Abstract
Physical astronomy as we know it today matured during the latter half of the twentieth century. It was preceded by a period Jean Eisenstaedt has dubbed the “low water mark” in general relativity (GR), covering roughly the period 1925 to 1955 (Eisenstaedt 1988b). Starting in the 1960s, however, a series of startling developments helped pave the way for what has since been called the “renaissance of general relativity,” which suddenly took on great significance for astrophysics and cosmology. In the days of Einstein and Eddington, one could imagine a gravitational field so strong that it would produce a black hole, a true space–time singularity. People talked about such things, but hardly anyone believed they could actually occur (Thorne 1994). Yet after Penrose and Hawking proved the celebrated singularity theorems (Earman 1999; Hawking and Ellis 1973), experts began to look for evidence that might confirm the existence of black holes. This was only one of many unexpected developments in GR that helped to inaugurate a revolutionary shift in our understanding of the universe. Truly momentous discoveries soon followed, leading to findings that would eventually shatter the quaint universe inhabited by Albert Einstein at the time he unveiled his general theory of relativity.
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Notes
- 1.
Scott Walter pointed out to me that, on a purely quantitative basis, there is no clear evidence of any ebb in publication numbers with respect to other branches of physics, particularly if unification theories as taken into account.
- 2.
This flurry of activity also involved a good deal of conceptual confusion, as recently discussed in Darrigol (2015).
- 3.
The passage in quotation marks was taken from de Sitter’s 1908 inaugural lecture as professor of astronomy in Leyden.
- 4.
Michel Janssen argues that this was the hidden agenda behind Einstein’s cosmological speculations, namely to show that the cosmological problem could be tackled within the framework of general relativity without encountering some kind of contradiction (Janssen 2014, 207–208).
- 5.
These letters can be found in CPAE 8B. (1998b). Hubert Goenner explored Weyl’s changing attitudes toward relativstic cosmology in his interesting paper Goenner (2001). Commenting on Weyl’s earliest work, Goenner was struck by how a mathematician of his caliber could have been misled by these special types of coordinates systems, which only cover part of the manifold, into thinking that the boundary of a coordinate batch contained a real singularity. To a modern expert on GR, this seems especially odd since de Sitter space–time has constant curvature and so is homogeneous and isotropic.
- 6.
For a survey of the connections between metrized projective geometries and their associated space–times, see Liebscher (2005).
- 7.
(Mercier and Kervaire (1955, 145); the question was posed by the Hambrug cosmologist Otto Heckmann).
- 8.
Isotropy here means with respect to the directions of light. Tits calls a Lorentzian manifold M isotropic at a point p if the isometries of M that fix p act transitively on the directions of light issuing from p, (ds 2 = 0). This is equivalent to requiring the existence of a space-like 3-plane ω containing p such that the isometries fixing p and ω act transitively on the lines of the light cone in ω.
- 9.
For a visual tour of de Sitter space and its various coordinatizatons and (partial) foliations, see Moschella (2005).
- 10.
Einstein had actually written words to this effect, but then he struck the sentence out before sending off his note. See Frenkel (2002).
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Acknowledgements
I am grateful to Michel Janssen, Erhard Scholz, and Scott Walter for their comments on an earlier version of this paper. This being a snapshot of a complex story, I have tried to tell part of it here without taking in other contemporaraneous developments that would require serious attention in a more comprehensive study. Historical and mathematical details connected with the Einstein–de Sitter debates and other related matters can be found in several of the references cited below.
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Rowe, D.E. (2018). Debating Relativistic Cosmology, 1917–1924. In: A Richer Picture of Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-67819-1_24
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