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).
References
Bergia, Silvio, and Lucia Mazzoni. 1999. Genesis and Evolution of Weyl’s Reections on de Sitter’s Universe. In The Expanding Worlds of General Relativity, Einstein Studies, ed. H. Goenner, et al., vol. 7, 325–342. Boston: Birkhäuser.
Bessel-Hagen, Erich. 1921. Über die Erhaltungsätze der Elektrodynamik. Mathematische Annalen 84: 258–276.
Coxeter, H.S.M. 1943. A Geometrical Background for de Sitter’s World. American Mathematical Monthly 50: 217–228.
CPAE 6. 1996. Collected Papers of Albert Einstein, Vol. 6: The Berlin Years: Writings, 1914–1917, ed. A.J. Kox et al. Princeton: Princeton University Press.
CPAE 7. 2002. Collected Papers of Albert Einstein, Vol. 7: The Berlin Years: Writings, 1918–1921, ed. Michel Janssen et al. Princeton: Princeton University Press.
CPAE 8A. 1998a. Collected Papers of Albert Einstein, Vol. 8A: The Berlin Years: Correspondence, 1914–1917, ed. Robert Schulmann et al. Princeton: Princeton University Press.
CPAE 8B. 1998b. Collected Papers of Albert Einstein, Vol. 8A: The Berlin Years: Correspondence, 1918, ed. Robert Schulmann et al. Princeton: Princeton University Press.
CPAE 10. 2006. Collected Papers of Albert Einstein, Vol. 10: The Berlin Years: Correspondence, May-December 1920, ed. Diana Kormos Buchwald et al. Princeton: Princeton University Press.
CPAE 13. 2012. Collected Papers of Albert Einstein, Vol. 13: The Berlin Years: Writings & Correspondence, January 1922 to March 1923, ed. Diana Kormos Buchwald et al. Princeton: Princeton University Press.
Darrigol, Olivier. 2015. Mesh and Measure in Early General Relativity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52: 163–187.
De Sitter, Willem. 1911. On the Bearing of the Principle of Relativity on Gravitational Astronomy. MNRAS 71: 388–415.
De Sitter, Willem. 1912. Absorption of Gravitation. Observatory 35: 387–393.
De Sitter, Willem. 1913. Some Problems of Astronomy. VII The Secular Variation of the Elements of the Four Inner Planets. Observatory 36: 296–303.
De Sitter, Willem. 1917a. On the Relativity of Inertia. Remarks Concerning Einstein’s Latest Hypothesis. Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings 19(1916–17): 1217–1225.
De Sitter, Willem. 1917b. On the Curvature of Space. Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings 20(1917–18): 229–243.
De Sitter, Willem. 1917c. On Einstein’s Theory of Gravitation, and its Astronomical Consequences. Third Paper, Royal Astronomical Society, Monthly Notices 78: 3–28.
De Sitter, Willem. 1918. Further Remarks on the Solutions of the Field Equations of Einstein’s Theory of Gravitation. Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings 20: 1309–1312.
De Sitter, Willem. 1920. On the Possibility of Statistical Equilibrium of the Universe. Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings 23(1920–22): 866–868.
Du Val, Patrick. 1924. Geometrical Note on de Sitter’s World. Philosophical Magazine 47: 930–938.
Earman, John. 1995. Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes. Oxford: Oxford University Press.
Earman, John. 1999. The Penrose-Hawking Singularity Theorems: History and Implications. In The Expanding Worlds of General Relativity, Einstein Studies, ed. H. Goenner, et al., vol. 7, 235–270. Boston: Birkhäuser.
Einstein, Albert. 1916. Näherungsweise Integration der Feldgleichungen der Gravitation, Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, physikalisch-math. Klasse, 1916: 688–696; Reprinted in (CPAE 6. 1996, 347–356).
Einstein, Albert. 1917. Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie, Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, physikalisch-math. Klasse, 1917, 142–152; Reprinted in (CPAE 6. 1996, 142–152).
Einstein, Albert. 1918a. Prinzipielles zur allgemeinen Relativitätstheorie. Annalen der Physik 55: 241–244; Reprinted in (CPAE 7. 2002, 38–41).
Einstein, Albert. 1918b. Kritisches zu einer von Hrn. De Sitter gegebenen Lösung der Gravitationsgleichungen, Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, physikalisch-math. Klasse, 270–272; Reprinted in (CPAE 7. 2002, 46–48).
Einstein, Albert. 1920. Aether und Relativitätstheorie. Berlin: Julius Springer; Reprinted in (CPAE 7. 2002, 306–320).
Einstein, Albert. 1922. Vier Vorlesungen über Relativitätstheorie gehalten im Mai 1921 an der Universität Princeton. Braunschweig: Vieweg, 1922; Reprinted in (CPAE 7. 2002, 497–569). English trans., The Meaning of Relativity, London: Methuen.
Eisenstaedt, Jean. 1988a. The Early Interpretation of the Schwarzschild Solution. In Einstein and the History of General Relativity, Einstein Studies, ed. Don Howard and John Stachel, vol. 1, 213–233. Boston: Birkhäuser.
Eisenstaedt, Jean. 1988b. The Low Water Mark of General Relativity, 1925–1955, In Einstein and the History of General Relativity, Einstein Studies, ed. Don Howard and John Stachel, vol. 1, 277–292. Boston: Birkhäuser.
Ellis, George F.R. 1988. The Expanding Universe: A History of Cosmology from 1917 to 1960. In Einstein and the History of General Relativity, Einstein Studies, ed. Howard, Don, and John Stachel, vol. 1, 367–432. Boston: Birkhäuser.
Frenkel, Viktor. 2002. Einstein and Friedmann. In Einstein Studies in Russia, Einstein Studies, ed. Balashov, Yuri, and Vladimir Vizgin, vol. 10, 1–16. Boston: Birkhäuser.
Goenner, Hubert. 2001. Weyl’s Contributions to Cosmology. In [Sch 2001a], pp. 105–137.
Hawking, S.W., and G.F.R. Ellis. 1973. The Large Scale Structure of Space-Time. Cambridge: Cambridge University Press.
Holton, Gerald. 1960. Notes on the Religious Orientation of Scientists. In Science Ponders Religion, ed. Harlow Shapley. New York: Appleton-Century-Crofts.
Janssen, Michel. 2014. ‘No Success like Failure …’: Einstein’s Quest for General Relativity, 1907–1920. In [Jan and Leh 2014], 167–227.
Janssen, Michel, and Christoph Lehner eds. 2014. The Cambridge Companion to Einstein. Cambridge: Cambridge University Press.
Kerszberg, Pierre. 1989. The Invented Universe: The Einstein-De Sitter Controversy (1916–1917) and the Rise of Relativistic Cosmology. Oxford: Clarendon Press.
Klein, Felix. 1871. Über die sogenannte Nicht-Euklidische Geometrie. Mathematische Annalen 4: 573–625; Reprinted in [Kl-GMA], vol. 1, 254–306.
Klein, Felix. 1872. Vergleichende Betrachtungen über neuere geometrische Forschungen. Erlangen: Deichert; Reprinted in [Kl-GMA], vol. 1, 460–497.
Klein, Felix. 1910. Über die geometrischen Grundlagen der Lorentzgruppe. Jahresbericht der Deutschen Mathematiker-Vereinigung, 19: 281–300; Reprinted in [Kl-GMA], vol. 1, 533–552.
Klein, Felix. 1917. Zu Hilberts erster Note über die Grundlagen der Physik. Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen 1917: 469–482; Reprinted in [Kl-GMA], vol. 1, pp. 553–567.
Klein, Felix. 1918a. Bemerkungen über die Beziehungen des de Sitter’schen Koordinatensystems B zu der allgemeinen Welt konstanter positiver Krümmung. Koninklijke Akademie van Wetenschappen te Amsterdam. Proceedings 20: 614–615.
Klein, Felix. 1918b. Über die Integralform der Erhaltungssätze und die Theorie der räumlich-geschlossenen Welt. Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen 1918: 394–423; Reprinted in [Kl-GMA], vol. 1, 586–612.
Kragh, Helge. 1996. Cosmology and Controversy. Princeton: Princeton University Press.
Liebscher, D.-E. 2005. The Geometry of Time. Weinheim: Wiley-VCH.
Lorentz, H.A., et al. 1922. Das Relativitäsprinzip. Eine Sammlung von Abhandlungen, 4th ed. Leipzig: Teubner. English trans., The Principle of Relativity, London: Methuen, 1923.
Martins, Roberto de Andrade. 1999. The Search for Gravitational Absorption in the early Twentieth Century. In The Expanding Worlds of General Relativity, Einstein Studies, ed. H. Goenner, et al., vol. 7, 1–44. Boston: Birkhauser.
Mercier, André, and Michel Kervaire eds. 1956. Fünfzig Jahre Relativitätstheorie/Cinquantenaire de la Théorie de la Relativité/Jubilee of Relativity Theory, Helvetica Physica Acta, Supplementum IV. Basel: Birkhäuser.
Minkowski, Hermann. 1909. Raum und Zeit. Physikalische Zeitschrift 10: 104111; English trans., The Principle of Relativity, London: Methuen, 1923: 73–91.
Moschella, Ugo. 2005. The de Sitter and anti-de Sitter Sightseeing Tour. Seminar Poincaré 1. http://www.bourbaphy.fr/moschella.pdf.
Noether, Emmy. 1918. Invariante Variationsprobleme, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse 235–257.
North, John. 1965. The Measure of the Universe: a History of Modern Cosmology. Oxford: Oxford University Press.
Norton, John. 1999. The Cosmological Woes of Newtonian Gravitation Theory. In The Expanding Worlds of General Relativity, Einstein Studies, ed. H. Goenner, et al., vol. 7, 271–324. Boston: Birkhauser.
Pais, Abraham. 1982. Subtle is the Lord. The Science and the Life of Albert Einstein. Oxford: Clarendon Press.
Pauli, Wolfgang. 1921. Relativitätstheorie, Encyklopädie der mathematischen Wissenschaften. 5: part 2 539–775; English trans., Theory of Relativity, London: Pergamon, 1958.
Pauli, Wolfgang. 1979. Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a., ed. Karl von Meyenn, Armin Hermann, Victor F. Weisskopf, Bd. 1. Heidelberg: Springer.
Robertson, H.P. 1933. Relativistic Cosmology. Review of Modern Physics 5: 62–90.
Röhle, Stefan. 2002. Mathematische Probleme in der Einstein-de Sitter Kontroverse, Examensarbeit, JGU Mainz, 2000, Max-Planck-Institut für Wissenschaftsgeschichte, Preprint Nr. 210.
Röhle, Stefan. 2007. Willem de Sitter in Leiden: ein Kapitel in der Entwicklung der relativistischen Kosmologie. Dissertation, JGU Mainz.
Rowe, David E. 1999. The Göttingen Response to General Relativity and Emmy Noether’s Theorems. In The Symbolic Universe. Geometry and Physics, 1890–1930, ed. Jeremy Gray, 189–233. Oxford: Oxford University Press.
Rowe, David E. 2006. Einstein’s Allies and Enemies: Debating Relativity in Germany, 1916–1920. In Interactions: Mathematics, Physics and Philosophy, 1860–1930, Boston Studies in the Philosophy of Science, ed. Vincent F. Hendricks, et al., vol. 251, 231–280. Dordrecht: Springer.
Rowe, David E. 2012. Einstein and Relativity. What Price Fame? Science in Context 25(2): 197–246.
Rowe, David E. 2015. Einstein und die Anfänge der relativistischen Kosmologie, 1917–1924. Mitteilungen der Mathematischen Gesellschaft Hamburg 35: 93–136.
Rynasiewicz, Robert. 1999. Kretschmann’s Analysis of Covariance and Relativity Principles. In The Expanding Worlds of General Relativity, Einstein Studies, ed. H. Goenner, et al., vol. 7, 431–462. Boston: Birkhauser.
Scholz, Erhard. 2001b. Weyls Infinitesimalgeometrie (1917–1925). In [Sch 2001a], 48–104.
Smeenk, Christopher. 2014. Einstein’s Role in the Creation of Relativstic Cosmology. In [Jan and Leh 2014], 228–269.
Thorne, Kip S. 1994. Black Holes and Time Warps: Einstein’s Outrageous Legacy. New York: W.W. Norton.
Weyl, Hermann. 1918. Raum-Zeit-Materie. Vorlesungen über allgemeine Relativitätstheorie. Berlin: Springer.
Weyl, Hermann. 1924. Massenträgheit und Kosmos. Ein Dialog, Die Naturwissenschaften 12: 197–204.
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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