Einsteins 1917 Static Model of the Universe: A Centennial Review

  Einstein’s 1917 Static Model of the Universe: A Centennial Review 

Cormac O’Raifeartaigh,a Michael O’Keeffe,a Werner Nahmb and Simon Mittonc

aSchool of Science and Computing, Waterford Institute of Technology, Cork Road, Waterford, Ireland bSchool of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 2, Ireland cSt Edmund’s College, University of Cambridge, Cambridge CB3 0BN, United Kingdom

Author for correspondence: coraifeartaigh@wit.ie

Abstract

We present a historical review of Einstein’s 1917 paper ‘Cosmological Considerations in the General Theory of Relativity’ to mark the centenary of a key work that set the foundations of modern cosmology. We find that the paper followed as a natural next step after Einstein’s development of the general theory of relativity and that the work offers many insights into his thoughts on relativity, astronomy and cosmology. Our review includes a description of the observational and theoretical background to the paper; a paragraph-by-paragraph guided tour of the work; a discussion of Einstein’s views of issues such as the relativity of inertia, the curvature of space and the cosmological constant. Particular attention is paid to little-known aspects of the paper such as Einstein’s failure to test his model against observation, his failure to consider the stability of the model and a mathematical oversight concerning his interpretation of the role of the cosmological constant. We recall the response of theorists and astronomers to Einstein’s cosmology in the context of the alternate models of the universe proposed by Willem de Sitter, Alexander Friedman and Georges Lemaître. Finally, we consider the relevance of the Einstein World in today’s ‘emergent’ cosmologies.

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1. Introduction

There is little doubt that Einstein’s 1917 paper ‘Cosmological Considerations in the General Theory of Relativity’ (Einstein 1917a) constituted a key milestone in 20th century physics. As the first relativistic model of the universe, the paper, later known as ‘Einstein’s Static Universe’ or the ‘Einstein World’, set the foundations of modern theoretical cosmology. In the present article, we commemorate the centenary of Einstein’s 1917 paper by presenting a detailed historical analysis of the work with an emphasis on the insights it provides into Einstein’s contemporaneous thoughts on relativity, astronomy and cosmology. To be sure, a description of the basic physics of the Einstein World can be found in any standard textbook on modern cosmology (Harrison 2000 pp 355-357; Coles and Lucchin 2002 pp 26-28). However, while the historical development of theoretical cosmology from this point onwards has been described in many accounts such as (North 1965 pp 81-129; Ellis 1986; Kragh 1996 pp 7-79; Duerbeck and Seitter 2000; Nussbaumer and Bieri 2009 pp 65–110), there have been surprisingly few detailed analyses of the 1917 paper itself, and even fewer studies of the emergence of the work from the general theory of relativity in the period 1915-1917.1 Indeed, it is probably safe to say that the paper is an example of a key scientific work that has been heavily cited but rarely analysed in detail. The present article aims to provide a detailed review of Einstein’s 1917 paper with an emphasis on the historical context of the work. Particular attention is paid to little-known aspects of this background such as: pre-relativistic models of the universe of similar geometry to the Einstein World; proposed modifications of Newton’s universal law of gravity before Einstein; the problem of boundary conditions at infinity in general relativity. As regards the 1917 memoir itself, particular attention is paid to lesser-known aspects of the paper such a mathematical confusion concerning Einstein’s interpretation of the cosmological constant term, Einstein’s failure to test his model against observation and his failure to consider the stability of his model.
Our review is informed by primary historical resources that have become available to Einstein scholars in recent years. In particular, we refer to many letters and papers written by Einstein and his colleagues in the years 1915-1921, recently published online in English

1 Some notable exceptions are (Kerzberg 1989a; Realdi and Peruzzi 2009; Weinstein 2013; Smeenk 2014). 3

translation by Princeton University Press.2 We also make use of the full text of Einstein’s 1917 paper, shown by kind permission of the Hebrew University of Jerusalem.

2. Historical context of the Einstein World

(i) Biographical considerations

Einstein’s manuscript ‘Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie’ or ‘Cosmological Considerations in the General Theory of Relativity’ (Einstein 1917a) was read to the Prussian Academy of Sciences on February 8th 1917 and published by th

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