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It is with great affection that I dedicate this paper to Vishu, a dear friend and valued colleague for many years.
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References
Albert Einstein, “Noherungsweise Integration der Feldgleichungen der Gravitation,” Preussische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1916): 688696, translated as “Approximative Integration of the Field Equations of Gravitation,” in The Collected Papers of Albert Einstein, vol. 6, The Berlin Years: Writings 1914–1917, English Translation of Selected Texts (Princeton University Press, 1997 ), Alfred Engel, transi., pp. 201–210.
Albert Einstein, “Uber Gravitationswellen,” Preussische Akademie der Wissenschaften ( Berlin ). Sitzungsberichte (1918): 154–167.
Albert Einstein, “Spielen Gravitationsfelder im Aufbau der materiellen Elementarteilchen eine wesentliche Rolle?,” Preussische Akademie der Wissenschaften (Berlin). Sitzungberichte (1919): 349–356; translated as “Do Gravitational Fields Play an Essential Part in the Structure of the Elementary Particles of Matter?” in The Principle of Relativity, Otto Blumenthal, ed., W. Perret and J. B. Jeffery, transis. (Methuen, London, 1923), reprint 1952 ( Dover, New York ), pp. 191–198.
There is an intriguing comment by Y. I. Frenkel, in a paper written for the Schilpp volume Albert Einstein: Philosopher- Scientist, but not submitted: “Einstein was probably the first to assimilate gravitational waves and the corresponding particles in a conversation with the author back in 1925” (quotation from Gennady E. Gorelik and Victor Y. Frenkel, “Matvei Petrovich Bronskin and Soviet Theoretical Physics in the Thirties”, Birkhauser, Cambridge, MA, 1994, p.85, cited hereafter).
Oskar Klein, “Zur füfdimensionalen Darstellung der Relativittstheorie,” Zeitschrift für Physik 46 (1927): 188 -xxx. Klein was working with Bohr in Copenhagen at this time, and his comments may well reflect Bohr’s views.
Werner Heisenberg and Wolfgang Pauli, “Zur Quantenelektrodynamik der Wellenfelder,” Zeitschrift für Physik 56 (1929): 1–61.
Leon Rosenfeld, “Zur Quantelung der Wellenfelder,” Annalen der Physik 5 (1930): 1113–152; “Uber die Gravitationswirkungen des Lichtes,” Zeitschrift für Physik 65 (1930): 589–599.
In response to a query from Pauli (see Pauli to Rosenfeld, 12 April 1931, in Wolfgang Pauli, “Scientific correspondence with Bohr, Einstein, Heisenberg and others”, vol.3, 1940–1949, Karl von Meyenn, ed., Springer Verlag, New York, 1993, p.746) Rosenfeld added a supplement to his paper showing that the gravitational self-energy of any one-photon state is infinite. Solomon soon showed that this divergence was not due to the zero-point energy of the field. See Jacques Solomon, “Nullpunktsenergie der Strahlung and Quantentheorie der Gravitation,” Zeitschrift für Physik 71 (1931): 162–170.
Rosenfeld himself later came to question the necessity of quantizing the gravitational field, and did not include his work on this topic in a collection of papers that he selected; instead he reprinted critical comments on field quantization, including arguments against the need for a quantum gravity. See Leon Rosenfeld, “On Quantization of Fields,” in Selected Papers of Leon Rosenfeld, Robert S. Cohen and John Stachel, eds. (Reidel, Dordrecht/Boston/London, 1979)(hereafter Rosenfeld 1979), pp.442–445, and “Quantum Theory and Gravitation,” ibid., pp.598–608.
See Wolfgang Pauli, Wissenschaftlicher Briefwechsel, vol. 2, 1930–1939, Karl von Meyenn, ed. (Springer Verlag, Berlin/Heidelberg/New York/Tokyo, 1985 ), Bohr to Pauli, 15 March 1934, p.308: “The idea was that the neutrino, for which one assumes a zero rest mass, could hardly be anything else than a gravitational wave with appropriate quantization” (transl. from Niels Bohr, Collected Works. vol. 7, Foundations of Quantum Phyics II (1933–1958), J. Kalcar, ed. (Elsevier, Amsterdam/Lausanne/New York/Oxford/Shannon/Tokyo, 1996), p.479). Fermi had evidently had a similar idea, but was aware of the problem of the different spins. See ibid., Pauli to Heisenberg 6 February 1934, p.277: “Fermi would prefer to make a connection between neutrinos and half gravitational quanta.” As late as November 1934, Pauli cautiously stated: “While up to now it has been held almost certain that gravitational phenomena play practically no role in nuclear physics, it now seems that the possibility cannot be immediately rejected, that the phenomena of beta-radiation could be connected with the square root of kappa [the gravitational constant] (”Raum, Zeit, and Kausalität lin der modernen Physik,“ Scientia 59 (1936): 65–76, p.76). This suggests that Pauli may have had in mind construction of a graviton from two neutrinos, along the lines of DeBroglie’s neutrino theory of light.
Dmitri Ivanovich Blokhintsev and F. M. Gal’perin, “Gipoteza neitrino i zakon sokhraneniya energii,” Pod znamenem marxisma (1934), no. 6, pp.147–157. As cited by Gorelik and Frenkel, they wrote: “The comparison displayed above indicates that the graviton and the neutrino have much in common, This probably testifies that in general the highly improbable process of graviton radiation becomes practically observable in beta-decay. If the neutrino turns out to be the graviton this would mean that contemporaray physics had approached the limits beyond which there would be no present insurmountable barrier between gravitation and electromagnetism. Due to theoretical considerations it is hard to identify gravitons with the neutrino since it is hard to admit that they have the same spin 1/2 as the neutrino. In this respect gravitons have much more in common with light quanta. It is impossible, however, to totally rule out a theoretical possibility of their identification. So far it is much more correct to regard the neutrino as an independent type of particle” (Gorelik and Frenkel 1994, p. 97 ).
Marcus Fierz, “über die relativistische Theorie kräftefreier Teilchen mit beliebigem Spin,” Helvetica Physica Acta 12 (1939): 3–37.
Wolfgang Pauli and Marcus Fierz, “über relativistische Wellengleichungen von Teilchen mit beliebigem Spin im elektromagnetischen Feld,” Helvetica Physica Acta 12 (1939): 297–300; ibid., “On relativistic wave equations for particles of arbitrary spin in an electromagnetic field,” Royal Society (London). Proceedings A173 (1939): 211–232.
See Pauli to Heisenberg, 10 June 1939, in Wolfgang Pauli, Wissenschafliche Briefwechsel, vol 2, 1930–1939, Karl von Meyenn, ed. (Springer, Berlin/Heidelberg/New York/Tokyo, 1985), p.662; and Heisenberg to Pauli, 12 June 1939, ibid., p.665.
See Wolfgang Pauli, Wissenschafliche Briefwechsel, vol 2, 1930–1939, Karl von Meyenn, ed. (Springer, Berlin/Heidelberg/New York/Tokyo, 1985), pp.833–901; the section on gravitation is on pp.897–901.
See, for example, Pauli to Schrödinger, 5 November 1939, ibid., p.823–825.
In 1934 Pauli also discussed “the three fundamental natural constants,” but added: “for the sake of simplicity we ignore gravitational phenomena for the present” (the article was not published until 1936 in Scientia; see the reference in note 10).
For Bronstein’s life and work, see Gorelik and Frenkel 1994.
Matvei Petrovich Bronstein, “Kvantovanie gravitatsionnykh voln [Quantization of gravitational waves],” Zhurnal Eksperimentalnoy i Teoreticheskoy Fiziki 6 (1936): 195–236.
Matvei Petrovich Bronstein, “Quantentheorie schwacher Gravitationsfelder,” Physikalische Zeitschrift der Sowjetunion 9 (1936): 140–157 (hereafter Bronstein, 1936b).
The German phrase—“Let him who doubts it pay a Thaler”— comes from the Grimm brother’s tale, “Der tapfere Schneider.”
Jacques Solomon, “Gravitation et Quanta,” Journal de Physique et de Radium 9 (1938): 479–485.
See Gorelik and Frenkel 1994, pp.144–147; and Lydia Chukovskaya, The Akhmatova Journals/ Volume I 1938–41 (Farrar, Strauss and Giroux, New York 1994 ).
See Leon Rosenfeld, “Jacques Solomon,” in Rosenfeld 1979, pp.297–301; Martha Cecilia Bustamente, “Jacques Solomon (1908–1942): Profil d’un physicien thèoricien dans la France des annèes trente,” Revue d’histoire des sciences 50, 49–87, 1997.
See D. van Dantzig, “Some possibilities of the future development of the notions of space and time,” Erkenntnis 7 (1938): 142–146; “On the Relation Between Geometry and Physics and the Concept of Space-time,” in Füenfzig Jahre Relativitäetstheorie, P. Kervaire, ed., Helvetica Physica Acta Supplementum IV, ( Birkhäuser, Basel 1956 ), pp. 48–53.
Indeed, in 1949 Bryce DeWitt, using Schwinger’s covariant technique, recalculated the gravitational self-energy of the photon and showed that it vanished identically. See Carl Bryce Seligman [DeWitt], “I. The Theory of Gravitational Interactions. II. The Interactions of Gravity With Light,” Ph.D. Thesis, Harvard University, December 1949. Note that DeWitt emphasized the need to quantize the full, nonlinear theory, and never regarded quantization of the linearized equations as more than a preliminary exercise.
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Stachel, J. (1999). The Early History of Quantum Gravity (1916–1940). In: Iyer, B.R., Bhawal, B. (eds) Black Holes, Gravitational Radiation and the Universe. Fundamental Theories of Physics, vol 100. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0934-7_31
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