5 7 6 D O C . 7 1 P R I N C E T O N L E C T U R E S
Einstein’s views on the role of what he called Mach’s principle in cosmology and for a discussion of
his correspondence with De Sitter and others on this subject.
[129]the same argument can be found in page proofs of Einstein 1918e (Doc. 4). See note 22 to that
[130]The manuscript has “〈zentrifugales Feld erzeugen〉.” For more on the Coriolis field, see Ein-
stein to Michele Besso, 31 July and 31 October 1916 (Vol. 8, Docs. 245 and 270).
[131]The fifth English edition (Einstein 1956) corrects to .”
[132]See Einstein and Grossmann 1913 (Vol. 4, Doc. 13), p. 307, for an earlier instance of this
claim. Einstein labels the increase in the gravitational potential energy of massive bodies as they
approach each other as an increase in their individual masses. However, because, as Einstein himself
argues in Einstein 1918f (Doc. 9), the total mass of a system is best defined in terms of its distant grav-
itational field, one cannot unambiguously assign individual masses to neighboring bodies.
[133]See Einstein’s paper on gravitational induction, Einstein 1912e (Vol. 4, Doc. 7).
[134]Thirring 1918, Lense and Thirring 1918. Einstein took great interest in Thirring’s work on
what has become known as the Lense-Thirring effect, or “dragging of inertial frames.” See the corre-
spondence with Hans Thirring in Vol. 8.
[135]For historical discussions of Mach’s principle, see Hoefer 1994 and Barbour and Pfister 1995.
[136]This is the cosmological model proposed in Einstein 1917b (Vol. 6, Doc. 43).
[137]See Einstein 1918e (Doc. 4), p. 243 and note 17.
[138]See Vol. 8, the editorial note, “The Einstein-De Sitter-Weyl-Klein Debate,” pp. 351–357.
[139]The first English edition (Einstein 1922d) corrects to on this line and the
[140]As discussed on pp. 32–33 and p. 53 of the book.
[141]Poincaré 1906. For a discussion, see Einstein 1919a (Doc. 17), note 11.
[142]In the theory presented in Einstein 1919a (Doc. 17), the cosmological constant emerges as a
negative pressure term (see Doc. 17, note 20, for further discussion). In the actual lectures, Einstein
presented a very similar argument. See the summary of Einstein’s last lecture by Adams (New York
Times, 14 May 1921, p. 10), which includes the remark: “Professor Einstein showed that this assump-
tion of pressure throughout the universe is wholly consistent with the general theory of relativity,
although it does not follow as a consequence of the theory.”
The phrase “in unserer phänomenologischen Darstellung” after “daß wir” is omitted from the sec-
ond German edition.
[143]The manuscript has “〈das Gesamtvolumen V der Welt〉” instead of “der Weltradius a.” In his
summary of the last lecture (for reference, see note 142), Adams wrote: “In order to determine the
size of the universe it is necessary to know the mean density of matter in it. But this is a quantity of
which we have no knowledge.”
[144]The last four paragraphs are not in the manuscript. Einstein sent a typescript of them as an
enclosure to Maurice Solovine, the translator of the French edition (see Solovine 1956, p. 22).
[145]In the actual lectures, Einstein gave a more elaborate version of these considerations, which
first appear in Einstein 1917b (Vol. 6, Doc. 43), sec. 1. In his summary of Einstein’s lecture of 13 May
1921, Adams wrote: “It has generally been thought that the universe is infinite in extent. Telescopes
of increasing power have brought more and more distant stars to our vision. If we imagine a sphere
of radius very large compared to the mean distance between the stars our first view is that as we
increase the radius of the sphere more and more a definite density of matter in the universe is
approached. The astronomer Seeliger first showed that such a view is definitely opposed to the New-
tonian law of gravitation, for this view immediately leads to the result that the gravitational field
would also increase beyond all limits as we go out toward infinity, and this would mean that the stellar
velocities would necessarily increase beyond all limits.
“Thus on the basis of Newton’s theory we should have to conclude that the mean density of matter
in the universe is zero. This could only be attained by assuming that the universe is an island floating
in infinite space free from matter. But this view is wholly unsatisfactory, and Seeliger attempted to
reconcile an infinite universe with finite density by assuming that matter of negative density is present


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