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 4 3

[Vol. 8, Docs. 460 and 470]). For further discussion of the role of Machian considerations in the gen-

esis of general relativity, see Hoefer 1994, 1995. For critical discussions of the role of “Mach’s prin-

ciple” in general relativity, see Barbour and Pfister 1995.

[6]Kretschmann 1917 begins by refuting the claim in Einstein 1916e (Vol. 6, Doc. 30), p. 776, that

a theory formulated in generally covariant form automatically satisfies a principle of relativity for

arbitrary motion.

[7]In Kretschmann 1917, p. 576, the author cites Einstein 1916e (Vol. 6, Doc. 30) for the term

“coincidences,” but refers to Kretschmann 1915 for further discussion of the concept. The latter paper

may actually have inspired Einstein’s point-coincidence argument (see Howard and Norton 1993, p.

53).

[8]The proposal in Kretschmann 1917 is to conceive of relativity principles as certain symmetry

principles. Under this proposal, a theory satisfies a relativity principle associated with a certain group

of transformations if those transformations map the sets of geodesics of all the space-times allowed

by that theory back onto themselves. General relativity does not satisfy any such relativity principle.

Kretschmann’s approach is mentioned approvingly in Gustav Mie to Einstein, 17–19 February 1918

(Vol. 8, Doc. 465). For further discussion, see Norton 1992, sec. 8; Norton 1993, sec. 5; and Ryna-

siewicz 1999.

[9]Einstein’s expectation was proven wrong by the discovery of generally covariant reformulations

of Newtonian theory in Cartan 1923 and Friedrichs 1927 (see Norton 1993, sec. 5.3).

[10]Einstein formulated the equivalence principle for the first time in Einstein 1907j (Vol. 2, Doc.

47), p. 454.

[11]In Einstein 1917b (Vol. 6, Doc. 43), p. 147, De Sitter was mentioned explicitly as disagreeing

with Einstein on this point. Later, Mie took De Sitter’s position (Gustav Mie to Einstein, 5 February

1918 [Vol. 8, Doc. 456]).

[12]Instead of “ich selbst . . . unbedingt notwendig”, Einstein wrote in the page proofs: “während

für mich selbst der eigentliche Reiz der Theorie mit diesem Prinzip steht und fällt”).

[13]Note that the solution to the linearized plane gravitational waves presented in Einstein 1918a

(Doc. 1) constitutes an approximate G-field with no matter component. Einstein clearly expected

exact, matter-free, plane-wave solutions in the theory because much later he expressed his surprise to

Max Born when he thought (wrongly) that he had proved their nonexistence (Einstein to Max Born,

undated letter [September 1936?]). Therefore, Einstein does not regard formal gravitational wave

solutions without matter as a counterexample to his proposition that matterless gravitational fields do

not exist.

[14]Einstein 1915i (Vol. 6, Doc. 25). Note that is the Ricci tensor, not the Einstein tensor of

modern notation.

[15]Einstein 1917b (Vol. 6, Doc. 43).

[16]Shortly after the publication of Einstein 1917b (Vol. 6, Doc. 43), De Sitter found a vacuum solu-

tion of the field equations with the cosmological term. It was in response to this solution that Einstein

formulated the requirement for which the term “Mach’s principle” is introduced in the present paper

(see Einstein to Willem de Sitter, 24 March 1917 [Vol. 8, Doc. 317]). Einstein had convinced himself

that the De Sitter solution has what would later be called an intrinsic singularity (see the following

document for further details). In Einstein to Rudolf Humm, 18 January 1918 (Vol. 8, Doc. 440), he

wrote that the De Sitter solution had thus strengthened his belief that eq. (2) does not allow solutions

that are both free of singularities and free of matter.

[17]Erwin Freundlich (1885–1964), Assistent at the Royal Prussian Observatory at Neubabelsberg

near Berlin, and Felix Klein had alerted Einstein to the possibility of an elliptic geometry, which is

obtained from the spherical geometry of the model proposed in Einstein 1917b (Vol. 6, Doc. 43) by

identifying antipodal points (see Einstein to Erwin Freundlich, after 18 February 1917 [Vol. 8, Doc.

300], and Einstein to Felix Klein, 26 March 1917 [Vol. 8, Doc. 319]).

[18]Both De Sitter and Mie had misconstrued what Einstein intended with his cosmological model,

suggesting that the model involves two kinds of matter: a homogeneously distributed “world matter,”

as De Sitter called it, producing the perfectly spherical spatial geometry of the model, and ordinary

matter causing local deviations from the spherical geometry. For Einstein’s response to these miscon-

struals, see Einstein to Willem de Sitter, 14 June 1917 (Vol. 8, Doc. 351), and Einstein to Gustav Mie,

Gμν