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Theory of relativity

2007-10-26T23:03:19Z

Tree111:

'''Relativity''' refers to two closely-related theories in [[physics]], and to a principle which led to the first theory. 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. At speeds approaching zero, Special Relativity is identical to Newton's Laws of Motion. Special Relativity was developed by [[Hendrik Lorentz]], [[Henri .ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html] However, some question whether the Theory of Special Relativity really restricts faster-than-light communication of information.</ref>
# The laws ofDNFSAIUHF9238709YYYYYYYYYYYYYYYYYYYYYYYYYYNCWIHNVKUDAFHCN97EY
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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</ref> <ref> http://csep10.phys.utk.edu/astr162/lect/galaxies/lensing.html </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>http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm</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).

==Time dilation==
[[Image:Light cone.png|right|thumb|Light-cone diagram]]
One important consequence of SR's postulates is that an observer in one reference frame will observe a clock in another frame to be "ticking" more slowly than in the observer's own frame. This can be proven mathematically using basic geometry.

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{v^{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>v</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light (3x108 ms-1).

Evidence for time dilation was discovered by studying [[muon decay]]. [[Muons]] are [[subatomic]] [[particles]] with a very short [[halflife]] (1.53 microseconds at rest) and a very fast speed (0.994c). By putting muon detectors at the top (D1) and bottom (D2) of a mountain with a separation of 1900m, 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 proving the theory.

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.

==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.

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{v^{2}}{c^{2}}}</math>

Where
:<math>l_0</math> is the "proper length" or the length of the object in the observed frame of reference.
:<math>v</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light (3x108 ms-1).

==Mass increase==

We also see that as a body moves with increasing velocity its [[mass]] also increases.

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 when it is at rest.
:<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.

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. But mass is not a vector, and the notion of the mass of an object having different values depending on the direction of an applied force is unacceptable. Accordingly, most physicists today avoid Einstein's original reliance on relativistic mass and his suggestion that mass increases. Instead, most physicists today teach that F=<math>\gamma</math>ma where <math>\gamma</math> varies with velocity as mass m remains constant. Force F is a vector and thus can handle the directional aspect of the relativistic effects better than the concept of relativistic mass can.

==Evidence for Relativity==
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.<ref>http://nobelprize.org/</ref>

In 1972, scientists flew extremely accurate clocks around the world in both directions on commercial airlines, and were directly able to observe the relativistic "twin paradox" the eastbound clock gained 273 ns and the westbound clock lost 59 ns, matching the predictions of general relativity to within experimental accuracy <ref>Hafele-Keating Experiment [http://www.answers.com/topic/hafele-keating-experiment]</ref> <ref>as described in [http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html What is the experimental basis of Special Relativity?], a personal web page, which cites Haefele and Keating (1972), ''Science'' Vol. 177 pp 166-170 as its source</ref> <ref>Sullivan, Walter (1972), "Relativity Theory Awaits Affirmation", September 23, 1972, p. 61. Note: Article refers to a different experiment, which Sullivan discusses, saying that if successful it would be "the second time within a year" that relativity had been confirmed, then proceeds to discuss Hafele[sic] and Keating's experiment as the first.</ref>

Predictions of relativity have historically been used to make the [[Global Positioning System]] ([[GPS]]) function properly. A 1996 article says:

:"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. But other obscure physicists having no connection with GPS design claim that Van Flandern is wrong about GPS, and insist that relativity provides the best explanation for its timing adjustments.<ref>''Ibid.''</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.

[[Image:Cassini-science-289.jpg|right|thumb|signal dipping into a gravity well around the [[sun]]]]
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>. There is also a satellite called [[Gravity Probe B]] currently in orbit about the Earth that is examining 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>. 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.<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.<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.

The [[perihelion]] of Mercury's [[orbit]] [[precession|precesses]] at a measurable rate, but even after 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|arcseconds]] per century. General relativity was developed in part to provide an estimate for this rate of precession that better matches observations.<ref>http://physics.ucr.edu/~wudka/Physics7/Notes_www/node98.html#SECTION032121000000000000000</ref> <ref> http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf</ref> <ref> http://farside.ph.utexas.edu/teaching/336k/lectures/node117.html</ref>

General relativity predicts twice as much bending in light as it passes near massive objects than Newton's theory predicts,<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> a phenomenon known as [[gravitational lens|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>

== Ostensible Paradoxes ==

The Theory of Relativity implies that physical constants like the speed of light 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>

"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 been complete failures. 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>

==Government Support for Relativistic research==
The Theory of Relativity enjoys a disproportionate share of federal funding of physics research today,<ref>The Democratic Congress insisted on the $250 million LIGO project despite substantial criticism by scientists that it was wasting scarce research dollars. John Travis, "LIGO: a $ 250 million gamble; Laser Interferometer Gravitational-Wave Observatory; includes related article," ''Science'' p. 612 (Apr. 30, 1993). "Adding to the acrimony is LIGO's $ 250 million price tag, which some hold responsible for NSF's recent funding woes." ''Id.''</ref>. In at least one case that research has been unsuccessful. The $365 million dollar LIGO project has failed to detect the gravity waves predicted by relativity.<ref>http://www.npr.org/programs/atc/features/2002/sept/gravitywaves/index.html</ref>

== Philosophical Impact of Relativity ==

There is a correlation between enthusiasm for the theory of relativity and political views,<ref>"Mistakenly, in the minds of many, the theory of relativity became relativism."[http://www.worldnetdaily.com/news/article.asp?ARTICLE_ID=38081]</ref> and 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 the theory of relativity and that may have hurt him professionally, even though his theory "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 never awarded a Nobel Prize just as other outspoken critics of scientific theories were passed over in granting the Nobel Prize to less-accompished colleagues.<ref>Other examples of scientists denied Nobel Prizes due to their criticisms of scientific theories are Sir [[Fred Hoyle]] and Dr. [[Raymond Damadian]]</ref>

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

[[Category:Physics]]

==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 Calculator - Learn Special Relativity Mathematics Mathematics of special relativity presented in as simple and comprehensive manner possible within philosophical and historical contexts.]

Theory of relativity

2007-10-26T23:02:49Z

Tree111:

'''Relativity''' refers to two closely-related theories in [[physics]], and to a principle which led to the first theory. 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. At speeds approaching zero, Special Relativity is identical to Newton's Laws of Motion. Special Relativity was developed by [[Hendrik Lorentz]], [[Henri .ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html] However, some question whether the Theory of Special Relativity really restricts faster-than-light communication of information.</ref>
# The laws ofDNFSAIUHF9238709YYYYYYYYYYYYYYYYYYYYYYYYYYNCWIHNVKUDAFHCN97EY
'GPA OJG98A3

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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</ref> <ref> http://csep10.phys.utk.edu/astr162/lect/galaxies/lensing.html </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>http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm</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).

==Time dilation==
[[Image:Light cone.png|right|thumb|Light-cone diagram]]
One important consequence of SR's postulates is that an observer in one reference frame will observe a clock in another frame to be "ticking" more slowly than in the observer's own frame. This can be proven mathematically using basic geometry.

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{v^{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>v</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light (3x108 ms-1).

Evidence for time dilation was discovered by studying [[muon decay]]. [[Muons]] are [[subatomic]] [[particles]] with a very short [[halflife]] (1.53 microseconds at rest) and a very fast speed (0.994c). By putting muon detectors at the top (D1) and bottom (D2) of a mountain with a separation of 1900m, 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 proving the theory.

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.

==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.

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{v^{2}}{c^{2}}}</math>

Where
:<math>l_0</math> is the "proper length" or the length of the object in the observed frame of reference.
:<math>v</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light (3x108 ms-1).

==Mass increase==

We also see that as a body moves with increasing velocity its [[mass]] also increases.

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 when it is at rest.
:<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.

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. But mass is not a vector, and the notion of the mass of an object having different values depending on the direction of an applied force is unacceptable. Accordingly, most physicists today avoid Einstein's original reliance on relativistic mass and his suggestion that mass increases. Instead, most physicists today teach that F=<math>\gamma</math>ma where <math>\gamma</math> varies with velocity as mass m remains constant. Force F is a vector and thus can handle the directional aspect of the relativistic effects better than the concept of relativistic mass can.

==Evidence for Relativity==
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.<ref>http://nobelprize.org/</ref>

In 1972, scientists flew extremely accurate clocks around the world in both directions on commercial airlines, and were directly able to observe the relativistic "twin paradox" the eastbound clock gained 273 ns and the westbound clock lost 59 ns, matching the predictions of general relativity to within experimental accuracy <ref>Hafele-Keating Experiment [http://www.answers.com/topic/hafele-keating-experiment]</ref> <ref>as described in [http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html What is the experimental basis of Special Relativity?], a personal web page, which cites Haefele and Keating (1972), ''Science'' Vol. 177 pp 166-170 as its source</ref> <ref>Sullivan, Walter (1972), "Relativity Theory Awaits Affirmation", September 23, 1972, p. 61. Note: Article refers to a different experiment, which Sullivan discusses, saying that if successful it would be "the second time within a year" that relativity had been confirmed, then proceeds to discuss Hafele[sic] and Keating's experiment as the first.</ref>

Predictions of relativity have historically been used to make the [[Global Positioning System]] ([[GPS]]) function properly. A 1996 article says:

:"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. But other obscure physicists having no connection with GPS design claim that Van Flandern is wrong about GPS, and insist that relativity provides the best explanation for its timing adjustments.<ref>''Ibid.''</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.

[[Image:Cassini-science-289.jpg|right|thumb|signal dipping into a gravity well around the [[sun]]]]
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>. There is also a satellite called [[Gravity Probe B]] currently in orbit about the Earth that is examining 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>. 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.<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.<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.

The [[perihelion]] of Mercury's [[orbit]] [[precession|precesses]] at a measurable rate, but even after 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|arcseconds]] per century. General relativity was developed in part to provide an estimate for this rate of precession that better matches observations.<ref>http://physics.ucr.edu/~wudka/Physics7/Notes_www/node98.html#SECTION032121000000000000000</ref> <ref> http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf</ref> <ref> http://farside.ph.utexas.edu/teaching/336k/lectures/node117.html</ref>

General relativity predicts twice as much bending in light as it passes near massive objects than Newton's theory predicts,<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> a phenomenon known as [[gravitational lens|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>

== Ostensible Paradoxes ==

The Theory of Relativity implies that physical constants like the speed of light 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>

"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 been complete failures. 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>

==Government Support for Relativistic research==
The Theory of Relativity enjoys a disproportionate share of federal funding of physics research today,<ref>The Democratic Congress insisted on the $250 million LIGO project despite substantial criticism by scientists that it was wasting scarce research dollars. John Travis, "LIGO: a $ 250 million gamble; Laser Interferometer Gravitational-Wave Observatory; includes related article," ''Science'' p. 612 (Apr. 30, 1993). "Adding to the acrimony is LIGO's $ 250 million price tag, which some hold responsible for NSF's recent funding woes." ''Id.''</ref>. In at least one case that research has been unsuccessful. The $365 million dollar LIGO project has failed to detect the gravity waves predicted by relativity.<ref>http://www.npr.org/programs/atc/features/2002/sept/gravitywaves/index.html</ref>

== Philosophical Impact of Relativity ==

There is a correlation between enthusiasm for the theory of relativity and political views,<ref>"Mistakenly, in the minds of many, the theory of relativity became relativism."[http://www.worldnetdaily.com/news/article.asp?ARTICLE_ID=38081]</ref> and 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 the theory of relativity and that may have hurt him professionally, even though his theory "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 never awarded a Nobel Prize just as other outspoken critics of scientific theories were passed over in granting the Nobel Prize to less-accompished colleagues.<ref>Other examples of scientists denied Nobel Prizes due to their criticisms of scientific theories are Sir [[Fred Hoyle]] and Dr. [[Raymond Damadian]]</ref>

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

[[Category:Physics]]

==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 Calculator - Learn Special Relativity Mathematics Mathematics of special relativity presented in as simple and comprehensive manner possible within philosophical and historical contexts.]

Theory of relativity

2007-10-26T23:01:41Z

Tree111: ldjfiwuhf

Talk:Electricity

2007-10-26T22:53:41Z

Tree111:

I'm doing this off the cuff, without references. When I'm through describing conductors, semiconductors, and insulators, I'll go back and revise my work with references. [[User:Navy Nuke|Navy Nuke]] 15:51, 15 March 2007 (EDT)

The section about atoms probably needs to be moved to a different section. Also a good detailed description of alternating current and direct current would be good. This would be a better way to describe electrical circuits(in terms of impedance, resistance, voltage, current, reactance, admittance).

Electricity

2007-10-26T22:51:23Z

Tree111:

[[Image:Htryt5.jpg|right|thumb|200px|Lightning strikes during a night-time thunderstorm. Energy is radiated as light when powerful electric currents flow through the Earth's atmosphere.]]
Electricity is the flow of electrons. Electrical charge is measured in Coloumbs. A basic element of electricity is the electric circuit. A circuit is a closed path that allows for movement of charges. Current is the name given to the movement of charges. The study of electricity involves the behavior of charges, current and voltage with the components that make up the electrical circuit. Electrical engineering has allowed many practical advances to be made, such as replacing [[steam power]]ed trains with more efficient electric ones.

==Polarity==

All materials that are known contain two basic components of electric charge: the [[proton]] and the [[electron]]. The proton is a basic particle with positive polarity, and the electron is the smallest amount of electric charge having negative polarity.
It is an arrangement of electrons and protons as basic particles of electricity that determines the electrical characteristics of substances. Although all matter has protons and electrons, most materials do not exhibit any evidence of electricity, because the number of protons and electrons are equal. The opposite electrical forces cancel each other out, and render materials like paper electrically neutral. In order to use electricity to do work, the protons and electrons must be separated. A battery can do electrical work because a chemical process separates electric charges to create an excess of electrons at its negative terminal and conversely, an excess of protons at its positive terminal. With separate and opposite charges at two terminals, electric energy can be supplied to a circuit connected to the battery.

==The Structure of an Atom Determines its Electrical Characteristics==

Although there are many possible ways protons and electrons could group themselves, they assemble in specific combinations that result in stable arrangement. Each stable arrangement of protons, electrons, and often [[neutron]]s makes one particular kind of atom, an [[element]]. Electrons orbit the nucleus of protons and neutrons at specific intervals, called "shells" or "energy levels." Each shell has a maximum number of electrons for stability.
It is the structure of the outermost shell of electrons in an element that determines how well it conducts electricity and its magnetic properties. If an element has fewer than eight electrons in its outermost shell, it can conduct electricity to some degree; the elements that have one electron in their outermost shell conduct electricity best. [[Gold]], [[silver]], and [[copper]] are the best conductors of electricity because their outermost electron shell has only one electron, and this allows the freest flow of electrical current because the opposition of an atom of these elements from taking on or loosing electrons is low.
Materials with electrons that tend to stay in their own orbits are called insulators, because they do not conduct electricity very well. However, these materials (except for the inert gases) can also take up extra electrons to complete their outer shells, and become negatively charged; they hold on to and store electrical charge, unlike conductors. Insulating materials like glass, plastic, rubber, paper, air, and mica are called dielectrics, meaning that they can take on and hold electrical charge. Insulators are useful when it is necessary to prevent current flow. They are also used in applications for storing electrical charge, as in capacitors, since a good conductor of electricity cannot store any charge.
Materials that can conduct more electrical charge than insulators, but less than conductors are called semiconductors. [[Carbon]], [[silicon]], and [[germanium]] are commonly used for transistors and other semiconductor components, with silicon being the most widely used.

==Resources==
Grob, Bertand ''Basic Electronics'' Fifth edition, 1984

[[Category:Physics]]
[[Category:Electricity]]