2O2 RELATIVITY, THE GENERAL THEORY
All the same, Einstein continued to adhere to flat space. It is perhaps significant
that, immediately following the lines just quoted, he continued, 'The measuring
rods as well as the coordinate axes are to be considered as rigid bodies. This is
permitted even though the rigid body cannot possess real existence.' The sequence
of these remarks may lead one to surmise that the celebrated problem of the rigid
body in the special theory of relativity stimulated Einstein's step to curved space,
later in 1912.*
It would be as ill-advised to discuss these papers in detail as to ignore them
altogether. It is true that their particular dynamic model for gravitation did not
last. Nevertheless, these investigations proved not to be an idle exercise. Indeed,
in the course of his ruminations Einstein made a number of quite remarkable
comments and discoveries that were to survive. I shall display these in the remain-
der of this chapter, labeling the exhibits A to F. However, in the course of the
following discussion, I shall hold all technicalities to a minimum.
Einstein begins by reminding the reader of his past result that the velocity of
light is not generally constant in the presence of gravitational fields:
A. ' ... this result excludes the general applicability of the Lorentz
transformation.'
At once a new chord is struck. Earlier he had said (I paraphrase), 'Let us see
how far we can come with Lorentz transformations.' Now he says, 'Lorentz trans-
formations are not enough.'
B. 'If one does not restrict oneself to [spatial] domains of constant c, then the
manifold of equivalent systems as well as the manifold of the transformations
which leave the laws of nature unchanged will become a larger one, but in turn
these laws will be more complicated' [!!].
Let us next unveil Einstein's first dynamic Ansatz for a theory of gravitation,
to which he was led by Eq. (11.6). He begins by again comparing a homogeneous
field in the frame S(x,y,z,t) with the accelerated frame E(£,77,fVr).** For small T
—terms O(r^3 ) are neglected—he finds
and the important relation
in which ca is fixed by the speed of the clock at the origin of £; acQ is the accel-
eration of this origin relative to S. Thus Ac = 0 in S. By equivalence Ac = 0 in
S (the A's are the respective Laplacians). 'It is plausible to assume that [Ac = 0]
"This point of view has been developed in more detail by Stachel [S4].
**I use again the notations of Chapter 9, which are not identical with those in I. In the frame S, the
light velocity is taken equal to unity.