Abstract
We present an analysis and translation of Einstein’s 1931 paper “Zum kosmologischen Problem der allgemeinen Relativitätstheorie” or “On the cosmological problem of the general theory of relativity”. In this little-known paper, Einstein proposes a cosmic model in which the universe undergoes an expansion followed by a contraction, quite different to the monotonically expanding Einstein-de Sitter model of 1932. The paper offers many insights into Einstein’s cosmology in the light of the first evidence for an expanding universe and we consider his views of issues such as the curvature of space, the cosmological constant, the singularity and the timespan of the expansion. A number of original findings concerning Einstein’s 1931 model are presented. We find that Einstein’s calculations of the present radius and matter density of the universe contain some anomalies: we suggest that his estimate of the age of the universe is based on a questionable calculation of Friedmann’s: we find that the model is not periodic, contrary to what is often stated. A first English translation of Einstein’s paper is included as an Appendix.
Similar content being viewed by others
Change history
20 July 2022
A Correction to this paper has been published: https://doi.org/10.1140/epjh/s13129-022-00040-1
References
Associated Press Report. 1931a. Prof. Einstein begins his work at Mt. Wilson. NYT, Jan 3, p. 1
Associated Press Report. 1931b. Redshift of nebulae a puzzle, says Einstein. NYT, Feb 12, p. 2
Bartusiak, M. 2009. The Day We Found the Universe. Vintage Books, New York
Belenkiy, A. 2012. Physics Today 65 (10): 38-43
Belenkiy, A. 2013. The waters I am entering no one yet has crossed: Alexander Friedmann and the origins of modern cosmology. Origins of the Expanding Universe 1912–1932, edited by M. Way and D. Hunter, Astron. Soc. Pacific. Conference Series 471: 71-96
Condon, E. 1925. The ages of the stars. Proc. Natl. Acad. Sci. 11: 125-130
de Sitter, W. 1917. On Einstein’s theory of gravitation and its astronomical consequences. Month. Not. Roy. Astron. Soc. 78: 3-28
de Sitter, W. 1930a. On the magnitudes, diameters and distances of the extragalactic nebulae, and their apparent radial velocities. Bull. Astron. Inst. Neth. 185: 157-171
de Sitter, W. 1930b. The expanding universe. Discussion of Lemaitre’s solution of the equations of the inertial field. Bull. Astron. Inst. Neth. 193: 211-218
Eddington, A.S. 1930. On the instability of Einstein’s spherical world. Month. Not. Roy. Astron. Soc. 90: 668-678
Eddington, A.S. 1931. The recession of the extra-galactic nebulae. Proc. Roy. Soc. A 133: 3-10
Einstein, A. 1905a. Zur Elektrodynamik bewegter Körper. Annal. Physik 17: 891-921 reprinted and translated in The Principle of Relativity (Dover, 1952), pp. 35-65
Einstein, A. 1905b. Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annal. Physik 17: 132-148
Einstein, A. 1917. Kosmologischen Betrachtungen zur allgemeinen Relativitätstheorie Sitzungsb. König. Preuss. Akad. 142-152, reprinted and translated in The Principle of Relativity (Dover, 1952), pp. 175-188
Einstein, A. 1923. Letter to H. Weyl, May 23
Einstein, A. 1931. Zum kosmologischen Problem der allgemeinen Relativitätstheorie. Sitzungsb. König. Preuss. Akad. 235-237
Einstein, A. 1934. Review of Relativity, Thermodynamics and Cosmology (Oxford University Press) by Richard Tolman. Science 80: 358
Einstein, A. 1945. On the cosmological problem. Appendix to The Meaning of Relativity. Princeton University Press, Princeton, New Jersey, 2nd edn. 109-132. Also available in later editions
Einstein, A. and W. Mayer. 1931a. Systematische Untersuchung über kompatible Feldgleichungen welche in einem Riemannschen Raume mit Fern-Parallelismus gesetzt werden können. Sitzungsb. König. Preuss. Akad. 257-265
Einstein, A. and W. Mayer. 1931b. Einheitliche Feldtheorie von Gravitation und Elektrizität. Sitzungsb. König. Preuss. Akad. 541-557
Einstein, A. and W. de Sitter, 1932. On the relation between the expansion and the mean density of the universe. Proc. Natl. Acad. Sci. 18: 213-214
Earman, J. and J. Eisenstaedt. 1999. Einstein and Singularities. Stud. Hist.Phil.Mod. Phys. 30 (2): 185-235
Eisenstaedt, J. 1989. ‘The low water-mark of general relativity 1925-1950’ in Einstein and the History of General Relativity, Einstein Studies vol 1, edited by J. Stachel and D. Howard. Birkhauser, Boston, Vol. 1, pp. 277-292
Eisenstaedt, J. 2006. The Curious History of Relativity: How Einstein’s Theory was Lost and Found Again. Princeton University Press
Eisinger, J. 2011. Einstein on the Road. Prometheus Books, New York
Friedmann, A. 1922. Über die Krümmung des Raumes. Zeit. Physik 10: 377-386
Friedmann, A. 1924. Über die Möglichkeit einer Welt mit constanter negative Krümmung des Raumes. Zeit. Physik. 21: 326-332
Gamow, G. 1956. The Evolutionary Universe. Sci. Amer. 195 (3): 136-156
Holder, R.D. and S. Mitton. 2013. Georges Lemaître: Life, Science and Legacy. Astrophysics and Space Science Library Series 395: XII. Springer Verlag
Hubble, E. 1929. A relation between distance and radial velocity among extra-galactic nebulae. Proc. Natl. Acad. Sci. 15: 168-173
Kuhn, T. 1962. The Structure of Scientific Revolutions. Cambridge University Press, Cambridge
Lemaître, G. 1927. Un univers homogène de masse constant et de rayon croissant, rendant compte de la vitesse radiale des nébeleuses extra-galactiques. Annal. Soc. Sci. Brux. Série A 47: 49-59
Lemaître, G. 1934. Evolution of the expanding universe. Proc. Natl. Acad. Sci. 20: 12-17
Lemaître, G. 1958. Rencontres avec Einstein. Rev. Quest. Sci. 129: 129-132
Livio, M. 2013. Brilliant Blunders: From Darwin to Einstein - Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe. Simon and Schuster.
North, J.D. 1965. The Measure of the Universe: A History of Modern Cosmology. Oxford University Press
Nussbaumer, H. and L. Bieri. 2009. Discovering the Expanding Universe. Cambridge University Press, Cambridge
Nussbaumer, H. 2013. Slipher’s redshifts as support for de Sitter’s model and the discovery of the dynamic universe. Origins of the Expanding Universe 1912–1932, edited by M. Way and D. Hunter, Astron. Soc. Pacific. Conference Series 471: 25-38
Nussbaumer, H. 2014. Einstein’s conversion from his static to an expanding universe. Eur. Phys. J. H, DOI: 10.1140/epjh/e2013-40037-6
O’Raifeartaigh, C. 2013. The contribution of V.M. Slipher to the discovery of the expanding universe. Origins of the Expanding Universe 1912–1932, edited by M. Way and D. Hunter, Astron. Soc. Pacific. Conference Series 471: 49-62
Pais, A. 1982. Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press, Oxford
Peacock, J.A. 2013. Slipher, galaxies and cosmological velocity fields. Origins of the Expanding Universe 1912–1932, edited by M. Way and D. Hunter, Astron. Soc. Pacific. Conference Series 471: 3-25
Peebles, P.J. and Ratra Bharat. 2003. The cosmological constant and dark energy. Rev. Mod. Phys. 75 (2): 559-606
Rindler, W. 1969. Essential Relativity: Special, General and Cosmological. Van Nostrand Reinhold Company New York. Reprinted 1977 Springer-Verlag New York, 2nd edn. Reprinted 2006. Oxford University Press
Robertson, H. 1929. On the foundations of relativistic cosmology. Proc. Natl. Acad. Sci. 15: 822-829
Solà, J. 2013. Cosmological constant and vacuum energy: old and new ideas. J. Phys.: Conf. Ser. 453: (1) 012015
Steinhardt, P.J. and N. Turok. 2007. Endless Universe: Beyond the Big Bang. Weidenfeld and Nicolson, London
Tolman, R.C. 1929. On the possible line elements for the universe. Proc. Natl. Acad. Sci. 15: 297-304
Tolman, R.C. 1930. More complete discussion of the time-dependence of the non-static line element for the universe. Proc. Natl. Acad. Sci. 16: 409-420
Tolman, R.C. 1931. On the theoretical requirements for a periodic behaviour of the universe. Phys. Rev. 38: 1758-1771
Tolman, R.C. 1932. On the behaviour of non-static models of the universe when the cosmological term is omitted. Phys. Rev. 39: 835-843
Tropp, E.A., V.Y. Frenkel and A.D. Chernin. 1993. Alexander A. Friedmann: The Man Who Made The Universe Expand. Cambridge University Press, Cambridge
Vibert Douglas, A. 1956. The Life of Arthur Stanley Eddington. Nelson and Sons Ltd.
Way, M. 2013. Dismantling Hubble’s Legacy? Origins of the Expanding Universe 1912–1932, edited by M. Way and D. Hunter, Astron. Soc. Pacific. Conference Series 471: 97-135
Weyl, H. 1923. Zur allgemeinen Relativitätstheorie. Physik Zeitschrift 24: 230-232
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
O’Raifeartaigh, C., McCann, B. Einstein’s cosmic model of 1931 revisited: an analysis and translation of a forgotten model of the universe. EPJ H 39, 63–85 (2014). https://doi.org/10.1140/epjh/e2013-40038-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjh/e2013-40038-x