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Line 7: − + − + + + − Relativity and [[quantum mechanics]] (the other physical theory comprising "modern physics") express non-classical effects at very different scales—relativity at very large scales and quantum mechanics at very small scales. This means that, to a high degree of accuracy, the two theories hardly conflict with each other in their closeness to classical phenomena. For example, one doesn't need to take quantum mechanics into consideration when calculating planetary precession. But approximations aren't good enough for serious physicists, and attempts to formulate a "grand unified theory", incorporating both theories, have been ongoing for about 80 years. This grand unification has still not been achieved, in the sense of gravity (general relativity) being incorporated into quantum mechanics, but there has been good success with special relativity. The ''Dirac equation'' was formulated by Paul Dirac in 1928 in order to bring special relativity into quantum mechanics, and it made the astonishing prediction of antiparticles. Such a particle (the positron) was discovered by Carl Anderson in 1932, and antiparticles are now a staple of particle physics. Special relativity is part of the ''standard model'' of particle physics, and that model is a ''relativistic quantum field theory''.<ref>The Theory of Almost Everything, Robert Oerter, ISBN 9-780452-287860</ref> Attempts to unify general relativity, that is, to unify gravity as a "fundamental force" on the same level as the electroweak and strong nuclear forces, have not yet been successful. Attempts in this direction involve such things as [[string theory]]. Such a "grand unification" is believed to involve the bizarre and presumably impossible to detect particle known as the [[graviton]].+ − − Line 56:
Line 56: − − ==Singularities in Relativity== − Relativity, like many areas of mathematics, physics, and engineering, has singularities in some of the governing equations. The most important singularities in the equations of relativity are the <math>\frac{1}{\sqrt{1-v^2/c^2}}</math> appearing in the Lorentz transform, and the <math>\frac{r}{c^2\,(r-a)}</math> appearing in the Schwartzschild metric at the event horizon.<ref>See [http://www.springerlink.com/content/u47l341u2q555455/] for further examples of singularities that can be made in the Riemann tensor.</ref>
Theory of relativity (view source)
Revision as of 20:18, December 12, 2009
, 20:18, December 12, 2009reverting liberal and misleading edits; a fraction of the reverted material may be worth reinserting, but should be done so without the liberal bias
*'''[[General theory of relativity|General Relativity]]''' (GR) is a theory which explains the laws of motion as viewed from accelerating reference frames and includes a geometric explanation for gravity. This theory was developed by [[David Hilbert]] and [[Albert Einstein]] as an extension of the postulates of Special Relativity.<ref>"[T]he German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein."[http://nobelprize.org/educational_games/physics/relativity/history-1.html Nobel Prize historical account]</ref> A dramatic but later discredited claim by Sir [[Arthur Eddington]] of experimental proof of General Relativity in 1919 made Einstein a household name.
*'''[[General theory of relativity|General Relativity]]''' (GR) is a theory which explains the laws of motion as viewed from accelerating reference frames and includes a geometric explanation for gravity. This theory was developed by [[David Hilbert]] and [[Albert Einstein]] as an extension of the postulates of Special Relativity.<ref>"[T]he German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein."[http://nobelprize.org/educational_games/physics/relativity/history-1.html Nobel Prize historical account]</ref> A dramatic but later discredited claim by Sir [[Arthur Eddington]] of experimental proof of General Relativity in 1919 made Einstein a household name.
Unlike most of physics, the theories 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> The equations for special relativity assume that it is forever impossible to attain a velocity faster than the speed of light and that all inertial frames of reference are equivalent, hypotheses that can never be fully tested. Relativity rejects Newton's [[action at a distance]], which is basic to Newtonian gravity and [[quantum mechanics]], but which has been observed in the precession of [[Mercury]]. 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.
Unlike most of physics, the theories 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>
Relativity has been met with much resistance in the scientific world. To date, a Nobel Prize has never been awarded for relativity. Louis Essen, the man credited with determining the speed of light, wrote many fiery papers against it such as ''The Special Theory of Relativity: A Critical Analysis''.<ref>http://ephysics.fileave.com/physics/Essen/oxford5-essen.pdf</ref>
More generally, and also unlike most of physics, the theories 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> The equations for special relativity assume that it is forever impossible to attain a velocity faster than the speed of light and that all inertial frames of reference are equivalent, hypotheses that can never be fully tested. Relativity rejects Newton's [[action at a distance]], which is basic to Newtonian gravity and [[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.
Relativity has been met with much resistance in the scientific world. To date, a Nobel Prize has never been awarded for relativity. Louis Essen, the man credited with determining the speed of light, wrote many fiery papers against it such as ''The Special Theory of Relativity: A Critical Analysis''.<ref>http://ephysics.fileave.com/physics/Essen/oxford5-essen.pdf</ref> Relativity also gravely conflicts with [[quantum mechanics]], 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 [[Newton]]ian 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<sup>2</sup> - c<sup>2</sup> t<sup>2</sup>). The (assumed) instantaneous transmission of [[Newton]]ian gravitational effects also contradicts special relativity.
Unlike [[Newton]]ian 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<sup>2</sup> - c<sup>2</sup> t<sup>2</sup>). The (assumed) instantaneous transmission of [[Newton]]ian gravitational effects also contradicts special 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>
== Special Relativity ==
== Special Relativity ==
Special relativity is the limiting case of general relativity where all gravitational fields are weak. Alternatively, special relativity is the limiting case of general relativity when all reference frames are inertial (non-accelerating and without gravity).
Special relativity is the limiting case of general relativity where all gravitational fields are weak. Alternatively, special relativity is the limiting case of general relativity when all reference frames are inertial (non-accelerating and without gravity).
==Lack of evidence for Relativity==
==Lack of evidence for Relativity==