Changes

''See [[Theory of Relativity]]'' for a comprehensive treatment of this topic.''

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

 

<br>''See [[Theory of relativity]]'' for a more "general" description of relativity.''

The '''General Theory of Relativity''' is an extension of [[Special theory of relativity|special relativity]], dealing with curved coordinate systems, accelerating frames of reference, curvilinear motion, and curvature of spacetime itself.  It could be said that general relativity is to special relativity as vector calculus is to vector algebra.  General relativity is best known for its formulation of gravity as a [[fictitious force]] arising from the curvature of spacetime.  In fact, "general relativity" and "Einstein's formulation of gravity" are nearly synonymous in many people's minds.

The general theory of relativity was first published by Marcel Grossman in 1913 and [[David Hilbert]] and [[Albert Einstein]] in 1916.

The general theory of relativity was first published by Marcel Grossman in 1913 and [[David Hilbert]] and [[Albert Einstein]] in 1916.

However, "even though General Relativity has passed many tests, most physicists don’t believe it is ultimately correct because it conflicts with [[quantum mechanics]]." [http://newsdesk.org/2010/08/conservapedia-calls-theory-of-relativity-a-liberal-conspiracy/]

However, "even though General Relativity has passed many tests, most physicists don’t believe it is ultimately correct because it conflicts with [[quantum mechanics]]." [http://newsdesk.org/2010/08/conservapedia-calls-theory-of-relativity-a-liberal-conspiracy/]

General relativity, like [[quantum mechanics]] (the other of the two theories comprising "modern physics") both have reputations for being notoriously complicated and difficult to understand.  In fact, in the early decades of the 20^th century, general relativity had a sort of cult status in this regard.  General relativity and quantum mechanics are both advanced college-level and postgraduate level topics.  Hence this article can't possibly give a comprehensive explation of general relativity at the expert level.  But we will attempt to give a rough outline, for lay people, of the general relativistic formulation of gravity.

General relativity, like [[quantum mechanics]] (the other of the two theories comprising "modern physics") both have reputations for being notoriously complicated and difficult to understand.  In fact, in the early decades of the 20th century, general relativity had a sort of cult status in this regard.  General relativity and quantum mechanics are both advanced college-level and postgraduate level topics.  Hence this article can't possibly give a comprehensive explanation of general relativity at the expert level.  But we will attempt to give a rough outline, for lay people, of the general relativistic formulation of gravity.

In the [[weak field approximation]], where velocities of moving objects are low and gravitational fields are not very severe, the theory of general relativity is said to ''reduce to'' the law of universal gravitation. That is to say, under those circumstances the equations of general relativity are mathematically equivalent to the equations of Newtonian gravitation.

In the weak field approximation, where velocities of moving objects are low and gravitational fields are not very severe, the theory of general relativity is said to ''reduce to'' the law of universal gravitation. That is to say, under those circumstances the equations of general relativity are mathematically equivalent to the equations of Newtonian gravitation.

Modern science does not say that Newtonian (classical) gravity is wrong.  It is obviously very very nearly correct.  In the weak field approximation, such as one finds in our solar system, the differences between general relativity and Newtonian gravity are miniscule.  It takes very sensitive tests to show the difference.  The history of those tests is a fascinating subject, and will be covered near the end of this article.  But in all tests conducted so far, where there are discrepancies between the predictions of general relativity and Newtonian gravity (or other competing theories for that matter), experimental results have shown general relativity to be a better description.

Modern science does not say that Newtonian (classical) gravity is wrong.  It is obviously very very nearly correct.  In the weak field approximation, such as one finds in our solar system, the differences between general relativity and Newtonian gravity are miniscule.  It takes very sensitive tests to show the difference.  The history of those tests is a fascinating subject, and will be covered near the end of this article.  But in all tests conducted so far, where there are discrepancies between the predictions of general relativity and Newtonian gravity (or other competing theories for that matter), experimental results have shown general relativity to be a better description.

The general theory of relativity is a ''metric theory,'' sometimes also called a ''geometric theory.'' Metric theories describe physical phenomena in terms of [[differential geometry]]. This stands in contrast to Isaac Newton's [[Law of Universal Gravitation]], which described gravity in terms of a [[vector field]].  In the case of general relativity, the theory relates ''stress-energy'' — an extension of the concept of [[mass]] — and the [[curvature]] of [[spacetime]]. In the words of physicist John Wheeler, "Space tells matter how to move, matter tells space how to curve."<ref>Misner, Thorne & Wheeler. ''Gravitation.'' (1973)</ref>

The general theory of relativity is a ''metric theory,'' sometimes also called a ''geometric theory.'' Metric theories describe physical phenomena in terms of [[differential geometry]]. This stands in contrast to Isaac Newton's [[Law of Universal Gravitation]], which described gravity in terms of a [[vector field]].  In the case of general relativity, the theory relates ''stress-energy'' — an extension of the concept of [[mass]] — and the [[curvature]] of [[spacetime]]. In the words of physicist John Wheeler, "Space tells matter how to move, matter tells space how to curve."<ref>Misner, Thorne & Wheeler. ''Gravitation.'' (1973)</ref>

==Coordinate Systems and Spacetime Diagrams==

==Coordinate Systems, Spacetime Diagrams, and Fictitious Forces==

 

 

 

 

 

A car is driving down the street, from left to right.  Figure 2 shows the same four events and two world lines, but with different calibration&mdash;the car's own coordinate system.  The car is driving 500 feet per minute, but in the opposite direction.  The event of my neighbor's arrival at my house is now at x=-2500.  It's way behind the car, though the car was directly in front of my house at t=0.

 

 

 

 

 

 

... In progress ...

See the "Study Guide" at the bottom of the page linked in the References section<ref>[http://www.thefullwiki.org/Introduction_to_general_relativity Introduction to general relativity]</ref> for an explanation of how fictitious forces (e.g. gravity) arise from "curved" coordinate systems on "spacetime".

==Qualitative Introduction to General Relativity==

==Qualitative Introduction to General Relativity==

===Orbits===

===Orbits===

General relativity provides one explanation for the precession of Mercury's perihelion, which was moving at a different speed than that predicted by a simple application of Newton's law of universal gravitation.  (Previous scientists had attempted to explain it by the gravitational pull of a hypothetical planet inside Mercury's orbit, which they called [[Vulcan]].  This could also be explained by altering the precise inverse-square relation of Newtonian gravity to distance, but that was disfavored by mathematicians due to its inelegance in integrating.)

General relativity provides the best known explanation for the precession of Mercury's perihelion, which was discovered in the 1840s to be following an orbit that was slowly precessing (rotating), rather than being fixed in space as Newtonian gravitation requires.  Actually, the effects of other planets on the precession has been known for a long time, but, when those effects are accounted for, there was still an "anomalous precession" of 43 arc seconds (an extremely tiny amount) per century.  Previous scientists had attempted to explain it by the gravitational pull of a hypothetical planet inside Mercury's orbit, which they called [[Vulcan]]; no such planet was found.  It could also have been explained, by a hypothesis put forward by Simon Newcomb and Asaph Hall, by altering the precise inverse-square relation of Newtonian gravity.  That theory was discarded, in the very early 20th century, when it was found to give wrong values for the orbit of the Moon.

===Gravitational Lensing===

===Gravitational Lensing===

''Main article:'' [[Gravitational lensing]]

''Main article:'' [[Gravitational lensing]]

General relativity predicts that the path of light will be distorted when it passes near a massive object.  In 1919, Sir [[Arthur Eddington]], an esteemed English astronomer, used this to test general relativity by observing the bending of starlight around the sun during a total [[solar eclipse]].<ref>Paul Johnson, British historian</ref>. (A smaller degree of bending could also be consistent with Newton's theory, if one hypothesized light to consist of particles.  However, that [[particle theory of light]] had gone out of favor previously.)  Eddington detected a bending of light, but his range of error overlapped both Einstein's and Newton's predictions.  Upon his return to England, Eddington declared that his observations proven the theory of relativity.  His experiment 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> [http://csep10.phys.utk.edu/astr162/lect/galaxies/lensing.html Gravitational Lensing] </ref><ref>[http://www.iam.ubc.ca/~newbury/lenses/glgallery.html]</ref>. Lorentz has this to say on the discrepancies between the empirical eclipse data and Einstein's predictions.

General relativity predicts that the path of light will be distorted when it passes near a massive object.  In 1919, Sir [[Arthur Eddington]], an esteemed English astronomer, used this to test general relativity by observing the bending of starlight around the sun during a total [[solar eclipse]].<ref>Paul Johnson, British historian</ref>  (A smaller degree of bending could also be consistent with Newton's theory, if one hypothesized light to consist of particles.  However, that [[particle theory of light]] had gone out of favor previously.)  Eddington detected a bending of light, but his range of error overlapped both Einstein's and Newton's predictions.  Upon his return to England, Eddington declared that his observations proven the theory of relativity.  His experiment 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>[http://csep10.phys.utk.edu/astr162/lect/galaxies/lensing.html Gravitational Lensing]</ref><ref>[http://www.iam.ubc.ca/~newbury/lenses/glgallery.html]</ref>  Lorentz has this to say on the discrepancies between the empirical eclipse data and Einstein's predictions.

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

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

{{Relativity}}

{{Relativity}}

==External Links==

==External links==

*Einstein, Albert (1916), [http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf "The Foundation of the General Theory of Relativity"] (PDF), Annalen der Physik 49

*Einstein, Albert (1916), [http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf "The Foundation of the General Theory of Relativity"] (PDF), Annalen der Physik 49

*[http://www.rareuniverse.org/general_science/general_relativity.html A simple explanation of General Relativity]

*[http://www.rareuniverse.org/general_science/general_relativity.html A simple explanation of General Relativity]