5 2 6 D O C U M E N T 3 7 0 C O M M E N T O N S E L E T Y Published in Annalen der Physik 69 (1922): 436–438. Received 25 September 1922, published 19 De- cember 1922. According to a three-page manuscript [1 016], written on the versos of Abs. 403, 409, and 419, the date of its completion is between 12 and 25 September 1922. [1]Selety 1922. For a historical analysis of the Einstein-Selety dialogue and its embedding in the contemporary discussion on how to reconcile Newtonian cosmology and Euclidean geometry with the problems mentioned, and with Mach’s principle, see Norton 1999, especially pp. 304–313, Kersz- berg 1989, pp. 356–358, and Jung 2005, especially pp. 134–140. [2]This model presupposes that the universe is made up of clusters that again consist of clusters and so on. A molecule and the Milky Way are such clusters. A cluster is added to a cluster higher in the hierarchy by being packed in an empty sphere with a radius larger than the radius of the cluster. This way, the mean density of clusters will decrease and, with infinite steps in hierarchy, will end up with an average zero density of the universe. Selety did not agree with Einstein’s assessment that the hypothesis of equivalence between the Milky Way and the nebulae was empirically refuted. He maintained that “the assumption is widely held that our Milky Way is one of many similar systems and that the spiral nebulae visible for us are other similar systems” (“die Annahme, daß unser Milchstraßensystem eines unter vielen seines- gleichen sei, ist weit verbreitet und daß die von uns gesehenen Spiralnebel andere derartige Syste- me seien” Selety 1922, p. 297). In the dispute among astronomers on whether the universe consists only of the Milky Way with all the sidereal systems belonging to it or, rather, of “island universes” (one of which being the Milky Way) with spiral nebulae in them, the years 1921–1922 showed an ad- vance of the first view, the Big Galaxy of Harlow Shapley (see Smith 1982, especially pp. 97–103). [3]“Nichtbuchten” should be “Nichtleuchten” (see the manuscript). The darkness of the night sky cannot be reconciled with an infinite and eternal universe, for in such a universe there must be a uni- form distribution of starlight (Olbers’s paradox). Hugo Seeliger noticed that Newton’s law of gravi- tation cannot be reconciled with an infinite universe in which matter is distributed uniformly, because the effect of gravitation at any point in space should be indeterminate. As discussed, e.g., in Einstein 1917b (Vol. 6, Doc. 43), Newton’s theory requires a center for the universe, where the density of mass is maximum. With the distance r from such a center, the density of stars should drop faster than to arrive at zero density at infinity: the stars make an island in infinite space. Apparently Einstein uses the expression “island universe” (“Inselwelt”) for Shapley’s Big Galaxy. [4]For Selety’s reaction to Einstein’s following criticism, see Selety 1923, 1924, and Selety to Ein- stein, 30 July 1923 [2 484]. [5]At this point it becomes clear that Einstein’s outlook on Mach’s principle has changed since the debate with De Sitter, Klein, and Weyl (see Vol. 8, the editorial note, “The Einstein-De Sitter-Weyl- Klein Debate,” pp. 351–356). Einstein had proposed his modified field equations in Einstein 1917b (Vol. 6, Doc. 43) with the explicit aim to ensure that, according to the field equations of general rela- tivity, the metric tensor representing the gravitational-inertial field is always uniquely determined by the energy-momentum tensor. However, De Sitter had shown that solutions to the new field equations exist for which this is not true, which Einstein acknowledged in Einstein to Felix Klein, 20 June 1918 (Vol. 8, Doc. 567), though at the same time pointing out that it did not qualify as a physical solution because it was not globally static (compare note 5 to Einstein 1922p [Doc. 340], Einstein’s critique of Friedmann’s nonstatic solution). Rather than abandoning Mach’s principle (as defined in Einstein 1918c [Vol. 7, Doc. 5]), at this point in the present document Einstein changed his way of using it: he argues that among all possible cosmological models we should choose one in which Mach’s principle holds, in particular, the spatially closed model proposed in Einstein 1917b. Thus, Mach’s principle is transformed from a criterion supposed to hold on the level of the field equations to a selection crite- rion among cosmological models. [6]See Einstein 1922c (Vol. 7, Doc. 71), especially pp. 63–70. 1 r2
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