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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 proposes time dilation and length contraction for observers moving relative to one another at very high ("relativistic") speeds.

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 proposes time dilation and length contraction for observers moving relative to one another at very high ("relativistic") speeds.

[[Image:600px-Albert Einstein Head.jpg|thumbnail|right|200px|

[[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). [https://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>]]

*"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). [https://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 to describe 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 put forward by [[Albert Einstein]]; its mathematical framework was independently developed and formalized 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." [https://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>

*'''[[Special theory of relativity|Special relativity]]''' (SR) is a theory to describe 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 put forward by [[Albert Einstein]]; its mathematical framework was independently developed and formalized 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." [https://www.britannica.com/eb/article-9052860/Hermann-Minkowski Hermann Minkowski -- ''Britannica Online Encyclopedia'' website]</ref><ref>[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Minkowski.html Hermann Minkowski, Biography]</ref>

*'''[[General theory of relativity|General Relativity]]''' (GR) is a theory to explain the laws of motion as viewed from accelerating reference frames and includes a geometric explanation for gravity.  This theory was originally developed by Einstein, with help from [[David Hilbert]] in its final mathematical formulation, as a generalization of the postulates of Special Relativity to account for non-inertial, accelerating observers, particularly those in a gravitational field.<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<ref>Stephen Hawking, ''Brief History of Time'' ("Their measurement had been sheer luck, or a case of knowing the result they wanted to get.").  Hawking was being kind.  In fact, Eddington excluded data that did not fit his preconceived view.  Further discrediting of Eddington's study was published by Earman, J., Glymour, C., Hist. Stud. Phys. Sci. 11, 49-85 (1980), and Collins, H. M., Pinch, T., The Golem: What Everyone Should Know About Science. Cambridge University Press (1993) (as cited in [http://www.nature.com/news/2007/070907/full/news070903-20.html#B2])</ref> claim by Sir [[Arthur Eddington]] of experimental proof of General Relativity in 1919 popularized the theory.

*'''[[General theory of relativity|General Relativity]]''' (GR) is a theory to explain the laws of motion as viewed from accelerating reference frames and includes a geometric explanation for gravity.  This theory was originally developed by Einstein, with help from [[David Hilbert]] in its final mathematical formulation, as a generalization of the postulates of Special Relativity to account for non-inertial, accelerating observers, particularly those in a gravitational field.<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<ref>Stephen Hawking, ''Brief History of Time'' ("Their measurement had been sheer luck, or a case of knowing the result they wanted to get.").  Hawking was being kind.  In fact, Eddington excluded data that did not fit his preconceived view.  Further discrediting of Eddington's study was published by Earman, J., Glymour, C., ''Hist. Stud. Phys. Sci.'' 11, 49-85 (1980), and Collins, H. M., Pinch, T., The Golem: What Everyone Should Know About Science. Cambridge University Press (1993) (as cited in [http://www.nature.com/news/2007/070907/full/news070903-20.html#B2])</ref> claim by Sir [[Arthur Eddington]] of experimental proof of General Relativity in 1919 popularized the theory.

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

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. Other critics of the theory are [[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> and 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 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. Other critics of the theory are [[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> and Louis Essen [1908-1997], the man credited with determining the speed of light. He wrote fiery papers and many feature articles of the subject in science journals with popular audiences 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>

There are some issues of continuity and limits arising in the mathematical analysis of the theory of relativity. See [[Counterexamples to Relativity]] for discussion of this point.

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 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. [https://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.

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. [https://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.

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 (''x''² - ''c''² ''t''²). 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]].

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]].

== Special Relativity ==

== Special Relativity ==

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 that of other parts of the universe. 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.

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 that of other parts of the universe. 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"''

The "anomalous precession" of Mercury's [[perihelion]] (slow shift of the orbit's major axis) is explained by the Theory of General Relativity, but not by Newtonian mechanics.  Some precession (5600 arcseconds per century) is caused by purely classical phenomena, mostly the gravitational attraction of other planets.  But a small amount (43 arcseconds per century) of the observed precession, goes beyond that which classical Newtonian mechanics can explain.  General relativity explains it accurately.

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.

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 quickly discarded when it gave very bad results for the Moon's orbit.  The relativistic explanation of the anomalous precession is disputed on the [[Counterexamples to Relativity]] page of Conservapedia.

British Historian Paul Johnson declared 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> [[Hendrik Lorentz]] had this to say on the discrepancies between the empirical eclipse data and Einstein's predictions.

British Historian Paul Johnson declared 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> [[Hendrik Lorentz]] had this to say on the discrepancies between the empirical eclipse data and Einstein's predictions.

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>

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>[https://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. 

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>  The [[Gravity Probe B]] satellite was put in orbit about the Earth to examine the effects of frame dragging and geodetic warping of space.  One report<ref>[https://www.nasa.gov/mission_pages/gpb/index.html NASA Gravity Probe B mission page]</ref> was that it showed "unprecedented precision", and one<ref>[http://einstein.stanford.edu/ Gravity Probe B project page]</ref> showed a 95% confidence that the measured effect was consistent with General Relativity.  Note, however, that one interpretation of Newtonian mechanics also predicts deflection of light by gravity.  This is the "light is particles" interpretation, and gives a deflection of 0.875 arcseconds, whereas the "light is waves" interpretation predicts a deflection of zero.  The experimentally measured deflection is 1.75 arcseconds, and is the value given by General Relativity (though Einstein's initial calculation was 0.875.).<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref>  

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>

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.

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.

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.

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

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

It is important to be aware that it is fairly rare for an experiment to '''prove''' a theory.  In general, experiments can only '''refute''' a theory.  They can also '''be consistent with''' a theory.  When enough experiments, especially experiments that investigate a wide variety of phenomena, are shown to be consistent with a theory, it lends credence to that theory.  When no other plausible theory can explain those observations, we can say that they '''validate''' the theory.  The Mercury observations are just one phenomenon.  By themselves they couldn't validate or prove GR.  And there was at one time another competing theory&mdash;the Newcomb-Hall exponent-fudging theory.  That one didn't hold up for things other than Mercury.  No other theory has come up explaining the phenomenon; GR has withstood the test of time.  That goes a long way toward validating GR.  There are many other observations and experiments, covering a wide variety of phenomena, described below&mdash;bending of light, gravitational time dilation, gravitational waves, geodetic precession, Shapiro effect, etc.  It is these widely disparate observations, and the lack of any alternative theories explaining any of them, that lead people to say that GR is "experimentally validated".

It is important to be aware that it is fairly rare for an experiment to '''prove''' a theory.  In general, experiments can only '''refute''' a theory.  They can also '''be consistent with''' a theory.  When enough experiments, especially experiments that investigate a wide variety of phenomena, are shown to be consistent with a theory, it lends credence to that theory.  When no other plausible theory can explain those observations, we can say that they '''validate''' the theory.  The Mercury observations are just one phenomenon.  By themselves they couldn't validate or prove GR.  And there was at one time another competing theory&mdash;the Newcomb-Hall exponent-fudging theory.  That one didn't hold up for things other than Mercury.  No other theory has come up explaining the phenomenon; SR and GR have withstood the test of time.  That goes a long way toward validating them.  There are many other observations and experiments, covering a wide variety of phenomena, described below&mdash;bending of light, gravitational time dilation, gravitational waves, geodetic precession, Shapiro effect, etc.  It is these widely disparate observations, ''and the lack of any alternative theories explaining any of them'', that lead people to say that SR and GR are "experimentally validated".

There's also the matter of simply "accepting" something, when a phenomenon is consistent with a theory that is already known to be valid.  The recoil from a gun is an example of this.  Everyone knows that there is a backward recoil when a gun is fired.  This is explained to people when they are first being taught how to use a gun, and they get used to it with practice.  The reason for the recoil is that it is an obvious consequence of Newtons' laws of motion.  But people don't specifically think about Newton's laws, or consider this to be a "proof", when they are firing a gun.  They just accept that the recoil is a known consequence of those laws.  Newton's laws of motion have been validated through thousands of experiments much more focused than the firing of a gun.

There's also the matter of simply "accepting" something, when a phenomenon is consistent with a theory that is already known to be valid.  The recoil from a gun is an example of this.  Everyone knows that there is a backward recoil when a gun is fired.  This is explained to people when they are first being taught how to use a gun, and they get used to it with practice.  The reason for the recoil is that it is an obvious consequence of Newtons' laws of motion.  But people don't specifically think about Newton's laws, or consider this to be a "proof", when they are firing a gun.  They just accept that the recoil is a known consequence of those laws.  Newton's laws of motion have been validated through thousands of experiments much more focused than the firing of a gun.

The [[Cockcroft and Walton Experiment|Cockcroft/Walton experiment]] is an example of this kind of acceptance.  The results are consistent (to within 5% when analyzed carefully) with Special Relativity, and many people consider it to be a validation of SR.  But there were too many other things going on, such as the use of the newly-invented particle accelerator, to make it a definitive test.  In any case, Special Relativity had already been validated through more focused and definitive tests.  There are no known alternative theories, published in the scientific literature or listed in [[Counterexamples to Relativity]], explaining this result.

The [[Cockcroft and Walton Experiment|Cockcroft/Walton experiment]] is an example of this kind of acceptance.  The results are consistent (to within 5% when analyzed carefully) with Special Relativity, and many people consider it to be a validation of SR.  But there were too many other things going on, such as the use of the newly invented particle accelerator, to make it a definitive test.  One would have to think very carefully about what assumptions have to be made about what is happening in the experiment if one wanted to use it to assert anything about [[E=mc²]].  However, famous as the experiment was at the time, it is no longer suggested as a validation of this formula.  Special Relativity had already been validated through more focused and definitive tests.  There are no known alternative theories, published in the scientific literature or listed in [[Counterexamples to Relativity]], explaining the loss of mass.  See [[Cockcroft and Walton Experiment]].

The anomalous behavior of the timing signals from [[GPS]] satellites is another example.  The phenomenon is well known&mdash;the system compensates for this; otherwise it wouldn't work&mdash;and the phenomenon is known to be a consequence of both special and general relativity.  But the GPS system should not be considered and experiment to test relativity.  No sensible person would build the GPS system as a test of relativity, if only because it exhibits two phenomena (time dilation of special relativity, 7 milliseconds per day, and time compression of general relativity, 45 milliseconds per day) that work against each other.  No one would design and experiment that tests two phenomena working against each other.  But the effect of both, 38 milliseconds per day, is well known, as is the reason for this.  There are no known alternative theories, published in the scientific literature or listed in [[Counterexamples to Relativity]], explaining this result.

The anomalous behavior of the timing signals from [[GPS]] satellites is another example.  The phenomenon is well known&mdash;the system compensates for this; otherwise it wouldn't work&mdash;and the phenomenon is known to be a consequence of both special and general relativity.  But the GPS system should not be considered and experiment to test relativity.  No sensible person would build the GPS system as a test of relativity, if only because it exhibits two phenomena (time dilation of special relativity, 7 milliseconds per day, and time compression of general relativity, 45 milliseconds per day) that work against each other.  No one would design an experiment that tests two phenomena working against each other.

 

The bending of light in a gravitational field is another example.  (In fact, it was the first, and, for a while, most famous piece of evidence in favor of GR, even though it was sloppily done.)  Newtonian physics also might predict the bending of light depending on whether one posits the "wave" formulation (deflection is zero) or the "particle" formulation (deflection is 0.875 arc seconds).  But the actual deflection is 1.75 arc seconds, and GR predicts this value.  The are no known versions of Newtonian gravity that get this larger value.

While the experimental tests for General Relativity are rather esoteric, those for Special Relativity are fairly straightforward.  So much so that the Michelson-Morley experiment could be said to have single-handedly established the case for SR&mdash;the logical syllogism leading from Michelson-Morley to SR and the Lorentz transform was fairly clear once people saw it.

While the experimental tests for General Relativity are rather esoteric, those for Special Relativity are fairly straightforward.  So much so that the Michelson-Morley experiment could be said to have single-handedly established the case for SR&mdash;the logical syllogism leading from Michelson-Morley to SR and the Lorentz transform was fairly clear once people saw it.

Relying on the usual assumptions&mdash;Newtonian mechanics, Galilean relativity, conservation of energy and momentum, the universality of the speed of light (that is, special relativity), the Equivalence Principle, and the geodesic equation in empty space (that is, general relativity), and the proper calibration of the instruments, observations of later eclipses, and the observations of quasar 3C273, confirm predictions of the theory, which is that the bending is 1.75 arc seconds.

Relying on the usual assumptions&mdash;Newtonian mechanics, Galilean relativity, conservation of energy and momentum, the universality of the speed of light (that is, special relativity), the Equivalence Principle, and the geodesic equation in empty space (that is, general relativity), and the proper calibration of the instruments, observations of later eclipses, and the observations of quasar 3C273, confirm predictions of the theory, which is that the bending is 1.75 arc seconds.

No [[Nobel Prize]] was awarded for this.  A few years later Einstein won the Nobel Prize for the (unrelated) [[Photoelectric effect]].

No Nobel Prize was awarded for this.  A few years later Einstein won the Nobel Prize for the (unrelated) [[Photoelectric effect]].

===Precession of the orbit of Mercury===

===Precession of the orbit of Mercury===

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.

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 1860 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 was based on observations going all the way back to about 1700.<ref>http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Pollock.pdf</ref>  It was calculated with great accuracy, and reported in 1859, by Urbain Leverrier.  This was long before relativity was formulated.

::One might wonder how astronomical observations accurate enough to measure such a tiny effect could have been made with the technology of that era.  A clever trick was used:  Solar transits of Mercury were observed and timed.  Some of these transits were timed with an accuracy of about 15 seconds.

:This created quite a problem&mdash;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.

:This created quite a problem&mdash;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.

:The approximation given at the end of Einstein's 1916 paper <ref>http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_GRelativity_1916.pdf "The Foundation of the General Theory of Relativity"</ref> is <math>24 \pi^3\frac{a^2}{T^2c^2 (1-e^2)}</math> revolutions per planet's "year", where a is the semi-major axis, T is the length of the planet's year, and e is the eccentricity.  A much simpler, but less accurate, approximation, designed to show how the precession relates to the planet's speed, is <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.  These are just approximations.  Getting an accurate value requires integrating the geodesic equation where Ricci's tensor is zero.

:The approximation given at the end of Einstein's 1916 paper <ref>http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_GRelativity_1916.pdf "The Foundation of the General Theory of Relativity"</ref> is <math>24 \pi^3\frac{a^2}{T^2c^2 (1-e^2)}</math> revolutions per planet's "year", where a is the semi-major axis, T is the length of the planet's year, and e is the eccentricity.  A much simpler, but less accurate, approximation, designed to show how the precession relates to the planet's speed, is <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.  These are just approximations.  Getting an accurate value requires integrating the geodesic equation of the Schwartzschild metric, where Ricci's tensor is zero.

: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.

: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.

:These error bars, and that of the general relativity prediction, all overlap.

:These error bars, and that of the general relativity prediction, all overlap.

:No Nobel Prize was was awarded for this.

 

The scientific community didn't have a lot of choice in how to measure the mechanical effects of general relativity in 1915.  The only manifestation that was known at the time was the precession of planetary orbits.  The orbit of Mercury was used because it has the highest precession of all the planets in the solar system.  This is because it moves faster than any other planet.  Though it is still nowhere near to being "relativistic", so the effect was extremely small.

 

#We now have access to much better examples of orbits affected by general relativity, showing the effect much more strongly than could have been done in 1915.  This is because orbiting bodies emit [[gravitational waves]], which remove energy from the system and make the orbit decay.  This effect is utterly impossible to observe in the case of Mercury's orbit, but it became possible with the discovery of pulsars in 1967.  Binary pulsars are sufficiently massive, and orbit sufficiently closely, that their decay can be observed.  This was observed for binary pulsar [[PSR B1913+16]], and Joseph Taylor and Russell Hulse were awarded the 1993 Nobel Prize for this.  The gravitational waves themselves were still far to weak to be observed directly.

 

 

People have argued at great length (often here at Conservapedia) over the total precession discrepancy (about 1 arcsecond per century according to an article cited at Wikipedia) and relativity's role in it, but in fact there are other phenomena that are vastly better suited to testing Einsteinian gravity.

===The Shapiro Effect===

===The Shapiro Effect===

In late 2015 (and announced in 2016), the LIGO instruments directly detected gravitational waves allegedly from colliding [[black hole]]s.  See [[Gravitational waves]].  Unlike the waves from orbiting pulsars, that could only be detected by the loss of rotation energy, the waves from colliding black holes were strong enough to be detected directly.  The assumptions required for this, in addition to those listed above, were that the objects emitting the radiation (generally believed to be black holes, of course) satisfy the Schwartzschild solution to relativistic mechanics.  The 2017 Nobel Prize in physics was awarded for this.

In late 2015 (and announced in 2016), the LIGO instruments directly detected gravitational waves allegedly from colliding [[black hole]]s.  See [[Gravitational waves]].  Unlike the waves from orbiting pulsars, that could only be detected by the loss of rotation energy, the waves from colliding black holes were strong enough to be detected directly.  The assumptions required for this, in addition to those listed above, were that the objects emitting the radiation (generally believed to be black holes, of course) satisfy the Schwartzschild solution to relativistic mechanics.  The 2017 Nobel Prize in physics was awarded for this.

Since that very early announcement, further observations of gravitational waves have continued to come in.<ref>ligo.org</ref>  In August 2019 the first detection of the gravitational waves from the merger of a [[black hole]] and a neutron star occurred.<ref>https://www.extremetech.com/extreme/296902-scientists-detect-first-ever-collision-between-black-hole-and-neutron-star</ref>

Since that very early announcement, further observations of gravitational waves have continued to come in.<ref>https://ligo.org</ref>  In August 2019 the first detection of the gravitational waves from the merger of a [[black hole]] and a neutron star occurred.<ref>https://ligo.org/news/index.php#O3updateAug19</ref>  This was event S190814bv, 870 million light years away, and hence actually occurred 870 million years ago.<ref>https://www.extremetech.com/extreme/296902-scientists-detect-first-ever-collision-between-black-hole-and-neutron-star</ref>

In 2018 an observation of the 3-body system PSR J0337+1715, consisting of 2 white dwarfs and a pulsar, was consistent with (and hence tended to confirm) general relativity under conditions of extremely high gravity, to enormous precision.  The assumptions made were the same as those listed above.  One of the researchers stated "If there is a difference [between observation and the prediction of the Equivalence Principle], it is no more than three parts in a million."<ref>https://www.nbcnews.com/mach/science/einstein-s-theory-relativity-passes-its-toughest-test-yet-ncna889021</ref>

In 2018 an observation of the 3-body system PSR J0337+1715, consisting of 2 white dwarfs and a pulsar, was consistent with (and hence tended to confirm) general relativity under conditions of extremely high gravity, to enormous precision.  The assumptions made were the same as those listed above.  One of the researchers stated "If there is a difference [between observation and the prediction of the Equivalence Principle], it is no more than three parts in a million."<ref>https://www.nbcnews.com/mach/science/einstein-s-theory-relativity-passes-its-toughest-test-yet-ncna889021</ref>

===Length contraction===

===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.

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 meter 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:

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

=== The Twin Paradox ===

=== 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 twin paradox is usually stated as a thought experiment involving two twins, one of whom is sent on a long journey in a spacecraft traveling at close to the speed of light, whilst the other remains on Earth. Time dilatation means that the traveling 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 problem can be resolved in two ways. One is to examine the effects of General Relativity: to come back to Earth, the traveling 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 traveling twin has traveled 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 ===

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 Ehrenfest Paradox considers a rigid wheel or disc rotating about 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>

The apparent paradox was finally resolved in 1975 by the Norwegian scientist Øyvind Grøn.<ref>http://www.physicsforums.com/showthread.php?t=224955</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>https://science.nasa.gov/headlines/y2004/21jul_llr.htm</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>https://science.nasa.gov/headlines/y2004/21jul_llr.htm</ref>

===Government Support for Relativistic research===

===Government Support for Relativistic research===