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Theory of relativity

2017-08-21T15:05:14Z

Geocentric: synchronization between altitudes on earth vs Einstein desynchronization

''See also [[Counterexamples to Relativity]].''

In physics, the '''theory of relativity''' is a scientific theory describing the effects due to the invariance of the speed of light. In particular, the meaning of space and time are altered by the motion of the observer. Relativity predicts phenomena such as time dilation and length contraction for observers moving relative to one another at very high ("relativistic") speed.

'''Relativity''' refers to two closely-related mathematical theories in [[physics]]:
[[Image:600px-Albert Einstein Head.jpg|thumbnail|right|200px|
*"I do not share the crusading spirit of the professional [[Atheism|atheist]] whose fervor is mostly due to a painful act of liberation from the fetters of religious indoctrination received in youth. I prefer an attitude of humility corresponding to the weakness of our intellectual understanding of nature and of our own being." - [[Albert Einstein]]<ref name="Isaacson390">Isaacson, Walter (2008). [http://books.google.com/books?id=cdxWNE7NY6QC&pg=PT390 ''Einstein: His Life and Universe''] (New York: Simon and Schuster), p. 390. Retrieved from GoogleBooks archive on February 19, 2015.</ref>]]
*'''[[Special theory of relativity|Special relativity]]''' (SR) is a theory which describes the laws of motion for non-accelerating bodies traveling at a significant fraction of the [[speed of light]]. As speeds approach zero, Special Relativity tends towards equivalence with [[Newton's Laws of Motion]]. Special Relativity was developed by [[Hendrik Lorentz]], [[Henri Poincaré]], and Hermann Minkowski,<ref>"German mathematician who developed the geometrical theory of numbers and who made numerous contributions to number theory, mathematical physics, and the theory of relativity." [http://www.britannica.com/eb/article-9052860/Hermann-Minkowski Hermann Minkowski -- Britannica Online Encyclopedia]</ref><ref>[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Minkowski.html Hermann Minkowski, Biography]</ref> and [[Albert Einstein]].

*'''[[General theory of relativity|General Relativity]]''' (GR) is a theory which explains the laws of motion as viewed from accelerating reference frames and includes a geometric explanation for gravity. This theory was developed by [[David Hilbert]] and [[Albert Einstein]] as a generalization of the postulates of Special Relativity.<ref>"[T]he German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein."[http://nobelprize.org/educational_games/physics/relativity/history-1.html Nobel Prize historical account]</ref> A dramatic but later discredited claim by Sir [[Arthur Eddington]] of experimental proof of General Relativity in 1919 made Einstein a household name.

These theories have augmented earlier approaches, such as [[Galilean Relativity]].

The theory of relativity is defended with religious-like zeal, such that no college faculty tenure, Ph.D degree, or Nobel Prize is ever awarded to anyone who dares criticize the theory, as the example of denying a Nobel Prize to the most accomplished physicist of the 20th century, [[Robert Dicke]], illustrates. Another critic of the theory was Louis Essen [1908-1997], the man credited with determining the speed of light. He wrote many fiery papers against it such as ''Relativity and Time Signals''<ref>http://gsjournal.net/Science-Journals/Journal%20Reprints-Relativity%20Theory/Download/3297</ref> and ''Relativity - Joke or Swindle?''.<ref>http://www.ekkehard-friebe.de/Essen-L.htm</ref> Perhaps the most famous website opposing relativity is this one, with its [[Counterexamples to Relativity]] page. The cornerstone item in that page involves the experimental measurements of the advance of the perihelion of Mercury that show a shift greater than predicted by Relativity, well beyond the margin of error.

The theory of relativity have discontinuities whereby the limit of a physical quantity as a variable (such as mass or velocity) approaches a fixed value is not the same as the physical quantity at the fixed value. For example, the limit of momentum as mass approaches 0 and velocity approaches the speed of light is not equal to the momentum of (massless) light.<ref>Discontinuities in General Relativity are also well-recognized. See, e.g., [http://www.springerlink.com/content/u47l341u2q555455/]</ref>

The theory of relativity consist of complex mathematical equations relying on several hypotheses. For example, at Hofstra University general relativity is taught as part of an upperclass math course on differential geometry, based on three stated assumptions.<ref>http://people.hofstra.edu/Stefan_Waner/diff_geom/tc.html</ref> Special relativity assumes that all observers in inertial frames of reference will measure the same value for the speed of light, '''c''' and that all inertial frames of reference are equivalent. These hypotheses that can never be fully tested. Relativity rejects Newton's [[action at a distance]], which is basic to Newtonian gravity and also found to be a consequence of [[quantum mechanics]]. The mathematics of relativity assume no exceptions, yet in the time period immediately following the origin of the universe the relativity equations could not possibly have been valid, since quantum effects would not be negligible (in the same way non-relativistic quantum mechanics is not valid when dealing with particles traveling near the speed of light).

The "continuous" nature of space and time postulated by relativity is in conflict with the "discrete" nature in [[quantum mechanics]],<ref>For example, Relativity claims that space and time are smooth and continuous, while [[quantum mechanics]] suggests otherwise. [http://www.csmonitor.com/Science/Cool-Astronomy/2010/1025/Is-the-universe-a-big-hologram-This-device-could-find-out.] Relativity also denies [[action-at-a-distance]], while quantum mechanics suggests otherwise. Relativity denies any role for chance, while quantum mechanics is heavily dependent on it.</ref> and although theories like [[string theory]] and [[quantum field theory]] have attempted to unify relativity and quantum mechanics, neither has been entirely successful or proven.

Unlike [[Classical mechanics|Newtonian physics]], in which space and time intervals are each invariant as seen by all observers, in SR the only invariant quantity is a quadratic combination of space and time intervals (x2 - c2 t2). The instantaneous transmission of Newtonian gravitational effects also contradicts relativity.

In quantum mechanics, the [[uncertainty principle]] suggests that virtual particles can sometimes travel faster than the speed of light which would violate causality, but "[t]he only known way to resolve this tension involves introducing the idea of antiparticles."<ref>http://nobelprize.org/nobel_prizes/physics/laureates/2004/wilczek-lecture.pdf (p. 102)</ref> Consequently, in 1928 Paul Dirac derived the Dirac equation, one of the first quantum mechanical equations compatible with special relativity, by which Dirac predicted the existence of antimatter. Four years later, antimatter (the positron) was discovered by Carl Anderson, as successfully predicted by relativistic quantum mechanics. [[Quantum field theory]], a generalization of quantum mechanics, is fully compatible with special relativity but not with general relativity, and still lacks a vital piece: evidence of the [[graviton]].

A famous critic of Theory of relativity is [[Nikola Tesla]], who called it a "...magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king ... its exponents are brilliant men but they are metaphysicists, not scientists...".<ref>[http://www.plasmacosmology.net/tesla.html New York Times, July 11, 1935, p23, c8]</ref>

== Special Relativity ==
Lorentz and Poincaré developed Special Relativity as way of understanding how Maxwell's equations for electromagnetism could be valid in different frames of reference. Einstein famously published an explanation of Poincaré's theory in terms of two assumptions (postulates):

# ''The [[speed of light]] is constant for all (inertial) observers, regardless of their velocities relative to each other.''
# ''The laws of physics are identical in all inertial reference frames.''

In layman's terms, these two assumptions can be restated as:
# It is impossible ever to transmit information faster than the speed of light.<ref>This assumption is commonly restated in this manner. For example, a discussion of hypothetical [[tachyons]] talks "about using tachyons to transmit information faster than the speed of light, '''in violation of Special Relativity'''."[http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html] However, there is some question whether the Theory of Special Relativity really restricts faster-than-light communication of information.</ref>
# The laws of physics are identical, without any variation, in every location throughout the universe.
# The laws of physics are identical, without any variation, no matter how fast something is traveling (in the absence of acceleration).

Or, in more concise, clearer terms, these assumptions are this:

#there is no [[action at a distance]] (because that would make observations dependent on the frame of reference)
#space and time are completely symmetric throughout the universe (because otherwise frames of reference would not be interchangeable)

When the assumptions are stated clearly as above, the weaknesses in the theory are more apparent. There “is” action at a distance in [[quantum entanglement]] and apparently also in gravity, as no gravitons can be found. However, no information has yet been transmitted via quantum entanglement, so while non-locality violates the spirit of relativity it is consistent with it if relativity is limited to the transmission of information. [[Quantum field theory]], an attempt to partially reconcile [[quantum mechanics]] with relativity, is incomplete at best. As to the second assumption, it is contrary to the [[arrow of time]], which illustrates the lack of symmetry in time. Logical defects include the incoherence of relativistic mass (see discussion below) and the lack of relativistic constraints near the beginning the universe (see above).

Special Relativity (SR) was initially developed by [[Henri Poincaré]] and [[Hendrik Lorentz]], working on problems in electrodynamics and the [[Michelson-Morley experiment]], which had not found any sign of Earth's orbital motion through the [[aether (science)|luminiferous aether]], which was believed to be the substance which carried electromagnetic waves. Special relativity alters [[Isaac Newton]]'s laws of motion by assuming that the speed of light will be the same for all observers, despite their relative velocities and the source of the light. (Therefore, if A sends a beam of light to B, and both measure the speed, it will be the same for both, no matter what the relative velocity of A and B. In Newtonian/Galilean mechanics, If A sends a physical object at a particular velocity towards B, and nothing slows it, the velocity of the object relative to B depends on the velocities of the object and of B relative to A.)

At low speeds (relative to light-speed), the Lorentz-Poincaré relativity equations are equivalent to Newton's equations. The media-promoted equation ''[[E=mc²]]'', implausibly suggests a relationship between typically unrelated concepts of energy, the rest mass of a body and the speed of light.

Under relativity, particles at low mass and low speed can be accurately approximated by [[classical mechanics]] (such as [[Isaac Newton]]'s laws of motion). At the two extremes, modeling the behavior of electrons requires that relativistic effects be taken into account (the chemically significant phenomenon of electron spin arises from relativity), and the course of light passing through a region containing many massive bodies such as galaxies will be distorted ([[classical mechanics]], in which light travels in straight lines, does not predict this). These are both experimentally confirmed (electron spin was known before relativity arose, and telescopic observations confirm that galactic clusters distort the paths of the light passing through them).

Many scientists have indicated problems with the postulates of special relativity. Paul Davies, formerly of Macquarie University and now at the University of Arizona believes that the speed of light has changed over time. Since the speed of light is a constant speed 'c' this indicates problems with the theory [http://news.bbc.co.uk/2/hi/science/nature/2181455.stm light speed]. Other engineers and scientists have written about problems in the basic set of special relativity equations. Based on the ideas of not Einstein but of the scientist Fitzgerald as well as others, a length contraction effect was predicted as an explanation of the failure of the Michelson-Morley experiment to detect Earth's orbital motion. This idea was taken up by Hendrik Lorentz and shown by others to be a useful mechanism by which theory could be forced into conformance with experimental results. However, in 2005, Michael Strauss a computer engineer invalidated much of Special Relativity theory by showing clear contradictions in the theory. [http://www.relativitycollapse.com relativity]

== General Relativity ==

::::''See the [[General theory of relativity]] page for more in-depth coverage of this topic.''

General Relativity is a theory of gravity that is compatible with Special Relativity. Einstein explains a thought experiment involving two elevators. The first elevator is stationary on the Earth, while the other is being pulled through space at a constant acceleration of g. Einstein realized that any physical experiment carried out in the elevators would give the same result. This realization is known as the equivalence principle and it states that accelerating frames of reference and gravitational fields are indistinguishable. General Relativity is the theory of gravity that incorporates Special Relativity and the equivalence principle.

General Relativity is a mathematical extension of Special Relativity. GR views space-time as a 4-dimensional [[manifold]], which looks locally like [[Minkowski space]], and which acquires [[curvature]] due to the presence of massive bodies. Thus, near massive bodies, the geometry of space-time differs to a large degree from [[Euclidean geometry]]: for example, the sum of the angles in a triangle is not exactly 180 degrees. Just as in classical physics, objects travel along [[geodesic]]s in the absence of external forces. Importantly though, near a massive body, geodesics are no longer straight lines. It is this phenomenon of objects traveling along geodesics in a curved spacetime that accounts for gravity.

The anomalous precession of Mercury's [[perihelion]] seems to support the Theory of General Relativity, though that is disputed on the[[Counterexamples to Relativity]] page. Keep in mind that the precession in question is the ''"anomalous"''
precession after the effects of other planets' gravitation action has been compensated for. Those other effects are much larger, and are purely Newtonian in nature. There was another explanation based on Newtonian gravity, involving a slight alteration to the precise inverse-square relation of Newtonian gravity to distance, but it was discarded when it gave very bad results for the Moon's orbit.

British Historian Paul Johnson declares the turning point in 20th century to have been when fellow Briton Sir [[Arthur Eddington]], an esteemed English astronomer, ventured out on a boat off Africa in 1919 with a local Army unit to observe the bending of starlight around the sun during a total eclipse. Upon his return to England declared that his observations proven the theory of relativity. In fact recent analysis of Eddington's work revealed that he was biased in selecting his data, and that overall his data were inconclusive about the theory of relativity. The prediction was later confirmed by more rigorous experiments, such as those performed by the [[Hubble Space Telescope]].<ref>[http://www.spaceimages.com/gravlen.html Hubble Gravitational Lens Photo]</ref><ref>[[Gravitational lensing]]</ref><ref>[http://www.iam.ubc.ca/~newbury/lenses/glgallery.html]</ref> Lorentz has this to say on the discrepancies between the empirical eclipse data and Einstein's predictions.

::''It indeed seems that the discrepancies may be ascribed to faults in observations, which supposition is supported by the fact that the observations at Prince's Island, which, it is true, did not turn out quite as well as those mentioned above, gave the result, of 1.64, somewhat lower than Einstein's figure.''<ref>Lorentz, H.A. [http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm The Einstein Theory of Relativity]</ref>

The prediction that light is bent by gravity is predicted both by Newtonian physics and relativity, but relativity predicts a larger deflection.

Special relativity is the limiting case of general relativity where all gravitational fields are weak. Alternatively, special relativity is the limiting case of general relativity when all reference frames are inertial (non-accelerating and without gravity).

==Lack of evidence for Relativity==
The Theory of relativity assumes that time is symmetric just as space is, but the biggest early promoter of relativity, Arthur Eddington, coined the term "[[arrow of time]]" admitting how time is ''not'' symmetric but is directional. The passage of time is tied to an increase in disorder, or [[entropy]]. The Theory of relativity cannot explain this, and implicitly denies it, specifically allowing for theoretical time travel (e.g., [[wormholes]]) and different rates of passage of time based on velocity and acceleration.

Claims that relativity was used to develop the [[Global Positioning System]] ([[GPS]]) are false. A 1996 article explains:

:"The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein's general theory of relativity would seem to require - transformations to and from the individual space vehicles (SVs), the Monitor Stations (MSs), and the users on the surface of the rotating earth, and the geocentric Earth Centered Inertial System (ECI) in which the SV orbits are calculated. There is a very good reason for the omission: the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter - less than one centimeter, for users on or near the earth."<ref>http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf</ref><ref>Some do claim that relativity is "vital" to GPS even though GPS developed independently of theoretical predictions and theoreticians disagree about how the relativistic effects for GPS should be calculated. ''See id. See also'' [http://www.rand.org/pubs/monograph_reports/MR614/MR614.appb.pdf]</ref>

This article, which was published in 1996, goes on to propose relativistic corrections that might be used to design more accurate GPS systems. Clocks on board GPS satellites require adjustments to their clock frequencies if they are to be synchronized with those on the surface of the Earth.

Tom Van Flandern, an astronomer hired to work on GPS in the late 1990s, concluded that "[t]he GPS programmers don't need relativity." He was quoted as saying that the GPS programmers "have basically blown off Einstein."<ref>http://archive.salon.com/people/feature/2000/07/06/einstein/index.html See also [http://www.metaresearch.org/solar%20system/gps/absolute-gps-1meter-3.ASP], where Van Flandern discusses how relativistic corrections might improve GPS accuracy.</ref> Asynchronization can be easily addressed through communications between the satellites and ground stations, so it is unclear why any theory would be needed for GPS. While Van Flandern believed that relativity is unnecessary for GPS, he also asserted that observations of GPS satellites supported both general and special relativity, writing that "we can assert with confidence that the predictions of relativity are confirmed to high accuracy over time periods of many days," with unrelated factors interfering with longer-term observations.<ref>http://www.metaresearch.org/cosmology/gps-relativity.asp</ref>

Some internet articles claim that GPS timing differences ''confirm'' the Theory of Relativity or its Lorentzian counterpart (which uses a preferred frame of reference). GPS clocks run slower in the weaker gravitation field of the satellites than on ground stations on Earth, with the effects predicted by general relativity far outweighing the effects predicted by special relativity. However, the articles claiming that the slower GPS satellite clocks confirm relativity do not address the effect, if any, of the weaker gravitational force under Newton's theory on the GPS satellite clocks, likely because in Newtonian Mechanics every clock in the universe keeps time at the same rate regardless of velocity, acceleration, or the presence or absence of force.

Currently, GPS satellites are synchronized to Coordinated Universal Time by radio signals from the ground; therefore, they cannot currently be used to test general relativity.<ref>[http://www.phys.lsu.edu/mog/mog9/node9.html "General Relativity in the Global Positioning System."] Neil Ashby, U. of Colorado</ref>

There are claims that the effects of relativity have been observed with the frequency shift of the signal being sent back to [[Earth]] several times as various spacecraft have dipped into the gravity wells around massive objects such as the [[sun]] (see image at right)<ref>[http://saturn.jpl.nasa.gov/news/press-releases-03/20031002-pr-a.cfm Saturn-Bound Spacecraft Tests Einstein's Theory]</ref> or Saturn.<ref>[http://www.newscientist.com/article/mg12517102.600-science-encounter-with-saturn-confirms-relativity-theory.html Encounter with Saturn confirms relativity theory]</ref> A satellite called [[Gravity Probe B]] was put in orbit about the Earth to examine the effects of frame dragging and geodetic warping of space,<ref>[http://www.nasa.gov/mission_pages/gpb/index.html NASA Gravity Probe B mission page]</ref><ref>[http://einstein.stanford.edu/ Gravity Probe B project page]</ref> but the results were inconclusive. Note, however, that Newtonian mechanics also predicts deflection of light by gravity, and in the initial theory of relativity it predicted the same amount of deflection, but only if we treat light as capable of being accelerated and decelerated like ordinary matter, which is contrary to all measurements and observations to date.<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> Adjustments to the theory of relativity resulted in a prediction of a greater deflection of light than that predicated by Newtonian mechanics, though it is debatable how much deflection Newtonian mechanics should predict.

None of the NASA spacecraft incorporates predictions of relativity into their own timing mechanisms, as Newtonian mechanics is adequate even for probes sent deep into space so long as they do not undergo accelerations near the speed of light or enter any massive gravity wells.<ref>There is no reported reliance on relativity by any space probe.</ref>

A decade of observation of the [[pulsar]] pair [[PSR 1913 16|PSR B1913+16]] detected a decline in its orbital period, which was attributed to a loss in energy by the system. It is impossible to measure the masses of the pulsars, their accelerations relative to the observers, or other fundamental parameters. Professors Joseph Taylor and Russell Hulse, who discovered the binary pulsar, found that physical values could be assigned to the pulsars to make the observed decline in orbital period consistent with the Theory of General Relativity, and for this they were awarded the 1993 [[Nobel Prize]] for Physics, which is the only award ever given by the Nobel committee for the Theory of Relativity.<ref>http://nobelprize.org/nobel_prizes/physics/laureates/1993/press.html</ref> In 2004, Professor Taylor utilized a correction to the derivative of the orbital period to fit subsequent data better to the theory. At most, assumptions can be made and altered to fit the data to the theory, rather than the data confirming the theory.

The [[perihelion]] of Mercury's [[orbit]] [[precession|precesses]] at a measurable rate, but even after accounting for gravitational perturbations caused all other planets in the [[solar system]], Newton's theory (assuming a precise inverse-square relationship for distance) predicts a rate of precession that differs from the measured rate by approximately 43 [[arcsecond]]s per century. While general relativity was developed on purely theoretical grounds, it was soon discovered that it explained these precession observations.<ref>http://physics.ucr.edu/~wudka/Physics7/Notes_www/node98.html#SECTION032121000000000000000</ref><ref>http://farside.ph.utexas.edu/teaching/336k/lectures/node117.html</ref> Newton's theory can also explain the Mercury precession by making tiny adjustments to parameters in the gravitational equation, but doing so would give the same precession for all orbiting bodies everywhere, a phenomenon which is not observed.

General relativity predicts twice as much bending in light as it passes near massive objects than Newton's theory might predict.<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> This phenomenon is known as [[gravitational lensing]]. A large number of instances of gravitational lensing have been observed, and it is now a standard astronomical tool.<ref>http://imagine.gsfc.nasa.gov/docs/features/news/grav_lens.html</ref><ref>http://astro.berkeley.edu/~jcohn/lens.html</ref><ref>http://www.iam.ubc.ca/~newbury/lenses/glgallery.html</ref> Note, however, that the extent of bending of light predicted by Newton's theory is open to debate, and depends on assumptions about the nature of light for gravitational purposes.<ref>http://cosmictimes.gsfc.nasa.gov/1919/guide/gravity_bends_starlight.html</ref>

In 1972, scientists flew extremely accurate clocks ("atomic clocks") around the world in both directions on commercial airlines, and claimed to observe relativistic time dilation; the eastbound clock gained 273 ns and the westbound clock lost 59 ns, matching the predictions of general relativity to within experimental accuracy.<ref>[http://www.answers.com/topic/hafele-keating-experiment Hafele-Keating Experiment]</ref> However, the inventor of the atomic clock, Louis Essen, declared that the experiment was inaccurate.<ref>Louis Essen, Electron. Wireless World 94 (1988) 238.</ref> Dr A. G. Kelly examined the raw data from the experiment and declared it inconclusive.<ref>A. G. Kelly,Reliability of Relativistic Effect Tests on Airborne Clocks, Monograph No.3 Feb.1996, The Institution of Engineers of Ireland, ISBN 1-898012-22-9</ref> The Nobel Committee chose not to honor this experiment for the significance that was claimed.

Despite [[censorship]] of dissent about relativity, evidence contrary to the theory is discussed outside of [[liberal]] universities.<ref>http://scitizen.com/screens/blogPage/viewBlog/sw_viewBlog.php?idTheme=8&idContribution=922</ref>

==Experiments that Fail to Prove Relativity==

Predictions of general relativity turn out to be obscure and difficult to test. The two most famous predictions were the bending of light in a gravitational field and the precession of the perihelia of orbiting planets.

*The first of these was famously tested during a total eclipse in 1919. That test was somewhat muddled by an incorrect initial calculation, by several people including Einstein himself, of what the effect would be, and some "cherry picking" of the data to be used.<ref>''Einstein's Luck'', John Waller, Oxford University Press, ISBN 0-19-860719-9</ref> The data selection could be considered "manipulation" or "fudging", by a person (Arthur Eddington) who had a personal stake in the outcome. His analysis techniques would not pass muster today.

:It should be noted that pre-relativistic (Newtonian) physics may also predict a bending, of half the observed value, depending on whether one uses the 17th century "corpuscular" formulation or the 19th century "wave" formulation.

:Nevertheless, it has been verified with ever-increasing precision in subsequent eclipses, and in the observations of quasar 3C273.

*The second "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury. There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun. These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century. This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

:Increasingly precise measurements of the precession demonstrate that it conflicts with General Relativity, despite claims of relativists for decades that it predicted the precession accurately in the amount of <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.<ref>That is a simple approximation, designed to relate the precession to the planet's speed relative to the speed of light. A more accurate approximation is <math>\frac{3GM}{c^2 a(1-e^2)}</math>, where a is the semi-major axis and e is the eccentricity.</ref> The conflict is greater than the margin of error, and many relativists avoid the discrepancy rather than address it.

==Experimental and Observational Evidence Confirming Relativity==

The different effects predicted by special relativity, compared to classical formulations, are extremely tiny. Most relativistic effects are negligible at the speeds of ordinary phenomena observed by humans. The effects only become significant when the speeds involved are a significant fraction of the speed of light, which is <math>3 \times 10^8</math> meters per second—such speeds are called ''relativistic''. (However, it's worth noting that ordinary magnetism can be considered an effect of relativity, dictated by the need for electrostatic theory to be correct under relativity. The speed of light in fact appears in the formulas ([[Maxwell's Equations]]) governing electricity and magnetism, though these equations were developed long before relativity was proposed.)

Because the effects of relativity are so tiny, scientists have been devising sophisticated and sensitive tests ever since the theory was formulated in 1905.

The most famous experiment, and the one that is commonly cited in textbooks as the experiment that established the case for relativity,<ref>Though relativity did not actually originate from this experiment</ref> was the [[Michelson-Morley experiment]]. This showed that all observers will obtain the same measured value for the speed of light (3x108 meters per second) no matter what their state of motion. This is the first of the two fundamental principles:
#''The [[speed of light]] is constant for all observers, regardless of their velocities relative to each other.''
#''The laws of physics are identical in all reference frames.''
(The second is just a restatement of Galilean relativity, that is, the "common sense" that had been accepted for centuries.)
A naive "common sense" interpretation of Galilean relativity would require that measurements of the speed of light (or anything else) by different observers would get results that differ by the observers' relative speeds, and hence that principle #1 can't be true. Special relativity fixes this apparent paradox.

All of special relativity derives for these two principles, plus assumptions of exact conservation of momentum and energy in all cases.

*At the end of Einstein's original 1905 paper [http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ "Does the Inertia of a Body Depend its Energy Content?"], he speculates on the possibility that the equation <math>E = m c^2</math>, which would normally be very hard to verify, could be verified with the extremely high energies of the newly discovered phenomenon of radioactivity.<ref>This equation is not related to [[quantum mechanics]].</ref> In the 1910s, with the invention of the mass spectrometer, it became possible to measure masses of nuclei accurately. This led to the clearing up of the mystery of atomic masses not being exact integers,and strongly suggested the existence of a "mass defect" (or "packing fraction") consistent with the mass-energy equivalence. In the 1930s, experiments with known nuclear reactions showed a very accurate correlation between the masses of the nuclei involved and the energy released. See [[Quantitative Analysis of Alpha Decay]].

*Another prediction of special relativity was time dilation in rapidly moving objects. This effect was most famously verified in the anomalously slow decay of relativistic cosmic muons.<ref>Some have suggested that other explanations are possible for this effect. We are trying to track this down.</ref> Time dilation has since been verified many times, and is routinely taken into account in all high-energy nuclear physics experiments, as in Hadron collision experiments.<ref>Experiments specifically designed to check dilation are rarely conducted any more.</ref>

[[Image:Cassini-science-289.jpg|right|thumb|The Shapiro effect: A spacecraft signal dipping into a gravity well around the [[Sun]] is delayed slightly.]]
As the 20th century progressed, tests of general relativity were proposed.

*One important "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury. There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun. These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century. This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

:This created quite a problem—physicists by then were accustomed to having their theories check out very accurately. One proposal that was made, by Simon Newcomb and Asaph Hall, was that the exponent of the radius in the gravitational formula wasn't exactly 2. He showed that, by choosing an exponent of <math>2+\delta</math>, the precession, as a fraction of a full orbit per planet's year, is <math>\delta/2</math>. By setting <math>\delta</math> to .000000157, that is, an exponent of 2.000000157, Newcomb was able to get a precession of .000000078 revolutions per Mercury year, or 43 arcseconds per Earth year. Whatever value is chosen for <math>\delta\,</math>, it gives the same precession, per revolution, for all orbiting bodies, but gravitational effects from other planets diminish that effect the further the planet is from the sun.

:A good approximation for the precession under general relativity is <math>\frac{3GM}{c^2 a(1-e^2)}</math> revolutions per planet's "year", where a is the semi-major axis and e is the eccentricity. A simpler but less accurate one is <math>3{}v^2/c^2</math>, where <math>v</math> is the planet's average orbital speed.

:While Newcomb's theory, and general relativity, don't lead to closed-form solutions, both theories can be solved numerically to as much precision as one desires.

:The following table shows some approximate parameters for the planets. Note that Mercury has the smallest orbit, and the fastest speed. Precession of planets other than Mercury is extremely hard to measure, but measurements of the actual anomalous precessions are in good agreement.<ref>http://www.mathpages.com/rr/s6-02/6-02.htm</ref>

{| class="wikitable"
|-
!Planet
!Period, seconds x 106
!Semimajor axis, meters x 109
!Speed, meters/second x 103
!Gravitational force, Newtons per kilogram
!Anomalous precession, arcseconds per (Earth) century, pure Newtonian mechanics
!Anomalous precession, Newtonian with exponent of 2.000000157
!Anomalous precession, general relativity
!Measured anomalous precession (estimated uncertainty)<ref>http://www.mathpages.com/rr/s6-02/6-02.htm</ref>
|-
|Mercury
|7.57
|58.9
|48
|.039
|0
|43
|43
|43.5(5)
|-
|Venus
|19.6
|108
|35
|.011
|0
|16.6
|9
|8(5)
|-
|Earth
|31.6
|150
|30
|.006
|0
|10.3
|4
|5(1)
|-
|Mars
|59.3
|227.9
|24
|.0025
|0
|5.5
|1.4
|
|-
|Jupiter
|374
|778.4
|13
|.0002
|0
|0.87
|0.07
|
|-
|Saturn
|929
|1426
|9.7
|.00006
|0
|0.35
|0.014
|
|-
|Uranus
|2651
|2870
|6.8
|.000016
|0
|0.12
|0.002
|
|-
|Neptune
|5200
|4498
|5.5
|.000007
|0
|0.063
|0.0008
|
|}

:Considering only the ''anomalous'' precession, that is, the precession that remains after all known other factors (other planets and asteroids, solar oblateness) have been accounted for, and using very accurate calculations rather than the approximations given above, general relativity predicts 42.98 ±0.04 arcseconds per century. Some observed values, as of 2008, are:
::: 43.11 ± 0.21 (Shapiro et al., 1976)
::: 42.92 ± 0.20 (Anderson et al., 1987)
::: 42.94 ± 0.20 (Anderson et al., 1991)
::: 43.13 ± 0.14 (Anderson et al., 1992)
::: (Source: [http://arxiv.org/PS_cache/astro-ph/pdf/9804/9804258v1.pdf Pijpers 2008])
:These error bars, and that of the general relativity prediction, all overlap.

*Another is the ''Shapiro effect'', involving time delay in radio signals passing through the gravity well of the Sun or a planet. Various spacecraft have confirmed this.

*Another is ''gravitational time dilation''. This is an effect separate from the time dilation of special relativity. It was tested by the Pound-Rebka experiment in 1959.

*Later in the 20th century, even more subtle phenomena were tested. One was the phenomenon of ''gravitational radiation'', or "gravitational waves". These waves are incredibly difficult to observe, and had never been observed until 2015. But extremely dense binary pulsars radiate gravitational waves with sufficient energy loss that, even though we can't detect the waves from Earth, we can see the effect of the energy loss from the radiation. The extreme precision of the timing of pulses from pulsars makes it possible to observe their energy loss with great accuracy. Observations by Hulse and Taylor of the pulsar pair known as B1913+16, if assumptions are made,<ref>Similar to the way Kepler chose orbital parameters to fit observed planetary motion to his theory</ref> could make the energy loss appear consistent with the predicted radiation. The rotating pulsars have moved such that Earth is now out of the beams, so those observations have been discontinued.

*In late 2015 (and announced in 2016), the LIGO instruments directly detected gravitational waves. See [[Gravitational waves]].

*An additional test of general relativity was performed with radio signals to the Cassini spacecraft.<ref>http://www.nature.com/nature/journal/v425/n6956/full/nature01997.html</ref>

*Two other effects, ''geodetic precession'' (also known as "de Sitter precession"), and ''frame dragging'' (also known as the "Lense-Thirring effect") were tested by the "Gravity Probe B" satellite early in the 21st century.<ref>http://prl.aps.org/accepted/L/ea070Y8dQ491d22a28828c95f660a57ac82e7d8c0</ref><ref>http://www.digitaljournal.com/article/306430</ref><ref>http://www.nap.edu/html/gpb/summary.html</ref><ref>http://www.sciencenews.org/view/generic/id/73870/title/Gravity_Probe_B_finally_pays_off_</ref><ref>http://www.nasa.gov/mission_pages/gpb/</ref><ref>http://einstein.stanford.edu/</ref><ref>http://spectrum.ieee.org/aerospace/space-flight/the-gravity-probe-b-bailout</ref><ref>http://www.engadget.com/2011/05/06/nasa-concludes-gravity-probe-b-space-time-experiment-proves-e/</ref> The precision required to observe this was phenomenal. The results were announced on May 4, 2011.

{{clear}}

==Predicted consequences of the Theories==
===Time dilation===

[[Image:Light cone.png|right|thumb|Light-cone diagram]]

Gravitational time dilation (explaining the desynchronization of clocks) between altitudes is incompatible with a correct physical description of a rising sun on earth (each time synchronized between altitudes) or the fact that two eclipses are separated by a same interval of time at all altitudes.

One important consequence of relativity is that an observer in one reference frame will not in general observe a clock in another frame to be "ticking" at the same rate as one in the observer's own frame.

In [[special relativity]], where acceleration and gravitational effects are ignored, this can be derived using basic geometry. The result is that clocks in all other [[inertial frames of reference]] other than the one you are in appear to tick slower. This can be summarised by the well known phrase "moving clocks run slow".

However, with [[general relativity]], there are similar effects such as gravitational time dilation where a clockthat is higher in a gravitational field runs faster. Often the effects of relativity are negligible. However the high precision required for the [[GPS|GPS system]] needs relativistic corrections. The rest of this section will concern only [[special relativity]].

The length of an event <math>t</math>, as seen by a (relative) stationary observer observing an event is given by:

<math> t = \frac{t_{0}} {\sqrt{1 - \frac{u^{2}}{c^{2}}}}</math>

Where
:<math>t_0</math> is the "proper time" or the length of the event in the observed frame of reference.
:<math>u</math> is the relative velocity between the [[inertial frame of reference|reference frames]].
:<math>c</math> is the speed of light (3x108 m s-1).

Evidence for time dilation was discovered by studying muon decay. [[Muons]] are [[subatomic particles]] with a short [[halflife]] of 1.53 microseconds. When produced by interactions of [[cosmic rays]] in the upper atmosphere, they have a speed around 0.994c. By putting muon detectors at the top (D1) and bottom (D2) of a mountain with a separation of 1900 m, scientists could measure accurately the proportion of muons reaching the second detector in comparison to the first. The proportion found was different to the proportion that was calculated without taking into account relativistic effects.

Using the equation for [[exponential decay]], they could use this proportion to calculate the time taken for the muons to decay, relative to the muon. Then, using the time dilation equation they could then work out the dilated time. The dilated time showed a good correlation with the time it took the [[muons]] to reach the second sensor, thereby supporting the existence of time dilation.

The time taken for a muon to travel from D1 to D2 as measured by a stationary observer is:

<math> t = \frac{s}{v} = \frac{1900}{0.994\times(3\times10^{8})} = 6.37\mu\textrm{s} </math>

The fraction of muons arriving at D2 in comparison to D1 was 0.732. (Given by <math> \frac{N}{N_0} = 0.732 </math>)

Since (from the equation for exponential decay) <math> \frac{N}{N_{0}} = e^{-\lambda t_{0}} </math> then

<math> t_{0} = \frac {ln(0.732)}{ln (0.2)} \times 1.53\times 10^{-6} = 0.689\mu\textrm{s}</math>

This gives the time for the proportion of decay to occur for an observer who is stationary, relative to the muon.

Putting this into the time dilation equation gives:

<math> t = \frac{t_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{0.689 \times{10^{-6}}}{\sqrt{1 - \frac{0.994^{2}}{1^{2}}}} = 6.3\times 10^{-6}\textrm{s}</math>

This is in good agreement with the value calculated above, thereby providing evidence to support time dilation.

Since either [[inertial frame of reference|reference frame]] is equally valid, from the [[muon]]'s point of view it sees the [[earth]] approach it at nearly the [[speed of light]]. Hence time passes faster for the muon (slower for an observer on the ground). This appears to be a contradiction. However, the [[muon]] sees the height of the mountain contracted and so travels a shorter distance in its own frame. See length contraction below.

====Time Dilation and Creation Science====

{{main|Starlight problem#Humphreys.27_model}}

Creation scientists such as physicists Dr. [[Russell Humphreys]] and Dr. [[John Hartnett]] have used relativistic time dilation to explain how the earth can be only 6,000 years old even though cosmological data (background radiation, supernovae, etc.) set a much older age for the universe.

====Derivation of Time Dilation====

Time dilation is most easily derived using the [[Lorentz transformation]]s, though geometrical solution is also straight forward. Using the transformation relating [[time]] between two [[Inertial frame of reference|frames of reference]], <math>t</math> and <math>t'</math>. We can find the time difference between two events that occur at the '''same''' location in space. The events shall be called event one and event 2. This results in the equations:

<math>t'_1 = \gamma \left(t_1 - \frac{ux}{c^2} \right) </math> 
<math>t'_2 = \gamma \left(t_2 - \frac{ux}{c^2} \right) </math>

where
:<math>\gamma</math> is the [[Lorentz factor]]
:<math>u</math> is the relative [[speed]] between [[Inertial frame of reference|reference frames]]
:<math>c</math> is the [[speed of light]]

Subtracting the top equation from the bottom produces the time between the events as measured in each reference frame, so:

<math>t'_2 - t'_1 = \gamma (t_2 - t_1)</math>

This the equation for time dilation and is the same equation as earlier.

===Length contraction===
When two inertial reference frames move past each other in a straight line with constant relative velocity, an observer in one reference frame would observe a metre rule in the other frame to be shorter along the direction parallel to the relative motion.

The length, <math>l</math>, of an object as seen by a (relative) stationary observer is given by:

<math> l = l_{0} \sqrt{1- \frac{u^{2}}{c^{2}}} = \frac{l_0}{\gamma}</math>

Where
:<math>l_0</math> is the "proper length" or the length of the object in its own [[inertial frame of reference|frame of reference]].
:<math>u</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light <math>3 \times 10^8 </math> m s-1
:<math>\gamma</math> is the [[Lorentz factor]]

====Derivation====

Length contraction may be derived using the [[Lorentz transformation]]s as with time dilation. This time we use the equation for <math>x</math>. In this case, the time in the undashed frame must be the '''same'''. Following the same procedure as above we find that:

<math>x'_2 -x'_1 = \frac{x_2 - x_1}{\gamma}</math>

This is the same as above with <math>x_2 - x_1</math> and <math>x'_2 - x'_1</math> being the lengths in the undashed and dashed frames respectively. Again, geometrical arguments may be used to achieve the same result.

===Mass increase===

For decades the theory of relativity taught that as a body moves with increasing velocity its [[mass]] also increases.<ref>For example, this was taught as recently as in the 1991 edition of the Encyclopedia Britannica.</ref>

Under this view, the mass, <math>m</math>, of an object as detected by a (relative) stationary observer is given by:

:<math> m = \frac{m_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>

Where
:<math>m_0</math> is the "rest mass" or the mass of the object measured by an observer in the same reference frame as the object.
:<math>v</math> is the relative velocity of the object.
:<math>c</math> is the speed of light (3x108 ms-1).

Since speed is relative, it follows that two observers in different inertial reference frames may disagree on the mass and kinetic energy of a body. Since all inertial reference frames are treated on an equal footing, it follows that mass and energy are interchangeable.

In recent years most physicists have shifted away from Einstein's original reliance on relativistic mass and his suggestion that mass increases{{Citation needed|date=January 2012}}. Instead, most physicists today teach that

:<math>F=\frac{d}{d\tau} p</math>

where
:<math>p</math> is the momentum defined by <math>\gamma m v</math>
:<math>\gamma</math> is the standard Lorentz factor
:<math>\tau</math> is the proper time

Force F defined this way is a [[vector]] and thus can handle the directional aspect of the relativistic effects better than the concept of relativistic mass can.
The abandonment by physicists of the concept of relativistic mass, however, has the consequence of undermining the traditional claim under relativity that

:<math>m - m_0 = \frac{E}{c^2}</math>

also popularly known as

:<math>E = m c^2</math>

Now a concept of the 4-momentum <math>p</math> of a particle is taught, such that the square of the magnitude of <math>p</math> satisfies:

<math>||p||^2 = -p_x^2-p_y^2-p_z^2+E^2 = m_0^2c^4</math>

in any inertial reference frame. The magnitude of the 4-momentum, in any inertial frame, equals the rest mass <math>m_0</math> of the particle (in units where <math>c=1</math>).

== Relativity in everyday life ==

Due to the small speeds and gravitational fields in normal life, relativistic phenomena such as time dilation and length contraction are rarely observed. However some things in everyday life can be explained using relativity:

*GPS, the satellites experience time dilation due to the difference in speed and the strength of gravitational field between the satellite and the ground. This is corrected by daily synchronisation between the ground and the atomic clocks in the satellites.
*While most elemental metals such as [[silver]], [[zinc]] and [[mercury]] have a silver/grey appearance, some metals like [[gold]] and [[copper]] do not. This difference can be explained using relativistic quantum mechanics.<ref>http://www.fourmilab.ch/documents/golden_glow/</ref>

== Paradoxes ==

The predictions of the theory of relativity throw up a number of apparent paradoxes and anomalies relating to the effects of time dilatation and length contraction. Whilst these paradoxes are consistent with the theory, they are contrary to everyday human experience and therefore can seem like impossibilities.

=== The Twin Paradox ===

The twin paradox is usually stated as a thought experiment involving two twins, one of whom is sent on a long journey in a spacecraft travelling at close to the speed of light, whilst the other remains on Earth. Time dilatation means that the travelling twin, on his return to Earth, is younger that the twin who has remained at home. However, because neither twin is in a special position - each being in an inertial frame of reference - the reverse must also be true, and so the twin remaining on Earth must be younger. Hence each twin is younger than the other - a paradox.

The problem can be resolved in two ways. One is to examine the effects of General Relativity: to come back to Earth, the travelling twin must undergo acceleration in order to reverse his course, causing temporal effects which make him permanently the younger. Alternatively, it can be explained entirely using Special Relativity and noting that the twins are not in symmetrical situations: the one on earth has remained in a single inertial frame of reference, whilst the travelling twin has travelled in two.<ref>http://mentock.home.mindspring.com/twins.htm</ref> Note that the length of the trip cannot be increased as to make the acceleration negligible.

=== The Ehrenfest Paradox ===

The Ehrenfest Paradox considers a rigid wheel or disc rotating a bout its axis at high speed (somewhat like a bicycle wheel spinning freely on its axle). The rim of the wheel travels at close to the speed of light and therefore undergoes length contraction, whereas the radius (the spokes, for the bicycle wheel) does not. Hence the circumference is no longer equal to 2<big><math>\pi</math></big>r, which is paradoxical.

The apparent paradox was finally resolved in 1975 by the Norwegian scientist Øyvind Grøn.<ref>http://www.physicsforums.com/showthread.php?t=224955</ref>

==Speed paradox==

One apparent inconsistency involves two spacecraft approaching each other. Suppose an observer on earth sees two spacecraft moving towards each other at half the [[speed of light]]. One travels in the positive x direction, the other in the negative. Therefore, they should each see the other approach them at the speed of light, an apparent contradiction given that no object with mass may travel at the [[speed of light]].

However, this is easily resolved by realising that adding the [[speed]]s is correct for [[Galilean relativity]]. Since the spacecraft are travelling at a significant fraction of the speed of light, it in not valid to use [[Galilean relativity]]. Therefore, the [[Lorentz transformation|velocity Lorentz transformations]] of special relativity must be used. Suppose the observer is in the undashed few and measures a speed <math>v_x</math>, then on the spacecraft travelling in the positive x direction, they measure speed <math>v_x^'</math>. The relevant equation is:

<math>v_x^' = \frac{v_x - u}{1- \frac{uv_x}{c^2}}</math>

Where <math>u</math> is the speed between the [[inertial frame of reference|inertial frames of reference]], in this case half the speed of light. <math>v_x</math> is also half the speed of light (but negative), and substituting in gives:

<math>v_x^' = -\frac{4}{5} c</math>

and so the paradox is resolved. If the observer on earth observes a beam of light, then the spacecraft also observes light travelling at the same speed, agreeing with the second postulate, that all observers in [[inertial frames of reference]] measure the same value for the speed of light.

== Variable Speed of Light ==

The Theory of Relativity implies that physical constants like c, the speed of light in a vacuum, have remained constant. But at least one study suggests that physical constants, and possibly even the speed of light, have changed as the universe has aged.<ref>James Glanz and Dennis Overbye, "Cosmic Laws Like Speed of Light Might Be Changing, a Study Finds," August 15, 2001.[http://www.nytimes.com/2001/08/15/science/15PHYS.html?ex=1185076800&en=d6467b6e3e346796&ei=5070]</ref>

"For the first time, scientists have experimentally demonstrated that sound pulses can travel at velocities faster than the speed of light, c. William Robertson's team from Middle Tennessee State University also showed that the group velocity of sound waves can become infinite, and even negative. ... Although such results may at first appear to violate special relativity (Einstein's law that no material object can exceed the speed of light), the actual significance of these experiments is a little different. These types of superluminal phenomena, Robertson et al. explain, violate neither causality nor special relativity, nor do they enable information to travel faster than c. In fact, theoretical work had predicted that the superluminal speed of the group velocity of sound waves should exist. 'The key to understanding this seeming paradox is that no wave energy exceeded the speed of light,' said Robertson."<ref>http://www.physorg.com/news88249076.html</ref>

"A team of researchers from the Ecole Polytechnique Fédérale de Lausanne (EPFL) has successfully demonstrated, for the first time, that it is possible to control the speed of light – both slowing it down and speeding it up – in an optical fiber, using off-the-shelf instrumentation in normal environmental conditions. Their results, to be published in the August 22 issue of Applied Physics Letters, could have implications that range from optical [[computing]] to the fiber-optic telecommunications industry."<ref>http://www.scienceblog.com/light.html</ref> Both slowing down and speeding up of light within a substance other than a vacuum is made possible, because the light travels through the material, and that material affects the speed of light, i.e. a photon hits an electron, which then exits and emits a slightly lower energy photon out in the direction that the original photon was traveling, thus maintaining conservation of momentum. No matter how transparent an object may appear, it radically impacts the speed of the light traveling through it, as demonstrated by the refractive production of a rainbow by a crystal, which Newton himself discovered.

This apparent change in speed can be explained, however, by noting that the constant c refers to the speed of light in a vacuum, i.e., when it is unimpeded. The speed of light when traveling through physical media is, in fact, variable.

"A pair of German physicists claim to have broken the speed of light - an achievement that would undermine our entire understanding of space and time. ... Dr Nimtz told New Scientist magazine: 'For the time being, this is the only violation of special relativity that I know of.'"<ref>http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/08/16/scispeed116.xml</ref>

==Pending research==

Today some physicists are working on hypothesizing how general relativity might have related to the other three forces of nature during the first fraction of a second of the [[Big Bang]]. Two of the more commonly studied attempts are [[string theory]] and [[loop quantum gravity]], but they have failed to produce any evidence that science mandates a science must have, and both typically take large amounts of work to even conform to what scientists believe. Critics increasingly point out that string theory and loop quantum gravity are largely untestable and unfalsifiable, and thus potentially unscientific under the principles of science advanced by [[Karl Popper]].<ref>See, for example, ''Not Even Wrong'', by Peter Woit</ref>

Relativity continues to be tested and some physics professors remain skeptical of the theory, such as University of Maryland physics professor Carroll Alley, who served as the principle physicist on the Apollo lunar project.<ref>http://science.nasa.gov/headlines/y2004/21jul_llr.htm</ref>

== Political aspects of relativity ==

Some [[liberal]] politicians have extrapolated the theory of relativity to metaphorically justify their own political agendas. For example, [[Democratic]] [[President of the United States of America|President]] [[Barack Obama]] helped publish an article by liberal law professor [[Laurence Tribe]] to apply the relativistic concept of "curvature of space" to promote a broad legal right to [[abortion]].<ref>Tribe, acknowledging help by Obama, argued that the [[Constitution]] should be interpreted to establish a right to federally funded [[abortion]] and that, more generally, ''[[Roe v. Wade]]'' does not go far enough. They insisted that a relativistic "curvature of space" could achieve this result by expanding application of the [[Constitution]] based on its impact on personal choice. "The ''[[Roe v. Wade]]'' opinion ignored the way in which laws regulating pregnant women may shape the entire pattern of relationships among men, women, and children. It conceptualized abortion not in terms of the intensely public question of the subordination of women to men through the exploitation of pregnancy, but in terms of the purportedly private question of how women might make intimately personal decisions about their bodies and their lives. That vision described a part of the truth, but only what might be called the Newtonian part. ... [A] change in the surrounding legal setting can constitute state action that most threatens the sphere of personal choice. And it is a 'curved space' perspective on how law operates that leads one to focus less on the visible lines of legal force and more on how those lines are bent and directed by the law's geometry." Laurence H. Tribe, The Curvature of Constitutional Space: What Lawyers Can Learn from Modern Physics, 103 Harv. L. Rev. 1, 16-17 (1989).</ref> As of June 2008, over 170 law review articles have cited this [[liberal]] application of the theory of relativity to legal arguments.<ref>Search conducted by [[User:Aschlafly]] in the LEXIS database "US Law Reviews and Journals, Combined," conducted June 1, 2008.</ref> Applications of the theory of relativity to change morality have also been common.<ref>"Mistakenly, in the minds of many, the theory of relativity became relativism."[http://www.worldnetdaily.com/news/article.asp?ARTICLE_ID=38081]</ref> Moreover, there is an unmistakable effort to censor or ostracize criticism of relativity.<ref>Although the [[Examples of Bias in Wikipedia|liberally biased Wikipedia]] contains lengthy criticisms of the subjects of many entries, and even though publications like ''The Economist'' recognize the lack of scientific satisfaction in the theory (see, e.g., "Weighing the Universe," The Economist (Jan. 25, 2007)), Wikipedia's entry on [http://en.wikipedia.org/wiki/Theory_of_Relativity Theory of Relativity] omits one word of criticism.</ref>

Physicist [[Robert Dicke]] of Princeton University was a prominent critic<ref>http://www.time.com/time/magazine/article/0,9171,943324,00.html</ref> of general relativity, and Dicke's alternative "has enjoyed a renaissance in connection with theories of higher dimensional space-time."<ref>"Initially a popular alternative to General Relativity, the Brans-Dicke theory lost favor as it became clear that omega must be very large-an artificial requirement in some views. Nevertheless, the theory has remained a paradigm for the introduction of scalar fields into gravitational theory, and as such has enjoyed a renaissance in connection with theories of higher dimensional space-time."[http://nedwww.ipac.caltech.edu/level5/Glossary/Essay_bekenstein.html]</ref> Despite being one of the most accomplished physicists in the 20th century, Dicke was repeatedly passed over for a [[Nobel Prize]], and in at least one case Dicke was insulted by the award being granted to others for contributions more properly credited to Dicke.

There has been little recognition by the Nobel Prize committee of either theory of relativity, and particularly scant recognition of the Theory of General Relativity. A dubious 1993 Nobel prize in physics was awarded Hulse and Taylor for supposedly finding the first evidence of gravitational waves in the orbital decay of the binary pulsar PSR1913+16.<ref>Weisberg, Joel M.; Taylor, Joseph H. (2003), "The Relativistic Binary Pulsar B1913+16"", in Bailes, M.; Nice, D. J.; Thorsett, S. E., Proceedings of "Radio Pulsars," Chania, Crete, August, 2002, ASP Conference Series</ref> A close reading of the paper reveals that that is based heavily on assumptions in trying to retrofit the data to the theory.

===Government Support for Relativistic research===
The Federal Government has funded the building of two gravity wave detectors: The first to test the principle, and the second (upgrade) to actually perform measurements. As a result of this work, on February 11, 2016, the LIGO team reported successful detection of gravitational waves caused by the merging of two black holes.<ref>https://www.ligo.caltech.edu/news/ligo20160211</ref>

{{Relativity}}

==See also==
*[[Attempts to prove E=mc²]]
*[[Counterexamples to Relativity]]
*[[Essay:Rebuttal to Counterexamples to Relativity]]
*[[Logical Flaws in E=mc²]]
*[[Essay:Rebuttal to Logical Flaws in E=mc²]]
*[[Quantitative Analysis of Alpha Decay]]
*[[Gravitational waves]]

== References ==
{{reflist|2}}

[[Category:Physics]]
[[Category:Science]]

==External links ==
*[http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm The Einstein Theory of Relativity, by H.A. Lorentz.]
*[http://www.relativitycalculator.com Relativity Science Calculator - Learn Special Relativity Mathematics ] The mathematics of special relativity presented in as simple and comprehensive manner possible within philosophical and historical contexts.
*[http://www.relativitycalculator.com/history_of_time_clocks.shtml Relativity Science Calculator - Philosophic Question: are clocks and time separable?]
*[http://www.relativityscience.com/twin_clock_paradox.shtml Relativity Science Calculator - Twin Clock Paradox]

Talk:Theory of relativity

2017-08-20T17:03:13Z

Geocentric: answer about synchronization on earth

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== Special relativity and evidence ==
Many objects have been accelerated to velocities near the speed of light (in particle colliders) and it is easily observed that the rate at which those objects speed up as a constant force is applied is (very precisely) consistent with special relativity and not Gallilean relativity. That is, as their measured speed approaches the speed of light, that speed increases less and less in response to each "push" even though the "pushes" remain the same strength, thus apparently violating Newton's F = ma. On the other hand, Einstein's famous E = gamma * mc^2 appears to describe their rate of acceleration very accurately. I don't understand how this article proposes to surmount that objection. [[User:ZeroThree|ZeroThree]] 15:47, 28 October 2012 (EDT)

== Mass depending on direction ==

The article states:
:''There is a logical difficulty, however, to an increase in relativistic mass. Such increase would only exist in the direction of motion, and the rest mass would remain intact with respect to a force applied in a direction orthogonal to velocity. Neither mass nor energy is a vector, and the notion of the mass of an object having different values depending on the direction of an applied force is illogical.''

As [[User:RSchlafly|RSchlafly]] on 8 July 2007 (EDT): ''This paragraph is nonsense [..] The relativistic mass applies no matter what the direction of the force is.''

[[User:AugustO|AugustO]] 15:45, 10 January 2012 (EST)

== Neutrinos now obey speed limit ==

The observation sited in the first sentence of this article has been discredited. [http://news.sciencemag.org/scienceinsider/2012/02/official-word-on-superluminal-ne.html?ref=hp] It appears that a loose fiber-optics cable is to blame for the misreadings. I suggest editing this first sentence, and any other mention of this in the article.--[[User:CarloP|CarloP]] 18:51, 2 March 2012 (EST)

:Issues concerning the neutrino experiment are not yet fully resolved. No problam: I replaced it with another counterexample.--[[User:Aschlafly|Andy Schlafly]] 19:12, 2 March 2012 (EST)

== Why does Conservapedia seek to discredit Relativity ==

Can someone explain why Conservapedia is so opposed to the Theory of Relativity?

Is there some philosophical or conservative/liberal basis for this opposition? [[User:RolandPlankton|RolandPlankton]] 18:32, 5 April 2012 (EDT)

:''Conservapedia'' seeks the truth, not merely what the [[lamestream media]] claim is the truth. Moreover, once one accepts a logical fallacy, then anything false can be proven from it.--[[User:Aschlafly|Andy Schlafly]] 23:34, 5 April 2012 (EDT)
:: Ahh.... But the fact that the conclusion is false does not necessarily render the basis false. I could say "Andy Schlafly founded Conservapedia and therefore I am a pig monkey." I am not a pig monkey, and even if I were, that has nothing to do with you founding this website. But you still did. [[User:Gregkochuconn|Gregkochuconn]] 09:58, 9 April 2012 (EDT)

:When looking around the internet, it is obvious that Conservapedia's classification of relativity as [[pseudoscience]] is a source of some amusement and contempt. Aschlafly, could you please answer the two questions I raised above? [[User:RolandPlankton|RolandPlankton]] 11:27, 9 April 2012 (EDT)

::Roland, liberal peer pressure from "around the internet" does not illuminate the truth. If what liberals on the internet said made a dime's bit of difference, then the [[Bible]] would not be the best selling book (by far) and the percentage of people who are [[conservative]] would not be growing (as it does).

::"Can someone explain why Conservapedia is so opposed to the Theory of Relativity?" Because it's false, it confuses people, it misleads people into stop reading the Bible, and its orthodoxy interferes with the advancement of science for the benefit of all. Other than that, it's not a bad theory!

::"Is there some philosophical or conservative/liberal basis for this opposition?" The only bias is by liberals who shout down any criticism of the theory. If the theory were so clearly true, then there would be no need for some liberals to rely on [[censorship]] in propping it up.--[[User:Aschlafly|Andy Schlafly]] 17:10, 9 April 2012 (EDT)

== GPS and Relativity ==

I note that anyone using a GPS is relying on the Theory of Relativity being true, since calculations derived from Relativity are used within a GPS. [[User:RolandPlankton|RolandPlankton]] 18:32, 5 April 2012 (EDT)

:GPS does '''''not''''' rely on the [[Theory of Relativity]], and this has been thoroughly explained on this site.--[[User:Aschlafly|Andy Schlafly]] 23:34, 5 April 2012 (EDT)

::Hi Aschlafly, I've located at least some of the discussion re GPS in the archives of this talk page, and there a lot of references for me to examine before I can make any further serious comments; certainly there are some references which appear to state that GPS relies on relativity. Can you perhaps draw my attention to what you consider the most important (half-dozen or so) references which indicate that the GPS system does NOT rely on relativity so that I have somewhere to start from? In the meantime I'll continue editing and improving less controversial articles as I have been doing for the last two months (my talk page lists nearly 40 articles I can usefully contribute to). [[User:RolandPlankton|RolandPlankton]] 14:17, 6 April 2012 (EDT)

:::This note 7 is on [[Counterexamples to Relativity]]:

::::Contrary to the claims of Relativists, the GPS system has never been based on Relativity. The Time Service Department, U.S. Navy, observed that "The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require" in part because "the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”

:::The Theory of Relativity does not even assert that it would require significant adjustments to GPS timing: the small effects claimed by the special and general theories nearly cancel each other out for orbiting satellites. From an engineering perspective, it makes far more sense simply to adjust the clocks using synchronization rather than relying on (dubious) theoretical claims.--[[User:Aschlafly|Andy Schlafly]] 14:36, 6 April 2012 (EDT)

Another false claim because of sloppy reading: In the same source by The Time Service Department, U.S. Navy, you can find how the authors Fliegel and DiEsposti describe what is happening to the clocks in the satellites:
''Since GPS receivers work in the time and not in the frequency domain, they handle the velocity, gravity, and acceleration shifts differently than described above. First, each GPS space vehicle (SV) clock is offset from its nominal rate by about -4.45 × 10-10 (= -38 microseconds per day) to allow for the relativistic offsets between the differences between the SV and the ground. Of this -38 microseconds per day, about -45 are due to the gravitational potential difference between the SV at its mean distance and the earth's surface, and +7 to the mean SV speed, which is about 3.87 km/sec. (p. 193).

The text is about the necessity of ''further'' corrections by the ''operational control system'' - there are corrections ''already'' installed in the clocks!

''The Theory of Relativity does not even assert that it would require significant adjustments to GPS timing:'' This sentence is wrong. It has shown to be wrong a couple of times, so it starts to become a lie. [[User:AugustO|AugustO]] 15:12, 6 April 2012 (EDT)

:The [[Theory of Relativity]] was not used to develop GPS, nor would it be sensible to waste time and money doing so. Synchronization is cheaper, simpler, and more reliable. The above quote does not contradict this obvious truth.--[[User:Aschlafly|Andy Schlafly]] 16:32, 6 April 2012 (EDT)

::The fact that these offsets are implemented in the clocks '''in accord with the theory of relativity''' as you can read in the very source you quoted shows that the [[Theory of Relativity]] is used in the GPS - and this from the very beginning of the project! Please, start to read your sources - completely! [[User:AugustO|AugustO]] 16:37, 6 April 2012 (EDT)

Please, before we get into any more debate, could someone supply some actual references (not quotes from) which state that relativity is not used in GPS? [[User:RolandPlankton|RolandPlankton]] 16:41, 6 April 2012 (EDT)

:Aschlafly took his quote from [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview] by Henry F. Fliegel and Raymond S. DiEsposti (though he probably isn't aware of this). The paper is about relativistic effects due to moving GPS-'''''receivers''''' (or GPS-receivers in high altitudes) and comes to the conclusion, that at the moment, they don't have to include additional relativistic corrections.

:Aschlafly interprets this as if ''no'' relativistic corrections are implemented in the GPS.
:However, in the paper itself, you will find the section I quoted above, where the authors describe such very corrections within the clocks of the satellites.
:I'm afraid that Aschlafly won't come up with ''some actual references (not quotes from) which state that relativity is not used in GPS'' as there aren't any.
:[[User:AugustO|AugustO]] 16:53, 6 April 2012 (EDT)

Folks, the burden of proof is on anyone who claims that the [[Theory of Relativity]] was used to design GPS. That burden includes describing who, when, where, how, and why. It didn't happen. And if it did, the person who wasted time and money on such a frivolous approach should explain the mistake, because engineers can simply synchronize the clocks far more accurately than the theory ever could.--[[User:Aschlafly|Andy Schlafly]] 18:15, 8 April 2012 (EDT)

:It looks to me as if you are trying to put impossible conditions prior to any debate. To avoid a lengthy debate all you have to do is produce some actual references which support your point of view. Is this too much to ask?

:If it didn't happen then you should be able to produce some evidence of this, so '''some actual references please'''. The only 'evidence' you have produced so far is an out-of-context quote from a paper which is concerned primarily with GPS receivers (that same paper mentions the use of relativity-related adjustments to the clocks on the GPS satellite transmitters). Surely you must have more than this. Will you accept evidence from engineers and companies involved in designing and building the GPS system? If not, why not? Who would you accept evidence from? The US Department of Defense? Do you seriously expect a member of the public to be able to access internal design documents as your "who, when, where, how, and why" statement implies?

:If you care to check my contribution history you will see that I am actively contributing non-controversial information to articles. This discussion re GPS etc. is only a small part of my activities on Conservapedia. Since I've barely started on considering and consolidating what evidence there is re GPS I would rather have a week or so to look at the evidence before getting into a debate. This should give you ample time to come up with some references to support the separation of GPS and relativity. Simple searches via Google turn up numerous instances where relativity is claimed to be relevant to GPS, but I can't find anything to the contrary and '''I need your help to do so'''. I would really like to see evidence from '''both sides''' of the discussion before entering the debate, so '''some actual references please'''. [[User:RolandPlankton|RolandPlankton]] 19:15, 8 April 2012 (EDT)

::Roland, you're requesting proof that something didn't happen. Moreover, someone with an engineering background (such as myself) would not expect it to have happened. It is like asking for a reference that no green cheese was found on the Moon. No such scientific reference is likely to exist, nor would anyone expect such a reference to exist.--[[User:Aschlafly|Andy Schlafly]] 19:28, 8 April 2012 (EDT)

:: Every single article on GPS says that relativistic adjustments are made to the satellite clocks. Some give the formulas and some give quantitative data on the adjustments. Textbooks explain why the adjustments are necessary. I don't see any reason to doubt that GPS uses relativistic adjustments. [[User:RSchlafly|RSchlafly]] 20:52, 8 April 2012 (EDT)

:::GPS does make synchronizing adjustments. Call them whatever you like, but those adjustments are not made based on predictions by the [[Theory of Relativity]]. Indeed, it would be a silly waste of time and money to synchronize in such a manner.--[[User:Aschlafly|Andy Schlafly]] 21:07, 8 April 2012 (EDT)
:::: Unless you drive the flying Delorean from ''Back to the Future'', relativity would say that its effect on your car when you're driving at normal speeds is so small it need not be accounting for. The normal error for GPS (about 40 feet) is many magnitudes higher than the error relativity would cause. Now, the GPS in the Flying DeLorean would be another issue. But until that's invented, let's not worry about it, ok? Of course, if you were orienteering, your speed would be even slower than if you were driving. Indeed, if you were moving at any normal speed (even a supersonic jet), relativity would be incredibly small (assuming that it exists as scientists explain it). [[User:Gregkochuconn|Gregkochuconn]] 22:14, 8 April 2012 (EDT)

:::::''GPS does make synchronizing adjustments'' Not only simple synchronizing: read the specifications for the GPS, read the sources ''in full'' which you are quoting, and you will see that all these engineers and scientists don't give a damn that you think that they are wasting ''time and money''.
:::::Aschlafly, your position is only tenable as you are willing to ignore most of the data which is presented to you. [[User:AugustO|AugustO]] 03:12, 9 April 2012 (EDT)

::Aschlafly, please correct me if I am misunderstanding you, but it seems to me that you believe very firmly that relativity has nothing to do with GPS, even though you are unwilling to present any evidence to support this belief, and wish to put severe restrictions on what 'proof' of the relationship other folks may present. I raised some five questions above as to what sort of evidence you might consider. Could you please answer these questions.

::I'd like to ask Mr. Schafly if he could explain what the clock adjustments on GPS satellites are for, the article is not clear, and neither is anything on this talk page.--[[User:Cahnkj|Cahnkj]] 00:44, 11 April 2012 (EDT)

:::Cahnkj, herewith a summary of the clock-adjustment situation as I (RolandPlankton) see it. Newton's equations of motions say nothing about how clocks keep time. Einstein's equations of relativity imply that identical clocks will vary in their timekeeping (tick at different rates) if they are travelling at different speeds, or if they are at different heights in a gravitational field, or if they are subject to different accelerations; see [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview]. Now the satellites used in the GPS system require very accurate clocks which are in step with ground-based clocks. The paper just quoted provides the various relativistic equations which apply - the satellites are travelling faster than a ground-based receiver, and are at a different height in a gravitational field. Prior to launch the clocks in the GPS satellites are deliberately set to a different tick rate from ground-based clocks, so that when they are in orbit the clocks will appear to tick at the same rate; the difference in tick rates is about 38 nanoseconds per day, and this adjustment can be calculated from the relevant relativistic equations.

:::But the problem is that Aschlafly rejects the Theory of Relativity, and hence rejects any calculation based on that. The only serious argument he has put forth on this current talk page (see preceding section) is an appeal to [http://en.wikipedia.org/wiki/Wikipedia:The_Truth the truth]; the quote he provides above is also demolished above. You may wish to consult [[Counterexamples to Relativity]], which is rebutted point by point in [[Essay:Rebuttal to Counterexamples to Relativity]].

:::Hope this doesn't add too much to the confusion. [[User:RolandPlankton|RolandPlankton]] 12:07, 11 April 2012 (EDT)

::::Mr. Schlafly states above that "the burden of proof is on anyone who claims that the Theory of Relativity was used to design GPS." (This is a fair requirement, and it seems as this has been done when AugustO referred to the Fliegel and DiEsposti paper above.)

::::But really, isn't the burden of proof on anyone who claims ''anything'' on this site, since Conservapedia Commandment #1 states that "everything you post must be true and verifiable" and Commandment #2 states that users should "always cite and give credit to <nowiki>[their]</nowiki> sources?" --[[User:AndreaM|AndreaM]] 19:03, 12 April 2012 (EDT)

:::::Good point. Anyone who asserts ''on this site'' that GPS was designed based on the [[Theory of Relativity]] needs to prove the claim. Note that the claim is implausible because it is cheaper, easier, and more precise to synchronize GPS based on observations rather than theoretical speculation. Also note that no [[Nobel Prize]] has been given for verification of the [[Theory of Relativity]] with GPS.--[[User:Aschlafly|Andy Schlafly]] 19:55, 12 April 2012 (EDT)

::::::Whether GPS was designed based on Relativity or not may be irrelevant. Whether or not Relativity is necessary for the clocks to run efficiently and accurately, also irrelevant. Observations of the satellites are still consistent with the predictions of General and Special Relativity as evidenced here: http://www.metaresearch.org/cosmology/gps-relativity.asp. Please not that this is an article by the same Tom Van Flandern quoted on this site as saying that relativity is unnecessary for GPS calculations, so I trust this is a source you will accept. Here he is saying here that while relativity may be UNNECESSARY for those calculations, it is still CONFIRMED by our observations.[[User:Williagz|Gus Williams]] 14:03, 13 May 2012 (EDT)

===A Separate Question for Mr. Schlafly About References===

::Aschlafly, as a separate issue, in view of of your apparent attitude to references, could I ask you to have a look at the articles I have been working on over the last two months: [[Pi]], [[Programming language]], [[Compiler]], and the work-in-progress [[Chomsky hierarchy]]. Obviously I'm only asking you to consider the changes I have made. In particular, can you check if the references are acceptable to you, and can you also check that the general style and level of writing is in accordance with Conservapedia's aims? The next article I intend to turn my intention to is [[Context-Free Grammar]], since it seems to me that this fails to satisfy [[Conservapedia:Guidelines#Style]] "Articles on complex topics need an introduction which assumes little or no previous knowledge". [[User:RolandPlankton|RolandPlankton]] 11:03, 9 April 2012 (EDT)

:::Roland, your good edits are appreciated and I've seen no complaints about them. I agree that the [[Context-Free Grammar]] would benefit from a better introduction and look forward to reading what you add there.--[[User:Aschlafly|Andy Schlafly]] 17:39, 9 April 2012 (EDT)

===READ THE MANUAL===
This debate seems pretty ridiculous, given that GPS is a public system with open specifications. If you're building a GPS receiver you do, in fact, need to compensate for relativistic effects. The correction equations that must be used on the receiving side equipment are given in the official GPS interface specification, IS-GPS-200G [http://www.gps.gov/technical/icwg/IS-GPS-200G.pdf], p.92. section 20.3.3.3.3.1: User Algorithm for SV Clock Correction.

<blockquote>
The polynomial defined in the
following allows the user to determine the effective SV PRN code phase offset referenced to the
phase center of the antennas with respect to GPS system time (t) at the time of data
transmission. The coefficients transmitted in subframe 1 describe the offset apparent to the two frequency
user for the interval of time in which the parameters are transmitted. This estimated
correction accounts for the deterministic SV clock error characteristics of bias, drift and aging, as
well as for the SV implementation characteristics of group delay bias and mean differential
group delay. '''Since these coefficients do not include corrections for relativistic effects, the user's equipment must determine the requisite relativistic correction. Accordingly, the offset given below includes a term to perform this function'''...
</blockquote>
I did not include the equations here, but they're given in the manual. --[[User:Smac56|Smac56]] 16:54, 7 December 2014 (EST)

== Why are adjustments needed to GPS? ==

A good question was raised above: if synchronization to GPS is not due to the [[Theory of Relativity]], then what is it due to?

And the answer is simply this: [[quantum mechanics]]. There are fundamental uncertainties, and those uncertainties will lead to clock differences. Otherwise a [[perpetual motion machine]] would be possible. It isn't.--[[User:Aschlafly|Andy Schlafly]] 22:50, 11 April 2012 (EDT)

Where to start with this. This is so bad it isn't even wrong. Could I respectfully suggest that you confine your efforts to areas you understand at least a little bit.

The impossibility of perpetual motion has nothing to do with quantum mechanics. It comes from the 2nd and 3rd laws of thermodynamics and predates quantum mechanics by at least 100 years.

The uncertainty principle is also completely irrelevant. If we imagine a 100 kg satellite moving at a velocity of approximately 100 km/s (this is three times the earth's velocity , so is a plausible and easy to handle number). If we know the satelites location to an uncertainty of 1cm then the uncertainty on its velocity implied by the uncertainty principle is 1 part in 10^39 (i.e. completely negligable).[[User:Jloveday|Jloveday]] 13:10, 14 April 2012 (EDT)

:Well, this is progress indeed. Could you please provide references to support the contention that the synchronization is required as a result of quantum mechanical effects?

:Also, as an aside, how do you say that fundamental uncertainties described by quantum mechanics relate to the impossibility of a perpetual motion machine? Not sure I follow you there. --[[User:JeromeKJ|JeromeKJ]] 23:36, 11 April 2012 (EDT)

::It's basic logic. Unless someone denies [[quantum mechanics]] and the fundamental uncertainties it describes -- and many [[Relativists]] do deny it -- then synchronization will be required as a logical result.--[[User:Aschlafly|Andy Schlafly]] 23:58, 11 April 2012 (EDT)

:::Do you have any references? --[[User:JeromeKJ|JeromeKJ]] 00:04, 12 April 2012 (EDT)

::::I haven't looked ... nor is it necessary to. I wouldn't look for references to confirm any logical statement.--[[User:Aschlafly|Andy Schlafly]] 00:14, 12 April 2012 (EDT)

:::::Really? Is it fair to say then that this contention that the synchronization is required as a result of quantum mechanical effects is not something that you have read about but rather something that you yourself concluded from your own knowledge of quantum mechanics and GPS systems? --[[User:JeromeKJ|JeromeKJ]] 00:21, 12 April 2012 (EDT)
:::::P.S. As a result of this discussion I found a couple of articles which appear to confirm that GPS satellites have their clocks adjusted by about 38,000 nanoseconds per day before launch in compliance with relitavistic predictions (both Special and General Relativity are taken into account). The articles are [http://metaresearch.org/cosmology/gps-relativity.asp here] and [http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html here]. Is there really any question that this is what is happening? I would think that if these sources are to be questioned that some sort of reference should be provided. A mere assertion that the adjustments are as a result of quantum mechanical effects and that it is a matter of logic would not usually be enough for any serious encyclopedia. --[[User:JeromeKJ|JeromeKJ]] 00:53, 12 April 2012 (EDT)

::::::The references are [[hearsay]]. Logic is far more compelling, more efficient, and more likely to lead to the correct result.

::::::To take the analogy mentioned above, if you agree that [[perpetual motion machines]] are impossible, what is the reason?--[[User:Aschlafly|Andy Schlafly]] 01:45, 12 April 2012 (EDT)

:Quantum mechanics gives a probabilistic model of phenomena. Indeed, the page you linked for quantum mechanics states:
::"If we measure such an observable, generally the wave function does not predict exactly which value we will obtain. Instead, the wave function gives us the probability that a certain value will be obtained."
:If this is the case, that means that Quantum mechanical phenomena are ''unpredictable''. How is it that clock adjustments can be made based on unpredictable events, ie, probabilities?
:I'd also like to know how the GPS system is affected by these phenomena.
:--[[User:Cahnkj|Cahnkj]] 01:51, 12 April 2012 (EDT)

Logic is a nice thing. But engineers like to calculate. So could you give us a Ballpark estimate for the quantum mechanic effects which come into play here? [[User:AugustO|AugustO]] 01:59, 12 April 2012 (EDT)

:(Edit conflict x2) Andy, as a lawyer I can assure you that hearsay is a [[legal]] concept which is of little use in this sort of scientific discussion. Whilst I understand that non-legally trained people sometimes confuse the nature and applicability of the concept, I can confirm that it has no relevance here.

:The difficulty here arises from your wanting to assert the truth of a matter without providing either references or even the basis for you own logic. Just saying "quantum mechanics" is hardly enlightening. Do you deny that GPS satellite clocks are adjusted by approximately 38,000 nanoseconds as referred to in the references that I provided? If not, do you say that there is a quantum calculation that accounts for that adjustment? What is that quantum calculation and what is it based on? I am really having difficulty in understanding the basis for all of this. --[[User:JeromeKJ|JeromeKJ]] 02:03, 12 April 2012 (EDT)

:Aschlafly, this reference [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview] has been pointed out to you several times already. Since it is published by folks actually working on the GPS system, I hardly think that it qualifies as 'hearsay'. It contains all the relevant relativistic equations, which are not really that complicated, and derives the 38 nanosecond figure quoted above. An assertion on scientific matters without any evidence can't really be taken seriously. Can we please see the quantum mechanical equations and calculations which come up with the same or similar result? [[User:RolandPlankton|RolandPlankton]] 09:49, 12 April 2012 (EDT)

:Aschlafly, I'm inclined to suspect that your disbelief in relativity is so strong that you are unwilling to consider any evidence which might indicate that relativity could be correct, and are hence flailing around looking for some other explanation as to what actually happens (GPS clock adjustment by 38 ns). Would you care to comment on my suspicion? [[User:RolandPlankton|RolandPlankton]] 09:49, 12 April 2012 (EDT)

Quote: "A logical statement is a declarative sentence that is either true or false." [http://www.ontotext.com/factforge/logical-statement].

So Aschlafly, why don't you need a reference to confirm a logical statement? Just because a statement is logical doesn't mean that it is true. [[User:RolandPlankton|RolandPlankton]] 16:53, 12 April 2012 (EDT)

: It would be helpful to have a more modern reference. GPS switched to a system of daily updates to the satellites. Maybe those relativistic formulas cause errors that require daily clock synchronizations to correct. Not likely. But to prove the point we ought to find a reference that says that the satellites still use the 38 ns/day relativistic adjustments, and that the daily corrections are much smaller than that. [[User:RSchlafly|RSchlafly]] 17:18, 12 April 2012 (EDT)
::The best I've found so far is [http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/GPS/Neil_Ashby_Relativity_GPS.pdf] from Physics Today, May 2002. This confirms the initial adjustment and mentions further on page 7: "Additional small frequency offsets arise from clock drift, environmental changes, and other unavoidable effects such as the inability to launch the satellite into an orbit with precisely the desired semimajor axis. The satellite clock frequencies are adjusted so that they remain as close as possible to the frequency of the Naval Observatory's clock ensemble." Unfortunately it doesn't give the actual size of the adjustments, thought the word 'small' does indicate it as being much less than the initial adjustment. I rather like the last sentence of this paper: "Ordinary users of the GPS, though they may not need to be aware of it, have thus become dependent on Einstein's conception of space and time." [[User:RolandPlankton|RolandPlankton]] 18:26, 12 April 2012 (EDT)

:::The lack of evidence, amid so much political pressure to prove it, is indicative that no proof can be found. Notice how no [[Nobel Prize]]s have been given for GPS confirming the [[Theory of Relativity]]?--[[User:Aschlafly|Andy Schlafly]] 21:01, 12 April 2012 (EDT)
:::If you want to use the [[Nobel Prize]] as evidence against relativity, might I direct you to:
:::http://www.nobelprize.org/educational/physics/relativity/
:::Where the official Nobel Prize website discusses various experiments related to relativity, and the relevant [[Nobel Prize]]s awarded for them.
:::--[[User:Cahnkj|Cahnkj]] 00:32, 13 April 2012 (EDT)

::::GPS is not even on that overly broad list.--[[User:Aschlafly|Andy Schlafly]] 00:43, 13 April 2012 (EDT)

::Aschlafly, I've tried to confine my evidence to items which not even you can claim as 'hearsay'. A simple Google search turns up hundreds of references linking GPS and relativity, but in view of your earlier dismissal of such as hearsay, I thought I'd better stick to indisputable items. At least there is some fairly convincing evidence linking GPS with relativity (including all the relevant equations and the result of applying these equations), unlike your assertion linking GPS with quantum mechanics, where you have produced precisely zero evidence. You still haven't responded to my comments and question re 'logical statements' above. So, where is the evidence for your assertion? [[User:RolandPlankton|RolandPlankton]] 02:46, 13 April 2012 (EDT)

:::There is no credible evidence that the [[Theory of Relativity]] had anything to do with the development of GPS. In addition, not even the pro-Relativity [[Nobel Prize]] [[liberals]] say that GPS proves the theory.

:::My comment about [[quantum mechanics]] was in response to a question about why synchronization is needed. Unless someone thinks that [[perpetual motion machines]] are possible (have you answered my question about that?), then synchronization will be needed.--[[User:Aschlafly|Andy Schlafly]] 11:00, 13 April 2012 (EDT)
::::Could you please clarify what the connection between synchronisation, quantum mechanics and perpetual motion machines is? From what I've learned, clock synchronisation between the satellites is necessary because any signal between them travels at a finite speed, namely the speed of light. Do you deny that? The claim is that in order to compute the signal travel time and thus to synchronize the clocks correctly, the relative velocities and the differences in gravitational potential due to the different altitudes of the satellites (and Earth's surface) have to be taken into account. Do you think that is wrong? --[[User:FrederickT3|FrederickT3]] 11:56, 13 April 2012 (EDT)

Lets stick to the subject (GPS and relativity); perpetual motion is a complete red herring, and I'm not sure how Nobel prizes come into the picture (we're debating science, not prizes).
On the basis of '''actual evidence produced''' in this discussion so far, I think that we can confidently state four facts:
#Prior to launch, the clock in a GPS satellite is set to run about 38 nanoseconds/day different from an otherwise identical clock on the earth's surface.
#When in orbit the GPS clock then appears to tick at the same rate as an identical clock on the earth's surface.
#Equations based on the theory of relativity accurately come up with this figure of around 38 nanoseconds.
#No evidence has been produced to show how quantum mechanics is involved.

If anyone disagrees with any of the above, they need to bear in mind ('''emphasis''' added):
:from Conservapedia:Commandments 1 Everything you post must be true and '''verifiable'''.
:from Conservapedia:Commandments 2 '''Always cite''' and give credit to your sources.
:from Conservapedia:Guidelines/Reliability 4 A major difference between Liberalism and Conservatism is how much each group is willing to have its pronouncements checked, its actions reviewed and evaluated.

Hope this summary helps. [[User:RolandPlankton|RolandPlankton]] 14:41, 13 April 2012 (EDT)

: That is the story as I have heard it. Except that I heard that the 38 ns/day adjustment was remotely switchable, because of relativity skeptics who did not believe that it would be necessary. I also don't agree that GPS is "dependent on Einstein's conception of space and time." The GPS system has the ability to measure the daily adjustments that it needs. So even with any relativity theory or Einstein conception, it could just make those 38 ns/day adjustments and GPS would have all the accuracy it has today. [[User:RSchlafly|RSchlafly]] 15:19, 13 April 2012 (EDT)

::In the summary I was careful to stick to facts supported by evidence, and to avoid saying "GPS is dependent on Einstein's conception of space and time", even though the two main references I have quoted do in fact say this. All I said was that the adjustment calculated according to relativity agrees with the actual adjustment, from which one might reasonably conclude, in this instance at least, that relativity is consistent with reality. [[User:RolandPlankton|RolandPlankton]] 15:44, 13 April 2012 (EDT)

::I note that no one has proposed any credible alternative theory as to why the orbiting clocks tick at a different speed from surface clocks, so until some better theory comes along I'm quite happy to stick with relativity. [[User:RolandPlankton|RolandPlankton]] 16:00, 13 April 2012 (EDT)

:In the last week, apart from one clarification question from [[User:RSchlafly|RSchlafly]], no one has challenged the 'four facts' summary I provided above. According I will shortly move a copy of this summary along with the relevant references in to the talk pages of other relevant articles, and will then update those articles to match. [[User:RolandPlankton|RolandPlankton]] 13:36, 21 April 2012 (EDT)

::Beware: in your fact #1, the correction is 38 '''micro'''seconds, not '''nano'''seconds. See [http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html]. My own rough calculations also agree that it's microseconds. [[User:JudyJ|JudyJ]] 15:05, 21 April 2012 (EDT)

::Well spotted, Judy. I've gone back to one of the sources and it is indeed 38 microseconds. Thank you for the correction. [[User:RolandPlankton|RolandPlankton]] 16:10, 21 April 2012 (EDT)
All right, can Andy Schlafly explain how adjusting the exponent in the law of gravity accounts for the orbits of the other planets? You know the reason why no one considers that as an alternative? Are you ready?! '''Because it doesn't work!''' And can you tell me why Einstein came up with GR? Was it to explain the orbit of Mercury? [[User:AndyFrankinson|AndyFrankinson]] 21:36, 28 April 2012 (EDT)

:::In response to your first question, the reason is purely political. Any grad student who suggests that tweaking the exponent in Newtonian mechanics is an interesting approach worth more attention will thereby eliminate his chances for obtaining a PhD.

:::In response to your second point, GR was tweaked to explain the Mercury perihelion precession, but now the more precisely observed data fail to match the theory. Grad students and Nobel Prize wannabes are clever enough to keep quiet about it now.--[[User:Aschlafly|Andy Schlafly]] 21:56, 28 April 2012 (EDT)

Andy: You make an interesting point about people not thinking that the Newcomb/Hall theory of planetary precession is an interesting approach—I hadn't thought about that aversion. I'm not sure why you think that people who take an interest in that theory would eliminate their chances of getting a PhD—people take an interest in historical aspects of science all the time. I can think of a few discarded scientific theories that are commonly discussed in science classes: The Ptolemaic theory of the solar system, the "plum pudding" model of the atom, and the phlogiston theory of combustion come to mind. The first two are very commonly taught in science classes. I think this is because they do a very good job of illustrating the scientific method and the value of careful analytical thinking. The phlogiston theory also illustrates careful thinking, but it isn't discussed in science classes nearly as much. My guess is that this is because it's harder to visualize. You can easily make a diagram in a textbook of the epicycles of Ptolemy and the ellipses of Kepler. And the model of electrons circling the nucleus, as per the Rutherford atom, is pretty much the logo for all things atomic. Lavoisier's (and others') experiments with combustion don't make for as dramatic an illustration.

The Simon Newcomb / Asaph Hall theory of planetary precession, unfortunately, seems to be even less photogenic. The effect being explained, 43 arcseconds per century, may be hard to get sudents excited about. But I doubt whether anyone jeopardizes their academic or research careers by being interested in it.

Idea: How about if I write some articles about the 4 theories (Ptolemy/Kepler, pudding/Rutherford, phlogiston/oxidation, and Newcomb/Einstein)? We could create a category for discarded scientific theories.

But I won't get to it any time soon. I'm very busy at Ameriwiki.

By the way, I have to thank you for the "E=mc^2" article. It really sharpened my thinking about the issues involved in special relativity, and it contributed to the outline of the articles I'm writing at Ameriwiki.

[[User:SamHB|SamHB]] 22:40, 2 May 2012 (EDT)

::: Ugh, the reasons GPS devices don't contain the "rigorous transformations" that relativity "would seem to require" is very simple. The satellites are in geosynchronous orbits, and the difference in time that relativity causes only need to be calculated once. From then on, it's simply a case of adding a few ns every day to the satellite clocks to account for this. I would've thought that was obvious to an expert. And only an expert should be attempting to write authoratively on the theory of relativity! A certificate in physics does not an expert make. [[User:LucoDaw|LucoDaw]] 15:09, 11 July 2012 (EDT)

== Logic and the GPS ==

*Atomic watches work on the Earth quite fine
*[[Quantum mechanics]] describe the physics of ''very small length and energy scales''
*Satellites are macroscopic objects.
*Even a precision of 1cm on the surface of the Earth isn't a very small length.

So which kind of logic tells us that quantum mechanical effects influence the synchronization of the clocks? Why are not only the scientists involved lying, but also their calculations?

For me it seems to be a logical conclusion that you, Aschlafly, are even more knowledgeable of Greek than of Science! [[User:AugustO|AugustO]] 08:21, 12 April 2012 (EDT)
:He's trying to apply the Heisenburg Uncertainty principle to satellites? Are you kidding me? That principle is used for things at the ATOMIC LEVEL! Using ANYTHING with regards to quantum mechanics in an argument about satellites is absurdism and/or ignorance of the subject matter! Seriously Andy, I know you hate the Theory of Relativity, but you should really leave science to those who understand it. [[User:JanSmuts|JanSmuts]] 16:04, 12 April 2012 (EDT)
::For someone who thinks that Brownian motion is about motion at the sub-atomic level your suggestions of scientific superiority ring hollow.--[[User:DavidEdwards|DavidEdwards]] 10:15, 13 April 2012 (EDT)

== Newtonian explanation of Mercury's precession ==

I removed the phrase "[precession can be understood by] factoring in the gravitational pull due to other planets". The first sentence of that paragraph says the opposite, that the extra precession cannot be understood "even after accounting for gravitational perturbations caused all other planets". Unless I'm reading it wrong, it sounded like a contradiction. [[User:Spielman|Spielman]] 16:51, 13 April 2012 (EDT)

:Where is the contradiction? If the exponent in Newtonian gravity is slightly adjusted, then it predicts the Mercury precession.--[[User:Aschlafly|Andy Schlafly]] 18:01, 13 April 2012 (EDT)

::I'm curious as to the justification for changing a formula in Newtonian gravity. Do you change it for every situation, or just for this one special case? Can you give us the adjusted formula, and specify the exact change? For such a change in physics which has been in use for over 250 years I would like to see a reference, preferably several good references. [[User:RolandPlankton|RolandPlankton]] 18:25, 13 April 2012 (EDT)
:::The old Newcomb-Hall hypothesis. [http://books.google.at/books?id=oKGlHjDzGjQC&lpg=PA379&dq=newcomb%20hall%20precession&pg=PA379#v=onepage&q=newcomb%20hall%20precession&f=false This book] says that it contradicts the observations of the orbit of the moon, which rules out a change of exponent of of the required magnitude. --[[User:FrederickT3|FrederickT3]] 18:30, 13 April 2012 (EDT)
::The contributors to this section might be pleased to see that the issue has been discussed, at great length, right here at Conservapedia. An entire debate page was created for it: [[Debate:What is the exponent of r in Newtonian gravity%3F]] This was a discussion that spilled over from [[Essay:Quantifying Open-Mindedness]].

::Furthermore, the subject was discussed on the relativity page itself, in the section [[Theory_of_relativity#Experimental_Verification_of_Relativity]]. There is a large chart showing the precessions of the planets under the Newcomb-Hall theory and under general relativity. They are the last two columns of the chart. The actual observations match the last column very well (see [http://www.mathpages.com/rr/s6-02/6-02.htm], taking into account that it's very hard to get accurate reading on the outer planets, since their precession is so small.

::One can see that the last two columns of the chart match only for Mercury. That is, Newcomb and Hall "tweaked" the exponent to the value of 2.000000157 in order to get Mercury's precession correct.

::Under the Newcomb-Hall theory, the precession of any orbiting body would be .000000078 revolutions per orbit. This works for Mercury, but is too high for the other planets, and way too high for the Moon. This is why the theory was discarded. With modern artificial satellites, such as the International Space Station, an orbit takes only an hour and a half, and the precession would be enormous. The clearly wrong value for the Moon is why the Newcomb-Hall theory was quickly discarded.

::Under general relativity, we know that the precession per orbit is proportional to the square of the planet's orbital velocity. Mercury has the highest velocity, so it has readily measurable precession. Artificial satellites are much slower, and the Moon is slower still.

::I personally don't see accepting the possible truth of such a thoroughly discredited theory as evidence of open-mindedness, but open-mindedness is admittedly a very tricky issue. [[User:SamHB|SamHB]] 18:11, 14 April 2012 (EDT)

::::"Mathematical physicists" (an [[oxymoron]] - I'll add it to the list) insisted that it was impossible for the exponent in Newtonian gravity to be anything other than '''''precisely''''' 2 (or -2). With the political push to promote the [[Theory of Relativity]], the influence of the mathematical physicists rose too, and that is what shut down the valid inquiry into whether the Newtonian exponent should be '''''precisely''''' 2 (or -2). But any logical inquiry must admit the possibility, or even the likelihood, that it would not be exactly 2 (or -2).--[[User:Aschlafly|Andy Schlafly]] 19:31, 13 April 2012 (EDT)

The issue here is not whether the exponent is precisely two or not but that you have to have a model which explains all (or at least as many as possible) observations. To get the precision of Mercury right you produce a model which then fails to explain the observed precession of every other body in the solar system. This seems to be a good experimental demonstration that Newcomb-Hall is wrong (or least inadequate as a model). [[User:Jloveday|Jloveday]] 15:32, 15 April 2012 (EDT)

:I'm not sure how [[User:Aschlafly|Andy Schlafly]] got us on the subject of the Newtonian exponent. My comment makes no mention of it. I'll answer his original question "where's the contradiction?": I quoted two sentences, both containing the phrase "other planets". One sentence said the precession '''can''' be understood by including the effects of the other planets, whereas the other said the precession '''cannot''' be understood that way. It is just rhetoric. The contradiction has little to do with physics. [[User:Spielman|Spielman]] 12:06, 16 April 2012 (EDT)

OK, how do you explain that adjusting the exponent in Newtonian gravity doesn't account for the orbits of the other planets? You say it has to do with politics. It has nothing to do with politics--the other theory just doesn't work! [[User:AndyFrankinson|AndyFrankinson]] 20:33, 11 May 2012 (EDT)

:I doubt the minor tweak in the exponent would affect the other orbits. The orbit of Mercury would be far more sensitive to such a tweak than anything else.

:The broader question remains: isn't the [[censorship]] of any alternative to the [[Theory of Relativity]] obvious? If the theory were correct, then there would be no need for [[liberals]] to censor debate or alternative theories.--[[User:Aschlafly|Andy Schlafly]] 20:25, 12 May 2012 (EDT)

::*''I doubt the minor tweak in the exponent would affect the other orbits.'' Do you have any calculations which would affirm this belief of yours? AFAIK, Simon Newcomb's and Asaph Hall's idea was discarded when excellent measurements for the Moon were made by Ernest W. Brown which didn't fit the predictions of Newcomb and Hall. This was in the early 20th century...
::*Today Computer simulations allow for an easy test of alternatives to Newton's exponent. Any student should be able to create one and see for himself that it doesn't work out.
::*The influence of the exponent on ''apsidal angles'' was discussed be Newton himself. It's still of interest today: a central system in which the exponent is 1 is easily imaginable (swing a weight on a spring around your head). And you will find publications on these subjects still today.
::That said:
::*Why don't you run a simulation for yourself?
::*''Alternative theories'' are discussed - and mostly discarded. That's the way physics works. Theories doesn't become true because you ''believe'' in them, they become more and more trustworthy when their predictions are verified over and over again.
::[[User:AugustO|AugustO]] 08:40, 13 May 2012 (EDT)

:::The Newcomb-Hall theory doesn't need anyone, liberal or otherwise, to censor it. It censors itself, by being wrong. It has been shown to be wrong many times, including Ernest Brown's observations, and some data published right here at [[Theory of relativity#Experiments that Fail to Prove Relativity|Conservapedia]].

:::Probably the best refutation at present is with artificial satellites, since their orbital period is so short. If you want to argue for the Newcomb-Hall theory, your best bet would be to find data showing that the periapsis of the International Space Station precesses by .013 degrees per month. That is an enormous precession, easily observed. The orbital eccentricity is only .001, but, since the ISS is so close and is in constant contact by radio and radar, there should be extremely good data. You should probably contact the author of the [http://www.heavens-above.com/ Heavens Above] web site. It has a huge amount of information on things like this.

:::I think that you will find that what you are up against is not liberals, but facts. [[User:JudyJ|JudyJ]] 12:44, 13 May 2012 (EDT)

== First sentence of article contradicted by the rest ==

Given that main body of the article now largely deals with the things GR can explain (including the precession of Mercury) should not the first sentance be changed?[[User:Jloveday|Jloveday]] 15:37, 15 April 2012 (EDT)

:GR is '''disproven''''' now by the precession of Mercury. See [[Counterexamples to Relativity]].--[[User:Aschlafly|Andy Schlafly]] 16:22, 21 April 2012 (EDT)

I checked [[Counterexamples to Relativity]] and the number for the observed precession in the note are unreferenced. To be credible there has to be a reference for this number.[[User:Jloveday|Jloveday]] 12:11, 22 April 2012 (EDT)

== Nobel Committee Criticism ==

That section of the article criticizes the Nobel Committee for not awarding a prize to a scientist who questions relativity, then immediately notes that no awards have been given for work related to relativity. Perhaps it'd be better to remove this contradiction; pick a poison and stick to it, so to speak. Alternatively, it may be more honest just to remove the section. --[[User:PaPatriot|PaPatriot]]

:What's contradictory about that? It's similar to how the Obama Administration won't appoint anyone who is [[pro-life]], and yet Obama won't campaign on being pro-[[abortion]]. That's not a contradiction.--[[User:Aschlafly|Andy Schlafly]] 20:07, 23 May 2012 (EDT)

== Bending of light in Newtonian gravity ==

All right, can someone show me exactly how light is bent by gravity in Newtonian gravity? Photons have zero mass, so, according to Newtonian gravity, they should not feel gravity. [[User:AndyFrankinson|AndyFrankinson]] 20:56, 25 June 2012 (EDT)

:*Newton's Corpuscular theory of light didn't state that the mass of the photons is zero. It was just obvious that it is very tiny
:*For the actual calculation, the mass of the photon cancels out
:*[[Johann Georg von Soldner]] did the calculations in 1801 - Newton's theroy was still going strong, then. ([http://de.wikisource.org/wiki/Ueber_die_Ablenkung_eines_Lichtstrals_von_seiner_geradlinigen_Bewegung Über die Ablenkung eines Lichtstrals von seiner geradlinigen Bewegung] English: ''On the Deflection of a Light Ray from its Rectilinear Motion''). The predicted effect was to tiny to be observed accurately in his time
:*Newton's corpuscular theory became unpopular since the 1820s, so this line of thought wasn't followed up.
:*Here is a modern re-calculation [http://arxiv.org/abs/0903.1031v6 Bending of light: A classical analysis]
:From Sendler's essay: ''Hoffentlich wird es niemand bedenklich finden, daß ich einen Lichtstral geradezu als schweren Körper behandle. Denn daß die Lichtstralen alle absoluten Eigenschaften der Materie besitzen, sieht man an dem Phänomen der Aberration, welches nur dadurch möglich ist, daß die Lichtstralen wirklich materiel sind. – Und überdies, man kann sich kein Ding denken, das existiren und auf unsere Sinne wirken soll, ohne die Eigenschaft der Materie zu haben. –''
:''Hopefully no one will take offense that I looked at a ray of light as an object of mass. That every ray of light has the absolute properties of matter is seen from the phenomenon of aberration, which is only possible because the rays are really material. — and furthermore, one can think of no thing which exists and interacts with our sense without having the properties of matter.''
:[[User:AugustO|AugustO]] 02:45, 26 June 2012 (EDT)
::Yeah, I've heard of that. But the photon has zero mass. [[User:AndyFrankinson|AndyFrankinson]] 20:20, 26 June 2012 (EDT)
:::Newtonian physics doesn't know about zero-mass particles, hence it doesn't make a unique prediction. One possible interpretation is to say "zero mass -> zero gravitational force -> no bending". Another interpretation is to take the mathematical limit of the equations for ''m''->0. Since ''ma = GMm/r2'', the mass of the photon cancels and you get ''a = GM/r2'', even in the limiting case ''m=''0. This leads to bending by half the amount as predicted by relativity (and observed). --[[User:FrederickT3|FrederickT3]] 22:47, 26 June 2012 (EDT)

== Conflation of Relativity and Relativism & Robert H. Dicke & Barack Obama ==

There appears to be significant resistance to relativity that is largely unfounded. The theory is in no way contradictory to Christian beliefs, or religion in general. As a conservative, right wing encycloepdia, I expect resistance to moral relativism.

From reading the article, it appears many of the authorship appear to conflate Einstein's relativity with moral relativism. The two concepts are entirely and utterly unrelated other than both containing the word "relativ". Newton's model of gravity as a simple inverse square law is a very close approximation to Einstein's model. The difference is Newton's is very slightly inaccurate and cannot be used where extreme accuracy is needed. Relativity can.

What's the difficulty with relativity here? The central premise is very basic and seems pretty self evident upon a little thought. There is no absolute frame of reference in a universe in which everything moves relative to everything else. Something can only be defined as moving with respect to (relative to) something else. And there you have it, general relativity.

There is also a problem with the section on Robert H. Dicke. He wasn't a major critic of relativity. Indeed, he developed some of the most stringent tests (relativity is highly falsifiable). It passed them. All.

I tracked down and read the article regarding relativity and law (Obama, etc.). It is quite a nice analogy, and is no way an attempt to use relativity to justify anything. The analogy is more closely related to the uncertainty principle - you cannot measure a particles position without changing or influencing it. You cannot just observe, as you have to intervene in order to do so. The same is true in American law (with a much stronger reliance on test cases, etc, than in say, English law). You cannot deal with one case without it having vast implications for others. That is all the paper is saying. Again, there is no agenda against conservatism or religion in this paper.

[[User:LucoDaw|LucoDaw]] 23:45, 5 July 2012 (EDT)

== Clocks on Trains - alternative theory ==

Someone better come up with a really good explanation as to why a clock on a train will show a different time to a clock next to the track, after the train has travelled for a length of time. This has been done, and relativity predicted the difference (due to time dilation). If relativity is definitely un-true (the premise of this article), then what IS causing the difference in times?

The above GPS argument makes a similar case, but trains are easier to understand. The difference in time on these clocks has nothing at all to do with quantum physics. Noone try and claim it is, and that they don't have to prove it because it's a logical statement. Anyone who thinks they can logically infer QM (which is inherently illogical by human perception) needs to see a shrink.

[[User:LucoDaw|LucoDaw]] 23:51, 5 July 2012 (EDT)

== Counterexamples to Recent Experiments ==

Recently, experiments have been published in Science, directly measuring general relativistic time dilation effects using atomic clocks placed about a metre apart. Do we have any idea how to refute this? The reference I provide is to a newspaper summary of the findings [http://www.independent.co.uk/news/science/einsteins-theory-is-proved--and-it-is-bad-news-if-you-own-a-penthouse-2088195.html]. I have also read the paper and see no loopholes.
--[[User:DanPW|DanPW]] 12:49, 20 July 2012 (EDT)

::We don't need to, and can't, refute this; it is true. This appears to be an update, over a much shorter distance, of the Pound-Rebka experiment of 1960 or so. [[User:SamHB|SamHB]] ([[User talk:SamHB|talk]]) 08:27, 15 July 2017 (EDT)

:Probably our best bet is personal attacks on the researcher, Chou, or possibly [[NIST]]. I suspect Chou was not born in this country. He may have an agenda to confuse American citizens. [[User:Spielman|Spielman]] 14:35, 20 July 2012 (EDT)

== Information and Relativistic Time Dilation? ==

The question is this: are laws of physics the results of predetermined relationships, or are they result of using information?

This seemingly has nothing to do with time dilation, mass increase and such. But it does. Read more about this important question:

[http://www.msg2act.com/physics/ch/index.shtml]

It turns out, there is a connection between information processing and SR/GR time dilation.

In a simplified way, the more information there is, the slower the rate of physical processes.

Antecedent to first concept of physics, main SR/GR results can be derived out of thin air, without postulates.

== Edit of 29 Oct 2014 ==

I think [[User:Dossas]] was right in having the article say what it is before criticizing it. Most pages on science have at least a sentence or two, at the beginning, saying what the subject is.

I have moved the bulk of the criticism (Louis Essen, etc.) up a few paragraphs. The link to his article ''The Special Theory of Relativity: A Critical Analysis'' was a dead link, but I found two other links that are equally fiery. And I put the "wouldn't get tenure" line into a better contextual place. That is, in with the paragraph about Essen. In fact, his ''Relativity and Time Signals'' paper has a quote at the top: "The theory is so rigidly held that young scientists dare not openly express their doubts" that you might want to put in, illustrating the "wouldn't get tenure" line. Though I haven't done that.

[[User:SamHB|SamHB]] 00:10, 30 October 2014 (EDT)

== An argument against relativity ==
I think I have a strong (theoretical) argument against the theory of relativity. Is there anyone who could help me by reviewing my stuff, by giving me a professional opinion? May email address: laszlogm@admarc.hu {{unsigned|Laszlogm}}

::I think things like this would be best played out in public. After all, this is a wiki, and Conservapedia has a long history of debating relativity issues openly. But if you really do want to promulgate it in private, my email is near the top of my user page. However, if you go that route, I very well may decide, based on what I see, to make it public somewhere here on CP.
::Your next choice might be simply to publish it directly, either on your own user or talk page, or at the bottom of this page (Talk pages are appended at the end, so they are in forward chronological order).
::Perhaps your best bet, if you are feeling really confident, is to add it to the [[Counterexamples to Relativity]] page. But I should advise you in advance: The bar for counterexamples is rather high, and, unless you really have a correct counterexample, your argument will be figuratively ripped to shreds, the way all the others have been.
::[[User:SamHB|SamHB]] 13:33, 11 January 2015 (EST)
== Einstein’s Relativity and Relativism: Why Einstein’s theory of relativity is actually a powerful argument for absolute truth. ==

Please read the article [http://evangelicalfocus.com/blogs/1297/Einsteins_Relativity_and_Relativism Einstein’s Relativity and Relativism: Why Einstein’s theory of relativity is actually a powerful argument for absolute truth.] [[User:Conservative|Conservative]] ([[User talk:Conservative|talk]]) 13:55, 11 February 2016 (EST)

== New heading ==

I have rarely laughed out loud as often as I did while reading this article. This must be satire, no? If not then I weep for humanity. {{unsigned|Nikib}}

:Yeah, sure you do. You might weep for closed-mindedness too.--[[User:Aschlafly|Andy Schlafly]] ([[User talk:Aschlafly|talk]]) 15:15, 2 July 2017 (EDT)

::You may consider it to be satire, but it is not. The story is more complicated than that. Conservapedia is probably the most prominent place on the internet where relativity is treated this way. There is probably no one on the planet that disparages and denies relativity more ferociously than Andy Schlafly. The [[counterexamples to relativity]] page is world-famous, has over 2 million page views, and dominates, by a wide margin, Google searches for the subject. If you think that all of us at CP are anti-relativity, you are wrong.

::You should know that there is sort of a custom at CP, for pages like this, that parts of pages above the table of contents are not to by edited except by Aschlafly, but the material below the table of contents is the consensus (in the usual way for a wiki) of the editor base, and that most editors try to have that part of the page be a factual exposition of the subject. If you would like to contribute to that, feel free. [[User:SamHB|SamHB]] ([[User talk:SamHB|talk]]) 15:37, 2 July 2017 (EDT)

== Gravitational time dilation ==

Each rising sun is a synchronization of time, every eclipses synchronize altitudes together from one eclipse to the other. Synchronization of events is incompatible with desynchronization of clocks. I prefer to believe in synchronization of eclipses than in desynchronization of clocks. But that is a choice. If you believe eclipses are desynchronized, it is God will, but you are not in the truth. If there were some (nano)seconds more at high altitudes between eclipses (slower rate), it would mean events happen quicker at low altitude (quicker rate of events in a time dilated frame???). What is your opinion?

User talk:Geocentric

2017-08-20T16:01:29Z

Geocentric: Answer about synchronization on earth

==Your edits to relativity==
I have reverted what you wrote. I think it is likely that you are simply trolling (and I might add that most people around here would block you instantly if they believed you were trolling, but I'm more patient and, in any case, do not have block powers), or perhaps that you are profoundly confused or ignorant. There has been a lot of ignorant writing about relativity here at Conservapedia, and I don't have a lot of patience for it.

Aside from the fact that the whole thing is what my 4th grade teacher would have called a "run-on sentence", the various phrases in that sentence do not make logical or grammatical sense. What does "is not accurate to describe" mean? What does the rising of the Sun have to do with the nanosecond accuracy with which relativity observations are made? The "possibility of multiverses" is largely driven by quantum mechanics, though it's all in the context of relativity. There are a lot of books on the subject, written for the lay public. Eclipses are typically separated by years, and the timing of them, at various altitudes, can be readily worked out. Worldlines are not the same. My worldline is different from yours. [[User:SamHB|SamHB]] ([[User talk:SamHB|talk]]) 21:52, 19 August 2017 (EDT)

God prevent me from trolling ! Each rising sun is a synchronization of time, every eclipses synchronize altitudes together from eclipse to the other. Synchronization of events is incompatible (not accurate) with desynchronization of clocks. I prefer to believe in synchronization of eclipses than in desynchronization of clocks. But that is a choice. If you believe eclipses are desynchronized, it is God will, but you are not in the truth. If there were some nanoseconds more at high altitudes between eclipses (slower rate), it would mean events happens quicker at low altitude (quicker rate of events in a time dilated frame???). Sincerely yours.[[User:Geocentric|Geocentric]] ([[User talk:Geocentric|talk]]) 12:01, 20 August 2017 (EDT)

Theory of relativity

2017-08-19T19:49:30Z

Geocentric: gravitational time dilation and worldlines

''See also [[Counterexamples to Relativity]].''

In physics, the '''theory of relativity''' is a scientific theory describing the effects due to the invariance of the speed of light. In particular, the meaning of space and time are altered by the motion of the observer. Relativity predicts phenomena such as time dilation and length contraction for observers moving relative to one another at very high ("relativistic") speed.

'''Relativity''' refers to two closely-related mathematical theories in [[physics]]:
[[Image:600px-Albert Einstein Head.jpg|thumbnail|right|200px|
*"I do not share the crusading spirit of the professional [[Atheism|atheist]] whose fervor is mostly due to a painful act of liberation from the fetters of religious indoctrination received in youth. I prefer an attitude of humility corresponding to the weakness of our intellectual understanding of nature and of our own being." - [[Albert Einstein]]<ref name="Isaacson390">Isaacson, Walter (2008). [http://books.google.com/books?id=cdxWNE7NY6QC&pg=PT390 ''Einstein: His Life and Universe''] (New York: Simon and Schuster), p. 390. Retrieved from GoogleBooks archive on February 19, 2015.</ref>]]
*'''[[Special theory of relativity|Special relativity]]''' (SR) is a theory which describes the laws of motion for non-accelerating bodies traveling at a significant fraction of the [[speed of light]]. As speeds approach zero, Special Relativity tends towards equivalence with [[Newton's Laws of Motion]]. Special Relativity was developed by [[Hendrik Lorentz]], [[Henri Poincaré]], and Hermann Minkowski,<ref>"German mathematician who developed the geometrical theory of numbers and who made numerous contributions to number theory, mathematical physics, and the theory of relativity." [http://www.britannica.com/eb/article-9052860/Hermann-Minkowski Hermann Minkowski -- Britannica Online Encyclopedia]</ref><ref>[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Minkowski.html Hermann Minkowski, Biography]</ref> and [[Albert Einstein]].

*'''[[General theory of relativity|General Relativity]]''' (GR) is a theory which explains the laws of motion as viewed from accelerating reference frames and includes a geometric explanation for gravity. This theory was developed by [[David Hilbert]] and [[Albert Einstein]] as a generalization of the postulates of Special Relativity.<ref>"[T]he German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein."[http://nobelprize.org/educational_games/physics/relativity/history-1.html Nobel Prize historical account]</ref> A dramatic but later discredited claim by Sir [[Arthur Eddington]] of experimental proof of General Relativity in 1919 made Einstein a household name.

These theories have augmented earlier approaches, such as [[Galilean Relativity]].

The theory of relativity is defended with religious-like zeal, such that no college faculty tenure, Ph.D degree, or Nobel Prize is ever awarded to anyone who dares criticize the theory, as the example of denying a Nobel Prize to the most accomplished physicist of the 20th century, [[Robert Dicke]], illustrates. Another critic of the theory was Louis Essen [1908-1997], the man credited with determining the speed of light. He wrote many fiery papers against it such as ''Relativity and Time Signals''<ref>http://gsjournal.net/Science-Journals/Journal%20Reprints-Relativity%20Theory/Download/3297</ref> and ''Relativity - Joke or Swindle?''.<ref>http://www.ekkehard-friebe.de/Essen-L.htm</ref> Perhaps the most famous website opposing relativity is this one, with its [[Counterexamples to Relativity]] page. The cornerstone item in that page involves the experimental measurements of the advance of the perihelion of Mercury that show a shift greater than predicted by Relativity, well beyond the margin of error.

The theory of relativity have discontinuities whereby the limit of a physical quantity as a variable (such as mass or velocity) approaches a fixed value is not the same as the physical quantity at the fixed value. For example, the limit of momentum as mass approaches 0 and velocity approaches the speed of light is not equal to the momentum of (massless) light.<ref>Discontinuities in General Relativity are also well-recognized. See, e.g., [http://www.springerlink.com/content/u47l341u2q555455/]</ref>

The theory of relativity consist of complex mathematical equations relying on several hypotheses. For example, at Hofstra University general relativity is taught as part of an upperclass math course on differential geometry, based on three stated assumptions.<ref>http://people.hofstra.edu/Stefan_Waner/diff_geom/tc.html</ref> Special relativity assumes that all observers in inertial frames of reference will measure the same value for the speed of light, '''c''' and that all inertial frames of reference are equivalent. These hypotheses that can never be fully tested. Relativity rejects Newton's [[action at a distance]], which is basic to Newtonian gravity and also found to be a consequence of [[quantum mechanics]]. The mathematics of relativity assume no exceptions, yet in the time period immediately following the origin of the universe the relativity equations could not possibly have been valid, since quantum effects would not be negligible (in the same way non-relativistic quantum mechanics is not valid when dealing with particles traveling near the speed of light).

The "continuous" nature of space and time postulated by relativity is in conflict with the "discrete" nature in [[quantum mechanics]],<ref>For example, Relativity claims that space and time are smooth and continuous, while [[quantum mechanics]] suggests otherwise. [http://www.csmonitor.com/Science/Cool-Astronomy/2010/1025/Is-the-universe-a-big-hologram-This-device-could-find-out.] Relativity also denies [[action-at-a-distance]], while quantum mechanics suggests otherwise. Relativity denies any role for chance, while quantum mechanics is heavily dependent on it.</ref> and although theories like [[string theory]] and [[quantum field theory]] have attempted to unify relativity and quantum mechanics, neither has been entirely successful or proven.

Unlike [[Classical mechanics|Newtonian physics]], in which space and time intervals are each invariant as seen by all observers, in SR the only invariant quantity is a quadratic combination of space and time intervals (x2 - c2 t2). The instantaneous transmission of Newtonian gravitational effects also contradicts relativity.

In quantum mechanics, the [[uncertainty principle]] suggests that virtual particles can sometimes travel faster than the speed of light which would violate causality, but "[t]he only known way to resolve this tension involves introducing the idea of antiparticles."<ref>http://nobelprize.org/nobel_prizes/physics/laureates/2004/wilczek-lecture.pdf (p. 102)</ref> Consequently, in 1928 Paul Dirac derived the Dirac equation, one of the first quantum mechanical equations compatible with special relativity, by which Dirac predicted the existence of antimatter. Four years later, antimatter (the positron) was discovered by Carl Anderson, as successfully predicted by relativistic quantum mechanics. [[Quantum field theory]], a generalization of quantum mechanics, is fully compatible with special relativity but not with general relativity, and still lacks a vital piece: evidence of the [[graviton]].

A famous critic of Theory of relativity is [[Nikola Tesla]], who called it a "...magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king ... its exponents are brilliant men but they are metaphysicists, not scientists...".<ref>[http://www.plasmacosmology.net/tesla.html New York Times, July 11, 1935, p23, c8]</ref>

== Special Relativity ==
Lorentz and Poincaré developed Special Relativity as way of understanding how Maxwell's equations for electromagnetism could be valid in different frames of reference. Einstein famously published an explanation of Poincaré's theory in terms of two assumptions (postulates):

# ''The [[speed of light]] is constant for all (inertial) observers, regardless of their velocities relative to each other.''
# ''The laws of physics are identical in all inertial reference frames.''

In layman's terms, these two assumptions can be restated as:
# It is impossible ever to transmit information faster than the speed of light.<ref>This assumption is commonly restated in this manner. For example, a discussion of hypothetical [[tachyons]] talks "about using tachyons to transmit information faster than the speed of light, '''in violation of Special Relativity'''."[http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html] However, there is some question whether the Theory of Special Relativity really restricts faster-than-light communication of information.</ref>
# The laws of physics are identical, without any variation, in every location throughout the universe.
# The laws of physics are identical, without any variation, no matter how fast something is traveling (in the absence of acceleration).

Or, in more concise, clearer terms, these assumptions are this:

#there is no [[action at a distance]] (because that would make observations dependent on the frame of reference)
#space and time are completely symmetric throughout the universe (because otherwise frames of reference would not be interchangeable)

When the assumptions are stated clearly as above, the weaknesses in the theory are more apparent. There “is” action at a distance in [[quantum entanglement]] and apparently also in gravity, as no gravitons can be found. However, no information has yet been transmitted via quantum entanglement, so while non-locality violates the spirit of relativity it is consistent with it if relativity is limited to the transmission of information. [[Quantum field theory]], an attempt to partially reconcile [[quantum mechanics]] with relativity, is incomplete at best. As to the second assumption, it is contrary to the [[arrow of time]], which illustrates the lack of symmetry in time. Logical defects include the incoherence of relativistic mass (see discussion below) and the lack of relativistic constraints near the beginning the universe (see above).

Special Relativity (SR) was initially developed by [[Henri Poincaré]] and [[Hendrik Lorentz]], working on problems in electrodynamics and the [[Michelson-Morley experiment]], which had not found any sign of Earth's orbital motion through the [[aether (science)|luminiferous aether]], which was believed to be the substance which carried electromagnetic waves. Special relativity alters [[Isaac Newton]]'s laws of motion by assuming that the speed of light will be the same for all observers, despite their relative velocities and the source of the light. (Therefore, if A sends a beam of light to B, and both measure the speed, it will be the same for both, no matter what the relative velocity of A and B. In Newtonian/Galilean mechanics, If A sends a physical object at a particular velocity towards B, and nothing slows it, the velocity of the object relative to B depends on the velocities of the object and of B relative to A.)

At low speeds (relative to light-speed), the Lorentz-Poincaré relativity equations are equivalent to Newton's equations. The media-promoted equation ''[[E=mc²]]'', implausibly suggests a relationship between typically unrelated concepts of energy, the rest mass of a body and the speed of light.

Under relativity, particles at low mass and low speed can be accurately approximated by [[classical mechanics]] (such as [[Isaac Newton]]'s laws of motion). At the two extremes, modeling the behavior of electrons requires that relativistic effects be taken into account (the chemically significant phenomenon of electron spin arises from relativity), and the course of light passing through a region containing many massive bodies such as galaxies will be distorted ([[classical mechanics]], in which light travels in straight lines, does not predict this). These are both experimentally confirmed (electron spin was known before relativity arose, and telescopic observations confirm that galactic clusters distort the paths of the light passing through them).

Many scientists have indicated problems with the postulates of special relativity. Paul Davies, formerly of Macquarie University and now at the University of Arizona believes that the speed of light has changed over time. Since the speed of light is a constant speed 'c' this indicates problems with the theory [http://news.bbc.co.uk/2/hi/science/nature/2181455.stm light speed]. Other engineers and scientists have written about problems in the basic set of special relativity equations. Based on the ideas of not Einstein but of the scientist Fitzgerald as well as others, a length contraction effect was predicted as an explanation of the failure of the Michelson-Morley experiment to detect Earth's orbital motion. This idea was taken up by Hendrik Lorentz and shown by others to be a useful mechanism by which theory could be forced into conformance with experimental results. However, in 2005, Michael Strauss a computer engineer invalidated much of Special Relativity theory by showing clear contradictions in the theory. [http://www.relativitycollapse.com relativity]

== General Relativity ==

::::''See the [[General theory of relativity]] page for more in-depth coverage of this topic.''

General Relativity is a theory of gravity that is compatible with Special Relativity. Einstein explains a thought experiment involving two elevators. The first elevator is stationary on the Earth, while the other is being pulled through space at a constant acceleration of g. Einstein realized that any physical experiment carried out in the elevators would give the same result. This realization is known as the equivalence principle and it states that accelerating frames of reference and gravitational fields are indistinguishable. General Relativity is the theory of gravity that incorporates Special Relativity and the equivalence principle.

General Relativity is a mathematical extension of Special Relativity. GR views space-time as a 4-dimensional [[manifold]], which looks locally like [[Minkowski space]], and which acquires [[curvature]] due to the presence of massive bodies. Thus, near massive bodies, the geometry of space-time differs to a large degree from [[Euclidean geometry]]: for example, the sum of the angles in a triangle is not exactly 180 degrees. Just as in classical physics, objects travel along [[geodesic]]s in the absence of external forces. Importantly though, near a massive body, geodesics are no longer straight lines. It is this phenomenon of objects traveling along geodesics in a curved spacetime that accounts for gravity.

The anomalous precession of Mercury's [[perihelion]] seems to support the Theory of General Relativity, though that is disputed on the[[Counterexamples to Relativity]] page. Keep in mind that the precession in question is the ''"anomalous"''
precession after the effects of other planets' gravitation action has been compensated for. Those other effects are much larger, and are purely Newtonian in nature. There was another explanation based on Newtonian gravity, involving a slight alteration to the precise inverse-square relation of Newtonian gravity to distance, but it was discarded when it gave very bad results for the Moon's orbit.

British Historian Paul Johnson declares the turning point in 20th century to have been when fellow Briton Sir [[Arthur Eddington]], an esteemed English astronomer, ventured out on a boat off Africa in 1919 with a local Army unit to observe the bending of starlight around the sun during a total eclipse. Upon his return to England declared that his observations proven the theory of relativity. In fact recent analysis of Eddington's work revealed that he was biased in selecting his data, and that overall his data were inconclusive about the theory of relativity. The prediction was later confirmed by more rigorous experiments, such as those performed by the [[Hubble Space Telescope]].<ref>[http://www.spaceimages.com/gravlen.html Hubble Gravitational Lens Photo]</ref><ref>[[Gravitational lensing]]</ref><ref>[http://www.iam.ubc.ca/~newbury/lenses/glgallery.html]</ref> Lorentz has this to say on the discrepancies between the empirical eclipse data and Einstein's predictions.

::''It indeed seems that the discrepancies may be ascribed to faults in observations, which supposition is supported by the fact that the observations at Prince's Island, which, it is true, did not turn out quite as well as those mentioned above, gave the result, of 1.64, somewhat lower than Einstein's figure.''<ref>Lorentz, H.A. [http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm The Einstein Theory of Relativity]</ref>

The prediction that light is bent by gravity is predicted both by Newtonian physics and relativity, but relativity predicts a larger deflection.

Special relativity is the limiting case of general relativity where all gravitational fields are weak. Alternatively, special relativity is the limiting case of general relativity when all reference frames are inertial (non-accelerating and without gravity).

==Lack of evidence for Relativity==
The Theory of relativity assumes that time is symmetric just as space is, but the biggest early promoter of relativity, Arthur Eddington, coined the term "[[arrow of time]]" admitting how time is ''not'' symmetric but is directional. The passage of time is tied to an increase in disorder, or [[entropy]]. The Theory of relativity cannot explain this, and implicitly denies it, specifically allowing for theoretical time travel (e.g., [[wormholes]]) and different rates of passage of time based on velocity and acceleration.

Claims that relativity was used to develop the [[Global Positioning System]] ([[GPS]]) are false. A 1996 article explains:

:"The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein's general theory of relativity would seem to require - transformations to and from the individual space vehicles (SVs), the Monitor Stations (MSs), and the users on the surface of the rotating earth, and the geocentric Earth Centered Inertial System (ECI) in which the SV orbits are calculated. There is a very good reason for the omission: the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter - less than one centimeter, for users on or near the earth."<ref>http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf</ref><ref>Some do claim that relativity is "vital" to GPS even though GPS developed independently of theoretical predictions and theoreticians disagree about how the relativistic effects for GPS should be calculated. ''See id. See also'' [http://www.rand.org/pubs/monograph_reports/MR614/MR614.appb.pdf]</ref>

This article, which was published in 1996, goes on to propose relativistic corrections that might be used to design more accurate GPS systems. Clocks on board GPS satellites require adjustments to their clock frequencies if they are to be synchronized with those on the surface of the Earth.

Tom Van Flandern, an astronomer hired to work on GPS in the late 1990s, concluded that "[t]he GPS programmers don't need relativity." He was quoted as saying that the GPS programmers "have basically blown off Einstein."<ref>http://archive.salon.com/people/feature/2000/07/06/einstein/index.html See also [http://www.metaresearch.org/solar%20system/gps/absolute-gps-1meter-3.ASP], where Van Flandern discusses how relativistic corrections might improve GPS accuracy.</ref> Asynchronization can be easily addressed through communications between the satellites and ground stations, so it is unclear why any theory would be needed for GPS. While Van Flandern believed that relativity is unnecessary for GPS, he also asserted that observations of GPS satellites supported both general and special relativity, writing that "we can assert with confidence that the predictions of relativity are confirmed to high accuracy over time periods of many days," with unrelated factors interfering with longer-term observations.<ref>http://www.metaresearch.org/cosmology/gps-relativity.asp</ref>

Some internet articles claim that GPS timing differences ''confirm'' the Theory of Relativity or its Lorentzian counterpart (which uses a preferred frame of reference). GPS clocks run slower in the weaker gravitation field of the satellites than on ground stations on Earth, with the effects predicted by general relativity far outweighing the effects predicted by special relativity. However, the articles claiming that the slower GPS satellite clocks confirm relativity do not address the effect, if any, of the weaker gravitational force under Newton's theory on the GPS satellite clocks, likely because in Newtonian Mechanics every clock in the universe keeps time at the same rate regardless of velocity, acceleration, or the presence or absence of force.

Currently, GPS satellites are synchronized to Coordinated Universal Time by radio signals from the ground; therefore, they cannot currently be used to test general relativity.<ref>[http://www.phys.lsu.edu/mog/mog9/node9.html "General Relativity in the Global Positioning System."] Neil Ashby, U. of Colorado</ref>

There are claims that the effects of relativity have been observed with the frequency shift of the signal being sent back to [[Earth]] several times as various spacecraft have dipped into the gravity wells around massive objects such as the [[sun]] (see image at right)<ref>[http://saturn.jpl.nasa.gov/news/press-releases-03/20031002-pr-a.cfm Saturn-Bound Spacecraft Tests Einstein's Theory]</ref> or Saturn.<ref>[http://www.newscientist.com/article/mg12517102.600-science-encounter-with-saturn-confirms-relativity-theory.html Encounter with Saturn confirms relativity theory]</ref> A satellite called [[Gravity Probe B]] was put in orbit about the Earth to examine the effects of frame dragging and geodetic warping of space,<ref>[http://www.nasa.gov/mission_pages/gpb/index.html NASA Gravity Probe B mission page]</ref><ref>[http://einstein.stanford.edu/ Gravity Probe B project page]</ref> but the results were inconclusive. Note, however, that Newtonian mechanics also predicts deflection of light by gravity, and in the initial theory of relativity it predicted the same amount of deflection, but only if we treat light as capable of being accelerated and decelerated like ordinary matter, which is contrary to all measurements and observations to date.<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> Adjustments to the theory of relativity resulted in a prediction of a greater deflection of light than that predicated by Newtonian mechanics, though it is debatable how much deflection Newtonian mechanics should predict.

None of the NASA spacecraft incorporates predictions of relativity into their own timing mechanisms, as Newtonian mechanics is adequate even for probes sent deep into space so long as they do not undergo accelerations near the speed of light or enter any massive gravity wells.<ref>There is no reported reliance on relativity by any space probe.</ref>

A decade of observation of the [[pulsar]] pair [[PSR 1913 16|PSR B1913+16]] detected a decline in its orbital period, which was attributed to a loss in energy by the system. It is impossible to measure the masses of the pulsars, their accelerations relative to the observers, or other fundamental parameters. Professors Joseph Taylor and Russell Hulse, who discovered the binary pulsar, found that physical values could be assigned to the pulsars to make the observed decline in orbital period consistent with the Theory of General Relativity, and for this they were awarded the 1993 [[Nobel Prize]] for Physics, which is the only award ever given by the Nobel committee for the Theory of Relativity.<ref>http://nobelprize.org/nobel_prizes/physics/laureates/1993/press.html</ref> In 2004, Professor Taylor utilized a correction to the derivative of the orbital period to fit subsequent data better to the theory. At most, assumptions can be made and altered to fit the data to the theory, rather than the data confirming the theory.

The [[perihelion]] of Mercury's [[orbit]] [[precession|precesses]] at a measurable rate, but even after accounting for gravitational perturbations caused all other planets in the [[solar system]], Newton's theory (assuming a precise inverse-square relationship for distance) predicts a rate of precession that differs from the measured rate by approximately 43 [[arcsecond]]s per century. While general relativity was developed on purely theoretical grounds, it was soon discovered that it explained these precession observations.<ref>http://physics.ucr.edu/~wudka/Physics7/Notes_www/node98.html#SECTION032121000000000000000</ref><ref>http://farside.ph.utexas.edu/teaching/336k/lectures/node117.html</ref> Newton's theory can also explain the Mercury precession by making tiny adjustments to parameters in the gravitational equation, but doing so would give the same precession for all orbiting bodies everywhere, a phenomenon which is not observed.

General relativity predicts twice as much bending in light as it passes near massive objects than Newton's theory might predict.<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> This phenomenon is known as [[gravitational lensing]]. A large number of instances of gravitational lensing have been observed, and it is now a standard astronomical tool.<ref>http://imagine.gsfc.nasa.gov/docs/features/news/grav_lens.html</ref><ref>http://astro.berkeley.edu/~jcohn/lens.html</ref><ref>http://www.iam.ubc.ca/~newbury/lenses/glgallery.html</ref> Note, however, that the extent of bending of light predicted by Newton's theory is open to debate, and depends on assumptions about the nature of light for gravitational purposes.<ref>http://cosmictimes.gsfc.nasa.gov/1919/guide/gravity_bends_starlight.html</ref>

In 1972, scientists flew extremely accurate clocks ("atomic clocks") around the world in both directions on commercial airlines, and claimed to observe relativistic time dilation; the eastbound clock gained 273 ns and the westbound clock lost 59 ns, matching the predictions of general relativity to within experimental accuracy.<ref>[http://www.answers.com/topic/hafele-keating-experiment Hafele-Keating Experiment]</ref> However, the inventor of the atomic clock, Louis Essen, declared that the experiment was inaccurate.<ref>Louis Essen, Electron. Wireless World 94 (1988) 238.</ref> Dr A. G. Kelly examined the raw data from the experiment and declared it inconclusive.<ref>A. G. Kelly,Reliability of Relativistic Effect Tests on Airborne Clocks, Monograph No.3 Feb.1996, The Institution of Engineers of Ireland, ISBN 1-898012-22-9</ref> The Nobel Committee chose not to honor this experiment for the significance that was claimed.

Despite [[censorship]] of dissent about relativity, evidence contrary to the theory is discussed outside of [[liberal]] universities.<ref>http://scitizen.com/screens/blogPage/viewBlog/sw_viewBlog.php?idTheme=8&idContribution=922</ref>

==Experiments that Fail to Prove Relativity==

Predictions of general relativity turn out to be obscure and difficult to test. The two most famous predictions were the bending of light in a gravitational field and the precession of the perihelia of orbiting planets.

*The first of these was famously tested during a total eclipse in 1919. That test was somewhat muddled by an incorrect initial calculation, by several people including Einstein himself, of what the effect would be, and some "cherry picking" of the data to be used.<ref>''Einstein's Luck'', John Waller, Oxford University Press, ISBN 0-19-860719-9</ref> The data selection could be considered "manipulation" or "fudging", by a person (Arthur Eddington) who had a personal stake in the outcome. His analysis techniques would not pass muster today.

:It should be noted that pre-relativistic (Newtonian) physics may also predict a bending, of half the observed value, depending on whether one uses the 17th century "corpuscular" formulation or the 19th century "wave" formulation.

:Nevertheless, it has been verified with ever-increasing precision in subsequent eclipses, and in the observations of quasar 3C273.

*The second "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury. There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun. These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century. This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

:Increasingly precise measurements of the precession demonstrate that it conflicts with General Relativity, despite claims of relativists for decades that it predicted the precession accurately in the amount of <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.<ref>That is a simple approximation, designed to relate the precession to the planet's speed relative to the speed of light. A more accurate approximation is <math>\frac{3GM}{c^2 a(1-e^2)}</math>, where a is the semi-major axis and e is the eccentricity.</ref> The conflict is greater than the margin of error, and many relativists avoid the discrepancy rather than address it.

==Experimental and Observational Evidence Confirming Relativity==

The different effects predicted by special relativity, compared to classical formulations, are extremely tiny. Most relativistic effects are negligible at the speeds of ordinary phenomena observed by humans. The effects only become significant when the speeds involved are a significant fraction of the speed of light, which is <math>3 \times 10^8</math> meters per second—such speeds are called ''relativistic''. (However, it's worth noting that ordinary magnetism can be considered an effect of relativity, dictated by the need for electrostatic theory to be correct under relativity. The speed of light in fact appears in the formulas ([[Maxwell's Equations]]) governing electricity and magnetism, though these equations were developed long before relativity was proposed.)

Because the effects of relativity are so tiny, scientists have been devising sophisticated and sensitive tests ever since the theory was formulated in 1905.

The most famous experiment, and the one that is commonly cited in textbooks as the experiment that established the case for relativity,<ref>Though relativity did not actually originate from this experiment</ref> was the [[Michelson-Morley experiment]]. This showed that all observers will obtain the same measured value for the speed of light (3x108 meters per second) no matter what their state of motion. This is the first of the two fundamental principles:
#''The [[speed of light]] is constant for all observers, regardless of their velocities relative to each other.''
#''The laws of physics are identical in all reference frames.''
(The second is just a restatement of Galilean relativity, that is, the "common sense" that had been accepted for centuries.)
A naive "common sense" interpretation of Galilean relativity would require that measurements of the speed of light (or anything else) by different observers would get results that differ by the observers' relative speeds, and hence that principle #1 can't be true. Special relativity fixes this apparent paradox.

All of special relativity derives for these two principles, plus assumptions of exact conservation of momentum and energy in all cases.

*At the end of Einstein's original 1905 paper [http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ "Does the Inertia of a Body Depend its Energy Content?"], he speculates on the possibility that the equation <math>E = m c^2</math>, which would normally be very hard to verify, could be verified with the extremely high energies of the newly discovered phenomenon of radioactivity.<ref>This equation is not related to [[quantum mechanics]].</ref> In the 1910s, with the invention of the mass spectrometer, it became possible to measure masses of nuclei accurately. This led to the clearing up of the mystery of atomic masses not being exact integers,and strongly suggested the existence of a "mass defect" (or "packing fraction") consistent with the mass-energy equivalence. In the 1930s, experiments with known nuclear reactions showed a very accurate correlation between the masses of the nuclei involved and the energy released. See [[Quantitative Analysis of Alpha Decay]].

*Another prediction of special relativity was time dilation in rapidly moving objects. This effect was most famously verified in the anomalously slow decay of relativistic cosmic muons.<ref>Some have suggested that other explanations are possible for this effect. We are trying to track this down.</ref> Time dilation has since been verified many times, and is routinely taken into account in all high-energy nuclear physics experiments, as in Hadron collision experiments.<ref>Experiments specifically designed to check dilation are rarely conducted any more.</ref>

[[Image:Cassini-science-289.jpg|right|thumb|The Shapiro effect: A spacecraft signal dipping into a gravity well around the [[Sun]] is delayed slightly.]]
As the 20th century progressed, tests of general relativity were proposed.

*One important "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury. There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun. These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century. This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

:This created quite a problem—physicists by then were accustomed to having their theories check out very accurately. One proposal that was made, by Simon Newcomb and Asaph Hall, was that the exponent of the radius in the gravitational formula wasn't exactly 2. He showed that, by choosing an exponent of <math>2+\delta</math>, the precession, as a fraction of a full orbit per planet's year, is <math>\delta/2</math>. By setting <math>\delta</math> to .000000157, that is, an exponent of 2.000000157, Newcomb was able to get a precession of .000000078 revolutions per Mercury year, or 43 arcseconds per Earth year. Whatever value is chosen for <math>\delta\,</math>, it gives the same precession, per revolution, for all orbiting bodies, but gravitational effects from other planets diminish that effect the further the planet is from the sun.

:A good approximation for the precession under general relativity is <math>\frac{3GM}{c^2 a(1-e^2)}</math> revolutions per planet's "year", where a is the semi-major axis and e is the eccentricity. A simpler but less accurate one is <math>3{}v^2/c^2</math>, where <math>v</math> is the planet's average orbital speed.

:While Newcomb's theory, and general relativity, don't lead to closed-form solutions, both theories can be solved numerically to as much precision as one desires.

:The following table shows some approximate parameters for the planets. Note that Mercury has the smallest orbit, and the fastest speed. Precession of planets other than Mercury is extremely hard to measure, but measurements of the actual anomalous precessions are in good agreement.<ref>http://www.mathpages.com/rr/s6-02/6-02.htm</ref>

{| class="wikitable"
|-
!Planet
!Period, seconds x 106
!Semimajor axis, meters x 109
!Speed, meters/second x 103
!Gravitational force, Newtons per kilogram
!Anomalous precession, arcseconds per (Earth) century, pure Newtonian mechanics
!Anomalous precession, Newtonian with exponent of 2.000000157
!Anomalous precession, general relativity
!Measured anomalous precession (estimated uncertainty)<ref>http://www.mathpages.com/rr/s6-02/6-02.htm</ref>
|-
|Mercury
|7.57
|58.9
|48
|.039
|0
|43
|43
|43.5(5)
|-
|Venus
|19.6
|108
|35
|.011
|0
|16.6
|9
|8(5)
|-
|Earth
|31.6
|150
|30
|.006
|0
|10.3
|4
|5(1)
|-
|Mars
|59.3
|227.9
|24
|.0025
|0
|5.5
|1.4
|
|-
|Jupiter
|374
|778.4
|13
|.0002
|0
|0.87
|0.07
|
|-
|Saturn
|929
|1426
|9.7
|.00006
|0
|0.35
|0.014
|
|-
|Uranus
|2651
|2870
|6.8
|.000016
|0
|0.12
|0.002
|
|-
|Neptune
|5200
|4498
|5.5
|.000007
|0
|0.063
|0.0008
|
|}

:Considering only the ''anomalous'' precession, that is, the precession that remains after all known other factors (other planets and asteroids, solar oblateness) have been accounted for, and using very accurate calculations rather than the approximations given above, general relativity predicts 42.98 ±0.04 arcseconds per century. Some observed values, as of 2008, are:
::: 43.11 ± 0.21 (Shapiro et al., 1976)
::: 42.92 ± 0.20 (Anderson et al., 1987)
::: 42.94 ± 0.20 (Anderson et al., 1991)
::: 43.13 ± 0.14 (Anderson et al., 1992)
::: (Source: [http://arxiv.org/PS_cache/astro-ph/pdf/9804/9804258v1.pdf Pijpers 2008])
:These error bars, and that of the general relativity prediction, all overlap.

*Another is the ''Shapiro effect'', involving time delay in radio signals passing through the gravity well of the Sun or a planet. Various spacecraft have confirmed this.

*Another is ''gravitational time dilation''. This is an effect separate from the time dilation of special relativity. It was tested by the Pound-Rebka experiment in 1959.

*Later in the 20th century, even more subtle phenomena were tested. One was the phenomenon of ''gravitational radiation'', or "gravitational waves". These waves are incredibly difficult to observe, and had never been observed until 2015. But extremely dense binary pulsars radiate gravitational waves with sufficient energy loss that, even though we can't detect the waves from Earth, we can see the effect of the energy loss from the radiation. The extreme precision of the timing of pulses from pulsars makes it possible to observe their energy loss with great accuracy. Observations by Hulse and Taylor of the pulsar pair known as B1913+16, if assumptions are made,<ref>Similar to the way Kepler chose orbital parameters to fit observed planetary motion to his theory</ref> could make the energy loss appear consistent with the predicted radiation. The rotating pulsars have moved such that Earth is now out of the beams, so those observations have been discontinued.

*In late 2015 (and announced in 2016), the LIGO instruments directly detected gravitational waves. See [[Gravitational waves]].

*An additional test of general relativity was performed with radio signals to the Cassini spacecraft.<ref>http://www.nature.com/nature/journal/v425/n6956/full/nature01997.html</ref>

*Two other effects, ''geodetic precession'' (also known as "de Sitter precession"), and ''frame dragging'' (also known as the "Lense-Thirring effect") were tested by the "Gravity Probe B" satellite early in the 21st century.<ref>http://prl.aps.org/accepted/L/ea070Y8dQ491d22a28828c95f660a57ac82e7d8c0</ref><ref>http://www.digitaljournal.com/article/306430</ref><ref>http://www.nap.edu/html/gpb/summary.html</ref><ref>http://www.sciencenews.org/view/generic/id/73870/title/Gravity_Probe_B_finally_pays_off_</ref><ref>http://www.nasa.gov/mission_pages/gpb/</ref><ref>http://einstein.stanford.edu/</ref><ref>http://spectrum.ieee.org/aerospace/space-flight/the-gravity-probe-b-bailout</ref><ref>http://www.engadget.com/2011/05/06/nasa-concludes-gravity-probe-b-space-time-experiment-proves-e/</ref> The precision required to observe this was phenomenal. The results were announced on May 4, 2011.

{{clear}}

==Predicted consequences of the Theories==

While relativity opens the possibility of multiverses (which is questionable), gravitational time dilation leading to desynchronization of clocks between altitudes is not accurate to describe a rising sun on earth or the fact that two eclipses are separated by a same interval of time at all altitudes (worldlines are the same on earth).

===Time dilation===

[[Image:Light cone.png|right|thumb|Light-cone diagram]]
One important consequence of relativity is that an observer in one reference frame will not in general observe a clock in another frame to be "ticking" at the same rate as one in the observer's own frame.

In [[special relativity]], where acceleration and gravitational effects are ignored, this can be derived using basic geometry. The result is that clocks in all other [[inertial frames of reference]] other than the one you are in appear to tick slower. This can be summarised by the well known phrase "moving clocks run slow".

However, with [[general relativity]], there are similar effects such as gravitational time dilation where a clockthat is higher in a gravitational field runs faster. Often the effects of relativity are negligible. However the high precision required for the [[GPS|GPS system]] needs relativistic corrections. The rest of this section will concern only [[special relativity]].

The length of an event <math>t</math>, as seen by a (relative) stationary observer observing an event is given by:

<math> t = \frac{t_{0}} {\sqrt{1 - \frac{u^{2}}{c^{2}}}}</math>

Where
:<math>t_0</math> is the "proper time" or the length of the event in the observed frame of reference.
:<math>u</math> is the relative velocity between the [[inertial frame of reference|reference frames]].
:<math>c</math> is the speed of light (3x108 m s-1).

Evidence for time dilation was discovered by studying muon decay. [[Muons]] are [[subatomic particles]] with a short [[halflife]] of 1.53 microseconds. When produced by interactions of [[cosmic rays]] in the upper atmosphere, they have a speed around 0.994c. By putting muon detectors at the top (D1) and bottom (D2) of a mountain with a separation of 1900 m, scientists could measure accurately the proportion of muons reaching the second detector in comparison to the first. The proportion found was different to the proportion that was calculated without taking into account relativistic effects.

Using the equation for [[exponential decay]], they could use this proportion to calculate the time taken for the muons to decay, relative to the muon. Then, using the time dilation equation they could then work out the dilated time. The dilated time showed a good correlation with the time it took the [[muons]] to reach the second sensor, thereby supporting the existence of time dilation.

The time taken for a muon to travel from D1 to D2 as measured by a stationary observer is:

<math> t = \frac{s}{v} = \frac{1900}{0.994\times(3\times10^{8})} = 6.37\mu\textrm{s} </math>

The fraction of muons arriving at D2 in comparison to D1 was 0.732. (Given by <math> \frac{N}{N_0} = 0.732 </math>)

Since (from the equation for exponential decay) <math> \frac{N}{N_{0}} = e^{-\lambda t_{0}} </math> then

<math> t_{0} = \frac {ln(0.732)}{ln (0.2)} \times 1.53\times 10^{-6} = 0.689\mu\textrm{s}</math>

This gives the time for the proportion of decay to occur for an observer who is stationary, relative to the muon.

Putting this into the time dilation equation gives:

<math> t = \frac{t_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{0.689 \times{10^{-6}}}{\sqrt{1 - \frac{0.994^{2}}{1^{2}}}} = 6.3\times 10^{-6}\textrm{s}</math>

This is in good agreement with the value calculated above, thereby providing evidence to support time dilation.

Since either [[inertial frame of reference|reference frame]] is equally valid, from the [[muon]]'s point of view it sees the [[earth]] approach it at nearly the [[speed of light]]. Hence time passes faster for the muon (slower for an observer on the ground). This appears to be a contradiction. However, the [[muon]] sees the height of the mountain contracted and so travels a shorter distance in its own frame. See length contraction below.

====Time Dilation and Creation Science====

{{main|Starlight problem#Humphreys.27_model}}

Creation scientists such as physicists Dr. [[Russell Humphreys]] and Dr. [[John Hartnett]] have used relativistic time dilation to explain how the earth can be only 6,000 years old even though cosmological data (background radiation, supernovae, etc.) set a much older age for the universe.

====Derivation of Time Dilation====

Time dilation is most easily derived using the [[Lorentz transformation]]s, though geometrical solution is also straight forward. Using the transformation relating [[time]] between two [[Inertial frame of reference|frames of reference]], <math>t</math> and <math>t'</math>. We can find the time difference between two events that occur at the '''same''' location in space. The events shall be called event one and event 2. This results in the equations:

<math>t'_1 = \gamma \left(t_1 - \frac{ux}{c^2} \right) </math> 
<math>t'_2 = \gamma \left(t_2 - \frac{ux}{c^2} \right) </math>

where
:<math>\gamma</math> is the [[Lorentz factor]]
:<math>u</math> is the relative [[speed]] between [[Inertial frame of reference|reference frames]]
:<math>c</math> is the [[speed of light]]

Subtracting the top equation from the bottom produces the time between the events as measured in each reference frame, so:

<math>t'_2 - t'_1 = \gamma (t_2 - t_1)</math>

This the equation for time dilation and is the same equation as earlier.

===Length contraction===
When two inertial reference frames move past each other in a straight line with constant relative velocity, an observer in one reference frame would observe a metre rule in the other frame to be shorter along the direction parallel to the relative motion.

The length, <math>l</math>, of an object as seen by a (relative) stationary observer is given by:

<math> l = l_{0} \sqrt{1- \frac{u^{2}}{c^{2}}} = \frac{l_0}{\gamma}</math>

Where
:<math>l_0</math> is the "proper length" or the length of the object in its own [[inertial frame of reference|frame of reference]].
:<math>u</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light <math>3 \times 10^8 </math> m s-1
:<math>\gamma</math> is the [[Lorentz factor]]

====Derivation====

Length contraction may be derived using the [[Lorentz transformation]]s as with time dilation. This time we use the equation for <math>x</math>. In this case, the time in the undashed frame must be the '''same'''. Following the same procedure as above we find that:

<math>x'_2 -x'_1 = \frac{x_2 - x_1}{\gamma}</math>

This is the same as above with <math>x_2 - x_1</math> and <math>x'_2 - x'_1</math> being the lengths in the undashed and dashed frames respectively. Again, geometrical arguments may be used to achieve the same result.

===Mass increase===

For decades the theory of relativity taught that as a body moves with increasing velocity its [[mass]] also increases.<ref>For example, this was taught as recently as in the 1991 edition of the Encyclopedia Britannica.</ref>

Under this view, the mass, <math>m</math>, of an object as detected by a (relative) stationary observer is given by:

:<math> m = \frac{m_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>

Where
:<math>m_0</math> is the "rest mass" or the mass of the object measured by an observer in the same reference frame as the object.
:<math>v</math> is the relative velocity of the object.
:<math>c</math> is the speed of light (3x108 ms-1).

Since speed is relative, it follows that two observers in different inertial reference frames may disagree on the mass and kinetic energy of a body. Since all inertial reference frames are treated on an equal footing, it follows that mass and energy are interchangeable.

In recent years most physicists have shifted away from Einstein's original reliance on relativistic mass and his suggestion that mass increases{{Citation needed|date=January 2012}}. Instead, most physicists today teach that

:<math>F=\frac{d}{d\tau} p</math>

where
:<math>p</math> is the momentum defined by <math>\gamma m v</math>
:<math>\gamma</math> is the standard Lorentz factor
:<math>\tau</math> is the proper time

Force F defined this way is a [[vector]] and thus can handle the directional aspect of the relativistic effects better than the concept of relativistic mass can.
The abandonment by physicists of the concept of relativistic mass, however, has the consequence of undermining the traditional claim under relativity that

:<math>m - m_0 = \frac{E}{c^2}</math>

also popularly known as

:<math>E = m c^2</math>

Now a concept of the 4-momentum <math>p</math> of a particle is taught, such that the square of the magnitude of <math>p</math> satisfies:

<math>||p||^2 = -p_x^2-p_y^2-p_z^2+E^2 = m_0^2c^4</math>

in any inertial reference frame. The magnitude of the 4-momentum, in any inertial frame, equals the rest mass <math>m_0</math> of the particle (in units where <math>c=1</math>).

== Relativity in everyday life ==

Due to the small speeds and gravitational fields in normal life, relativistic phenomena such as time dilation and length contraction are rarely observed. However some things in everyday life can be explained using relativity:

*GPS, the satellites experience time dilation due to the difference in speed and the strength of gravitational field between the satellite and the ground. This is corrected by daily synchronisation between the ground and the atomic clocks in the satellites.
*While most elemental metals such as [[silver]], [[zinc]] and [[mercury]] have a silver/grey appearance, some metals like [[gold]] and [[copper]] do not. This difference can be explained using relativistic quantum mechanics.<ref>http://www.fourmilab.ch/documents/golden_glow/</ref>

== Paradoxes ==

The predictions of the theory of relativity throw up a number of apparent paradoxes and anomalies relating to the effects of time dilatation and length contraction. Whilst these paradoxes are consistent with the theory, they are contrary to everyday human experience and therefore can seem like impossibilities.

=== The Twin Paradox ===

The twin paradox is usually stated as a thought experiment involving two twins, one of whom is sent on a long journey in a spacecraft travelling at close to the speed of light, whilst the other remains on Earth. Time dilatation means that the travelling twin, on his return to Earth, is younger that the twin who has remained at home. However, because neither twin is in a special position - each being in an inertial frame of reference - the reverse must also be true, and so the twin remaining on Earth must be younger. Hence each twin is younger than the other - a paradox.

The problem can be resolved in two ways. One is to examine the effects of General Relativity: to come back to Earth, the travelling twin must undergo acceleration in order to reverse his course, causing temporal effects which make him permanently the younger. Alternatively, it can be explained entirely using Special Relativity and noting that the twins are not in symmetrical situations: the one on earth has remained in a single inertial frame of reference, whilst the travelling twin has travelled in two.<ref>http://mentock.home.mindspring.com/twins.htm</ref> Note that the length of the trip cannot be increased as to make the acceleration negligible.

=== The Ehrenfest Paradox ===

The Ehrenfest Paradox considers a rigid wheel or disc rotating a bout its axis at high speed (somewhat like a bicycle wheel spinning freely on its axle). The rim of the wheel travels at close to the speed of light and therefore undergoes length contraction, whereas the radius (the spokes, for the bicycle wheel) does not. Hence the circumference is no longer equal to 2<big><math>\pi</math></big>r, which is paradoxical.

The apparent paradox was finally resolved in 1975 by the Norwegian scientist Øyvind Grøn.<ref>http://www.physicsforums.com/showthread.php?t=224955</ref>

==Speed paradox==

One apparent inconsistency involves two spacecraft approaching each other. Suppose an observer on earth sees two spacecraft moving towards each other at half the [[speed of light]]. One travels in the positive x direction, the other in the negative. Therefore, they should each see the other approach them at the speed of light, an apparent contradiction given that no object with mass may travel at the [[speed of light]].

However, this is easily resolved by realising that adding the [[speed]]s is correct for [[Galilean relativity]]. Since the spacecraft are travelling at a significant fraction of the speed of light, it in not valid to use [[Galilean relativity]]. Therefore, the [[Lorentz transformation|velocity Lorentz transformations]] of special relativity must be used. Suppose the observer is in the undashed few and measures a speed <math>v_x</math>, then on the spacecraft travelling in the positive x direction, they measure speed <math>v_x^'</math>. The relevant equation is:

<math>v_x^' = \frac{v_x - u}{1- \frac{uv_x}{c^2}}</math>

Where <math>u</math> is the speed between the [[inertial frame of reference|inertial frames of reference]], in this case half the speed of light. <math>v_x</math> is also half the speed of light (but negative), and substituting in gives:

<math>v_x^' = -\frac{4}{5} c</math>

and so the paradox is resolved. If the observer on earth observes a beam of light, then the spacecraft also observes light travelling at the same speed, agreeing with the second postulate, that all observers in [[inertial frames of reference]] measure the same value for the speed of light.

== Variable Speed of Light ==

The Theory of Relativity implies that physical constants like c, the speed of light in a vacuum, have remained constant. But at least one study suggests that physical constants, and possibly even the speed of light, have changed as the universe has aged.<ref>James Glanz and Dennis Overbye, "Cosmic Laws Like Speed of Light Might Be Changing, a Study Finds," August 15, 2001.[http://www.nytimes.com/2001/08/15/science/15PHYS.html?ex=1185076800&en=d6467b6e3e346796&ei=5070]</ref>

"For the first time, scientists have experimentally demonstrated that sound pulses can travel at velocities faster than the speed of light, c. William Robertson's team from Middle Tennessee State University also showed that the group velocity of sound waves can become infinite, and even negative. ... Although such results may at first appear to violate special relativity (Einstein's law that no material object can exceed the speed of light), the actual significance of these experiments is a little different. These types of superluminal phenomena, Robertson et al. explain, violate neither causality nor special relativity, nor do they enable information to travel faster than c. In fact, theoretical work had predicted that the superluminal speed of the group velocity of sound waves should exist. 'The key to understanding this seeming paradox is that no wave energy exceeded the speed of light,' said Robertson."<ref>http://www.physorg.com/news88249076.html</ref>

"A team of researchers from the Ecole Polytechnique Fédérale de Lausanne (EPFL) has successfully demonstrated, for the first time, that it is possible to control the speed of light – both slowing it down and speeding it up – in an optical fiber, using off-the-shelf instrumentation in normal environmental conditions. Their results, to be published in the August 22 issue of Applied Physics Letters, could have implications that range from optical [[computing]] to the fiber-optic telecommunications industry."<ref>http://www.scienceblog.com/light.html</ref> Both slowing down and speeding up of light within a substance other than a vacuum is made possible, because the light travels through the material, and that material affects the speed of light, i.e. a photon hits an electron, which then exits and emits a slightly lower energy photon out in the direction that the original photon was traveling, thus maintaining conservation of momentum. No matter how transparent an object may appear, it radically impacts the speed of the light traveling through it, as demonstrated by the refractive production of a rainbow by a crystal, which Newton himself discovered.

This apparent change in speed can be explained, however, by noting that the constant c refers to the speed of light in a vacuum, i.e., when it is unimpeded. The speed of light when traveling through physical media is, in fact, variable.

"A pair of German physicists claim to have broken the speed of light - an achievement that would undermine our entire understanding of space and time. ... Dr Nimtz told New Scientist magazine: 'For the time being, this is the only violation of special relativity that I know of.'"<ref>http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/08/16/scispeed116.xml</ref>

==Pending research==

Today some physicists are working on hypothesizing how general relativity might have related to the other three forces of nature during the first fraction of a second of the [[Big Bang]]. Two of the more commonly studied attempts are [[string theory]] and [[loop quantum gravity]], but they have failed to produce any evidence that science mandates a science must have, and both typically take large amounts of work to even conform to what scientists believe. Critics increasingly point out that string theory and loop quantum gravity are largely untestable and unfalsifiable, and thus potentially unscientific under the principles of science advanced by [[Karl Popper]].<ref>See, for example, ''Not Even Wrong'', by Peter Woit</ref>

Relativity continues to be tested and some physics professors remain skeptical of the theory, such as University of Maryland physics professor Carroll Alley, who served as the principle physicist on the Apollo lunar project.<ref>http://science.nasa.gov/headlines/y2004/21jul_llr.htm</ref>

== Political aspects of relativity ==

Some [[liberal]] politicians have extrapolated the theory of relativity to metaphorically justify their own political agendas. For example, [[Democratic]] [[President of the United States of America|President]] [[Barack Obama]] helped publish an article by liberal law professor [[Laurence Tribe]] to apply the relativistic concept of "curvature of space" to promote a broad legal right to [[abortion]].<ref>Tribe, acknowledging help by Obama, argued that the [[Constitution]] should be interpreted to establish a right to federally funded [[abortion]] and that, more generally, ''[[Roe v. Wade]]'' does not go far enough. They insisted that a relativistic "curvature of space" could achieve this result by expanding application of the [[Constitution]] based on its impact on personal choice. "The ''[[Roe v. Wade]]'' opinion ignored the way in which laws regulating pregnant women may shape the entire pattern of relationships among men, women, and children. It conceptualized abortion not in terms of the intensely public question of the subordination of women to men through the exploitation of pregnancy, but in terms of the purportedly private question of how women might make intimately personal decisions about their bodies and their lives. That vision described a part of the truth, but only what might be called the Newtonian part. ... [A] change in the surrounding legal setting can constitute state action that most threatens the sphere of personal choice. And it is a 'curved space' perspective on how law operates that leads one to focus less on the visible lines of legal force and more on how those lines are bent and directed by the law's geometry." Laurence H. Tribe, The Curvature of Constitutional Space: What Lawyers Can Learn from Modern Physics, 103 Harv. L. Rev. 1, 16-17 (1989).</ref> As of June 2008, over 170 law review articles have cited this [[liberal]] application of the theory of relativity to legal arguments.<ref>Search conducted by [[User:Aschlafly]] in the LEXIS database "US Law Reviews and Journals, Combined," conducted June 1, 2008.</ref> Applications of the theory of relativity to change morality have also been common.<ref>"Mistakenly, in the minds of many, the theory of relativity became relativism."[http://www.worldnetdaily.com/news/article.asp?ARTICLE_ID=38081]</ref> Moreover, there is an unmistakable effort to censor or ostracize criticism of relativity.<ref>Although the [[Examples of Bias in Wikipedia|liberally biased Wikipedia]] contains lengthy criticisms of the subjects of many entries, and even though publications like ''The Economist'' recognize the lack of scientific satisfaction in the theory (see, e.g., "Weighing the Universe," The Economist (Jan. 25, 2007)), Wikipedia's entry on [http://en.wikipedia.org/wiki/Theory_of_Relativity Theory of Relativity] omits one word of criticism.</ref>

Physicist [[Robert Dicke]] of Princeton University was a prominent critic<ref>http://www.time.com/time/magazine/article/0,9171,943324,00.html</ref> of general relativity, and Dicke's alternative "has enjoyed a renaissance in connection with theories of higher dimensional space-time."<ref>"Initially a popular alternative to General Relativity, the Brans-Dicke theory lost favor as it became clear that omega must be very large-an artificial requirement in some views. Nevertheless, the theory has remained a paradigm for the introduction of scalar fields into gravitational theory, and as such has enjoyed a renaissance in connection with theories of higher dimensional space-time."[http://nedwww.ipac.caltech.edu/level5/Glossary/Essay_bekenstein.html]</ref> Despite being one of the most accomplished physicists in the 20th century, Dicke was repeatedly passed over for a [[Nobel Prize]], and in at least one case Dicke was insulted by the award being granted to others for contributions more properly credited to Dicke.

There has been little recognition by the Nobel Prize committee of either theory of relativity, and particularly scant recognition of the Theory of General Relativity. A dubious 1993 Nobel prize in physics was awarded Hulse and Taylor for supposedly finding the first evidence of gravitational waves in the orbital decay of the binary pulsar PSR1913+16.<ref>Weisberg, Joel M.; Taylor, Joseph H. (2003), "The Relativistic Binary Pulsar B1913+16"", in Bailes, M.; Nice, D. J.; Thorsett, S. E., Proceedings of "Radio Pulsars," Chania, Crete, August, 2002, ASP Conference Series</ref> A close reading of the paper reveals that that is based heavily on assumptions in trying to retrofit the data to the theory.

===Government Support for Relativistic research===
The Federal Government has funded the building of two gravity wave detectors: The first to test the principle, and the second (upgrade) to actually perform measurements. As a result of this work, on February 11, 2016, the LIGO team reported successful detection of gravitational waves caused by the merging of two black holes.<ref>https://www.ligo.caltech.edu/news/ligo20160211</ref>

{{Relativity}}

==See also==
*[[Attempts to prove E=mc²]]
*[[Counterexamples to Relativity]]
*[[Essay:Rebuttal to Counterexamples to Relativity]]
*[[Logical Flaws in E=mc²]]
*[[Essay:Rebuttal to Logical Flaws in E=mc²]]
*[[Quantitative Analysis of Alpha Decay]]
*[[Gravitational waves]]

== References ==
{{reflist|2}}

[[Category:Physics]]
[[Category:Science]]

==External links ==
*[http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm The Einstein Theory of Relativity, by H.A. Lorentz.]
*[http://www.relativitycalculator.com Relativity Science Calculator - Learn Special Relativity Mathematics ] The mathematics of special relativity presented in as simple and comprehensive manner possible within philosophical and historical contexts.
*[http://www.relativitycalculator.com/history_of_time_clocks.shtml Relativity Science Calculator - Philosophic Question: are clocks and time separable?]
*[http://www.relativityscience.com/twin_clock_paradox.shtml Relativity Science Calculator - Twin Clock Paradox]