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]