x x v i I N T R O D U C T I O N T O V O L U M E 7
in such an accelerated frame can be said to dissipate gravitational energy as heat.
That energy cannot be represented by a tensor, for in a Lorentz frame in Minkowski
space-time there is no gravitational energy present. More generally, the energy
associated with the gravitational field at some point in one frame of reference is
transferred someplace else or into some other form of energy in the new frame. In
the modern language that arises directly out of this debate (see, e.g., Pauli 1921,
sec. 61; Eddington 1922, p. 280), one says that the energy associated with a gravi-
tational field cannot be localized to any (sufficiently small) part of a system,
although the total energy of a closed system is still conserved.
In Einstein 1918f (Doc. 9), Einstein does not advance this argument. Instead, he
argues more generally that an integral form of the energy conservation law is the
appropriate one, showing that the integral of a closed system’s total energy is
invariant and conserved, and is measurable only at a great distance from the source,
where he shows it is identical with the Schwarzschild mass of the system. In keep-
ing with his interest in cosmology, much of the paper is taken up with a discussion
of the total energy of his closed static model of the universe. The physics behind
Einstein’s formulation of the energy law gradually became more transparent with
the advances in the derivation of the conservation law made by mathematicians
such as Felix Klein (with whom Einstein corresponded at length on this topic in
1918; see the Introduction to Vol. 8, sec. VIII), culminating in the formulation of
Emmy Noether’s celebrated theorems on the relation between symmetries and con-
servation laws in physics (Noether 1918).
Einstein’s struggle to convince his colleagues of the validity of his energy con-
servation law shows that, in some respects, he continued to be isolated in his
approach to research, in spite of the growing number of physicists and mathemati-
cians interested in the general theory. As he remarks at the beginning of Doc. 9,
“nearly all my colleagues still raise objections to my definition of the momentum-
energy theorem.” Even the publication of Doc. 9 did not persuade his critics. Klein
found its argument easy to follow but unconvincing (Felix Klein to Einstein, 16
June 1918 [Vol. 8, Doc. 566]), although he was soon able to put it into a form that
satisfied him (Felix Klein to Einstein, 5 July 1918 [Vol. 8, Doc. 581]). The techni-
cal language of general relativity was still in its infancy at this time and impaired
Einstein’s efforts to explain himself even to his most receptive colleagues. The
pseudotensor controversy shows how the precision of the available language
improved rapidly through fruitful exchanges between physicists and mathemati-
cians. However, this initial promise remained unfulfilled until after Einstein’s
death, as physicists largely turned away from sustained research on the theory from
the mid-twenties on. Nevertheless, Einstein was conscious of the need to educate
physicists about his theory, a task he addresses at the end of this volume, with the