244 RELATIVITY, THE GENERAL THEORYunable to find generally covariant gravitational field equations [El7] and that
Einstein had given a 'physical argument' for the impossibility of such general
covariance. Now, late in 1914, Einstein reproduced this same argument in his
long paper. Not only did he still believe it, but he prefaced it with the remark that
'we must restrict this requirement [of general covariance] if we wish to be in full
agreement with the law of causality' [E22]. This remark is understandable in the
context of Einstein's unjustified criterion that the metric tensor g^ should be
uniquely determined by its source, the energy momentum tensor. In the 1914
paper he returned to the division of space-time into two domains L, and L 2 , as
described in Section 12d. Recall that he had found g^ ¥= g^ in the matter-free
region L 2. This time, he wrote this inequality in more detail: g^x) =£ g'^x'). But,
he now adds, grua(x') = g'm(x'(x)) = /^(x). Anyone familiar with tensor fields
will not be shocked by the fact that g^x) ¥= /^(x). Einstein, on the other hand,
concluded from this inequality that generally covariant gravitational field equa-
tions are inadmissible. In 1914 not only did he have some wrong physical ideas
about causality but in addition he did not yet understand some elementary math-
ematical notions about tensors [HI]. Once again he insisted that the gravitational
field equations can be covariant only under linear transformations.*
Einstein next proceeded to show that this restricted covariance uniquely deter-
mines the gravitational Lagrangian, provided that the latter is assumed to be
homogeneous and of the second degree in the (ordinary, noncovariant) first deriv-
atives of the gp, [E24]. In the course of 1915 he realized, however, that this
'argument for the determination of the Lagrange function of the gravitational field
was entirely illusory, since it could easily be modified in such a way that [this
Lagrangian]. .. could be chosen entirely freely' [E25].
The mathematical details of the October 1914 paper are of no interest for the
understanding of the evolution of the general theory and will be omitted. This
paper gave rise to a correspondence between Einstein and Levi-Civita, early in
- The latter pointed out some technical errors. Einstein was grateful for hav-
ing these brought to his attention. Above all, however, he was happy to have
finally found a professional who took a keen interest in his work. 'It is remarkable
how little my colleagues are susceptible to the inner need for a real relativity the-
ory. ... It is therefore doubly gladdening to get to know better a man like you'
[E26].
In summary, toward the end of 1914 Einstein could look back on a year which
had brought major changes to his personal life and his professional career. He
was still essentially alone in his convictions about the future of relativity theory
and confused about some of its crucial features. One year later, he had corrected
his conceptual errors, completed the theory, and seen others participate actively in
its development.
"The slight extension of the set of allowed transformations given in the second Einstein-Grossmann
paper [E23] (Section 12d) must have been found shortly afterward.