Field Theories of Gravitation: the First Fifty Years

Abstract It did not take Einstein long to realize that the collaboration with Grossmann [E1] had led to some conclusions that defeated the very task he had set himself. Let us briefly recapitulate the developments in his thinking about gravitation up to the spring of 1913. Late in 1907 he discovered the singular position of gravitation in the theory of relativity. He realized that the question was not how to incorporate gravitation into the special theory but rather how to use gravitation as a means of breaking away from the privileged position of covariance for uniform relative motion to covariance for general motion. In his Prague days, the analysis of the motion of light in an inhomogeneous gravitational field taught him that the light velocity depends on the gravitational potential and that therefore the framework of the special theory of relativity was too narrow [E2]. Toward the end of his stay in Prague, the technical concept of general covariance took shape in his mind and the fundamental role of the metric tensor as the carrier of gravitation became clear. The first steps toward the tensor theory of gravitation, taken with Grossmann, led him to conclude that the gravitational field equations can be covariant only with respect to linear transformations.