D O C . 4 F O U N D A T I O N S O F G E N E R A L R E L A T I V I T Y 3 3

4. “On the Foundations of the

General Theory of Relativity”

[Einstein 1918e]

Received 6 March 1918

Published 24 May 1918

In: Annalen der Physik 55 (1918): 241–244.

A number of recent publications give me occasion to return to the foundations of

general relativity, in particular the discerning paper by Kretschmann which was re-

cently published in these annals 53, number 16. My aim here is merely to empha-

size the basic ideas, while I presume the theory to be known.

The theory, as I see it today, is based upon three fundamental aspects which,

however, are by no means independent of one another. They shall be briefly

sketched and characterized, and then illuminated from a few aspects in the follow-

ing.

a. Principle of Relativity. Nature’s laws are merely statements about temporal-

spatial coincidences; therefore, they find their only natural expression in gener-

ally covariant equations.

b. Principle of Equivalence. Inertia and gravity are phenomena identical in na-

ture. From this and from the special theory of relativity it follows necessarily

that the symmetric “fundamental tensor” determines the metric properties

of space, the inertial behavior of bodies in this space, as well as the gravitational

effects. We shall call the state of space which is described by this fundamental

tensor the “G-field.”

c. Mach’s

Principle.1

The G-field is completely determined by the masses of the

bodies. Since mass and energy are—according to the results of the special theory

of relativity—the same, and since energy is formally described by the symmetric

1

Up to now I have not kept the principles (a) and (c) clearly separated; but this was con-

fusing. I have chosen the term “Mach’s principle” because this principle is a generalization

of Mach’s claim that inertia has to be reduced upon interaction of the bodies.

[p. 241]

[1]

[2]

[3]

gμν) (

[4]

[p. 242]

[5]