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Essay:Hubble redshift in Einstein's universe

2011-10-02T13:36:46Z

JimJast: /* Derivation of Hubble "constant" */ typo

#REDIRECT Hubble redshift in Einstein's universe
This essay is an original work of '''W. Jim Jastrzebski''', file 160-12.htm [[User:JimJast|JimJast]] 13:00, 27 August 2011 (EDT) Unofficial PhD program supervised by prof. Józef Namysłowski, The Institute of Theoretical Physics, University of Warsaw, Room 139, Hoża 69, 00-681 Warsaw, Poland

==Abstract==

It is shown that the observed features of Hubble redshift can be explained within the framework of Einstein's general relativity. The observed Hubble redshift could be attributed to thus far unnoticed mechanism of time dilation coupled to curvature of space. Einstein's universe regains its status as a viable model predicting cosmological observations such as the ''apparent'' expansion of space and the observed acceleration of this expansion.

==Derivation of Hubble "constant"==

Consider Einstein's homogeneous universe filled with dust (with a particle of dust corresponding to a galaxy). Let photons move through this dust
interacting with it only gravitationally. We will assume that energy conservation holds and that Newton's approximation can be applied. With these assumptions one can readily calculate energy transfer from photons to dust. To the observer at some distance from the light source this energy transfer will manifest itself as a change in wavelength, which is exactly what was observed by Hubble. The relativistic interpretation of this result allows the derivation of Hubble redshift (HR), including discovery that Hubble "constant" depends on the distance between the place in deep space and the observer.

Let <math>E_d=E_o-E</math> be the gravitational energy acquired by the dust due to gravitational
interaction between dust and photons of energy <math>E</math> and initial energy <math>E_o</math>
and let <math>\Lambda=4 \pi G \rho/c^2</math>, where <math>G</math> is Newtonian gravitational constant, <math>\rho</math> is density of dust, and
<math>c</math> is speed of light (which makes accidentally <math>\Lambda</math> equal to the cosmological constant of Einstein's universe or
<math>1/R^2</math>, where <math>R</math> is radius of Einstein's universe).

The linear density of Newtonian gravitational force acting on dust (force per unit length), which is identically equal to <math>d^2E/d^2r</math>, where <math>r</math> is distance travelled by photons, can be written, using relativistic relation between mass and energy <math>(mass = Energy / c^2)</math> as <math>4\pi G\rho(E_o-E_d)/c^2</math> leading to equation <ref>See [[Essay:Demystified gravitation]] for step-by-step derivation of eq. (1)</ref>

:<math>d^2E/dr^2 = \Lambda E </math> ...... (1)

Substituting <math>1/R^2</math> for <math>\Lambda</math> and solving the equation with initial conditions <math>E(r=0)=E_o</math> and <math>(dE/dr)(r=0)=-E_o/R</math> (meaning selecting a solution that makes physical sense) one gets

:<math>E / E_o=exp(-r/R)</math> ...... (2)

Since in Einstein's general relativity (EGR) there is nothing else but time dilation and the curvature of space as the media controlling gravitation, EGR interpretation of the above result is that time is
running slower at a distance from (any) observer according to relation
:<math>d\tau/dt = exp( - r / R )</math> ...... (3),

where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''Hubble Time
Dilation'' (HTD) in honor of its discoverer, and as distinguished from the ''gravitational time dilation'' predicted by Einstein.

After differentiating the above equation at <math>r = 0</math> we get a relation between the HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space <math>\Lambda = 1/R^2</math> as

:<math>(d^2\tau/dtdr)^2-\Lambda=0</math> ...... (4)

and it suggests the existence of antisymmetric part of Ricci tensor in time domain, named here tentatively <math>H_{\mu\nu}</math> or
Hubble Tensor (HT), such that <math>H_{\mu\nu}+ R_{\mu\nu} = 0</math> indicating that the spacetime is intrinsically flat as proposed by Narlikar and Arp<ref>Narlikar, J. & Arp, H. Flat spacetime cosmology - a unified framework
for extragalactic redshifts, 1993, Astrophysical Journal, Part 1 (ISSN
0004-637X) vol. 405, no. 1, The American Astronomical Society, p. 51-56,
Bibliographic code: 1993 ApJ...405...51N
</ref> and required by the law of conservation of energy.

It follows from equation (2) or (3) equivalently, that the redshift, produced by HTD, is equal to
:<math>Z=(E_o-E)/E=exp(r/R)-1</math> ...... (5)

simulating the expansion of space, with the ''Hubble "constant"'' of this apparent expansion at
<math>r = 0</math>
:<math>H_o= c / R</math> ...... (6)

For Einstein's universe of density <math>\rho = 6 \times 10^{-27}kg/m^3</math> Hubble constant <math>H_o=70km/s/Mpc</math>. After expanding the ''Hubble "constant"'', <math>H(t)</math> into ''Taylor series'' around <math>t = 0</math> the acceleration of this apparent expansion is approximately equal to

:<math>dH / dt = - H_o^2/2 </math> ...... (7)

which agrees within one standard deviation with 1998 observations by the Supernova Cosmology Project team<ref>Kuznetsova N, Barbary K, et al, A New Determination of the High-Redshift
Type Ia Supernova Rates with the Hubble Space Telescope Advanced Camera
for Surveys, 2008, The Astrophysical Journal, Volume 673, Issue 2, The
American Astronomical Society, pp. 981-998, Bibliographic Code: 2008
ApJ...673..981K, [href="http://supernova.lbl.gov/]"</ref>.

==Conclusions==

The analysis of Hubble time dilation (HTD) can be carried out using Einstein's general relativity and the law of conservation of energy.

The observed HTD can be attributed to the geometry of spacetime of the stationary homogeneous dust universe. Such a model may bo oversimplified,
however, it does reproduce the essential properties of HTD, and allows one to estimate the measured properties of the universe such as the average
density of space and the acceleration of its apparent expansion. While the formula for Hubble redshift, equation (5), can be derived directly from equation (2) obtained using Newtonian approximation, it is equation (3) that expresses the essential transition from Newtonian approach in which space and time are distinct, to a general
relativistic spacetime. Excelent agreement of the calculated acceleration of apparent expansion of this model universe with the measured value, lends additional support for the model.

==Acknowledgments==

Over the years the author has benefited from discussions with many people too numerous to to list them here. The members of the faculty of the
Institute of Theoretical Physics, Warsaw, Poland were kind enough to spare their time and offer critique which helped in clarifying the ideas expressed in the above manuscript.

==References==
<references/>

[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-10-01T20:57:40Z

JimJast: /* Step by step derivation of cosmological redshift */ adding the paper with derivation of Hubble redshift

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" is our "Euclidean space"
<ref>

"Flat" or "Euclidean" means "3-space" (x, y, z space) in which any "2-sphere" (since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime is flat''.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between ''the now'' and ''the past'' or ''the future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which ''spacetime is "curved"'') (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its ''[[curvature of spacetime]]''. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for 3 physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian approximate equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact, its action only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe theory (EUT), is a theory of universe from which the "expansion of univrese" was eliminated through the calculation of [[intrinsic redshift]], that showed that the alleged expansion is a relativistic illusion due to the curvature of space.

The EUT is almost the same as Einstein's stationary model universe of 1917 that was Einstein's guess, very close to the present EUT model of universe. It has common with the present EUT model the proved only in 1985, and therefore unknown to Einstein, the lack of expansion, that in original Einstein's model has been acheived via introduction of [[cosmological constant]], and therefore with purely mathematical means <ref>

And one has to remember that math is not [[science]].

</ref>.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some astronomers that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, in 1985, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which in EUT simulates accelerating expansion of space with acceleration

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EUT over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is really an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their hypothesis of creation and evolution of universe called the [[Big Bang]] hypothesis, which assumes creation of energy in the [[Big Bang]] event.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, and left his [[cosmological constant]] as it was. He also told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis and named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains ever since a mystery for them to solve.

The establishment scientific journals still resist the publication of the truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the [[Big Bang]] as a way of creation of the universe).

EUT sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics contained in the following sections.

First easy to notice feature of EUT is that the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EUT is therefore described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. the mentioned "[[cosmological constant]]"). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding since its [[intrinsic redshift]] turned to be represented by [[Hubble constant]] equal

:<math>H_o=c/R_E</math>,

where <math>c</math> is speed of light in vacuum and <math>R_E</math> is [[Einstein's radius of universe]], which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EUT may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EUT (also unsure but at least better theory than the [[Big Bang]] that contains errors, which we don't see in EUT, hoping that in EUT there are none).

</ref>.

The EUT is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EUT which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with acceleration confirmed to one standard deviation by Supernova cosmology Project.

The EUT explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies the density of space of universe as about

:<math>6\times 10^{-27}kg/m^3</math>.

The EUT explains also why the above [[Hubble constant|Hubble "constant"]], in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EUT.

Therefore the EUT explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. the EUT is in fact an extension of Einstein's general realativity but it may not be called by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion.

===Step by step derivation of cosmological redshift===

To see the whole one page paper describing the derivation for physicists and/or astronomers look at [[Essay:Hubble redshift in Einstein's universe]].
To see step-by-step derivation for high school students look at following steps:

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einsteinian universe===

Here is the metric of universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric

:<math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The EUT metric seems to be the simplest metric with required by Einsteinian property of non symmetry of metric <ref>

Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.

</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from [[Noether's Theorem]]) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric

:<math>d\tau^2=dt^2-dr^2/c^2</math>.

I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation

:<math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math>

that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by

:<math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-10-01T19:22:45Z

JimJast: /* Metric of Einsteinian universe */

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" is our "Euclidean space"
<ref>

"Flat" or "Euclidean" means "3-space" (x, y, z space) in which any "2-sphere" (since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime is flat''.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between ''the now'' and ''the past'' or ''the future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which ''spacetime is "curved"'') (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its ''[[curvature of spacetime]]''. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for 3 physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian approximate equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact, its action only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe theory (EUT), is a theory of universe from which the "expansion of univrese" was eliminated through the calculation of [[intrinsic redshift]], that showed that the alleged expansion is a relativistic illusion due to the curvature of space.

The EUT is almost the same as Einstein's stationary model universe of 1917 that was Einstein's guess, very close to the present EUT model of universe. It has common with the present EUT model the proved only in 1985, and therefore unknown to Einstein, the lack of expansion, that in original Einstein's model has been acheived via introduction of [[cosmological constant]], and therefore with purely mathematical means <ref>

And one has to remember that math is not [[science]].

</ref>.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some astronomers that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, in 1985, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which in EUT simulates accelerating expansion of space with acceleration

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EUT over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is really an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their hypothesis of creation and evolution of universe called the [[Big Bang]] hypothesis, which assumes creation of energy in the [[Big Bang]] event.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, and left his [[cosmological constant]] as it was. He also told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis and named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains ever since a mystery for them to solve.

The establishment scientific journals still resist the publication of the truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the [[Big Bang]] as a way of creation of the universe).

EUT sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics contained in the following sections.

First easy to notice feature of EUT is that the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EUT is therefore described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. the mentioned "[[cosmological constant]]"). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding since its [[intrinsic redshift]] turned to be represented by [[Hubble constant]] equal

:<math>H_o=c/R_E</math>,

where <math>c</math> is speed of light in vacuum and <math>R_E</math> is [[Einstein's radius of universe]], which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EUT may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EUT (also unsure but at least better theory than the [[Big Bang]] that contains errors, which we don't see in EUT, hoping that in EUT there are none).

</ref>.

The EUT is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EUT which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with acceleration confirmed to one standard deviation by Supernova cosmology Project.

The EUT explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies the density of space of universe as about

:<math>6\times 10^{-27}kg/m^3</math>.

The EUT explains also why the above [[Hubble constant|Hubble "constant"]], in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EUT.

Therefore the EUT explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. the EUT is in fact an extension of Einstein's general realativity but it may not be called by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einsteinian universe===

Here is the metric of universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric

:<math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The EUT metric seems to be the simplest metric with required by Einsteinian property of non symmetry of metric <ref>

Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.

</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from [[Noether's Theorem]]) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric

:<math>d\tau^2=dt^2-dr^2/c^2</math>.

I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation

:<math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math>

that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by

:<math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Talk:Essay:Demystified gravitation

2011-10-01T19:18:06Z

JimJast: missing signing

JimJast, I hope you don't mind, but I did a few minor spelling corrections per Spellcheck.--[[User:JamesWilson|JamesWilson]] 19:47, 22 August 2011 (EDT)

:Hi Jim, I'm grateful (except that I noticed it since we had an edit conflict). Luckily I recovered and now I'm editing my essay at school (while I'm waiting to meet the prof. who blocked my access to physics server to learn the reason for my blocking). They have speller in school so it makes my job easier though I appreciate if you could from time to time read my stuff since I mostly work from home with my speller being a dictionary and school speller being British. [[User:JimJast|JimJast]] 15:18, 1 October 2011 (EDT)

Essay:Demystified gravitation

2011-10-01T19:07:14Z

JimJast: /* Hubble tensor */ Noether's Theorem

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" is our "Euclidean space"
<ref>

"Flat" or "Euclidean" means "3-space" (x, y, z space) in which any "2-sphere" (since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime is flat''.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between ''the now'' and ''the past'' or ''the future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which ''spacetime is "curved"'') (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its ''[[curvature of spacetime]]''. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for 3 physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian approximate equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact, its action only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe theory (EUT), is a theory of universe from which the "expansion of univrese" was eliminated through the calculation of [[intrinsic redshift]], that showed that the alleged expansion is a relativistic illusion due to the curvature of space.

The EUT is almost the same as Einstein's stationary model universe of 1917 that was Einstein's guess, very close to the present EUT model of universe. It has common with the present EUT model the proved only in 1985, and therefore unknown to Einstein, the lack of expansion, that in original Einstein's model has been acheived via introduction of [[cosmological constant]], and therefore with purely mathematical means <ref>

And one has to remember that math is not [[science]].

</ref>.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some astronomers that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, in 1985, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which in EUT simulates accelerating expansion of space with acceleration

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EUT over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is really an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their hypothesis of creation and evolution of universe called the [[Big Bang]] hypothesis, which assumes creation of energy in the [[Big Bang]] event.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, and left his [[cosmological constant]] as it was. He also told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis and named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains ever since a mystery for them to solve.

The establishment scientific journals still resist the publication of the truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the [[Big Bang]] as a way of creation of the universe).

EUT sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics contained in the following sections.

First easy to notice feature of EUT is that the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EUT is therefore described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. the mentioned "[[cosmological constant]]"). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding since its [[intrinsic redshift]] turned to be represented by [[Hubble constant]] equal

:<math>H_o=c/R_E</math>,

where <math>c</math> is speed of light in vacuum and <math>R_E</math> is [[Einstein's radius of universe]], which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EUT may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EUT (also unsure but at least better theory than the [[Big Bang]] that contains errors, which we don't see in EUT, hoping that in EUT there are none).

</ref>.

The EUT is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EUT which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with acceleration confirmed to one standard deviation by Supernova cosmology Project.

The EUT explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies the density of space of universe as about

:<math>6\times 10^{-27}kg/m^3</math>.

The EUT explains also why the above [[Hubble constant|Hubble "constant"]], in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EUT.

Therefore the EUT explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. the EUT is in fact an extension of Einstein's general realativity but it may not be called by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einsteinian universe===

Here is the metric of universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric

:<math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from [[Noether's Theorem]]) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric

:<math>d\tau^2=dt^2-dr^2/c^2</math>.

I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation

:<math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math>

that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by

:<math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-10-01T19:04:33Z

JimJast: fixing EU as EUT + some corrections

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" is our "Euclidean space"
<ref>

"Flat" or "Euclidean" means "3-space" (x, y, z space) in which any "2-sphere" (since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime is flat''.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between ''the now'' and ''the past'' or ''the future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which ''spacetime is "curved"'') (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its ''[[curvature of spacetime]]''. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for 3 physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian approximate equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact, its action only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe theory (EUT), is a theory of universe from which the "expansion of univrese" was eliminated through the calculation of [[intrinsic redshift]], that showed that the alleged expansion is a relativistic illusion due to the curvature of space.

The EUT is almost the same as Einstein's stationary model universe of 1917 that was Einstein's guess, very close to the present EUT model of universe. It has common with the present EUT model the proved only in 1985, and therefore unknown to Einstein, the lack of expansion, that in original Einstein's model has been acheived via introduction of [[cosmological constant]], and therefore with purely mathematical means <ref>

And one has to remember that math is not [[science]].

</ref>.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some astronomers that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, in 1985, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which in EUT simulates accelerating expansion of space with acceleration

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EUT over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is really an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their hypothesis of creation and evolution of universe called the [[Big Bang]] hypothesis, which assumes creation of energy in the [[Big Bang]] event.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, and left his [[cosmological constant]] as it was. He also told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis and named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains ever since a mystery for them to solve.

The establishment scientific journals still resist the publication of the truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the [[Big Bang]] as a way of creation of the universe).

EUT sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics contained in the following sections.

First easy to notice feature of EUT is that the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EUT is therefore described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. the mentioned "[[cosmological constant]]"). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding since its [[intrinsic redshift]] turned to be represented by [[Hubble constant]] equal

:<math>H_o=c/R_E</math>,

where <math>c</math> is speed of light in vacuum and <math>R_E</math> is [[Einstein's radius of universe]], which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EUT may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EUT (also unsure but at least better theory than the [[Big Bang]] that contains errors, which we don't see in EUT, hoping that in EUT there are none).

</ref>.

The EUT is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EUT which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with acceleration confirmed to one standard deviation by Supernova cosmology Project.

The EUT explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies the density of space of universe as about

:<math>6\times 10^{-27}kg/m^3</math>.

The EUT explains also why the above [[Hubble constant|Hubble "constant"]], in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EUT.

Therefore the EUT explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. the EUT is in fact an extension of Einstein's general realativity but it may not be called by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einsteinian universe===

Here is the metric of universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric

:<math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric

:<math>d\tau^2=dt^2-dr^2/c^2</math>.

I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation

:<math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math>

that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by

:<math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Noether's Theorem

2011-10-01T12:59:01Z

JimJast: adding link to John Baez

'''Noether's theorem''' is a mathematical theorem that relates [[symmetry|symmetries]] of a [[Hamiltonian]] or [[Lagrangian Dynamics|Lagrangian]] system to conserved quantities. The theorem states that for every continuous symmetry there is a conservation law. For example, the invariance of time translation (i.e, the laws of physics do not change with time) leads to the conservation of energy. The invariance of spatial translation (i.e, the laws of physics are the same everywhere) leads to conservation of momentum.
==See also==
[http://math.ucr.edu/home/baez/noether.html Noether's Theorem in a Nutshell]
[[Category:Mathematics]]
[[Category:Physics]]

Noether's Theorem

2011-10-01T12:50:14Z

JimJast: adding redirect to (Noether theorem)

#REDIRECT Noether theorem
'''Noether's theorem''' is a mathematical theorem that relates [[symmetry|symmetries]] of a [[Hamiltonian]] or [[Lagrangian Dynamics|Lagrangian]] system to conserved quantities. The theorem states that for every continuous symmetry there is a conservation law. For example, the invariance of time translation (i.e, the laws of physics do not change with time) leads to the conservation of energy. The invariance of spatial translation (i.e, the laws of physics are the same everywhere) leads to conservation of momentum.
[[Category:Mathematics]]
[[Category:Physics]]

Essay:Demystified gravitation

2011-09-30T23:33:39Z

JimJast: /* Introduction to Einsteinian universe */ style and typos

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe (EU), is a theory of universe from which the "expansion of univrese" was eliminated through the calculation of [[intrinsic redshift]], that showed that the alleged expansion is a relativistic illusion due to the curvature of space.

The EU is almost the same as Einstein's stationary model universe of 1917 that was Einstein's guess, very close to the present EU model of universe. It has common with the present model the proved only in 1985, and therefore unknown to Einstein, the lack of expansion, that in original Einstein's model has been acheived via [[cosmological constant]].

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some astronomers that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which in EU simulates accelerating expansion of space with acceleration

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EU over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is really an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their openly false hypothesis of creation and evolution of universe called the [[Big Bang]] hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, and left his [[cosmological constant]] as it was. He also told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis and named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains a mystery for them ever since.

The establishment scientific journals still resist the publication of the truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the [[Big Bang]] as a way of creation of the universe).

Einteinian gravitation sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics contained in the following sections.

First easy to notice feature of EU is that the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EU is therefore described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. the mentioned [[cosmological constant]]). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding since its [[intrinsic redshift]] turned to be represented by [[Hubble constant]] equal

:<math>H_o=c/R_E</math>,

where <math>c</math> is speed of light in vacuum and <math>R_E</math> is [[Einstein's radius of universe]], which means that derivation may be right if the Newtonian calculations come out with [[Einstein's radius of universe]]!

It also means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EU may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EU (also unsure but at least better theory than the Big Bang that contains errors, which we don't see in EU, hoping that there are none).

</ref>.

The EU is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EU which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with acceleration confirmed to one standard deviation by Supernova cosmology Project.

The EU explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EU explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EU.

Therefore the EU explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. EU is in fact an extension of Einstein's general realativity but it may not be used by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of universe===

Here is the metric of universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-30T23:03:40Z

JimJast: shortening

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe (EU), is a theory of universe from which the "expansion of univrese" was eliminated through the calculation of [[intrinsic redshift]], that showed that the alleged expansion is a relativistic illusion due to the curvature of space.

The EU is almost the same as Einstein's stationary model universe of 1917 that was Einstein's guess, very close to the present EU model of universe. It has common with the present model the proved only in 1985, and therefore unknown to Einstein, the lack of expansion, that in original Einstein's model has been acheived via [[cosmological constant]].

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some astronomers that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which in EU simulates accelerating expansion of space with acceleration

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EU over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is really an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their openly false hypothesis of creation and evolution of universe called the [[Big Bang]] hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, and left his cosmological constant as it was. He also told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis and named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains a mystery ever since.

The establishment scientific journals still resist the publication of the truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the [[Big Bang]] as a way of creation of the universe).

Einteinian gravitation sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics contained in the following sections.

First easy to notice feature of EU is that the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EU is therefore described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. the mantioned [[cosmological constant]]). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding since its [[intrinsic redshift]] turned to be represented by [[Hubble constant]] equal

:<math>H_o=c/R_E</math>,

where <math>c</math> is speed of light in vacuum and <math>R_E</math> is [[Einstein's radius of universe]], which means that derivation may be right if the Newtonian calculations come out with [[Einstein's radius of universe]]!

It also means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EU may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EU (also unsure but at least better theory than the Big Bang that contains errors, which we don't see in EU, hoping that there are none).

</ref>.

The EU is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EU which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with acceleration confirmed to one standard deviation by Supernova cosmology Project.

The EU explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EU explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EU.

Therefore the EU explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. EU is in fact an extension of Einstein's general realativity but it may not be used by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of universe===

Here is the metric of universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-30T21:57:17Z

JimJast: /* Introduction to Einsteinian universe */ improving style

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe (EU), is a theory of universe from which the "expansion of univrese" got eliminated through the calculation of [[intrinsic redshift]], that showed that the alleged expansion is a relativistic illusion due to the curvature of space.

Basics of its gravitation have been explained in part 1 of this essay. Now, knowing how the ''apparent gravitational force'' has been generated let's look at the whole universe controlled by this apparent force.

First easy to notice feature is that in EU the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EU is described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. [[cosmological constant]]). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvature of space]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EU may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EU (also unsure but at least better theory than the Big Bang that contains errors, which we don't see in EU, hoping that there are none).

</ref>.

The EU is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EU which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EU explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EU explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EU.

Therefore the EU explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. EU is in fact an extension of Einstein's general realativity but it may not be used by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917 that was Einstein's guess very close to the contemporary picture of universe. It has common with the present model proved only in 1985 and therefore unknown to Einstein the lack of expansion.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to EU simulates accelerating expansion of space with

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EU over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is an illusion but the news has been never published yet (in 2011) and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their openly false hypothesis of evolution of universe called the [[Big Bang]] hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, left his cosmological constant as it was. Told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis while it would become obvious that the universe is not expanding named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains a mystery since the establishment scientific journals still resist to publish truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics conteined in the following sections.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-30T21:43:39Z

JimJast: /* Einstein's universe */ typos

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe (EU), is a contemporary theory of universe. Basics of its gravitation have been explained in part 1 of this essay. Now, knowing how the ''apparent gravitational force'' has been generated let's look at the whole universe controlled by this apparent force.

First easy to notice feature is that in EU the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EU is described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. [[cosmological constant]]). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvature of space]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EU may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EU (also unsure but at least better theory than the Big Bang that contains errors, which we don't see in EU, hoping that there are none).

</ref>.

The EU is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EU which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EU explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EU explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EU.

Therefore the EU explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. EU is in fact an extension of Einstein's general realativity but it may not be used by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917 that was Einstein's guess very close to the contemporary picture of universe. It has common with the present model proved only in 1985 and therefore unknown to Einstein the lack of expansion.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to EU simulates accelerating expansion of space with

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EU over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is an illusion but the news has been never published yet (in 2011) and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their openly false hypothesis of evolution of universe called the [[Big Bang]] hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, left his cosmological constant as it was. Told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis while it would become obvious that the universe is not expanding named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains a mystery since the establishment scientific journals still resist to publish truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics conteined in the following sections.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-30T21:35:39Z

JimJast: /* Introduction to Einsteinian universe */ cleaning

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe (EU), is a contemporary theory of universe. Basics of its gravitation have been explained in part 1 of this essay. Now, knowing how the ''apparent gravitational force'' has been generated let's look at the whole universe controlled by this apparent force.

First easy to notice feature is that in EU the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EU is described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. [[cosmological constant]]). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvature of space]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EU may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EU (also unsure but at least better theory than the Big Bang that contains errors, which we don't see in EU, hoping that there are none).

</ref>.

The EU is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EU which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EU explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EU explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EU.

Therefore the EU explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. EU is in fact an extension of Einstein's general realativity but it may not be used by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917 that was Einstein's guess very close to the contemporary picture of universe. It has common with the present model proved only in 1985 and therefore unknown to Einstein the lack of expansion.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to EGR simulates accelerating expansion of space with

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EGR over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is an illusion but the news has been never published yet (in 2011) and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their openly false hypothesis of evolution of universe called the [[Big Bang]] hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, left his cosmological constant as it was. Told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis while it would become obvious that the universe is not expanding named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains a mystery since the establishment scientific journals still resist to publish truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics conteined in the following sections.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-30T21:19:21Z

JimJast: /* Introduction to Einsteinian universe */

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe (EU), is a contemporary theory of universe. Basics of its gravitation have been explained in part 1 of this essay. Now, knowing how the ''apparent gravitational force'' has been generated let's look at the whole universe controlled by this apparent force.

First easy to notice feature is that in EU the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EU is described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. [[cosmological constant]]). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvature of space]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EGR (also unsure but at least better theory than the Big Bang that contains errors, which we don't see in EGR, hoping that there are none).

</ref>.

The EU is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EU explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EU explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EU.

Therefore the EU explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. EU is in fact an extension of Einstein's general realativity but it may not used be by this name because the [[relativists]] highjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion in some minds.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917 that was Einstein's guess very close to the contemporary picture of universe. It has common with the present model proved only in 1985 and therefore unknown to Einstein the lack of expansion.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to EGR simulates accelerating expansion of space with

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EGR over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is an illusion but the news has been never published yet (in 2011) and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their openly false hypothesis of evolution of universe called the [[Big Bang]] hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, left his cosmological constant as it was. Told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis while it would become obvious that the universe is not expanding named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains a mystery since the establishment scientific journals still resist to publish truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics conteined in the following sections.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Redshift

2011-09-29T20:52:50Z

JimJast: /* Support for the Big Bang theory */

The '''redshift''' of a given object is a measure of the amount that the wavelength of its emitted or reflected electromagnetic radiation has increased. This increase in wavelength is due to the relative motion of a source with respect to an observer; a light emitting source moving away from an observer will have its spectrum shifted toward longer (in optical light, redder) wavelengths. In practice this is analogous to the Doppler shifting of sound waves emitted from a moving source. Light emitted from a source moving towards an observer will experience a blueshift. In the case of redshift, however, most of the redshift is believed to be due not to the object moving through space, but to the expansion of space itself.

== Support for the Big Bang theory ==

The Hubble redshift in absorption and emission lines in the spectra of distant cosmic objects, discovered by Edwin Hubble in 1929, is claimed as a source of evidence for the [[Big Bang theory]].<ref>Edwin Hubble (1929). [http://www.pnas.org/cgi/reprint/15/3/168/ "A relation between distance and radial velocity among extra-galactic nebulae"]. Proceedings of the National Academy of Sciences 15: 168–173.</ref> The redshift, the expanded wavelength of light, suggests that these objects are moving away from Earth due to the expansion of the universe. It also suggests that the universe is undergoing accelerating expansion for an unknown reason.

Actually the reason is known and confirmed by Supernova Cosmology Project team in 1998 with accuracy to one standard deviation (the second term of Taylor series of Hubble "constant" as function of time is causing the illusion of accelerating expansion of space with
:<math>dH/dt=-H_o^2/2</math>,
where <math>dH/dt</math> is apparent acceleration of expansion of space,
:<math>H_o=c/R_E</math>,
is Hubble constant, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is "Einstein radius", or radius of curvature of space, about 13 billion light years). Scientific journals are niether publishing it nor allow to put it through peer review process. If they did then the Big Bang hypothesis would collapse which might harm [[relativists]].

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

==References==

<references/>

[[Category:Astronomy]]

Essay:Demystified gravitation

2011-09-29T19:40:04Z

JimJast: /* Introduction to Einsteinian universe */ typo

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe (EU), is a contemporary theory of universe. Basics of its gravitation have been explained in part 1 of this essay. Now, knowing how the ''apparent gravitational force'' has been generated let's look at the whole universe controlled by this apparent force.

First easy to notice feature is that in EU the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EU is described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. [[cosmological constant]]). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvature of space]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EGR (also unsure but at least better theory than the Big Bang that contains errors, which we don't see in EGR, hoping that there are none).

</ref>.

The EU is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EU explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EU explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EU explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. EU is in fact an extension of Einstein's general realativity but it may not used be by this name because the [[realtivists]] jighjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion in some minds.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917 that was Einstein's guess very close to the contemporary picture of universe. It has common with the present model proved only in 1985 and therefore unknown to Einstein the lack of expansion.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to EGR simulates accelerating expansion of space with

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EGR over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is an illusion but the news has been never published yet (in 2011) and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their openly false hypothesis of evolution of universe called the [[Big Bang]] hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, left his cosmological constant as it was. Told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis while it would become obvious that the universe is not expanding named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains a mystery since the establishment scientific journals still resist to publish truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics conteined in the following sections.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-29T19:37:50Z

JimJast: /* Introduction to Einsteinian universe */ replacing EGR with EU

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe (EU), is a contemporary theory of universe. Basics of its gravitation have been explained in part 1 of this essay. Now, knowing how the ''apparent gravitational force'' has been generated let's look and the whole universe controlled by this apparent force.

First easy to notice feature is that in EU the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EU is described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about or didn't care. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. [[cosmological constant]]). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvature of space]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EGR (also unsure but at least better theory than the Big Bang that contains errors, which we don't see in EGR, hoping that there are none).

</ref>.

The EU is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EU explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EU explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EU explains most of numerical results that the [[Big Bang]] cosmology is unable to explain. EU is in fact an extension of Einstein's general realativity but it may not used be by this name because the [[realtivists]] jighjacked this name for their pseudo scientific hypothesis of the [[Big Bang]] which, when used, might have caused a confusion in some minds.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917 that was Einstein's guess very close to the contemporary picture of universe. It has common with the present model proved only in 1985 and therefore unknown to Einstein the lack of expansion.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to EGR simulates accelerating expansion of space with

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EGR over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is an illusion but the news has been never published yet (in 2011) and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their openly false hypothesis of evolution of universe called the [[Big Bang]] hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, left his cosmological constant as it was. Told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis while it would become obvious that the universe is not expanding named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains a mystery since the establishment scientific journals still resist to publish truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics conteined in the following sections.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-29T19:18:23Z

JimJast: /* Introduction to Einsteinian universe */ grammar

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe. Basics of its gravitation have been explained in part 1 of this essay. Now, knowing how the ''apparent gravitational force'' has been generated let's look and the whole universe controlled by this apparent force.

First easy to notice feature is that in EGR the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EGR is described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. [[cosmological constant]]). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EGR (also unsure but at least better theory than the Big Bang that contains errors, which we don't see in EGR, hoping that there are none).

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917 that was Einstein's guess very close to the contemporary picture of universe. It has common with the present model proved only in 1985 and therefore unknown to Einstein the lack of expansion.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to EGR simulates accelerating expansion of space with

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EGR over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is an illusion but the news has been never published yet (in 2011) and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their openly false hypothesis of evolution of universe called the [[Big Bang]] hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, left his cosmological constant as it was. Told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis while it would become obvious that the universe is not expanding named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains a mystery since the establishment scientific journals still resist to publish truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics conteined in the following sections.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-29T19:12:26Z

JimJast: rearranging sections + some improvements

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian universe, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe. Basics of its gravitation have been explained in part 1 of this essay. Now, knowing how the ''apparent gravitational force'' has been generated let's look and the whole universe controlled by this apparent force.

First easily to notice feature is that in EGR the universe has been always approximately the same. It has been never changing, beyond trivial movements of celestial bodies. The EGR is described by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as e.g. [[cosmological constant]]). The new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know
<ref>

Theories are never "right" unless they pass all the possible tests of their validity, which the [[Big Bang]] hypohtesis was not able to pass and that's why it has to be replaced with EGR (also unsure but at least better theory than the Big Bang that contains errors, which we don't see in EGR, hoping that there are none).

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917 that was Einstein's guess very close to the contemporary picture of universe. It has common with the present model proved only in 1985 and therefore unknown to Einstein the lack of expansion.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

When the ''"cosmological constant"'' turned out to be unnecessary, since it turned out that the Hubble redshift is not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to EGR simulates accelerating expansion of space with

:<math>dH/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by EGR over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation showed that the expansion of universe is an illusion but the news has been never published yet (in 2011) and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their openly false hypothesis of evolution of universe called the [[Big Bang]] hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his stationary universe, left his cosmological constant as it was. Told his secretary not to let in anyone who wants to talk to him about the universe.
<ref>

Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.

</ref>

The [[relativists]] were not able to remove cosmological constant since it might have ruined their [[Big Bang]] hypothesis while it would become obvious that the universe is not expanding named it "[[dark energy]]" creating this way new mystery for themselves to solve (at the taxpayers expense) and so the "[[dark energy]]" remains a mystery since the establishment scientific journals still resist to publish truth about the universe (that it operates according to Einstein's plan and that the Einsteinian gravitation, does not allow the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend and repeat the Newtonian physics conteined in the following sections.

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Hubble redshift

2011-09-28T13:27:39Z

JimJast: Created page with "The same thing as intrinsic redshift of our universe."

The same thing as [[intrinsic redshift]] of our universe.

Cosmological redshft

2011-09-28T13:23:27Z

JimJast: Created page with "The same thing a intrinsic redshift of the universe."

The same thing a [[intrinsic redshift]] of the universe.

Essay:Demystified gravitation

2011-09-28T13:09:54Z

JimJast: /* Future of Hubble tensor */

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neat Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-28T13:03:34Z

JimJast: /* Introduction */

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. Without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''future''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontaneously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't believe in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neet Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Hubble redshift in Einstein's universe

2011-09-28T12:52:51Z

JimJast: /* Derivation of Hubble "constant" */

#REDIRECT Hubble redshift in Einstein's universe
This essay is an original work of '''W. Jim Jastrzebski''', file 160-12.htm [[User:JimJast|JimJast]] 13:00, 27 August 2011 (EDT) Unofficial PhD program supervised by prof. Józef Namysłowski, The Institute of Theoretical Physics, University of Warsaw, Room 139, Hoża 69, 00-681 Warsaw, Poland

==Abstract==

It is shown that the observed features of Hubble redshift can be explained within the framework of Einstein's general relativity. The observed Hubble redshift could be attributed to thus far unnoticed mechanism of time dilation coupled to curvature of space. Einstein's universe regains its status as a viable model predicting cosmological observations such as the ''apparent'' expansion of space and the observed acceleration of this expansion.

==Derivation of Hubble "constant"==

Consider Einstein's homogeneous universe filled with dust (with a particle of dust corresponding to a galaxy). Let photons move through this dust
interacting with it only gravitationally. We will assume that energy conservation holds and that Newton's approximation can be applied. With these assumptions one can readily calculate energy transfer from photons to dust. To the observer at some distance from the light source this energy transfer will manifest itself as a change in wavelength, which is exactly what was observed by Hubble. The relativistic interpretation of this result allows the derivation of Hubble redshift (HR), including discovery that Hubble "constant" depends on the distance between the place in deep space and the observer.

Let <math>E_d=E_o-E</math> be the gravitational energy acquired by the dust due to gravitational
interaction between dust and photons of energy <math>E</math> and initial energy <math>E_o</math>
and let <math>\Lambda=4 \pi G \rho/c^2</math>, where <math>G</math> is Newtonian gravitational constant, <math>\rho</math> is density of dust, and
<math>c</math> is speed of light (which makes accidentally <math>\Lambda</math> equal to the cosmological constant of Einstein's universe or
<math>1/R^2</math>, where <math>R</math> is radius of Einstein's universe).

The linear density of Newtonian gravitational force acting on dust (force per unit length), which is identically equal to <math>d^2E/d^2r</math>, where <math>r</math> is distance travelled by photons, can be written, using relativistic relation between mass and energy <math>(mass = Energy / c^2)</math> as <math>4\pi G\rho(E_o-E_d)/c^2</math> leading to equation <ref>See [[Essay:Demystified gravitation]] for step-by-step derivation of eq. (1)</ref>

:<math>d^2E/dr = \Lambda E </math> ...... (1)

Substituting <math>1/R^2</math> for <math>\Lambda</math> and solving the equation with initial conditions <math>E(r=0)=E_o</math> and <math>(dE/dr)(r=0)=-E_o/R</math> (meaning selecting a solution that makes physical sense) one gets

:<math>E / E_o=exp(-r/R)</math> ...... (2)

Since in Einstein's general relativity (EGR) there is nothing else but time dilation and the curvature of space as the media controlling gravitation, EGR interpretation of the above result is that time is
running slower at a distance from (any) observer according to relation
:<math>d\tau/dt = exp( - r / R )</math> ...... (3),

where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''Hubble Time
Dilation'' (HTD) in honor of its discoverer, and as distinguished from the ''gravitational time dilation'' predicted by Einstein.

After differentiating the above equation at <math>r = 0</math> we get a relation between the HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space <math>\Lambda = 1/R^2</math> as

:<math>(d^2\tau/dtdr)^2-\Lambda=0</math> ...... (4)

and it suggests the existence of antisymmetric part of Ricci tensor in time domain, named here tentatively <math>H_{\mu\nu}</math> or
Hubble Tensor (HT), such that <math>H_{\mu\nu}+ R_{\mu\nu} = 0</math> indicating that the spacetime is intrinsically flat as proposed by Narlikar and Arp<ref>Narlikar, J. & Arp, H. Flat spacetime cosmology - a unified framework
for extragalactic redshifts, 1993, Astrophysical Journal, Part 1 (ISSN
0004-637X) vol. 405, no. 1, The American Astronomical Society, p. 51-56,
Bibliographic code: 1993 ApJ...405...51N
</ref> and required by the law of conservation of energy.

It follows from equation (2) or (3) equivalently, that the redshift, produced by HTD, is equal to
:<math>Z=(E_o-E)/E=exp(r/R)-1</math> ...... (5)

simulating the expansion of space, with the ''Hubble "constant"'' of this apparent expansion at
<math>r = 0</math>
:<math>H_o= c / R</math> ...... (6)

For Einstein's universe of density <math>\rho = 6 \times 10^{-27}kg/m^3</math> Hubble constant <math>H_o=70km/s/Mpc</math>. After expanding the ''Hubble "constant"'', <math>H(t)</math> into ''Taylor series'' around <math>t = 0</math> the acceleration of this apparent expansion is approximately equal to

:<math>dH / dt = - H_o^2/2 </math> ...... (7)

which agrees within one standard deviation with 1998 observations by the Supernova Cosmology Project team<ref>Kuznetsova N, Barbary K, et al, A New Determination of the High-Redshift
Type Ia Supernova Rates with the Hubble Space Telescope Advanced Camera
for Surveys, 2008, The Astrophysical Journal, Volume 673, Issue 2, The
American Astronomical Society, pp. 981-998, Bibliographic Code: 2008
ApJ...673..981K, [href="http://supernova.lbl.gov/]"</ref>.

==Conclusions==

The analysis of Hubble time dilation (HTD) can be carried out using Einstein's general relativity and the law of conservation of energy.

The observed HTD can be attributed to the geometry of spacetime of the stationary homogeneous dust universe. Such a model may bo oversimplified,
however, it does reproduce the essential properties of HTD, and allows one to estimate the measured properties of the universe such as the average
density of space and the acceleration of its apparent expansion. While the formula for Hubble redshift, equation (5), can be derived directly from equation (2) obtained using Newtonian approximation, it is equation (3) that expresses the essential transition from Newtonian approach in which space and time are distinct, to a general
relativistic spacetime. Excelent agreement of the calculated acceleration of apparent expansion of this model universe with the measured value, lends additional support for the model.

==Acknowledgments==

Over the years the author has benefited from discussions with many people too numerous to to list them here. The members of the faculty of the
Institute of Theoretical Physics, Warsaw, Poland were kind enough to spare their time and offer critique which helped in clarifying the ideas expressed in the above manuscript.

==References==
<references/>

[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-24T20:46:43Z

JimJast: /* Reformatted value of Hubble constant */

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''furture''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontanously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't belive in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], the same as <math>\Delta H_o</math>, <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neet Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-24T20:02:19Z

JimJast: /* Quantative aspects of gravitational force */

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''furture''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontanously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't belive in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>) then

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math>, more accurately than the Newtonian force given by the Newtonian equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neet Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-24T19:56:24Z

JimJast: /* Qualitative aspects of gravitational force */

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''furture''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontanously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't belive in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain ''apparent force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the ''tendency of particle <math>m</math> to move towards the most most probable position'' of this particle, ''position of its lowest energy''. Something that the particle is '''''pushed''''' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a ''quantum effect of particle trying to assume its most probable position of its lowest enery''.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>)

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math> and more accurately than the Newtonian force given by the equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neet Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-24T19:41:21Z

JimJast: /* Qualitative aspects of gravitational force */

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''furture''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontanously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't belive in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both conventions is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain apparent ''force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of '''''apparent attraction''''': the tendency of particle <math>m</math> to move towards the most most probable position of this particle, position of its lowest energy. Something that the particle is ''pushed'' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a quantum effect of particle trying to assume its most probable position of its lowest enery.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>)

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math> and more accurately than the Newtonian force given by the equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neet Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-24T19:32:56Z

JimJast: /* Qualitative aspects of gravitational force */

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''furture''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontanously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't belive in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math> in both notations is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain apparent ''force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of '''''apparent attraction''''': the tendency of particle <math>m</math> to move towards the most most probable position of this particle, position of its lowest energy. Something that the particle is ''pushed'' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a quantum effect of particle trying to assume its most probable position of its lowest enery.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>)

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math> and more accurately than the Newtonian force given by the equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neet Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-24T19:31:33Z

JimJast: /* Qualitative aspects of gravitational force */ missing dot

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''furture''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontanously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't belive in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time
<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative.

:<math>g_{oo}</math>

in both notations is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain apparent ''force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of '''''apparent attraction''''': the tendency of particle <math>m</math> to move towards the most most probable position of this particle, position of its lowest energy. Something that the particle is ''pushed'' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a quantum effect of particle trying to assume its most probable position of its lowest enery.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>)

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math> and more accurately than the Newtonian force given by the equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neet Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-23T18:03:43Z

JimJast: /* Reformatted value of Hubble constant */ typo

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''furture''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontanously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't belive in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative <math>g_{oo}</math> in both notations is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain apparent ''force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of '''''apparent attraction''''': the tendency of particle <math>m</math> to move towards the most most probable position of this particle, position of its lowest energy. Something that the particle is ''pushed'' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a quantum effect of particle trying to assume its most probable position of its lowest enery.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>)

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math> and more accurately than the Newtonian force given by the equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis of their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neet Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Essay:Demystified gravitation

2011-09-23T17:54:21Z

JimJast: /* Atempt to get the rate of expansion of space */

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''furture''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontanously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't belive in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative <math>g_{oo}</math> in both notations is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain apparent ''force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of '''''apparent attraction''''': the tendency of particle <math>m</math> to move towards the most most probable position of this particle, position of its lowest energy. Something that the particle is ''pushed'' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a quantum effect of particle trying to assume its most probable position of its lowest enery.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>)

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math> and more accurately than the Newtonian force given by the equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe "is expanding" and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also knew that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously meant that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis if their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neet Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Conservation law

2011-09-23T17:28:15Z

JimJast: grammar

'''Conservation law''' is a [[physical law]] that says that some physical quantity is conserved, which means ''never changes''. Examples of ''conserved quantities'' in physics are energy and momentum along 3 axes. So we have at least 4 independent conservation laws of momentum along axis 1, momentum along axis 2, momentum along axis 3, and energy, that is considered axis 4 by some autors or axis 0 by others. Usually mathematicians use diferent convention for numbering axes than physicists, who number axes starting from 0 for ''energy'', and so on for other axes (e.g. t, x, y, z where t denotes ''time'', and the rest relate to ''space'').
[[Category:Physics]]

Physical law

2011-09-23T15:13:46Z

JimJast: Created page with "'''Physical law''' is a law of nature that ''"as far as we know"'' is ''"true"'' which in this case means that it never yet was observed as being violated by nature (or anybody t..."

'''Physical law''' is a law of nature that ''"as far as we know"'' is ''"true"'' which in this case means that it never yet was observed as being violated by nature (or anybody thought by the given person to be controlling the nature) and therefore it is reliable in ''scientific sense''.

[[Category:Physics]]

Conservation law

2011-09-23T14:44:55Z

JimJast: style

'''Conservation law''' is a [[physical law]] that says that some physical quantity is conserved, which means ''never changes''. Examples of ''conserved quantities'' in physics are energy and momentum along 3 axies. So we have at least 4 independent conservation laws of momentum around axis 1, momentum along axis 2, momentum along axis 3, and energy, that is considered axis 4 by some autors or axis 0 by others. Usually mathematicians use diferent convention for numbering axes than physicists, who number axes starting from 0 for ''energy'', and so on for other axes (e.g. t, x, y, z where t denotes ''time'', and the rest relate to ''space'').
[[Category:Physics]]

Conservation law

2011-09-23T14:43:21Z

JimJast:

'''Conservation law''' is a [[physical law]] that says that some physical quantity is conserved, which means ''never changes''. Examples of ''conserved quantities'' in physics are energy and momentum along 3 axies. So we have at least 4 independent conservation laws of momentum around axis 1, momentum along axis 2, momentum along axis 3, and energy, that is considered axis 4 by some autors or axis 0 by others. Usually mathematicians use diferent convention for numbering axes than physicists, who number axes starting from 0 for ''energy'', and so on for other axes (e.g. t, x, y, z where t denotes time, and the rest relate to ''space'').
[[Category:Physics]]

Conservation law

2011-09-23T14:39:25Z

JimJast: Created page with "'''Conservation law''' is a physical law that says that some physical quantity is conserved, which means ''never changes''. Examples of ''conserved quantities'' in physics ar..."

'''Conservation law''' is a [[physical law]] that says that some physical quantity is conserved, which means ''never changes''. Examples of ''conserved quantities'' in physics are energy and momentum along 3 axies. So we have at least 4 independent conservation laws of momentum around axis 1, momentum around axis 2, momentum around axis 3, and energy, that is considered axis 4 by some autors or axis 0 by others. Usually mathematicians use diferent convention for numbering axes than physicists, who number axes starting from 0 for ''energy'', and so on for other axes (e.g. t, x, y, z where t denotes time, and the rest relate to ''space'').

Essay:Demystified gravitation

2011-09-23T13:42:53Z

JimJast: /* Introduction */ grammar

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"
<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''furture''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontanously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think, "together" as Wheeler's hypothetic "momenergy" in which energy is assumed to be able to be converted into momentum and v.v).

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but generally don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists
<ref>

According to the legend only two physicists, Albert Einstein and Arthur Eddington, understood relativity since when a journalist told Eddington that he heard that only three people in the whole world understood relativity, Eddington asked him: "Yeah? Who is the third?"

</ref>.
I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton
<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.
Newton was wise man and didn't belive in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative <math>g_{oo}</math> in both notations is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain apparent ''force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of '''''apparent attraction''''': the tendency of particle <math>m</math> to move towards the most most probable position of this particle, position of its lowest energy. Something that the particle is ''pushed'' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a quantum effect of particle trying to assume its most probable position of its lowest enery.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>)

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math> and more accurately than the Newtonian force given by the equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe is expanding and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also new that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously ment that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis if their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neet Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Cargo cult science

2011-09-23T13:18:08Z

JimJast: Undo revision 918629 by LesCoyle (talk)

'''Cargo cult science''' is a name invented by [[Richard Feynman]] to name an apparent "scientific activity" that many scientists are engaged in that only looks like scientific activity because of use of language proper for this particular branch of science but not containing any substance beyond similarity to [[science]].

The name came from natives of New Guinea and other Pacific islands who build in jungle something that looks like controll towers in hope that gods seeing them will send them cargo planes with all those goods that other people enjoy receiving from gods, as those natives imagine the reasons for gods sending cargo planes to the earth.

One example of a cargo cult science is [[Complementary and Alternative Medicine]] another is the [[Big Bang|Big Bang hypothesis]].
[[Category:Science]]
[[Category:Pseudoscience]]

Einstein's radius

2011-09-22T01:08:18Z

JimJast:

'''Einstein's radius''' is the radius of curvature of stationary (or less properly called "static") Einstein's universe model that was proposed by Einstein in 1917 and later given up after consensus of astronomers assumed that the universe is expanding. In 1985 it turned out that expansion is only a relativistic illusion produced by coupling of time with space but [[relativists]] didn't accept that and started to suppress notion of illusion by not allowing publications of papers explaining this illusion
<ref>

See [[Essay:Hubble redshift in Einstein's universe]] and also Einstein's paper dropped from the bibloigraphy of Einstein's papers in 1973 ''"Gravitation"'' in which Einstein advocated non symmetric metric tensor of spacetime while the Big Bang [[relativists]] assume symmetric metric in that book.

</ref>. [[Relativists]] insisted that it is not an illusion but a real expansion. Though no scientific theory of expansion could be constructed as it contradicted the conservation laws (conservation of energy and conservation of momentum separately) so the hypothesis of expansion became a true [[cargo cult science]] as described by [[Richard Feynman]] in his rant against [[relativists]].

The illusion of expansion is explained in [[Gravitation demystified]] and so '''Einstein's radius''' would be about 13 billion light years. The number coming from division of speed of light by [[Hubble constant]] that represent the [[intrinsic redshift]] in the universe that is result of Newtonian calculation of [[dynamical friction]] of photons in a stationary [[Einstein's universe]]
<ref>
See the step-by-step derivation of [[intrinsic redshift]] and [[Hubble constant]] in [[Gravitation demystified]] that an intelligent high school student may follow.
</ref>.
The exact value of '''Einstein's radius''' predicted theoretically as value at which the Einstein's field equation is stable or derived from [[intrinsic redshift]] of photons, is

:<math>R_E=c/\sqrt{4\pi G\rho}</math>,

where <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the density of space of universe.

==Rreferences==
<references/>

[[Category:Cosmology]]
[[Category:Astronomy]]
[[Category:Physics]]

Einstein's radius

2011-09-22T01:02:48Z

JimJast:

'''Einstein's radius''' is the radius of curvature of stationary (or less properly called "static") Einstein's universe model that was proposed by Einstein in 1917 and later given up after consensus of astronomers assumed that the universe is expanding. In 1985 it turned out that expansion is only a relativistic illusion produced by coupling of time with space but [[relativists]] didn't accept that and started to suppress notion of illusion by not allowing publications of papers explaining this illusion
<ref>

See [[Essay:Hubble redshift in Einstein's universe]] and also Einstein's paper dropped from the bibloigraphy of Einstein's papers in 1973 ''"Gravitation"'' in which Einstein advocated non symmetric metric tensor of spacetime while the Big Bang [[relativists]] assume symmetric metric in that book.

</ref>. [[Relativists]] insisted that it is not an illusion but a real expansion. Though no scientific theory of expansion could be constructed as it contradicted the conservation laws (conservation of energy and momentum) so the hypothesis of expansion became a true [[cargo cult science]] as described by [[Richard Feynman]] in his rant against [[relativists]].

The illusion of expansion is explained in [[Gravitation demystified]] and so '''Einstein's radius''' would be about 13 billion light years. The number coming from division of speed of light by [[Hubble constant]] that represent the [[intrinsic redshift]] in the universe that is result of Newtonian calculation of [[dynamical friction]] of photons in a stationary [[Einstein's universe]]
<ref>
See the step-by-step derivation of [[intrinsic redshift]] and [[Hubble constant]] in [[Gravitation demystified]] that an intelligent high school student may follow.
</ref>.
The exact value of '''Einstein's radius''' predicted theoretically as value at which the Einstein's field equation is stable or derived from [[intrinsic redshift]] of photons, is

:<math>R_E=c/\sqrt{4\pi G\rho}</math>,

where <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the density of space of universe.

==Rreferences==
<references/>

[[Category:Cosmology]]
[[Category:Astronomy]]
[[Category:Physics]]

Essay:Demystified gravitation

2011-09-22T00:42:48Z

JimJast: /* Introduction */

#REDIRECT Gravitation demystified
This essay is an original work by '''W. Jim Jastrzebski'''.

:[[User:JimJast|JimJast]] 09:43, 22 August 2011 (EDT)

==Demystifying gravitation==

===Introduction===

I'm writing this essay to explain to people interested in gravitation how it works according to Einsteinian physics.

Between 1905 and 1915 the theory of gravitation switched from Newtonian math to Einsteinian physics and many Newton's problems got solved, mostly due to the fact that the space is not flat ("flat space" means the same as "Euclidean space"<ref>

"Flat" or "Euclidean" means our regular (x,y,z) space called also "3-space" in which any 3D sphere (called also "2-sphere" since its surface has only 2 dimensions) of surface area <math>4\pi r^2</math> contains volume of space <math>(4/3)\pi r^3</math>.

</ref>) but is curved having certain [[curvature of space]] and the time reflects faithfully this [[curvature of space]] through the gravitational [[time dilation]] in such way that the whole ''spacetime'' is flat.

This global flatness of spacetime is an important feature. without it the movement of certain geometrical structures (tensors) that describe things in space and time (therefore in 4 dimensions: 3 in space and 1 in time) wouldn't have the property of keeping the strict conservation of energy and momentum between the ''now'' and the ''past'' or the ''furture''. There wouldn't be any [[conservation law]]s valid in the universe. The things would be spontanously created from nothing and disappearing without trace from one moment to another just by the virtue of mathematical manipulation (as it happens in the [[Big Bang]] hypothesis in which spacetime is "curved") (luckily not in this universe of ours since then we would be forced to believe in "ghosts" while they would be created and disappear without no reason whatsoever). The creationist might be happy but the [[science]] wouldn't be as we know it today. Now in [[science]] neither energy nor momentum can't be created from nothing as it is assumed in the [[Big Bang]] hypothesis with its [[curvature of spacetime]]. [[Conservation law]]s assure that energy and momentum are conserved separately (not as some [[relativists]] think "together" as Wheeler's hypothetic "momenergy").

This essay is meant to explain this strange physics of [[gravitation]], with which we deal every day but don't understand it, don't know how it operates and where the "gravitational force" is coming from, except for some physicists<ref>

According to a legend only two of them Albert Einstein and Arthur Eddington, since when a journalist told Eddington that he heard that only three people in the entire world understand relativity, Eddington asked him "who is the third?"

</ref>.

I hope it soon will be clear to the readers that [[gravitation]] contains no mystery and is probably the simplest physics around and could hardly work in a different manner.

There may be readers who might think that it should be left working as Newtonian math seemed to work when everybody and his brother thought that objects in the universe attract each other. Though it won't be true since gravitation doesn't work this way. Even according to Newton<ref>

Quote from Newton [according to wikipedia]: ''"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."''

</ref>.

Newton was wise man and didn't belive in things that he thought are impossible. Then there were many things seemingly impossible. Though gravitation was obviously possible. How did it work?

The description of gravitation starts with the next section.

===How gravitational force is generated===

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2(x)</math> ...... (1)

where <math>c^2(x)</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time<ref>

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

:<math>d\tau/dt=\sqrt{g_{oo}}</math>,

in sign convention used in physics, where times are considered to be positive and distances negative <math>g_{oo}</math> in both notations is time-time component of metric of spacetime, which means that

:<math>E=mc^2 \sqrt{g_{oo}(x)}</math>

is not a constant but a function of displacement <math>x</math> in relation to the particle and we may take its non vanishing derivative with respect to displacement to calculate ''"gravitational force"''.

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force

:<math>F=-dE/dx</math> ...... (2)

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (1) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain apparent ''force'', pushing mass <math>m</math> towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of '''''apparent attraction''''': the tendency of particle <math>m</math> to move towards the most most probable position of this particle, position of its lowest energy. Something that the particle is ''pushed'' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation. We may say that gravitational force is a quantum effect of particle trying to assume its most probable position of its lowest enery.

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

This is the whole qualitatative mystery of how ''"gravitational force"' is generated in Einsteinian physics.

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.

====Quantative aspects of gravitational force====

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>)

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the ''"gravitational force"'' comes out as <math>F=ma</math> and more accurately than the Newtonian force given by the equation

:<math>F_N=GMm/r^2</math> ...... (6),

where G is Newtonian gravitational constant. The small difference between those two forces (Newtonian <math>F_N</math> and Einsteinian <math>F</math>) comes from the difference between flat space of Newtonian math and the [[curvature of space|curved space]] of Einsteinian physics that is responsible for equation (4).

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

Einstein's universe is Einstein's stationary (or "static" as some cosmologists call it) model universe of 1917.

To keep Einstein's field equation of this stationary model stable, and not knowing yet about the ''"[[Hubble time dilation]]"'', discovered by Edwin Hubble over a decade later, and suggesting to some cosmologists that the universe might be expanding, Einstein added his ''"cosmological constant"'' to his field equation that stopped the alleged expansion of his model universe. Later he called this cosmological constant ''"the biggest blunder of his life"''.

In 1985 the ''"cosmological constant"'' turned out to be unnecessary since it turned out that the Hubble redshift might be not caused by expansion of the universe but by the time runing slower at the deep space galaxies in curved space, which according to ''Einsteinian gravitation'' (see below) simulates accelerating expansion of space with

:<math>dH(t)/dt=-H_o^2/2</math>

as observed in 1998 by the Supernova Cosmology Project team of astronomers and therefore predicted by ''Einsteinian gravitation'' over 80 years earlier.

The agreement of value of alleged acceleration of space with the results of observations of Supernova Cosmology Project within one standard deviation suggest that the expansion of universe is an illusion but the news has been never published yet and is not likely to be published soon (except in conservapedia).

Publishing of such a news would destroy the credibility of estblishment cosmologists and their beloved though openly false hypothesis of evolution of universe called the Big Bang hypothesis.

Around 1929 Edwin Hubble discovered cosmological redshift that [[relativists]] started to consider a sign that the universe is expanding. Then Einstein gave up working on his universe and it has been forgotten for some time.

Einstein told his secretary not to let in anyone who wants to talk to Einstein about the universe<ref>Story told to the author by Roy J. Glauber who was at the time Einstein's assistant in Princeton University in N.J. and later, for one year, author's physics teacher at Harvard, Cambridge, MA.</ref>.

Also the Einsteinian gravitation, not allowing the expansion of universe, does not allow the Big Bang as a way of creation of the universe. It sugests that the universe is stationary (with Newtonian arguments based on relativity of time, which any intelligent high school student should easily comprehend).

===Step by step derivation of cosmological redshift===

====Step 1. Assumptions ====

:The basic assumption is as in any cosmological theory, that space of our universe is homogeneous and filed up with dust of galaxies with one galaxy corresponding to one dust particle (or a few). Average density of this dust is <math>\rho</math> and this is rather important for further calculations. Additionally we assume that <math>\pi</math> is what it usually is, <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant. So the overall picture of our universe is rather simple. It is not expanding. No hidden [[magic]].

:Now light starts radiating from some arbitrary ''"point zero"'' and photons start interacting wirh galaxies through ''"dynamical friction of photons"'' (the gravitational effect known in astronomy as ''"dynamical friction"'' but in this case acting on photons instead its usual action on heavier objects like stars). The gravitational energy of our "dust" gained through this dynamical friction contained in a ball of "dust" of radius <math>r</math> around "point zero" is <math>E_d(r)</math>. This number is needed later to adjust the whole energy of "dust" to make the calculations exact (approximation is causing problems resulting as usually from approximations that all astrophysicists who wanted to make approximate calculations, including me, had, so I know that it has to be done exactly).

:After photons of energy <math>E_o</math> are radiated out from arbitrarily placed center of coordinate system called "point zero" (point with radial coordinate <math>r=0</math> in homogeneous space making the space inhomogeneous and therefore the Newtonian "gravitational force" starts pushing the "dust" away from "point zero" this force is equal, from Newtonian equation for "gravitational force"

::<math>F_{galaxy}(r)=(G/c^2)[E_o-E_d(r)]m_{galaxy} /r^2,</math> <ref>

Explanation of the above equation:
It comes from the Newtonian force being <math>F=GMm/r^2</math> and <math>M</math>, the source of gravitational "repulsive force" being replaced by <math>M=E/c^2</math> according to Einstein's physics. <math>E</math> in this equation is difference of original mass of "dust" causing the "Newtonian repulsion" adjusted by in general tiny <math>E_d(r)</math> causing "attraction" (acting in opposite direction than the "repulsive" <math>M</math>). It is similar to a gravitational effect of a bubble of air "repulsing" gravitationally their sorounding water in a tank of water plus tiny effect of attraction by <math>E_d(r)</math>, the tiny gravitational energy of accumulated within the bubble

</ref>

:and

::<math>F_{galaxy}(r)=-dE_{galaxy}(r)/dr</math>

:where <math>E_{galaxy}(r)</math> is gravitational energy of "dust particle" (galaxy) gained from the action of light through the "dynamical friction of photons on this particular "dust particle" (really a galaxy, or a few) at distance <math>r</math> from "point zero" <ref>

Usually people neglect influence of a single photon on a Galaxy since it looks to them as "negligible". Though it is not '''exact''' but they think that no harm is done by small negligence of exactness of math. It is wrong approach as it is demonstrated below where exact calculations produce Hubble constant roughly as it is observed. And agreement of theory with observation is a good indicator that the theory may be right as '''Einsteinian gravitation''' explaining the phenomenon of redshift in ''Einstein's universe'' might be.

</ref>

==== Step 2: Integrating the mass of galaxies ====
:... of spherical shell of radius <math>r</math> of galaxies around "point zero" and thickness <math>dr</math> gives number

::<math>m_{shell}=4 \pi \rho r^2dr</math>,

:where <math>m_{shell}</math> is the mass of whole thin (of thickness <math>dr</math>) shell of galaxies of radius <math>r</math> and

::<math>F_{shell}=(G/c^2)[E_o-E_d(r)m_{shell}/r^2</math>

==== Step 3. Calculating sum of all forcess acting on the shell ====
:Substituting number from step 2 for the mass of galaxy resulting in

::<math>F_{shell}(r)=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

:and
::<math>F_{shell}(r)=-dE_{shell}(r)/dr</math>.

:and so

::<math>-dE_{shell}(r)/dr=(4\pi G\rho/c^2)[E_o-E_d(r)]dr</math>.

==== Step 4. Integrating both sides of above equation ====
::<math>-d E_d(r)/dr =(4 \pi G \rho/c^2)\int[E_o-E_d(r)]dr</math>.
:... over all spherical shells between "point zero" and <math>r</math> to get total energy of "dust" absorbed from photons, and then '''differentiating both sides with respect to''' <math>r</math> '''to get rid of integral on the right side''' of this equation, we get finally the starting <math>E_d(r)</math> where subscript <math>d</math> now, as before, means ''"volume of universe of radius <math>r</math> around point zero"''

::<math>-d^2 E_d(r)/dr^2 =(4 \pi G \rho/c^2)[E_o-E_d(r)]</math>.

==== Step 5: Setting differential equation controlling the redshift ====
:Substituting <math>E_d(r)=E_o-E(r)</math> where <math>E(r)</math> is energy of photons at distance <math>r</math> from their source and <math>1/R_E^2=4\pi G\rho/c^2</math>, number called in cosmology "curvature of space of Einstein's universe" (or <math>R_E=</math>"Einstein's radius of universe"), we get

::<math>d^2E(r)/dr^2=E(r)/R_E^2</math>

==== Step 6: Solving the above equation ====
:with initial conditions <math>E(r=0)=E_o</math>
:and <math>(dE/dr)(r=0)=-E_o/R_E</math> meanig selecting a solution that makes physicsl sense) one gets solution

::<math>E/E_o=exp(-r/R_E)</math>

==== Step 7: Slowing of proper time in deep space ====
:Since in Einsteinian general relativity (EGR) there is nothing else but the time dilation and the curvature of space as the media controlling gravitation the EGR interpretation of the above result is that the time is running slower at a distance from (any) observer according to relation

::<math>d\tau/dt=exp(-r/R_E)</math>,

:where <math>\tau</math> is proper time in deep space and <math>t</math> is coordinate time at observer. The effect might be called ''"Hubble Time Dilation"'' (HTD) in honor of its discoverer, and as distinguished from the gravitational time dilation predicted by Einstein. It is the above equation that expresses the esential transition from Newtonian approach in which space and time are distinct, to general relativistic spacetime. It demonstrates also the '''essential relativity of time''' of Einsteinian theory.

:Excelent agreement of the shown in step 11 '''acceleration of apparent expansion''' of this model universe with the value measured by the Supernova Cosmology Project team of astonomers lends strong additional support for this model.

==== Step 8. Flatness of spacetime ====
:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.

:So all the pieces of puzzle seem to fit the ''"principle of conservation of all components of 4-momentum"''. They contradict the speculations of authors of 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler who maintain that the spacetime is curved and that only the magnitude of stress-energy tensor is conserved (infamous Wheeler's "Momenergy"). The Einsteinian conclusion is still that the spacetime is intrinsically flat (as proven by elementary tensor calculus) and therefore the universe is not expanding and therefore it must be eternal, as once assumed by the Einsteinian gravitation.

:But look at the further steps, even more interesting.

==== Step 9. Hubble redshift ====
:It follows from results of steps 6 and 7 equivalently, that the redshift, produced by HTD, is equal to

::<math>Z=(\lambda-\lambda_o)/\lambda_o=(E_o-E)/E=exp(r/R_E)-1</math>,

:where <math>\lambda</math> is "shifted" wavelength, <math>\lambda_o</math> is original wavelength, etc.

==== Step 10. The same thing in form of Hubble "constant"====
:Such redshift simulates the expansion of space, with Hubble constant of this apparent expansion at <math>r=0</math> equal

::<math>H_o=c/R_E</math>

:It is observed as about

::<math>H_o=</math>70km/s/Mpc

:which implies that the radius of curvature of space of Einstein's model universe, <math>R_E</math> is about 13Gly (13 billion light years). Very tough to measure but luckily very easy to calculate. And BTW, this value of <math>H_o</math> implies the density of our universe about

::<math>6\times 10^{-27}kg/m^3</math>,

:which is within about one standard deviation from what is observed.

==== Step 11. Apparent accelerating expansion of space ====
:After expanding Hubble "constant" <math>H(t)</math> into Taylor series around <math>t=0</math> acceleration of this apparent expansion is approximately equal

::<math>dH/dt=-H_o^2/2</math>.

:the above value agrees within one standard deviation (maximum available accuracy for testind results of a theory) with 1998 observations by the Supernova Cosmology Project team of astronomers.

:So the "accelerating expansion of our universe" blamed on mysterious "dark energy" for which cosmologists look since 1998 is just the Taylor term of expansion series of Hubble constant which is no constant but exponential function as shown in steps 6 or 7 (first as Newtonian result and second as Einsteinian interpretation of this Newtonian result). Cosmologists also call it "cosmological constant" (the ''"biggest blunder of Einstein's life"'') which can be shown not to exist at all. It might be eliminated from Einstein's field equation in rather straight forward manner.

===Metric of Einstein's universe===

Here is the metric of Einstein's universe with radial coordinate only (angular coordinates dropped for isotropy of the model):

:<math>d\tau^2=exp(-2r/R_E)dt^2+2sinh(2r/R_E)dtdr/c-exp(2r/R_E)dr^2/c^2</math>,

where <math>\tau</math> is proper time, <math>r</math> is radial coordinate, <math>t</math> is coordinate time, <math>R_E</math> is radius of curvature of space of Einstein's universe (Einstein's radius of universe). This metric approximates to Minkowski metric <math>d\tau^2=dt^2-dr^2/c^2</math> for <math>r</math><<<math>R_E</math>.

The Einstein's universe metric seems to be the simplest metric with required by Einstein's property of non symmetry of metric <ref>Einstein's 1950 paper ''"On the Generalized Theory of Gravitation"'', published in April 1950 issue of ''"Scientific American"''. This paper was not placed for some reason in detailed bibliography of Einstein's papers of 1973 ''"Gravitation"'', by Misner, Thorne, and Wheeler. The reason might be that this book assumes at the onset the symmetric metric of spacetime while Einstein excluded such possibility possibly for it potential of creation of energy from nothing utilized indeed later in ''"Gravitation"'' in the form of Big Bang hypothesis. For this reason ''"Gravitation"'' might be considered advocating a creationist cosmology, as contrasted by stationary cosmology of '''Einsteinian gravitation'''.</ref>.

==Demystifying universe==

===Introduction to Einsteinian universe===

The Einsteinian gravitation, or rather the Einsteinian General Relativity (EGR), as it should be more properly called, is a contemporary theory of universe and its [[gravitation]]. In EGR the universe has been always approximately the same, never changing, beyond trivial movements of celestial bodies. The EGR is described generally by the [[Perfect cosmological principle]].

The theory is called ''"Einsteinian"'' since it's Einsteinian type theory, except a bit deeper since it includes elements that Einstein didn't know about. For this reason there are also a few flaws which had to be dealt with and removed (as [[cosmological constant]]). Those new elements and recognition of flaws showed up after 1985 when it turned out that the universe is not expanding (as it was obviosly neither expanding when Newton tried to describe it Without yet knowing though about the [[curvatures of spacetime]]. Yet almost purely Newtonian solution, with accuracy to

:<math>E=mc^2</math>,

where <math>E</math> is energy contained in any mass <math>m</math> and <math>c</math> is speed of light in vacuum, comes out with [[Einstein's radius of universe]]!

Which means that Einstein must have been doing something right assuming the [[perfect cosmological principle]] already in 1917. And so the EGR may be also "right" as far as we know<ref>

Theories are never really "right" unless they pass all the possible tests of their validity which the Big Bang hypohtesis was not able to pass and that's why it had to be replaced with EGR.

</ref>.

The EGR is explaning how the relativity of time and space (notions of non existence of absolute time and absolute space) are working in stationary, neither expanding nor contracting, eternal universe that has neither the beginning nor the end.

The EGR which except explaining the mechanism of gravitational force as ''inertial force'' pushing masses towards their most probable positions of minimum energy in which it reveals its quantum nature, explains also why due to relativity of time in curved space the universe ''looks as if it were expanding'', and expansion were accelerating with

:<math>dH/dt=-H_o^2/2</math>,

where <math>dH/dt</math> is a change of [[Hubble constant]] with distance from observer <math>r</math> converted to time <math>t</math> through <math>r=ct</math>, <math>H_o</math> is [[Hubble constant|Hubble "constant"]] near the Earth (at <math>t=0</math>).

The EGR explains why the value of [[Hubble constant|Hubble "constant"]] <math>H(t)</math>, which in reality is an exponential function, since the redshift is in reality an exponential function of distance (or time, since <math>r=ct</math>, distance <math>r</math> is the same as time <math>t</math> multiplied by speed of light), so the redshift

:<math>Z=exp(r/R_E)-1</math>,

where <math>R_E</math> is "[[Einstein's radius]]" of universe, and the [[Hubble constant]] equal approximately

:<math>H_o=Z/r=v/c/r=70km/s/Mpc</math>

implies density of space of universe as

:<math>6\times 10^{-27}kg/m^3</math>.

The EGR explains also why the above [[Hubble constant|Hubble "constant"]] in which <math>v</math> is '''apparent''' recession speed of a galaxy, is really

:<math>H_o=c/R_E</math>.

''"[[Einstein's radius of universe]]"'' <math>R_E</math> in the above equation equals roughly 13 billion light years is implied by the above value of [[Hubble constant|Hubble "constant"]] and why it should be consistent with minimum of angular diameters of galaxies between redshifts Z=1 and Z=2 which is additional test of EGR.

Therefore the EGR explains most of numerical results that the [[Big Bang]] cosmology is unable to explain.

===Critique of the Big Bang hypothesis (BBH)===

First of all there is no expansion of universe as it was proven by application of high school calculus to simple task of predicting the amount of [[intrinsic redshift]] in the universe in BBH. Lack of expansion disqualifies the BBH.

Since humans are not easily convinced by one proof of invalidity of certain assumption and easier by multiple proofs, there are more flaws of BBH:

* curvature of spacetime of the universe, allegedly causing gravitation, while gravitation is most likely caused by particles assuming the most probable position in flat spacetime formed by 10 curvatures of spacetime, while "curved spacetime" might produce disappearing of physical objects not observed in nature (unless they are socks in a washing machine), and creation of physical objects "out of blue" (neither observed in nature),

* symmetric metric tensor of spacetime, allegedly causing a need for assuming that spacetime is "expanding" while Einstein specifically presented the demand that metric tensor '''''must be non symmetric'''''<ref>

Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950, ''"Scientific American"'', dropped from bibliography of Einstein's papers in Misner, Thorne, and Wheeler's 1973 ''"Gravitation"''.

</ref> and possibly non Riemannian,

* quasars at cosmological distances (forced by the lack of alternative mechanism of the redshift except the expansion),

* "[[dark energy]]" (forced by the lack of alternative mechanism of the redshift except the expansion),

* to be continued

==History of Einsteinian gravitation (personal experience)==

===Atempt to get the rate of expansion of space===

I was all my life interested in physics though not in gravitation. I thought that gravitation works approximately as Newtonian equation say and there is nothing special about Newtonian force being
:<math>F_N=GMm/r^2</math>

Of course I "knew" that the universe is expanding and speed of expansion (called [[Hubble constant]])
is about 70km/s/Mpc. I also new that photons interact with masses in the universe that have to influence those photons slightly diminishing their momentum. All this was "known". What was not known was how much of their momentum photons lose flying through the universe, due to the presence of matter in the universe. I tried to calculate it approximately but got the results always between zero and infinity depending on my approximations, which obviously ment that my approximations were wrong.

In February 1985 I decided that it is crazy not to be able to calculate such a simple thing. I decided not to use any approximations this time and I calculated, with high school calculus, Newtonian math, and a little of Einsteinian physics (limited to equation <math>E=mc^2</math>) how much of cosmological [[redshift]] in the universe is due to the expansion of space and how much is due to the Newtonian interaction between photons and the masses of universe that as I learned from Ned Wright <ref>Edward L. (Ned) Wright, Astronomy
professor from UCLA, who advises through e-mail on problems within astronomy to anybody who has such problems. </ref> was called [[dynamical friction]].

I wanted to find out what is the real rate of expansion of space after subtracting the result of my calculations <math>\Delta H_o</math> from the [[Hubble constant]] <math>H_o</math> that, as I thought then, contained the total redshift: coming from the expansion of space and from [[dynamical friction]].

I thought that I can adjust the [[Hubble constant]] <math>H_o</math> by subtracting from it <math>\Delta H_o</math> to get the real rate of expansion of space. I thought that the rate of expansion was too high since nobody bothered with making those calculations of [[dynamical friction]]. When I asked astrophysicists they all kept saying that the dynamical friction must be "negligible" for photons since if it were not then someone would have calculated it already, and no one heard that it was ever done. Consequently no one knew how "negligible" it is.

===Surprise! Surprise! No expansion?!===

The result turned out to be <math>\Delta H_o= \sqrt{4 \pi G \rho}</math>, where <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the mass density of universe <ref>

See step-by-step calculations in [http://conservapedia.com/Essay:Demystified_gravitation#Step_by_step_derivation_of_cosmological_redshift]

</ref> but also that it is the whole [[Hubble constant]] of our universe. There was nothing left for the expansion of space.

It means that the cosmological [[redshift]] might be the result of interaction of photons with the masses of universe due to [[dynamical friction]] and none due to the expansion of space. Necessary conclusion was that the space of our universe is not expanding and the redshift is due [[dynamical friction]] of photons only (as Fritz Zwicky once suspected, just couldn't prove it with his math).

Could I with mine (or rather Newton's and Einstein's)?

===Checking the results and the first rejection===

To be sure that I didn't make any mathematical error I gave those results to a math professor who was teaching general relativity a few years earlier to check them<ref>Prof. Tadeusz Bałaban, presently tenured professor at [[Rutgers University]] in New Jersey, who checked my calculations in February 1985 before saying that they don't contain any mathematical error, after which I sent them to ''[["Nature"]]'', where the editor rejected them for his disbelief of them without any peer review. </ref>, and when he assured me that there was no math error I sent the results to ''[["Nature"]]'', which I subscribed to at that time, on February 12, 1985, for final verification and possible publication. Then I got a response from ''[["Nature"]]'': ... 20 February 1985, ''"I am afraid that we cannot publish your paper which is too speculative to be appropriate for Nature."'' Dr Philip Campbell, Physical Science Editor.

===Studying general relativity===

After the rejection letter from Dr Campbell, I asked him which part of my paper he considered "speculative" and sent the paper to ''"Physical Review Letters"''. It rejected it as well but after the referee said he does not understand it recommending rejection. Then I asked for a referee who understands gravitation and got one with whom I discussed the subject for many weeks learning in the meantime the general relativity mostly from his questions. Then I enrolled in the general relativity two semester course at Harvard University, Cambridge, MA to find out why such pretty paper can't be published. On March 28, 1985 came response from Dr Campbell: ''"Maybe our judgement is at fault but, based on that judgement, our decision must remain against publication."''

====Reformatted value of Hubble constant====

The first thing that I learned from my general relativity course in Harvard was that my result

:<math>\Delta H_o= \sqrt{4 \pi G \rho}</math>

can be written as

:<math>H_o=c/R_E</math>,

where <math>H_o</math> is as before [[Hubble constant]], <math>c</math> is speed of light in vacuum, and <math>R_E</math> is [[Einstein's radius of universe]].

To make a long story short I wrote another paper based on my newly acquired knowledge of general relativity, using in it already my reformatted Hubble constant being now equal <math>H_o=c/R_E</math> and arguing with a referee for several weeks explaining also except the reasons for the necessity of the universe being stable the temperature of MCBR (Microwave Cosmic Background Radiation) and how it allows the calculation of average size of pieces of non luminous matter.

The referee seemed to be impressed but not knowing what else might be my weak points and being not able to refute my results for any mathematical or physical problems decided that he will reassess their rejection on the basis if their little interest to the readers of ''"Physical Review Letters"''. Which the referee did and so my next rejection was for the presumed little interest of the readers in cosmology.

====Ratio of radius of Earth orbit to itself====

In the meantime I became the nuisance to the professor teaching my general relativity course. After he told us that we don't need just listen but are supposed to ask questions if we don't understand something. The first question he heard from the audience was "how come the ratio of radius of planet orbit to radius of Earth orbit is exectly one for the Earth?" After everybody started laughing at the silliness of the question I got less intimidated by the presence so many wise physicists around me and asked ''"if space expands with speed greater than the speed of light, what will be the speed that galaxies move with in respect to a guy connected by long pole to one of galaxies? Wouldn't it be greater than speed of light?"

The question was followed by long silence during which our teach was thinking intesively. After the silence became too long, he said ''"I teach this course for four years already and nobody ever asked me such a question so I need more time to think about it, just come to me tomorrow before the lecture so I have more time to think. I'm not really a [[relativists|relativist]] but a particle physicists, I just teach this course"''.

The question wasn't answered neither next day (''"no time"'') nor ever. I just learned that general realtivity is not a simple subject known to any physicist. So I started learning it and think about it on my own.

====Getting rid of cosmological constant====

First idea that came to my mind was that if the Einstein's value of [[cosmological constant]] stabilizes the universe then one should come up with such a constant that changes together with <math>R</math> (contraction of Ricci tensor) in such way that their sum vanishes. I called this hypothetical constant "contraction of ''[[Hubble tensor]]''" in honor of discoverer of [[Hubble redshift]]. To have a contraction one needs also a tensor itself so I needed a ''[[Hubble tensor]]'' as well. It would be a tensor having such properties that its contraction multiplied by half of metric would be equal exactly <math>\Lambda_E</math> (Einstein's value of [[cosmological constant]]). I just learned lately from a mathematician in my school, that such arangement is possible if the metric is non symmetric. Which it is, since it was metric required by Einstein for the spacetime <ref>Einstein, A., ''"On the Generalized Theory of Gravitation"'', April 1950 issue of ''"Scientific American"''. Einstein's paper has been dropped from the bibliography of Einstein's papers in 1973 ''"Gravitation"'' by Misner, Thorne, and Wheeler.</ref>.

====Hubble tensor====

Furthermore to make the spacetime flat to comply with the principle of conservation of energy and momentum (that followed from Noether theorem) I needed the missing antisymmetric part of Ricci tensor that would represent the "curvature of time" (the term coined by [[Richard Feynman]]) that would compensate the [[curvature of space]] represented by Ricci tensor to make the spacetime flat ([[Minkowski]]). [[Hubble tensor]] seemed an ideal candidate to fill up this place.

The metric that I assumed for Einsteinian universe is non symetric and degenerate (with vanishing determinant) and yet is approximates to very neet flat [[Minkowski]] metric <math>d\tau^2=dt^2-dr^2/c^2</math>. I sent this proposal of new Einstein field equation in January 1986 to ''"Rapid communications of Physical Review Letters"''. They received it on January 27, 1986, and rejected on March 14, 1986 by the same referee who rejected my previous stuff about Newtonian calculation of [[Hubble constant]] in [[Einstein's universe]].

====Future of Hubble tensor====

The assumption of existence of [[Hubble tensor]] leads to very neet Einsteinian equation <math>R_{\mu\nu}-g_{\mu\nu}R/2=8\pi T_{\mu\nu}+g_{\mu\nu}H/2</math> that is the same as the present Einstein field equation but without his [[cosmological constant]] replaced by <math>\Lambda=-H/2</math>, where <math>H</math> is contraction of [[Hubble tensor]].

To be continued... [[User:JimJast|JimJast]] 12:08, 24 August 2011 (EDT)

==See also==
*[[Counterexamples to Relativity]]

==References==
<References/>

[[Category: Astronomy]]
[[Category: Cosmology]]
[[Category: Physics]]

Einstein's radius

2011-09-21T23:41:02Z

JimJast: Undo revision 919013 by FindlayT (talk)

'''Einstein's radius''' is the radius of curvature of stationary (or less properly called "static") Einstein's universe model that was proposed by Einstein in 1917 and later given up after consensus of astronomers assumed that the universe is expanding. In 1985 it turned out that expansion is only a relativistic illusion produced by coupling of time with space but [[relativists]] didn't accept that and started to suppress notion of illusion by not allowing publications of papers explaining this illusion
<ref>

See [[Essay:Hubble redshift in Einstein's universe]].

</ref>. [[Relativists]] insisted that it is not an illusion but a real expansion. Though no scientific theory of expansion could be constructed as it contradicted the conservation laws (conservation of energy and momentum) so the hypothesis of expansion became a true [[cargo cult science]] as described by [[Richard Feynman]] in his rant against [[relativists]].

The illusion of expansion is explained in [[Gravitation demystified]] and so '''Einstein's radius''' would be about 13 billion light years. The number coming from division of speed of light by [[Hubble constant]] that represent the [[intrinsic redshift]] in the universe that is result of Newtonian calculation of [[dynamical friction]] of photons in a stationary [[Einstein's universe]]
<ref>
See the step-by-step derivation of [[intrinsic redshift]] and [[Hubble constant]] in [[Gravitation demystified]].
</ref>.
The exact value of '''Einstein's radius''' predicted theoretically as value at which the Einstein's field equation is stable or derived from [[intrinsic redshift]] of photons, is

:<math>R_E=c/\sqrt{4\pi G\rho}</math>,

where <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the density of space of universe.

==Rreferences==
<references/>

[[Category:Cosmology]]
[[Category:Astronomy]]
[[Category:Physics]]

Einstein's radius

2011-09-21T23:29:30Z

JimJast:

'''Einstein's radius''' is the radius of curvature of stationary (or less properly called "static") Einstein's universe model that was proposed by Einstein in 1917 and later given up after consensus of astronomers assumed that the universe is expanding. In 1985 it turned out that expansion is only a relativistic illusion produced by coupling of time with space but [[relativists]] didn't accept that and started to suppress notion of illusion by not allowing publications of papers explaining this illusion
<ref>

See [[Essay:Hubble redshift in Einstein's universe]].

</ref>. [[Relativists]] insisted that it is not an illusion but a real expansion. Though no scientific theory of expansion could be constructed as it contradicted the conservation laws (conservation of energy and momentum) so the hypothesis of expansion became a true [[cargo cult science]] as described by [[Richard Feynman]] in his rant against [[relativists]].

The illusion of expansion is explained in [[Gravitation demystified]] and so '''Einstein's radius''' would be about 13 billion light years. The number coming from division of speed of light by [[Hubble constant]] that represent the [[intrinsic redshift]] in the universe that is result of Newtonian calculation of [[dynamical friction]] of photons in a stationary [[Einstein's universe]]
<ref>
See the derivation of [[intrinsic redshift]] and [[Hubble constant]] in [[Gravitation demystified]].
</ref>.
The exact value of '''Einstein's radius''' predicted theoretically as value at which the Einstein's field equation is stable or derived from [[intrinsic redshift]] of photons, is

:<math>R_E=c/\sqrt{4\pi G\rho}</math>,

where <math>c</math> is speed of light in vacuum, <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is the density of space of universe.

==Rreferences==
<references/>

[[Category:Cosmology]]
[[Category:Astronomy]]
[[Category:Physics]]

Cargo cult science

2011-09-21T01:31:30Z

JimJast:

Halton Arp

2011-09-21T00:43:52Z

JimJast:

'''Halton Arp''' is an American astronomer, the author of 1987 book ''"Quasars, redshifts and controversies"''
<ref>
Arp, Halton, 1987, ''"Quasars, redshifts and controversies"'', Interstallar Media,2153 Russel Street, Berkeley, CA, ISBN 0-941325-00-8.
</ref>
who for the reason of not believing in the Big Bang hypothesis was taken away the telescope time from, and in this way forced to emmigrate from the US. He presently lives in Germany continuing his reaserch of [[quasar]]s that he considers local to their galaxies rather than remote objects at cosmological distances. In 1993 Arp co-athored with J. Narlikar a paper on geometry of spacetime
<ref>
Narlikar, J. & Arp, H., 1993, ''"Flat spacetime cosmology - a unified framework for extragalactic redshifts"'', Astrophysical Journal, Part 1 (ISSN 0004-637X) vol. 405, no. 1, The American Astronomical Society, p.51-56, Bibliographic code: 1993 ApJ...405...51N
</ref> that proposed the idea of flat spacetime (also proposed by others)
<ref>
See a detailed explanation of the mechanism of Einsteinian gravitation [[Gravitation demystified]]. It explains the Einsteinian gravitational force as ''inertial push'' at the quantum level in ''[[flat spacetime]]''.
</ref>.
Arp's research contradicts the idea of expanding universe and confirms the idea that the universe is stationary as it was shown with relativistic physics and Newtonian math in 1985, when it was discovered that the [[Hubble constant]] of stationary universe is
:<math>H_o=c/R_E=\sqrt{4\pi G\rho}</math>,
where <math>c</math> is speed of light in vacuum, <math>R_E</math> is radius of curvature of space (called ''"[[Einstein's radius]]"''), <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is density of space
<ref>
See [[Essay:Hubble redshift in Einstein's universe]]. Except conservapedia (and briefly in RW, before access to the paper were blocked by the University of Warsaw, Poland) it was never published by any mainstream scientific journal and therefore remains unknown to the physicists and astronomers
</ref> and so the cosmological redshift is exactly Arp's [[Intrinsic redshift]] with which one may measure the average density of universe (and possibly also the density of space around [[quasar]]s).

:<math>H_o=70km/s/Mpc</math> implies

:<math>\rho=6\times 10^{-27}kg/m^3</math>

==References==
<References/>

[[Category:Cosmology]]
[[Category:Astronomy]]
[[Category:Physics]]

Halton Arp

2011-09-21T00:37:03Z

JimJast:

'''Halton Arp''' is an American astronomer, the author of 1987 book ''"Quasars, redshifts and controversies"''
<ref>
Arp, Halton, 1987, ''"Quasars, redshifts and controversies"'', Interstallar Media,2153 Russel Street, Berkeley, CA, ISBN 0-941325-00-8.
</ref>
who for the reason of not believing in the Big Bang hypothesis was taken away the telescope time from, and in this way forced to emmigrate from the US. He presently lives in Germany continuing his reaserch of [[quasar]]s that he considers local to their galaxies rather than remote objects at cosmological distances. In 1993 Arp co-athored with J. Narlikar a paper on geometry of spacetime
<ref>
Narlikar, J. & Arp, H., 1993, ''"Flat spacetime cosmology - a unified framework for extragalactic redshifts"'', Astrophysical Journal, Part 1 (ISSN 0004-637X) vol. 405, no. 1, The American Astronomical Society, p.51-56, Bibliographic code: 1993 ApJ...405...51N
</ref> that proposed the idea of flat spacetime (also proposed by others)
<ref>
See a detailed explanation of the mechanism of Einsteinian gravitation [[Gravitation demystified]]. It explains the Einsteinian gravitational force as ''inertial push'' at the quantum level in ''[[flat spacetime]]''.
</ref>.
Arp's research contradicts the idea of expanding universe and confirms the idea that the universe is stationary as it was shown with relativistic physics and Newtonian math in 1985, when it was discovered that the [[Hubble constant]] of stationary universe is
:<math>H_o=c/R_E=\sqrt{4\pi G\rho}</math>,
where <math>c</math> is speed of light in vacuum, <math>R_E</math> is radius of curvature of space (called ''"[[Einstein's radius]]"''), <math>G</math> is Newtonian gravitational constant, and <math>\rho</math> is density of space
<ref>
See [[Essay:Hubble redshift in Einstein's universe]]. Except conservapedia (and briefly in RW, before access to the paper were blocked by the University of Warsaw, Poland) it was never published by any mainstream scientific journal and therefore remains unknown to the physicists and astronomers
</ref> and so the cosmological redshift is exactly Arp's [[Intrinsic redshift]] with which one may measure the average density of universe

:<math>H_o=70km/s/Mpc</math> implies

:<math>\rho=6\times 10^{-27}kg/m^3</math>

==References==
<References/>

[[Category:Cosmology]]
[[Category:Astronomy]]
[[Category:Physics]]

Halton Arp

2011-09-21T00:18:05Z

JimJast:

'''Halton Arp''' is an American astronomer, the author of 1987 book ''"Quasars, redshifts and controversies"''
<ref>
Arp, Halton, 1987, ''"Quasars, redshifts and controversies"'', Interstallar Media,2153 Russel Street, Berkeley, CA, ISBN 0-941325-00-8.
</ref>
who for the reason of not believing in the Big Bang hypothesis was taken away the telescope time from, and in this way forced to emmigrate from the US. He presently lives in Germany continuing his reaserch of [[quasar]]s that he considers local to their galaxies rather than remote objects at cosmological distances. In 1993 Arp co-athored with J. Narlikar a paper on geometry of spacetime
<ref>
Narlikar, J. & Arp, H., 1993, ''"Flat spacetime cosmology - a unified framework for extragalactic redshifts"'', Astrophysical Journal, Part 1 (ISSN 0004-637X) vol. 405, no. 1, The American Astronomical Society, p.51-56, Bibliographic code: 1993 ApJ...405...51N
</ref> that proposed the idea of flat spacetime (also proposed by others)
<ref>
See a detailed explanation of the mechanism of Einsteinian gravitation [[Gravitation demystified]]. It explains the Einsteinian gravitational force as ''inertial push'' at the quantum level in ''[[flat spacetime]]''.
</ref>.
Arp's research contradicts the idea of expanding universe and confirms the idea that the universe is stationary as it was shown with relativistic physics and Newtonian math in 1985, when it was discovered that the [[Hubble constant]] of stationary universe is
:<math>H_o=c/R_E</math>,
where <math>c</math> is speed of light in vacuum, and <math>R_E</math> is radius of curvature of space (called ''"[[Einstein's radius]]"'')
<ref>
See [[Essay:Hubble redshift in Einstein's universe]]. Except conservapedia (and briefly in RW, before access to the paper were blocked by the University of Warsaw, Poland) it was never published by any mainstream scientific journal and therefore remains unknown to the physicists and astronomers
</ref> and so the cosmological redshift is exactly Arp's [[Intrinsic redshift]] with which one may measure the average density of the universe.

==References==
<References/>

[[Category:Cosmology]]
[[Category:Astronomy]]
[[Category:Physics]]

Halton Arp

2011-09-21T00:15:57Z

JimJast:

'''Halton Arp''' is an American astronomer, the author of 1987 book ''"Quasars, redshifts and controversies"''
<ref>
Arp, Halton, 1987, ''"Quasars, redshifts and controversies"'', Interstallar Media,2153 Russel Street, Berkeley, CA, ISBN 0-941325-00-8.
</ref>
who for the reason of not believing in the Big Bang hypothesis was taken away the telescope time from, and in this way forced to emmigrate from the US. He presently lives in Germany continuing his reaserch of [[quasar]]s that he considers local to their galaxies rather than remote objects at cosmological distances. In 1993 Arp co-athored with J. Narlikar a paper on geometry of spacetime
<ref>
Narlikar, J. & Arp, H., 1993, ''"Flat spacetime cosmology - a unified framework for extragalactic redshifts"'', Astrophysical Journal, Part 1 (ISSN 0004-637X) vol. 405, no. 1, The American Astronomical Society, p.51-56, Bibliographic code: 1993 ApJ...405...51N
</ref> that proposed the idea of flat spacetime (also proposed by others)
<ref>
See a detailed explanation of the mechanism of Einsteinian gravitation [[Gravitation demystified]]. It explains the Einsteinian gravitational force as ''inertial push'' at the quantum level in ''[[flat spacetime]]''.
</ref>.
Arp's research contradicts the idea of expanding universe and confirms the idea that the universe is stationary as it was shown with relativistic physics and Newtonian math in 1985, when it was discovered that the [[Hubble constant]] of stationary universe is
:<math>H_o=c/R_E</math>,
where <math>c</math> is speed of light in vacuum, and <math>R_E</math> is radius of curvature of space (''"[[Einstein's radius]]"'')
<ref>
See [[Essay:Hubble redshift in Einstein's universe]]. Except conservapedia (and briefly in RW, before access to the paper were blocked by the University of Warsaw, Poland) it was never published by any mainstream scientific journal and therefore remains unknown to the physicists and astronomers
</ref> and so the cosmological redshift is exactly Arp's [[Intrinsic redshift]] with which one may measure the average density of the universe.

==References==
<References/>

[[Category:Cosmology]]
[[Category:Astronomy]]
[[Category:Physics]]

Halton Arp

2011-09-21T00:11:59Z

JimJast:

'''Halton Arp''' is an American astronomer, the author of 1987 book ''"Quasars, redshifts and controversies"''
<ref>
Arp, Halton, 1987, ''"Quasars, redshifts and controversies"'', Interstallar Media,2153 Russel Street, Berkeley, CA, ISBN 0-941325-00-8.
</ref>
who for the reason of not believing in the Big Bang hypothesis was taken away the telescope time from, and in this way forced to emmigrate from the US. He presently lives in Germany continuing his reaserch of [[quasar]]s that he considers local to their galaxies rather than remote objects at cosmological distances. In 1993 Arp co-athored with J. Narlikar a paper on geometry of spacetime
<ref>
Narlikar, J. & Arp, H., 1993, ''"Flat spacetime cosmology - a unified framework for extragalactic redshifts"'', Astrophysical Journal, Part 1 (ISSN 0004-637X) vol. 405, no. 1, The American Astronomical Society, p.51-56, Bibliographic code: 1993 ApJ...405...51N
</ref> that proposed the idea of flat spacetime (also proposed by others)
<ref>
See a detailed explanation of the mechanism of Einsteinian gravitation [[Gravitation demystified]]. It explains the Einsteinian gravitational force as ''inertial push'' at the quantum level in ''[[flat spacetime]]''.
</ref>.
Arp's research contradicts the idea of expanding universe and confirms the idea that the universe is stationary as it was shown with relativistic physics and Newtonian math in 1985, when it was discovered that the [[Hubble constant]] of stationary universe is
:<math>H_o=c/R_E</math>,
where <math>c</math> is speed of light in vacuum, and <math>R_E</math> is radius of curvature of space (''"[[Einstein's radius]]"'')
<ref>
See [[Essay:Hubble redshift in Einstein's universe]]. Except conservapedia (and briefly in RW, before access to the paper were blocked by the University of Warsaw, Poland) it was never published by any mainstream scientific journal and therefore remains unknown to the physicists and astronomers
</ref> and so the Hubble redshift is exactly Arp's ''"[[Intrinsic redshift]]"''.

==References==
<References/>

[[Category:Cosmology]]
[[Category:Astronomy]]
[[Category:Physics]]