General Relativity
Einstein was not content
with the special theory of relativity, because it was in contradiction
with Newton's theory of gravitation. Newtonian gravitation was a very
successful theory. In particular, it accounted for the motion of the planets
to high precision. However, it has a peculiar property that had even bothered
Newton. It implies instantaneous transmission of the gravitation force
between two objects across great distances.
Einstein knew this had
to be wrong, because special relativity implies that no signal can be
transmitted faster than the speed of light. Einstein provided the resolution
around 1915 with a new theory of gravitation, which he called the general
theory of relativity. It agrees with the Newtonian theory for low speeds
and weak gravitational fields, but differs from it at high speeds and
strong fields.
The theory had several
immediate observational successes. First it implied a small correction
to the orbit of the planet Mercury that accounted for a small discrepancy
between the orbit implied by the Newtonian theory and the observed orbit.
(The effect is too small to be observed for the other planets.) Second,
it predicted that light from a distant star passing near to the limb of
sun would be bent by a small but measurable angle. The measurement was
made by Eddington during a solar eclipse.
The observations confirmed
the theoretical prediction, and Einstein became an international celebrity.
Other predictions of the theory  such as the existence of black holes
and of gravitational radiation  have been confimed much more recently.
The thing that impressed
other physicists most about the general theory of relativity is that it
is based on very general physical principles  the equivalence principle
and general coordinate invariance  and very beautiful mathematical concepts.
The relevant mathematics is called differential geometry (specifically,
Riemannian geometry). The idea is that gravity is a manifestation of the
curvature of spacetime. Also, the geometry of spacetime is determined
by the distribution of energy and momentum. The basic equation of motion
is
In this equation G_{mn} describes
the spacetime geometry, G is Newton's constant characterizing
the strength of gravitation, and T_{mn}
describes the distribution of energy and momentum.
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