4 2 D O C . 4 F O U N D AT I O N S O F G E N E R A L R E L AT I V I T Y

Published in Annalen der Physik 55 (1918): 241–244. Received 6 March 1918, published 24 May

1918. A set of page proofs for this document (Klaus Mie, Kiel [79 091.1]) was enclosed with Einstein

to Gustav Mie, 24 March 1918 (Vol. 8, Doc. 493). Significant differences between the document and

the page proofs are noted.

[1]Kretschmann 1917. As can be inferred from the introduction of Einstein 1918c (Doc. 5), the

other recent publications referred to at the beginning of this sentence include several papers by

Willem de Sitter (De Sitter 1916c, 1917a, 1917b, 1917c).

[2]For a concise discussion of the three principles listed below, see Norton 1993, sec. 3.7.

[3]In Einstein’s first systematic exposition of the foundations of general relativity (Einstein 1916e

[Vol. 6, Doc. 30]; see especially pp. 772 and 776), the general principle of relativity was still defined

in terms of the equivalence of frames of reference in arbitrary states of motion. General covariance,

Einstein wrote, guaranteed that the theory satisfied this principle. It was as part of the argument for

general covariance that Einstein introduced the so-called point-coincidence argument, the core of

which is in the present document turned into the statement of the relativity principle itself. Einstein

had originally put forward the point-coincidence argument as part of the resolution of the so-called

hole argument against generally covariant field equations (see Einstein to Paul Ehrenfest, 26 Decem-

ber 1915 and 5 January 1916 [Vol. 8, Docs. 173 and 180] and Einstein to Michele Besso, 3 January

1916 [Vol. 8, Doc. 178]; see Norton 1984, 1987 and Stachel 1989, 1993a for historical discussions).

[4]Einstein originally introduced the term “equivalence principle” for the equivalence of an accel-

erated frame of reference in Minkowski space-time and a frame at rest in a homogeneous gravitational

field. For a careful formulation of this version of the principle, see Einstein 1916p (Vol. 6, Doc. 40).

This formulation reappears, for instance, in Einstein 1922c (Doc. 71), p. 37. Although it was pre-

sented as a heuristic principle for finding the theory rather than as one of the theory’s main tenets, the

original formulation can be seen as a special case of the equivalence principle as it is formulated in

the present paper. The Minkowski metric not only encodes the inertial structure of Minkowski space-

time, expressed in the coordinates of any accelerated frame, it also represents a gravitational field. The

Minkowksi metric is thus a special case of an inertio-gravitational field. In effect, Einstein had used

this special case to draw conclusions about inertio-gravitational fields in general (see Norton 1985,

secs. 7 and 12). The new formulation of the equivalence principle may have been partly in response

to attempts by Willem de Sitter (1872–1934), Professor of Astronomy at the University of Leyden,

and Gustav Mie to distinguish between an inertial and a gravitational component of the metric field

in the cosmological model introduced in Einstein 1917b (Vol. 6, Doc. 43). See also note 18 and Vol.

8, the editorial note, “The Einstein-De Sitter-Weyl-Klein Debate,” pp. 351–357.

[5]In the context of the “Entwurf” theory of Einstein and Grossmann 1913 (Vol. 4, Doc. 13), Ein-

stein had sought to abolish absolute space and time and establish the relativity of arbitrary motion in

two different ways, which can be seen as corresponding to principles (a) and (c). He tried to ensure,

first, that the field equations of the theory have the same form in all frames of reference and, second,

that a particle’s inertia can be reduced to its interaction with other particles (see, for instance, Einstein

1914o [Vol. 6, Doc. 9], pp. 1030–1032 and p. 1085). When, in November 1915, the “Entwurf” field

equations were replaced by generally covariant ones, the first of these two requirements was satisfied

automatically. The discussion in sec. 2 of Einstein 1916e (Vol. 6, Doc. 30) suggests that Einstein orig-

inally thought general covariance guaranteed that the second requirement was satisfied as well (see

also Einstein to Michele Besso, 31 July 1916 [Vol. 8, Doc. 245]). However, by the fall of 1916, if not

earlier, he realized that this is not the case: the metric field, and thereby inertia, is not only determined

by matter but also by boundary conditions. The recognition of this problem formed the starting point

of his correspondence with De Sitter on these matters. Initially, Einstein suggested that a complete

relativity of inertia was not that important to him anymore now that his theory was generally covariant

(Einstein to Willem de Sitter, 4 November 1916 [Vol. 8, Doc. 273]). It was precisely to achieve full

relativity of inertia, however, that he subsequently introduced a static, spatially closed cosmological

model—thus avoiding the need for boundary conditions—and added the cosmological term to the

field equations to allow this model as a solution (Einstein 1917b [Vol. 6, Doc. 43]). The requirement

that matter fully determines the metric field thereupon became the embodiment of the relativity of

arbitrary motion for Einstein, although he did not distinguish it carefully from the requirement of gen-

eral covariance (see, in particular, Einstein to Gustav Mie, 2 February 1918 and 22 February 1918