D O C . 9 E N E R G Y C O N S E RVAT I O N 4 7
9. “The Law of Energy Conservation
in the General Theory of Relativity” and
“Note Added in Proof”
[Einstein 1918f]
Submitted 16 May 1918
Published 30 May 1918
In: Königlich Preußische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1918):
448–459.
While the general theory of relativity has found the approval of most theoretical
physicists and mathematicians, almost all colleagues still raise objections to my
formulation of the momentum-energy
theorem.1
Since I am convinced the
formulation is correct, I shall present my point of view on this question in the
following, and with the necessary
detail.2
§1. The Formulation of the Theorem and the Objections Raised
According to the energy theorem there is a sum, defined in a specific way and
extended over the parts of each (isolated) system, the energy, which does not
change in value in the course of time, irrespectively of the kind of process the sys-
tem may experience. Oringinally, the theorem is an integral theorem just as the the-
orem of momentum is, which is formed from three similar conservation equations.
The special theory of relativity fused the four conservation theorems into one dif-
ferential law that expresses the vanishing of the divergence of the “energy tensor.”
1
See for example E. Schrödinger, Phys. Zeitschrift. 19 (1918), 4–7; H. Bauer, Phys.
Zeitschr. 19 (1918), 163. G. Nordström, in contrast, shares my interpretation of the energy
theorem; see his recent paper “Jets over de massa van een stoffelijkstelsel,” Amsterdamer
Akademie-Ber. 26 (1917), pp. 1093–1108.
2
In order not to have to repeat known things, I use the results of my presentation of the
foundations of the theory given in my paper “Hamiltonsches Prinzip und allgemeine Rela-
tivitätstheorie” (these Berichte 42 [1916], pp. 1111–1116). Equations from this paper are
denoted with “l.c.”
[p. 448]
[1]
[2]