Changes

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'' website]</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 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 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.

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.

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.

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.

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 ==

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.

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.  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 [[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 an experiment that tests two phenomena working against each other.

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.

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===

: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===

===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===