General Theory of Relativity
After 1905, Einstein continued working in all three of his works in the 1905 papers. He made important contributions to the quantum theory, but increasingly he sought to extend the special theory of relativity to phenomena involving acceleration. The key to an elaboration emerged in 1907 with the principle of equivalence, in which gravitational acceleration was held a priori indistinguishable from acceleration caused by mechanical forces; gravitational mass was therefore identical with inertial mass. Einstein elevated this identity, which is implicit in the work of Isaac Newton, to a guiding principle in his attempts to explain both electromagnetic and gravitational acceleration according to one set of physical laws. In 1907 he proposed that if mass were equivalent to energy, then the principle of equivalence required that gravitational mass would interact with the apparent mass of electromagnetic radiation, which includes light. By 1911, Einstein was able to make preliminary predictions about how a ray of light from a distant star, passing near the Sun, would appear to be attracted, or bent slightly, in the direction of the Sun's mass. At the same time, light radiated from the Sun would interact with the Sun's mass, resulting in a slight change toward the infrared end of the Sun's optical spectrum. At this juncture Einstein also knew that any new theory of gravitation would have to account for a small but persistent anomaly in the perihelion motion of the planet Mercury.
About 1912, Einstein began a new phase of his gravitational research,
with the help of his mathematician friend Marcel Grossmann, by phrasing
his work in terms of the tensor calculus of Tullio Levi-Civita and Gregorio
Ricci-Curbastro. The tensor calculus greatly facilitated calculations in
four-dimensional space-time, a notion that Einstein had obtained from Hermann
Minkowski's 1907 mathematical elaboration of Einstein's own special theory
of relativity. Einstein called his new work the general theory of relativity.
After a number of false starts, he published the definitive form of the
general theory in late 1915. In it the gravitational field equations were
covariant; that is, similar to Maxwell's equations, the field equations
took the same form in all equivalent frames of reference. To their advantage
from the beginning, the covariant field equations gave the observed perihelion
motion of the planet Mercury. In its original form, Einstein's general relativity
has been verified numerous times in the past 60 years, especially during
solar-eclipse expeditions when Einstein's light-deflection prediction could
be tested.