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Cyclic Models of the Relativistic Universe: The Early History

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Beyond Einstein

Part of the book series: Einstein Studies ((EINSTEIN,volume 14))

Abstract

Relativistic models of an expanding universe followed by contraction, or a big bang followed by a big crunch, were first proposed by A. Friedmann in 1922 and nine years later by A. Einstein. In the period ca. 1922–1960, the more speculative idea of a large and possibly infinite number of cycles was discussed by R. Tolman in particular. To some cosmologists, the idea was philosophically appealing because it seemed to justify an eternal yet dynamic universe without an absolute beginning in time. During the 1950s models of this kind, sometimes known as Phoenix models, were investigated by a few cosmologists of whom the most important were A. Dauvillier, W. Bonnor, and H. Zanstra.

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Notes

  1. 1.

    For the cosmological constant, I have substituted the symbol Λ for Friedmann’s λ (which is also the symbol Einstein used in his article of 1917). An English translation of Friedmann’s paper appears in several versions, e.g. Lang and Gingerich (1979, 838–843).

  2. 2.

    Friedmann (2000, 109). The book was translated into French in 1997 (Luminet 1997, 99–214) and into German three years later (Friedmann 2000), introduced and annotated by Georg Singer.

  3. 3.

    Steinhardt and Turok (2007, 177) suggest that Einstein’s choice of investigating the periodic Friedmann solution was a result of his “philosophical predilections” and fascination of Spinoza’s philosophy. The suggestion lacks documentary evidence as well as plausibility. See O’Raifeartaigh and McCann (2014) for a detailed analysis of Einstein’s paper and an English translation of it.

  4. 4.

    Hubble’s name was systematically misspelled as “Hubbel”.

  5. 5.

    Tolman to Einstein, 14 September 1931, a response to Einstein to Tolman, 27 June 1931. Courtesy the Einstein Archives and Princeton University Press. Tolman’s reference to his forthcoming paper was to Tolman (1931b).

  6. 6.

    Takeuchi wrote several papers on relativity, quantum theory, and cosmology in the years about 1930, some of them in the proceedings of the Physico-Mathematical Society and others in the Zeitschrift für Physik. For example, he investigated the hypothesis of a decreasing velocity of light within the framework of evolutionary cosmology, concluding that the decrease was only about 1 cm/sec/year (Takeuchi 1930).

  7. 7.

    In fact, Boltzmann never advocated or discussed an oscillating universe. In 1895 he developed a remarkable scenario of a kind of multiverse, including “worlds” with a reversed entropic order, but he did not consider a series of such worlds changing periodically in time (Boltzmann 1895).

  8. 8.

    A similar speculation appeared in (Robertson 1932, 224), who suggested that the universe “was originally shrinking and, having reached a finite lower limit, began to expand”.

  9. 9.

    The lecture was not published, but a brief summary of it appeared in Nature, vol. 127, p. 790. The blackboard Einstein used, provided with his calculations of the cyclic universe, was kept and can be seen at the Museum of the History of Science in Oxford. The formulae on the blackboard correspond closely to those in his published paper. See O’Raifeartaigh and McCann (2014).

  10. 10.

    Lemaître (1933) was reprinted in 1972 in Pontifical Academiae Scientiarum Scripta Varia, no. 36: 107–181. In 1997 an English translation by M. A. H. MacCallum appeared in General Relativity and Gravitation (Lemaître 1997).

  11. 11.

    Relativistic thermodynamics started much earlier. For a critical survey of the early development, see Liu and Chuang (1992).

  12. 12.

    Science 80 (1934): 358. A more visible result of Einstein’s stay in Pasadena was a brief paper he wrote jointly with Tolman and Boris Podolsky on the philosophical problems of quantum mechanics (Einstein et al. 1931).

  13. 13.

    All considerations of the entropy of the universe, whether supposed to be closed or not, rest on the assumption that the idea of entropy can be applied to the universe as a whole. It was and still is rarely realized that this is a questionable assumption. According to Robert Wald, there is “no reason to expect that there will be a meaningful notion of the ‘total entropy of the universe’ ” (Wald 2006, 396).

  14. 14.

    For an in-depth analysis of the history of singularity theorems, see Earman (1999).

  15. 15.

    Zanstra (1957) appeared separately as circular no. 11 of the Astronomical Institute of the University of Amsterdam. It is not included in the ISI Web of Science and has not received attention by historians of science. The paper was abstracted in the Astronomischer Jahresbericht (vol. 57, 1957: 124–125) but not in the Physics Abstracts.

  16. 16.

    It would seem that the steady-state universe, based on the perfect cosmological principle, satisfied all three principles, but Zanstra argued that it failed on account of the third principle.

  17. 17.

    Zanstra gave an exposition of his metaphysical beliefs, which included telepathy and other parts of parapsychology, in a series of lectures at the philosophy department of the University of Michigan 1959–1960. The lectures were published as Zanstra (1962).

  18. 18.

    Lemaître (1934). In cosmology the equation of state is given by a dimensionless number w ≡ p∕ρ, where p is the pressure and ρ the energy density equal to the mass density times c 2. For an ordinary gas, w = 0, whereas for radiation and relativistic matter, as in the early universe, w = 1∕3. It can be shown that for any w < −1∕3, the expansion of the universe is accelerating. One example is dark energy in the form of the cosmological constant, where w = −1. The even more extreme case w < −1 is characteristic of so-called phantom energy.

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Acknowledgements

I thank the Caltech Institute Archives for permission to quote from Tolman’s unpublished correspondence. Tilman Sauer kindly provided me with copies of letters between Einstein and Tolman, for which I am grateful.

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  1. Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100, Copenhagen, Denmark

    Helge Kragh

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  1. Helge Kragh
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  1. Institut für Mathematik, Johannes Gutenberg-Universität, Mainz, Germany

    David E. Rowe

  2. Institut für Mathematik, Johannes Gutenberg-Universität, Mainz, Germany

    Tilman Sauer

  3. Centre François Viète, Université de Nantes, Nantes Cedex, France

    Scott A. Walter

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Kragh, H. (2018). Cyclic Models of the Relativistic Universe: The Early History. In: Rowe, D., Sauer, T., Walter, S. (eds) Beyond Einstein. Einstein Studies, vol 14. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-7708-6_8

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