Abstract
In the mid-1950s, John Archibald Wheeler radically changed his research agenda, from nuclear physics to general relativity, establishing in Princeton one of the most important hubs of the renaissance of relativity. We reconstruct Wheeler’s turnaround based on his notebooks and a series of talks he gave in this period, including a talk in Japan, which is here published in English for the first time. Wheeler’s motivation is then analyzed in terms of the notion of the untapped potential of general relativity, which has been identified as the key epistemic factor in the renaissance of general relativity.
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Notes
- 1.
Wheeler apparently resented the term “relativist,” feeling that it implied too narrow a specialization on relativity (Bartusiak 2015, 91). We will still be using this term to denote a physicist with expertise in general relativity, making no value judgments about that physicist’s expertise in other areas of physics.
- 2.
Oral History Interview by Gloria Lubkin and Charles Weiner, conducted on 5 April 1967. https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4958. Accessed 11 September 2019.
- 3.
Wheeler’s transition has also been recently studied by Dean Rickles (2018). That analysis focuses more on a before-after comparison, as well as on the geon paper and its aftermath, not on the details of Wheeler’s transition, as we do in this paper. It thus makes good complementary reading.
- 4.
I shall be referring to this collection simply as “Wheeler Papers” throughout the text. Other archives consulted are the Albert Einstein Archives at the Hebrew University of Jerusalem, Israel (“Einstein Papers”), the Gregory Breit Papers (MS 1465) at the Archives at Yale, New Haven, CT, USA (“Breit Papers”) and the Richard P. Feynman Papers (FeynmanRP2) at the Caltech Archives, Pasadena, CA, USA (“Feynman Papers”).
- 5.
As analyzed in detail in (Blum 2019). That book and this chapter represent key case studies for work of the research group Historical Epistemology of the Final Theory Program at the Max Planck Institute for the History of Science.
- 6.
https://www.aip.org/history-programs/niels-bohr-library/oral-histories/5063-1. Accessed 11 September 2019. For WL see footnote 2.
- 7.
- 8.
We shall have no more to say about “Everything as Scattering,” which was here mentioned only to illustrate the early traces of daring conservatism in Wheeler’s thinking. This notion was very influential in Feynman’s later diagrammatic formulation of renormalized QED, which did effectively become a pure scattering theory, see Blum (2017).
- 9.
Oral History Interview by Charles Weiner, 5 March 1966. https://www.aip.org/history-programs/niels-bohr-library/oral-histories/5020-2. Accessed 14 September 2020.
- 10.
The number of pages that this manuscript has depends on how exactly one counts, e.g., if one includes handwritten inserts, typed pages containing just one extraneous paragraph, and figure captions. A case can certainly be made for 27.
- 11.
We would like to thank André Bernard of the John Simon Guggenheim Memorial Foundation for making this and other documents available to us. The entire dossier relating to Wheeler’s application and Scholarship is on file at the Guggenheim Foundation. It contains Wheeler’s application (where the above quote is to be found in Item 3, pp. 1–2), as well as several letters quoted below.
- 12.
Letter from Wheeler to Bohr, 21 January 1950. Archives for the History of Quantum Physics, Bohr Scientific Correspondence, Microfilm 34.
- 13.
One reason for Wheeler’s return to action-at-a-distance gravity after so many years appears to have been that it had by then become abundantly clear that quantum gravity would suffer from similar divergence difficulties as QED, difficulties that in electrodynamics the Wheeler-Feynman absorber theory had aimed to solve. Since these difficulties could not be solved by renormalization in the case of gravity, it appeared attractive to revisit the old AAD formulation. This was pointed out to us by Daniel Wesley, who co-authored the AAD gravity paper with Wheeler as an undergraduate student, in an email to one of the authors (AB), 11 April 2019.
- 14.
We will also be using a notation that Wheeler introduced only after his letter to Einstein. This is additionally motivated by the fact that reproducing Wheeler’s notation in the Einstein letter presents somewhat of a typesetting challenge.
- 15.
In general, the forward light cone might intersect the other world line more than once. The liaison was supposed to be a single-valued function that singles out one of those points and thus constituted an object somewhat more restricted than a light cone.
- 16.
In general, it is of course possible to first move along the forward light cone from world line a to world line b and then back, along the backward light cone, to world line a and arrive at a point different from the point one started out from, when conjugate points are involved. In the liaison framework, this issue is avoided: As mentioned in footnote 15, the liaison has to be a single-valued function, and thus it was natural on many levels for Wheeler to simply define the backward liaisons as the inverses of the forward ones.
- 17.
The two-body solutions by Weyl and Levi-Cività that Einstein was referring to are discussed in detail in an editorial footnote of the Collected Papers of Albert Einstein (Kormos-Buchwald et al. 2018, 437).
- 18.
We will be citing frequently from Wheeler’s first two relativity notebooks, which we will be abbreviating as WR1 and WR2, respectively. These notebooks are to be found in Wheeler Papers, Section V, Volumes 39 and 40.
- 19.
Interview on 10 July 1984 with Churchill Eisenhart conducted by William Aspray, available at https://www.princeton.edu/mudd/finding_aids/mathoral/pmc09.htm. Accessed 17 July 2016. In this interview, Churchill Eisenhart also recalls that the manuscript for Wheeler and Eisenhart’s book disappeared under mysterious circumstances after Luther Eisenhart’s death.
- 20.
For biographical information on Eisenhart, see Lefschetz (1969).
- 21.
Kaiser erroneously gives the year of Wheeler’s first course as 1954/1955. The 52/53 course, which is well documented by Wheeler’s notebook, indeed did not yet show up in the Princeton course catalogue. A course on relativity by Wheeler is listed for 1953/1954. This course catalogue had not been available to Kaiser at the time he wrote his paper.
- 22.
On Wheeler’s role in ensuring that the institutionalization of research in general relativity would take place in the disciplinary context of physics, see Lalli (2017).
- 23.
- 24.
He had been pointed to these mathematical works by Arthur Wightman; WR1, p.121.
- 25.
For more details, see Blum and Rickles (2018).
- 26.
This assessment is based on Lehmkuhl (2019).
- 27.
According to the recollections of Wheeler’s student Marcel Wellner, Einstein had apparently not thought about Mach’s principle in a long time (Wheeler 1979) when it came up during the visit of Wheeler’s class. But less than a year after that visit, Einstein was asked about the matter again, by Felix Pirani. Einstein expressed his surprise at the renewed interest, opening his letter of 2 February 1954 (Einstein Papers, 17–447) with the words: “There is a lot of talk about Mach’s principle.” By that time, apparently having rethought the matter following the meeting with Wheeler and his students, Einstein had convinced himself that the principle was obsolete, telling Pirani: “In my opinion, one should not speak of Mach’s principle at all any more.”
- 28.
Arthur Komar offered a more specific account of Einstein’s dismissal of Einstein-Rosen bridges, recalling: “John Wheeler asked him about the Einstein-Rosen bridge. Why had he first introduced it and then dropped it again? Einstein answered that he had initially believed that the bridge connects two almost plane surfaces in a unique manner. When he, however, discovered that they did not have a unique structure, the bridge seemed to him to be too cumbersome, unattractive, and ambiguous” (Wheeler 1979). (John Wheeler fragte ihn über die Einstein-Rosen-Brücke. Warum habe er sie zunächst eingeführt und dann wieder fallengelassen? Einstein antwortete, dass er zunächst glaubte, die Brücke verbinde zwei fast ebene Flächen in eindeutiger Weise. Als er jedoch entdeckte, dass sie keine eindeutige Struktur war, schien ihm die Brücke zu schwerfällig, unattraktiv und vieldeutig.) These still rather vague recollections might be of Einstein referring to the fact that he had hoped that multi-bridge solutions to the Einstein equations might be so constrained as to enforce equal masses for the individual bridges, thereby addressing the problem discussed earlier of explaining why only a few different mass values for elementary particles were observed. He ultimately appears to have concluded that no such constraints would arise, as stated in a letter to Richard Tolman of 23 May 1935 (Einstein Papers, 23–32): “One does not see why the ponderable and electric masses cannot be arbitrarily large or different, when several are present.” Many thanks to Dennis Lehmkuhl for discussions on the Einstein-Rosen paper and for making this letter available to us.
- 29.
According to the notebook (Wheeler Papers, Box 156) that Wheeler kept during his stay in Japan, the translation was done by Takahiko Yamanouchi; Japan Notebook p. 51.
- 30.
In a manuscript entitled “The Zero Rest Mass Fundamental Field Hypothesis” (WR, p. 101), which we shall discuss later in more detail, Wheeler ascribes this vision of a theory with no free parameters to Einstein. We have not been able to find relevant statements in Einstein’s work.
- 31.
Wheeler here also invoked, for the first time, Bohr as the godfather of daring conservatism, because Bohr had applied “electrostatics to very small distances” in his atomic model.
- 32.
No correspondence between Wheeler and Reines or Cowan from 1953 is extant, but Reines in turn was clearly aware of Wheeler’s contemporaneous elevation of the neutrino to central stage. In his Nobel lecture, Reines makes an inside joke, remarking without mentioning Wheeler: “While we were engaged in this background test, some theorists were rumored to be constructing a world made predominantly of neutrinos!”
- 33.
Here Wheeler was following in the footsteps of a number of famous physicists who had attempted to derive the value of the fine structure constant (which for a long time looked like it might be precisely 1/137) in the preceding decades. See Kragh (2003).
- 34.
Indeed, Einstein appears to have been impressed. While first remarking that he “abhorred” the idea of first constructing the classical field theory and then quantizing it, he then conceded (according to Wheeler’s notes) that “it was the first time he had ever heard describe a way that [quantum theory] might get through, found it very attractive.”
- 35.
While Wheeler (1961) would later conclude that point singularities were not a valid approximation for any reasonable model of matter (which by that time for him meant geons and wormholes), there is no indication that he (or anybody else) harbored such doubts in 1953/1954, given that the concepts and in particular the conception of matter that these conclusions were based on had not been developed yet.
- 36.
The paper is included in WR2, p. 101, as an insert. This copy is noteworthy also for some remarks in the margins in which Wheeler explicitly connects his conservative heuristic in physics with conservatism in politics, noting: “To defend well established physical ideas as unpopular as defending well established political parties. People like to criticize. Religion the great defender.” In this connection it appears pertinent to mention that Wheeler’s conservative stance (in physics), as outlined in the Tokyo talk, was explicitly criticized by the Japanese physicist Shoichi Sakata, an outspoken Marxist (Staley 2001). In discussions on September 18 at the conference in Kyoto, a week after Wheeler’s lecture, Sakata remarked: “I am convinced the future theory should not be the progressive improvement of the present theory. At the Tokyo meeting, Professor Wheeler pointed out that there are two methods of approaching the truth, that is, Saigo Takamori’s method and Sugawara Michizane’s method. But in Japan Professor Tomonaga had pointed out that there are two ways, namely, a non-reactionary conservative way and also a revolutionary way. This is our common sense.” (Proceedings of the international conference of theoretical physics, Kyoto and Tokyo 1954, 34–35).
- 37.
Here Wheeler already pondered the possibility of having “outgoing lines of force […] understood in terms of lines coming in from an ‘internal universe,”’ an idea that would later mature into his notion of a wormhole.
- 38.
Here Wheeler encountered some conservative resistance from Wightman, who objected to Wheeler’s predilection for path integrals, arguing instead that one should “improve & understand present formalism,” i.e., pursue axiomatic quantum field theory. Even Feynman appears to have been doubtful about the “general utility” of the path integral, as he had not yet been able to properly accommodate fermions.
- 39.
The AAPT was conducting its winter meeting in parallel with the American Physical Society, which conducted its annual meeting at Columbia University from 28 to 30 January 1954 (Physical Review, Volume 94, pp. 742ff), so that there were also many research physicists in the audience.
- 40.
The lecture was never published, but there is an extant transcript in the Wheeler Papers, Box 182, in a folder entitled “Fields and Particles.” The Richtmyer Lecture Memorial Award had been established in 1941 to honor Floyd Richtmyer, one of the founders of the AAPT (https://www.aapt.org/Programs/awards/richtmyer.cfm). Accessed 14 September 2019. Many of the previous lectures had been published in the AAPT’s journal, the American Journal of Physics (e.g., Slater 1951; Vleck 1950; DuBridge 1949). Wheeler had plans to publish his lecture there as well, and the folder contains two revised versions of the original lecture transcripts, which were clearly supposed to lead up to a publication. The folder also contains some correspondence between Wheeler and Thomas Osgood, editor of the American Journal of Physics, such as a letter from Osgood of 28 January 1957, which begins: “Here is my annual letter of inquiry about the manuscript of the paper ‘Fields and Particles’ that you gave as Richtmyer Memorial Lecture during the meeting of the American Association of Physics Teachers in New York, January 28–30, 1954. It ought to be published without delay.” Wheeler in fact cited the paper in the first footnote of the geon paper as “to be published.” That long footnote (a specialty of Wheeler, to which this footnote here is a sort of tribute) also contained a reference to Wheeler’s Tokyo talk and “the point of view ascribed by the author to Sugawara-no-Michizane,” making the entire footnote rather enigmatic for the average American reader of The Physical Review.
- 41.
This passage is from Philippians 4:8, where it reads “honest” instead of “honored”, “just” instead of “judged”, and “report” instead of “repute.” We have given the quote as it appears in the lecture transcript, and it is to be assumed that the transcriber simply misheard these three words. Wheeler corrected all three in the later manuscripts of the Richtmyer Lecture mentioned in footnote 40.
- 42.
Then still referred to as a “Kugelblitz” or, in the words of the person who transcribed the lecture, “cugoflix.”
- 43.
Many thanks to the Physical Society of Japan for letting us publish this translation free of charge.
- 44.
The authors would also like to thank Lisa Onaga and Masato Hasegawa (both Max Planck Institute for the History of Science) for additional input. We have freely edited the translation based on our understanding of the context and the physics involved, so all mistakes should be considered ours.
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Blum, A.S., Brill, D. (2020). Tokyo Wheeler or the Epistemic Preconditions of the Renaissance of Relativity. In: Blum, A.S., Lalli, R., Renn, J. (eds) The Renaissance of General Relativity in Context. Einstein Studies, vol 16. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-50754-1_5
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