THE EINSTEIN-GROSSMANN COLLABORATION 213the great transition to Riemannian geometry must have taken place during the
week prior to August 16, as is indicated by Einstein's letter to Hopf.
These conclusions are in harmony with my own recollections of a discussion
with Einstein in which I asked him how the collaboration with Grossmann began.
I have a vivid though not verbatim memory of Einstein's reply: he told Grossmann
of his problems and asked him to please go to the library and see if there existed
an appropriate geometry to handle such questions. The next day Grossmann
returned (Einstein told me) and said that there indeed was such a geometry, Rie-
mannian geometry. It is quite plausible that Grossmann needed to consult the
literature since, as we have seen, his own field of research was removed from
differential geometry.
There is a curiously phrased expression of thanks to Grossmann which, I
believe, comes close to confirming this recollection of mine. It is found at the end
of the introduction to Einstein's first monograph on general relativity, written in
1916: 'Finally, grateful thoughts go at this place to my friend the mathematician
Grossmann, who by his help not only saved me the study of the relevant mathe-
matical literature but also supported me in the search for the field equations of
gravitation' [E21].
Finally, there is a recollection which I owe to Straus [S6], who also remembers
that Einstein was already thinking about general covariance when he met Gross-
mann. Einstein told Grossmann that he needed a geometry which allowed for the
most general transformations that leave Eq. 12.1 invariant. Grossmann replied
that Einstein was looking for Riemannian geometry. (Straus does not recall that
Einstein had asked Grossmann to check the literature.) But, Grossmann added,
that is a terrible mess which physicists should not be involved with. Einstein then
asked if there were any other geometries he could use. Grossmann said no and
pointed out to Einstein that the differential equations of Riemannian geometry
are nonlinear, which he considered a bad feature. Einstein replied to this last
remark that he thought, on the contrary, that was a great advantage. This last
comment is easily understood if we remember that Einstein's Prague model had
taught him that the gravitational field equations had to be nonlinear since the
gravitational field necessarily acts as its own source (see Eq. 11.14).
Having discussed what happened in July and early August 1912,1 turn to the
question of how it happened. Einstein gave the answer in 1921:
The decisive step of the transition to generally covariant equations would cer-
tainly not have taken place [had it not been for the following consideration].
Because of the Lorentz contraction in a reference frame that rotates relative to
an inertial frame, the laws that govern rigid bodies do not correspond to the
rules of Euclidean geometry. Thus Euclidean geometry must be abandoned if
noninertial frames are admitted on an equal footing. [E22]Let us pursue Einstein's 'decisive step' a little further.
In June Einstein had written to Ehrenfest from Prague, 'It seems that the