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== General Relativity ==

== General Relativity ==

General Relativity is a theory of gravity that is compatible with Special Relativity.  Einstein explains a thought experiment involving two elevators.  The first elevator is stationary on the Earth, while the other is being pulled through space at a constant acceleration of g.  Einstein realized that any physical experiment carried out in the elevators would give the same result.  This realization is known as the equivalence principle and it states that accelerating frames of reference and gravitational fields are indistinguishable.  General Relativity is the theory of gravity that incorporates Special Relativity and the equivalence principle.   

General Relativity is a theory of gravity that is compatible with Special Relativity.  Einstein explains a thought experiment involving two elevators.  The first elevator is stationary on the Earth, while the other is being pulled through space at a constant acceleration of g.  Einstein realized that any physical experiment carried out in the elevators would give the same result.  This realization is known as the equivalence principle and it states that accelerating frames of reference and gravitational fields are indistinguishable.  General Relativity is the theory of gravity that incorporates Special Relativity and the equivalence principle.   

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 [[Euclidean geometry]]: for example, the sum of the angles in a triangle is not exactly 180 degrees. 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 [[Euclidean geometry]]: for example, the sum of the angles in a triangle is not exactly 180 degrees. 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.

At one time the anomalous precession of Mercury's [[perihelion]] seemed to support the Theory of General Relativity, but increasingly accurate measurements show a divergence of the data from the theory.<ref>[[Counterexamples to Relativity]].</ref> There are other explanations based in Newtonian gravity, such as factoring in the pull of the other planets on Mercury's orbit.  One Newtonian explanation requires a slight alternation to the precise inverse-square relation of Newtonian gravity to distance, which is disfavored by mathematicians due to its inelegance in integrating.

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"''

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.

British Historian Paul Johnson declares the turning point in 20th century to have been when fellow Briton Sir [[Arthur Eddington]], an esteemed English astronomer, ventured out on a boat off Africa in 1919 with a local Army unit to observe the bending of starlight around the sun during a total eclipse.  Upon his return to England declared that his observations proven the theory of relativity.  In fact recent analysis of Eddington's work revealed that he was biased in selecting his data, and that overall his data were inconclusive about the theory of relativity. The prediction was later confirmed by more rigorous experiments, such as those performed by the [[Hubble Space Telescope]] <ref>[http://www.spaceimages.com/gravlen.html Hubble Gravitational Lens Photo]</ref><ref> [[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.

British Historian Paul Johnson declares the turning point in 20th century to have been when fellow Briton Sir [[Arthur Eddington]], an esteemed English astronomer, ventured out on a boat off Africa in 1919 with a local Army unit to observe the bending of starlight around the sun during a total eclipse.  Upon his return to England declared that his observations proven the theory of relativity.  In fact recent analysis of Eddington's work revealed that he was biased in selecting his data, and that overall his data were inconclusive about the theory of relativity. The prediction was later confirmed by more rigorous experiments, such as those performed by the [[Hubble Space Telescope]] <ref>[http://www.spaceimages.com/gravlen.html Hubble Gravitational Lens Photo]</ref><ref> [[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.