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Field Theories of Gravitation:
the First Fifty Years
13a. Einstein in Vienna
It did not take Einstein long to realize that the collaboration with Grossmann [El ]
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.
By August 1913, it had become clear to him that this last result spelled disaster.
He expressed this in a letter to Lorentz: .. .'My faith in the reliability of the
theory still fluctuates. ... The gravitational equations unfortunately do not have
the property of general covariance. Only their covariance for linear transforma-
tions is assured. However, the whole faith in the theory rests on the conviction
that acceleration of the reference system is equivalent to a gravitational field.
Thus, if not all systems of equations of the theory. .. admit transformations other
than linear ones, then the theory contradicts its own starting point [and] all is up
in the air' (sie steht dann in der Luft) [E3].
Thoughts such as these must have been on Einstein's mind when he traveled
to Vienna, where on September 23 he had to present a paper before the Natur-
forscherversammlung.* He was going to report not only on his own work but also
*At that meeting, Einstein met and complimented Friedrich Kottler, who had been the first to write
the Maxwell equations in generally covariant form, though not in connection with a theory of grav-
itation [Kl]. Kottler's later involvement with general relativity was less successful [E3a].228