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The Reichenbach–Einstein Debate on the Geometrization of the Electromagnetic field View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Institutional Research Information System University of Turin Studies in History and Philosophy of Modern Physics 54 (2016) 35–51 Contents lists available at ScienceDirect Studies in History and Philosophy of Modern Physics journal homepage: www.elsevier.com/locate/shpsb ‘…But I still can't get rid of a sense of artificiality’: The Reichenbach–Einstein debate on the geometrization of the electromagnetic field Marco Giovanelli a,b,n a Universität Tübingen, Forum Scientiarum, Doblerstrae 33, 72074 Tübingen, Germany b Einstein Papers Project, Caltech M/C 20-7, 1200 East California Blvd., Pasadena, CA 91125, USA article info abstract Article history: This paper analyzes correspondence between Reichenbach and Einstein from the spring of 1926, Received 6 December 2015 concerning what it means to ‘geometrize’ aphysicalfield. The content of a typewritten note that Accepted 10 April 2016 Reichenbach sent to Einstein on that occasion is reconstructed, showing that it was an early version of Section 49 of the untranslated Appendix to his Philosophie der Raum-Zeit-Lehre, on which Reichenbach Keywords: was working at the time. This paper claims that the toy-geometrization of the electromagnetic field Hans Reichenbach that Reichenbach presented in his note should not be regarded as merely a virtuoso mathematical Albert Einstein exercise, but as an additional argument supporting the core philosophical message of his 1928 fi fi Uni ed eld theories monograph. This paper concludes by suggesting that Reichenbach's infamous ‘relativization of geo- General relativity metry’ was only a stepping stone on the way to his main concern—the question of the ‘geometrization Geometrization of gravitation’. & 2016 Elsevier Ltd. All rights reserved. When citing this paper, please use the full journal title Studies in History and Philosophy of Modern Physics Aber ich kann auch da das Gefühl des Künstlichen nicht form (including a transcription of the quite heavy mathematical los werden—Reichenbach to Einstein, March 16, 1926 apparatus), and the typescript is preserved in the Reichenbach Archives in Pittsburgh (HR, 041-2101). However, the publication must have been withdrawn subsequently. Except for a ‘dead link’ to a no-longer-existing Section 46 on page 17, even today many 1. Introduction readers of The Philosophy of Space and Time might be unaware that such an Appendix ever existed. In the late 1950s, Hans Reichenbach's second wife Maria The decision not to publish the Appendix is understandable. Reichenbach edited an English translation (Reichenbach, 1958)of The text is quite demanding for readers unaccustomed to the his Philosophie der Raum-Zeit-Lehre (Reichenbach, 1928). This edi- formalism, and struggling through it may not have been worth tion was missing a long Appendix entitled ‘Die Weylsche Erwei- terung des Riemannschen Raumbegriffs und die geometrische the effort. After Einstein's death in 1955, the very project of a fi Deutung der Elektrizität’ (‘Weyl's Extension of Riemann's Concept uni ed theory of gravitation and electromagnetism, which of Space and the Geometrical Interpretation of Electromagnetism’). Reichenbach discusses with a plethora of technical details, was A translation of the Appendix was prepared in a nearly publishable nearly unanimously regarded as a relic of the past (but see Tonnelat, 1955)—not least of which by Hermann Weyl, one of the project's initiators (Weyl, 1956). In the same spirit, in an English Abbreviation: AEA, The Albert Einstein Archives at The Hebrew University of translation of a selection of Reichenbach's writings from the late – – Jerusalem (1879 1955); CPAE, Albert Einstein (1987 ). The Collected Papers of “ Albert Einstein. Ed. by John Stachel et al. 14 vols. Princeton: Princeton University 1970s (Reichenbach, 1978), the pages dealing with Weyl's gen- Press; HR, Archives of Scientific Philosophy: The Hans Reichenbach Papers eralization of Riemannian space” were omitted because, as the (18911953); SN, Vienna Circle Foundation—Wiener Kreis Stichting: Schlick Nachlass editors write, they had “no historical significance” (Reichenbach, (1882–1936) n 1978,2:3). Correspondence address: Universität Tübingen, Forum Scientiarum, Doblerstrae 33, 72074 Tübingen, Germany Only a year later, however, a pathbreaking paper by Coffa E-mail addresses: [email protected], [email protected] (1979) proved that this judgment was hasty. Rediscovering Weyl http://dx.doi.org/10.1016/j.shpsb.2016.04.001 1355-2198/& 2016 Elsevier Ltd. All rights reserved. 36 M. Giovanelli / Studies in History and Philosophy of Modern Physics 54 (2016) 35–51 and Reichenbach's ‘elective affinities’, Coffa began (with a nice then approving, reaction to the note. Section 5 shows what pun) a fertile line of research which, much later, would bear fruit Reichenbach's Philosophie der Raum-Zeit-Lehre looks like if read in the work of Ryckman (1995, 1996, 2005), Rynasiewicz (2005) from the perspective of the Appendix. Finally, analyzing Reich- and others (see also Giovanelli, 2013b). It was in this context that enbach's attitude towards Einstein's distant parallelism field the- Coffa provided perhaps the first and only detailed analysis of the ory, Section 6 emphasizes the differences that existed behind untranslated Appendix to the Philosophie der Raum-Zeit-Lehre.In Reichenbach and Einstein's apparent agreement on the issue of fact, Coffa read the Appendix as single-mindedly trying to “exhibit geometrization. This paper concludes by suggesting that Reich- the vacuity of Weyl's enterprise” (Coffa, 1979, 295). Here, however, enbach's well-known ‘relativization of geometry’ was only a Coffa's major achievement becomes a hindrance. Despite the stepping stone on the way to his main concern—the question of Appendix's somewhat misleading title, by interpreting it exclu- the ‘geometrization of gravitation’. sively in terms of the Weyl–Reichenbach debate, we do not fully grasp its meaning. Letters between Reichenbach and Einstein, preserved in the 2. Reichenbach's Γ-critique and his note on the unified field 1 Einstein Archives in Jerusalem (AEA), suggest that the Appendix theories should be read more broadly. In the spring of 1926, Reichenbach, after making some remarks on Einstein's newly published metric- On June 5, 1925 Einstein, who had just returned from a long affine theory (Einstein, 1925b), sent him a note offering what looks trip to South America (see his travel diary, CPAE, Vol. 14, Doc. 455, like his own attempt at a unified field theory. Reichenbach's note March 5–May 11, 1925), wrote to Michele Besso about the state of turns out to have been an early draft of Section 49 of the Appendix, his research on a unified theory of the gravitational and elec- on which he was working at the time. Einstein's objections and tromagnetic fields (Goenner, 2004; Sauer, 2014; Vizgin, 1994). He Reichenbach's replies reveal that criticism of Weyl's theory was revealed to Besso that he had become disillusioned with the only part of the story. Reichenbach was mainly interested in the whole “Weyl–Eddington–Schouten line of thinking,” the frame- very idea of the ‘geometrization’ of a physical field. At the time, work in which he had been working in the previous years,2 and many believed that if general relativity geometrized the gravita- that he was already “on another track, that is physically more tional field, then it was also plausible to geometrize the other grounded” (Einstein to Besso, June 5, 1925; Speziali, 1972,240). known field—the electromagnetic field. To challenge this view, The paper Einstein was referring to—the first in which the term Reichenbach conducted what might be called an ‘epistemological ‘unified field theory’ appears in the title—was presented at the experiment’. Prussian Academy during its July 9, 1925 session (Einstein, Reichenbach constructed a toy-theory establishing a connection 1925b). between electricity and geometry which, he argued, was just as Einstein described “the egg” he “recently laid” to Besso some good as the one general relativity established between gravitation weeks later (Einstein to Besso, July 28, 1925; Speziali, 1972, 209– τ and geometry. Reichenbach's theory, however, was clearly not as 210). The theory introduced an affine connection (Γμν) (from successful as general relativity. Thus, Reichenbach could provide which the Riemann and Ricci tensor Rμν are derived), and inde- ‘ ’ fi experimental evidence that the geometrization of a physical eld pendently the metric tensor gμν (and its correspondent contra- μν μν cannot be regarded in itself as a physical achievement. As soon as variant tensor g and tensor density g ). Einstein then built the ‘ ’ μν Einstein understood the ironical nature of Reichenbach's enter- scalar densityR H ¼ g Rμν and postulated the independent varia- μν τ prise, he immediately agreed with him. As Lehmkuhl (2014) has tion δ H dt ¼ 0, with respect to the g and Γμν (Ferraris, recently shown, it was in his correspondence with Reichenbach that Francaviglia, & Reina, 1982). After some manipulation he obtained, Einstein pointed out, for the first time, that general relativity had at first approximation, the already-known laws of gravitation and μν not geometrized the gravitational field. electromagnetism. The symmetric part of the g represents the As we shall see, Einstein and Reichenbach's opinions about the ‘gravitational potentials’, and the antisymmetric part the ‘electro- geometrization issue were only superficially similar. However, magnetic field strength’ (Einstein to Besso, July 28, 1925; Speziali, reading Reichenbach's 1928 monograph against the background of 1972, 209–210). this issue reveals a quite different view of his interpretation of Einstein's enthusiasm for this approach was again a flash in the general relativity. If general relativity dressed the gravitational field pan. The paper was published in September, but by Christmas of in a geometrical ‘cloak’, as Reichenbach put it, “one should not 1925 Einstein confessed his skepticism to Besso, revealing that he confuse the cloak [Gewand] with the body which it covers” had returned to a set of field equations he had presented in 1919 (Reichenbach, 1928, 354; tr.
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