"On the History of Unified Field Theories. Part II. (ca. 1930 – ca. 1965)"
Hubert F. M. Goenner 
1 Introduction
2 Mathematical Preliminaries
2.1 Metrical structure
2.2 Symmetries
2.3 Affine geometry
2.4 Differential forms
2.5 Classification of geometries
2.6 Number fields
3 Interlude: Meanderings – UFT in the late 1930s and the 1940s
3.1 Projective and conformal relativity theory
3.2 Continued studies of Kaluza–Klein theory in Princeton, and elsewhere
3.3 Non-local fields
4 Unified Field Theory and Quantum Mechanics
4.1 The impact of Schrödinger’s and Dirac’s equations
4.2 Other approaches
4.3 Wave geometry
5 Born–Infeld Theory
6 Affine Geometry: Schrödinger as an Ardent Player
6.1 A unitary theory of physical fields
6.2 Semi-symmetric connection
7 Mixed Geometry: Einstein’s New Attempt
7.1 Formal and physical motivation
7.2 Einstein 1945
7.3 Einstein–Straus 1946 and the weak field equations
8 Schrödinger II: Arbitrary Affine Connection
8.1 Schrödinger’s debacle
8.2 Recovery
8.3 First exact solutions
9 Einstein II: From 1948 on
9.1 A period of undecidedness (1949/50)
9.2 Einstein 1950
9.3 Einstein 1953
9.4 Einstein 1954/55
9.5 Reactions to Einstein–Kaufman
9.6 More exact solutions
9.7 Interpretative problems
9.8 The role of additional symmetries
10 Einstein–Schrödinger Theory in Paris
10.1 Marie-Antoinette Tonnelat and Einstein’s Unified Field Theory
10.2 Tonnelat’s research on UFT in 1946 – 1952
10.3 Some further developments
10.4 Further work on unified field theory around M.-A. Tonnelat
10.5 Research by and around André Lichnerowicz
11 Higher-Dimensional Theories Generalizing Kaluza’s
11.1 5-dimensional theories: Jordan–Thiry theory
11.2 6- and 8-dimensional theories
12 Further Contributions from the United States
12.1 Eisenhart in Princeton
12.2 Hlavatý at Indiana University
12.3 Other contributions
13 Research in other English Speaking Countries
13.1 England and elsewhere
13.2 Australia
13.3 India
14 Additional Contributions from Japan
15 Research in Italy
15.1 Introduction
15.2 Approximative study of field equations
15.3 Equations of motion for point particles
16 The Move Away from Einstein–Schrödinger Theory and UFT
16.1 Theories of gravitation and electricity in Minkowski space
16.2 Linear theory and quantization
16.3 Linear theory and spin-1/2-particles
16.4 Quantization of Einstein–Schrödinger theory?
17 Alternative Geometries
17.1 Lyra geometry
17.2 Finsler geometry and unified field theory
18 Mutual Influence and Interaction of Research Groups
18.1 Sociology of science
18.2 After 1945: an international research effort
19 On the Conceptual and Methodic Structure of Unified Field Theory
19.1 General issues
19.2 Observations on psychological and philosophical positions
20 Concluding Comment

18 Mutual Influence and Interaction of Research Groups

18.1 Sociology of science

18.1.1 Princeton and UFT

Einstein’s unified field theory makes a good example for showing that the influence of a model scientist may be as important in driving research as ideas coming from physics or mathematics themselves. A realistic impression seems to be that most in the group of young workers busy with Einstein’s UFT after the second world war were enticed by Einstein’s fame and authority – perhaps mediated through the prestige of their professorial advisers. They went into the field despite its being disdained by mainstream-physicists. In view of the success of quantum field theory, it could hardly have been the methods and conceptions used in UFT that attracted them. In fact, many of those who wrote a doctoral thesis in the field dropped the subject quickly afterwards in favor of general relativity proper, or of some other field. It would be unfair to give too much importance to J. R. Oppenheimer’s reckless rating of 1935 (unpublished at the time), i.e., “Princeton is a madhouse: its solipsistic luminaries shining in separate & helpless desolation. Einstein is completely cuckoo” (Letter of J. R. Oppenheimer to his brother Frank from 11 January 1935 in [462], p. 190.) After all, much later during his time as director of the Institute for Advanced Study there, he supported people working on versions of UFT like R. L. Arnowitt who stayed at the Princeton Institute for Advanced Study from 1954 to 1956 and expressly thanked him in a paper ([5], p. 742). Nevertheless, while highly respected, Einstein and his theories lived there in splendid scientific isolation.

18.1.2 Mathematics and physics

Looking at the mutual “directions of influence” between mathematics and physics in the field described here, we may distinguish three fruitful exchanges. It is known that the mathematician Grossmann provided Einstein with the Ricci-calculus as a means of formulating General Relativity within Riemannian geometry. This very theory then radiated back into mathematics and helped to further study the previously introduced most general concept of affine connection (G. Hessenberg, T. Levi-Civita, E. Cartan, H. Weyl). Next, the transfer of this new geometrical concept into physics led to the unified field theories of Eddington, Einstein, and Schrödinger [138, 546, 548]. It seems to me that after this third interaction mathematics (geometry) no longer did profit from physical theory: the conceptual development of metric-affine geometry took place independently within mathematics (L. P. Eisenhart, O. Veblen, J. M. Thomas, T. Y. Thomas). Einstein’s approach to a connection by way of the compatibility equation (30*) was of very limited interest for mathematics. This was expressed most clearly by Schouten:

“[…] in the end there is nothing but an X4 [a 4-dimensional manifold] with only two fields g (ij) and g [ij] and that […] the differential concomitants of these fields are ordinary concomitants of g(ij),g[ij], the curvature tensor of the symmetric connection belonging to g(ij) and the covariant derivatives of these quantities with respect to this connection. […] It may be useful to introduce this new connection in order to get some heuristic principles […]. But nothing really new can ever arise from following this course.” ([540], p. 184.)

Unified field theory has stimulated the fantasy of mathematicians such that they investigated conformal geometry [670] and projective geometry [538], or even ventured to apply odd geometries to geometrize physics. We have met some of them (Finsler, Sphere-, Lyra geometries). Certainly, mathematicians also both helped theoretical physicists to solve their equations and invented new equations for UFT. Unfortunately, to the exact solutions of such equations found, in most cases no physical meaning could be given. In physics, the next step in unification would be taken only in the 1960s through the joining of the weak and electromagnetic interactions in electroweak theory with gravitation being left aside, however. In mathematics, important developments leading to differential topology as well as to the theory of fiber bundles originated with E. Cartan among others – not with any of the theoretical physicist connected to the unified field theories of Einstein and Schrödinger. Gauge theory, seen as a development starting from Kaluza–Klein theory, and, more recently, string-theory (M-theory) then presented further examples for a fruitful interaction between physics and mathematics.

18.1.3 Organization and funding

Apart from the creative abilities of the individual scientist, knowledge production depends on the institutional organization of research and the ways of communication among researchers. Thus, within a review of the history of physics, beside the conceptional developments, questions pertaining to the sociology of science cannot easily be omitted.

During the period looked at, both, changes in the funding of scientific research, and in the institutional organization toward team work and less interaction with teaching, i.e., away from university research along Humboldt’s idea of a close link between teaching and research, still were going on. In Germany, this development had begun with the establishment of the Kaiser Wilhelm Institutes (KWI, now Max Planck Institutes) since 1911, a combination of private and state funding, together with “Helmholtz-Gesellschaft”, “Stifterverband”, and most influential, the “Notgemeinschaft der deutschen Wissenschaft” predecessor of “Deutsche Forschungsgemeinschaft” since 1920 [676]. In France, where state-funding was the rule, the apparently not very successful “Caisse des recherches scientifiques” (1910 – 1934) was replaced by CNRS (Centre National de la Recherche Scientifique) only in 1939, right after the beginning of World War II. Of particular interest for the present review is the foundation of the Institut Henri Poincaré (IHP) in 1926 [579] which was built with private money but did not provide salaries. In the United States mostly private sponsors were involved; e.g., the Carnegie Corporation (1911), the Rockefeller Foundation (1913) and Einstein’s “home” institution, the Princeton Institute for Advanced Study (PIAS) (since the 1930s). The Dublin Institute for Advanced Studies in Ireland (DIAS) was founded in 1935, but funded by the government (Department of Education).300 In Great Britain, after the Great War a mixture of state and private funding (University grants commission, Science Research Council) persisted, coordinated in part by the Royal Society. After the 2nd world war 35 Research Associations have sprung up.

Looking at four main figures in UFT, Einstein’s and Hlavatý’s research thus depended on private donors while Schrödinger in Dublin, Lichnerowicz, and Mme. Tonnelat in Paris were state-funded. Within this external framework, there existed micro-structures pertaining to the inner workings of the particular research groups.

18.2 After 1945: an international research effort

During the second world war, communications among the various scientists investigating UFT came to a halt – with the exception of the correspondence between nobel prize winners Einstein and Schrödinger. That the exchange between libraries then only slowly began to resume is clear from a letter of A. Lichnerowicz to W. Pauli of 6 October 1945: “In France, only one copy of Mathematical Review and one copy of the series Annals [of Mathematics] exist. Concerning the paper of Einstein published in 1941 at Tucuman, I know about it only through the report in Mathematical Review; it never reached France” ([489*], p. 317).301View original Quote

From hindsight, after the second world war, research in classical unified field theory developed into a world-wide research effort. However, at the time it was no concerted action with regard to funding and organization; the only agreement among researchers consisted in the common use of scientific methods and concepts. As described in detail above in Sections 7 to 9, since the 1920s, it had been mainly Albert Einstein (1879 – 1955) who had pursued research on UFT if we put aside H. Weyl and A. S. Eddington. Since his separation from Berlin, most important actors of the 1930s and 1940s were Einstein himself in Princeton, and somewhat later (from 1943 on) Erwin Schrödinger (1887 – 1961) in Dublin. After the war, in Paris the mathematician André Lichnerowicz (1915 – 1998) became interested in mathematical problems related with UFT, and a student of Louis de Broglie, and later professor Marie-Antoinette Tonnelat (1912 – 1980), built a sizable group working in the field. From the 1950s on Vavlav Hlavatý (1894 – 1969) in Bloomington/Indiana and his collaborators contributed prominently to the field. The Italian groups around Bruno Finzi (1899 – 1974) and Maria Pastori (1895 – 1975) were not as influential in the 1960s, perhaps because they wrote exclusively in Italian, published mostly in Italian journals and seemingly deemed networking less important although there were connections to France and the USA (cf. Sections 10 to 15).

18.2.1 The leading groups

The internal structure of the research “groups” differed greatly: in Princeton (as in Berlin), Einstein never had doctoral students but worked with post-docs like Peter Bergmann, Bannesh Hoffmann, Valentine Bargmann, Leopold Infeld, Bruria Kaufman, and Ernst Straus302. At the time, further people interested in unified field theory came to the Princeton Institute for Advanced Study (PIAS), e.g., Tullio Levi-Civita (1936), Vaclav Hlavatý (1937), Luis A. Santaló (1948 – 49) from Argentina, M. S. Vallarta from Mexico (1952), Wolfgang Pauli (1940 – 1946; 1949 – 50), Richard Lee Ingraham (1952 – 53), R. L. Arnowitt (1954 – 55), both from the USA, and D. W. Sciama (1954 – 55) from Great Britain. Schrödinger also worked with scientifically advanced people, mostly independent scholars at DIAS (J. McConnell, A. Papapetrou, O. H. Hittmair, L. Bass, F. Mautner, B. Bertotti). Unlike this, A. Lichnerowicz at the Collège de France and Mme. Tonnelat at the Institut Henri Poincaré (IHP) worked with many doctoral students. M.-A. Tonnelat had also two experienced collaborators whom she had not advised for her doctoral theses: Stamatia Mavridès [1954 – 57] and Judith Winogradzki [1954 – 59]. None of these scientists in Paris have been scholars at the Princeton Institute; possibly, they did not belong to the proper network.

The following students and young scientists wrote their PhD theses in M.-A. Tonnelat’s group at the IHP or were interacting intensely with her on the Einstein–Schrödinger type of Unified Field Theories, and on linear theories of gravitation: Jacques Lévy – Thèse 1957; Pham Tan Hoang – Thèse 1957; Dipak K. Sen – Thèse, 1958; Jean Hély – Thèse 1959; Marcel Bray – Thèse 1960; Liane Bouche, née Valere – Thèse 1961; Huyen Dangvu – Thèse 1961; Mme. Aline Surin, née Parlange – Thèse 1963; Nguyên, Phong-Chau; – Thèse 1963; Philippe Droz-Vincent – Thèse 1963;303 Sylvie Lederer – Thèse 1964; Huyen Dangvu – Thèse 1966, Rudolphe Bkouche – Thèse 196?. S. Kichenassamy wrote his thesis with her on general relativity in 1958. That M.-A. Tonnelat advised doctoral students also on subjects outside of unified field theory is shown by the thesis of 1974 on classical renormalization by Th. Damour [99].

Scientists and PhD students closer to A. Lichnerowicz besides Yvonne Bruhat / Fourès(-Bruhat) / Choquet-Bruhat – Thèse 1951, but unlike her working on Unified Field Theories, were: Yves Thiry – Thèse 1950; Pham Mau Quan – Thèse 1954; Josette Charles, née Renaudie – Thèse 1956; Françoise Maurer, née Tison – Thèse 1957; Françoise Hennequin, née Guyon – Thèse 1958; Pierre V. Grosjean – Thèse 1958; Robert Vallée – Thèse 1961; Albert Crumeyrolle – Thèse 1961; Marcel Lenoir – Thèse 1962; Jean Vaillant – Thèse 1964;304 Claude Roche – Thèse 1969; Alphonse Capella – Thèse 1972?. Eliane Blancheton wrote her thesis in general relativity in 1961.

Y. Thiry also supervised doctoral students. Among them is P. Pigeaud with a thesis on the application of approximations in JordanThiry theory [495]. The thesis adviser for Monique Signore-Poyet was Stamatia Mavridès (Thesis 1968).305

The relationship between M.-A. Tonnelat and A. Lichnerowicz must have been friendly and cooperative; he seems to have been the more influential in the faculty: having become a professor at the prestigious Collège de France while her application had not been successful ([92], p. 330). For the examination of Tonnelat’s PhD-students, since 1960, Lichnerowicz was presiding the commission; she belonged to the two (or rarely three) examiners. Before Lichnerowicz, G. Darmois had been presiding several times. Tonnelat was backed by L. de Broglie; she became his successor as director of the “Centre de physique théorique” of Paris University (Sorbonne) in 1972.

From the Italian groups around Bruno Finzi and Maria Pastori (Milano) also a sizable number of doctoral degrees resulted. People working in UFT were: Paulo Udeschini (Pavia); Emilio Clauser (Milano); Elisa Brinis-Udeschini (Milano); Laura Gotusso (Milano); Bartolomeo Todeschini (Milano); Franco De Simoni (Pisa); Franca Graiff (Milano) [Student of M. Pastori]; Laura Martuscelli [Student of M. Pastori]; Angelo Zanella (Milano); Luigia Mistrangioli.

Of the seven doctoral students of V. Hlavatý,306 two were involved in work on UFT: Robert C. Wrede [PhD 1956] and Joseph Francis Schell [PhD 1957].

We notice the considerable number of female collaborators and PhD students both in France and Italy in comparison with all the other countries. In Germany, in particular, no woman scientist has worked in UFT in the period studied.

18.2.2 Geographical distribution of scientists

Research on UFT was done on all continents but essentially centered in Europe and in the United States of America. The contributing scientists came from more than 20 different countries. The largest number of researchers in UFT, between 1955 and 1956, worked in Paris. To a lesser extent work on UFT was done also in Asia, notably in Japan since the 1930s and in India since the 1950s. In the 1970s and 1980s, many papers on exact solutions of the Einstein–Schrödinger theory and alternatives were published by Indian scientists. In the early 1960s, V. Hlavatý had a coworker from India (R. S. Mishra). Of the six papers on UFT published by S. N. Bose in Calcutta from 1953 – 1955, five appeared in French journals, perhaps due to his contacts established during his previous stay in Paris in 1924/25.

Did those involved in UFT move from one place to another one? During the period considered, the mobility of scientists in Europe was seriously hampered by the Nazi-regime, the second world war and the ensuing occupation of Eastern Europe by the USSR (“cold war”). While doing their main work, the group leaders Einstein, Schrödinger, Lichnerowicz, and Tonnelat remained at the same place, respectively. After the war had ended, Tonnelat visited Schrödinger in Dublin. Because of the political situation, Hlavatý left his native Czechoslovakia, went to Paris as a guest professor at the Sorbonne (1948). He also spent some time in Princeton following an invitation by Einstein before obtaining a position at the University of Indiana. A. Papapetrou (1907 – 1997) who had obtained a doctoral degree at the Polytechnical University of Stuttgart, Germany, and had been professor in Athens, Greece, during 1940 – 1946, was the only major contributor to UFT who changed his positions several times. He first worked in Dublin until 1948, then at the University of Manchester until 1952 when he went to Berlin. There, he headed a group in general relativity at the Academy of Sciences of the GDR until 1962. From then on he stayed in Paris at the Institut Henri Poincaré until his retirement as a “Directeur de recherche” of the CNRS. Of course, there had always been exchanges between Paris and other centers, but they were not concerned with research on UFT. In 1946/47, the French mathematician Cecile Morette-[DeWitt] (1922 –) originally affiliated with the Joliot-Curie group, spent a year at the Institute for Advanced Studies in Dublin. She did not work with Schrödinger on UFT but with P. H. Peng on mesons. Another well-known French mathematician, Yvonne Choquet-Bruhat, who had written her dissertation with A. Lichnerowicz, in 1951/52 was at PIAS.

John Archibald Wheeler must have spent some time in Paris in 1949; he worked on atomic and nuclear physics, though. In 1957 the quantum field theorist Arthur Wightman was a guest scientist at the University of Paris and in 1963/64 and 1968/69 at IHES (Institut des Hautes Études Scientifiques) near Paris. Stanley Deser was a Guggenheim fellow and guest professor at the Sorbonne (University of Paris) in 1966/67, and in 1971/72 as a Fulbright Fellow. Tonnelat and Mavridès visited the Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Brazil, as guest professors in 1971. A. Lichnerowicz visited Princeton University in 1974, i.e., outside the period considered here.

18.2.3 Ways of communications

In 1923 to 1925, when research in classical unified field theory started, the only ways of communication among scientists apart from personal visits or encounters during the rare international conferences, were notes on paper in the form of personal letters by surface mail (Einstein and Pauli are famous for their postcards), and publications in scientific journals. Correspondence sometimes included manuscripts or proof sheets. Both, Einstein and Hlavatý left an enormous correspondence.307 The most notable change in available services during the period 1930 – 1960 was the introduction of air mail and wireless services (world wide telex, since the 1930s) including radio broadcasts.308 Radio broadcast as well as gramophone records (Einstein in Berlin!) were used mainly for educational purposes. In principle, telegrams also would have been available but they were unwieldy and too expensive for the communication of scientific content. To a lesser degree, the same may apply to the still costly telephone calls even within the same town.

The main meeting places seem to have been seminars of the various groups as there were in Paris:

  • Séminaire Janet (Séminaire de mécanique analytique et de mécanique céleste);
  • Séminaire de l’école normale supérieure;
  • Séminaire Théories physiques Institut Henri Poincaré [with invited talks by Einstein, Bonnor, Stephenson, Sciama, and others];
  • Séminaire de Physique théorique (Séminaire Louis de Broglie).
  • Séminaire de Physique mathématique du Collège de France (A. Lichnerowicz).
  • Séminaire sur la Mécanique quantique et les particules élémentaires (J. Winogradzki).

In London, a seminar on unified field theory existed at the University College (Imperial College) (ca. 1945 – ca. 1955) [G. Stephenson, C. Kilmister (1924 – 2010)], and continued at Kings College as a seminar on general relativity and cosmology initiated by the group around H. Bondi [F. Pirani, W. Bonnor, P. Higgs] (late 1950s – 1977).


In total, about 150 – 170 scientists did take part in research on UFT between 1930 and 1965. If we distinguish three age cohorts according to year of birth, then in the group born until 1900 we find 27 people, from 1901 – 1920 three more (30), and after 1921 18 persons. This is a biased preliminary survey among less than 50 % of all involved, because the birth dates of the then doctoral students, of not so well known researchers, and of many scientists in India and Japan could not yet be obtained. Another grouping would be concerned with the differentiation between mathematicians and theoretical/mathematical physicists working in the field: roughly one third of the contributors to UFT were mathematicians.

Knowledge production in UFT is reflected by a yearly average of 18 papers published.309 The maximum of a 5-year-average in published papers per year at a peak of 40 papers occurred in the years just before and just after Einstein’s death, i.e., in 1953 – 1957; the minimum with 4 papers in the period 1939 – 1943, i.e., during the years of the second world war. Looking at the absolute number of total yearly publications in UFT which appeared in Comptes Rendus de l’Académie des Sciences, Paris (French groups), and their percentage relative to papers on general relativity likewise published in Comptes Rendus, we conclude that the number of papers on UFT at most reached 20% of the papers on general relativity.

Do preferred journals exist in which researchers in the field of UFT published their research articles? Certainly, Einstein preferred the Annals of Mathematics, edited by Princeton University and, since 1933, co-edited by the Institute for Advanced Study. Likewise, Schrödinger used the Proceedings of the Royal Irish Academy and the Communications of the Dublin Institute for Advanced Studies, the organ of his home institution; M.-A. Tonnelat chose the Comptes Rendus de l’Academie des Sciences, Paris to which she had easy access through her former teacher L. de Broglie.310 Likewise, Lichnerowicz and the members of the French groups published first in Comptes Rendus. Finally, V. Hlavatý published mostly in a journal of his institution, Indiana University, i.e., in Journal of Rational Mechanics and Analysis. Thus, the main proponents of UFT did not have to submit their papers to an external refereeing process. However, all of the main figures did at some occasions; M.-A. Tonnelat and her coworkers also published in Journal de Physique et le Radium, Cahiers de Physique, and in Nuovo Cimento.311 V. Hlavatý sent his papers also to Italy (Rendiconti del Seminario Matematico dell’Università degli Studi di Padova, Rendiconti del Seminario Matematico, Università e Politecnico di Torino, Annali di Matematica), and to the Netherlands (Nieuw archief voor wiskunde), A. Lichnerowicz published in Rendiconti del Seminario Matemàtico e Fisico di Milano, etc. This remark is not meant as a criticism of quality but perhaps as an indication concerning the inaccessibility of many physics journals for papers on UFT.312

As mentioned above, during the period considered (mid-1930s – mid-1960s) continuous communication almost exclusively happened via surface mail or, later, also by air mail. Thus, it is understandable that Schrödinger’s papers, published during the war in the Proceedings of the Irish Academy, were not readily available in France, Italy, the USA, India or Japan. Schrödinger himself acknowledged having received information by correspondence with Einstein prior to publication of the Einstein–Straus-paper ([551], p. 44, footnote 3). Also, G. Bandyopadhyay in India learned of De Simoni’s paper of 1954 only later (before 1963) through Bonnor ([11], p. 660). Of course, after the second world war, communication sped up. Nevertheless, Japanese and Indian researchers in the field of UFT seemingly did not read French journals because no references to Tonnelat are given in papers by Takeno and Ikeda [297, 298]. However, in a note added in proof, Takeno and his co-authors then in 1951 acknowledged having received information about a paper by Tonnelat of the year before [602]. Rao [504] included Tonnelat’s book of 1955 and a paper by Mavridès of 1955 in his bibliography, but the way of listing shows that he might not have had them in his hands.

Although missing language skills did not forestall progress in the development of UFT, it might have been slowed down by it, in part. Knowledge of English and French was standard throughout Europe. Researchers in the United States apparently did not read articles in French. The large groups in Paris published mainly in French; the groups in Italy stuck to Italian such that the dissemination of their results occurred mostly via French authors (e.g., the books of M.-A. Tonnelat), or through occasional visitors like Corben. The German language had virtually vanished for use in publications about UFT after the second world war.


In order to obtain an impression of how people in the field interacted, the questions about co-authorships, inside and outside the various groups, may be asked. It was not to be expected that some of the group leaders, senior professors of the old style, would join to write a paper. This did not even occur between “colleagues” Marie-Antoinette Tonnelat and André Lichnerowicz in Paris if we leave aside the jointly edited proceedings of the Royaumont conference. As co-authors, we most often have the combination of group leader and co-worker/PhD student: Einstein & Straus, Einstein & Kaufman etc., Schrödinger & Mautner, Schrödinger & Papapetrou etc, M.-A. Tonnelat & Liane Bouche, M.-A. Tonnelat & Sylvie Lederer; A. Lichnerowicz & Y. Thiry, A. Lichnerowicz & Y. Fourès-Bruhat, Hlavatý & Sáenz. Remarkably, Tonnelat did not publish in UFT jointly with her co-workers Judith Winogradzki (1916 – 2006) and Stamatia Mavridès. Winogradzki worked on UFT from 1954 – 1956 and then on spinors. Mavridès on UFT from 1954 – 1957, and also on Tonnelat’s Euclidean theory of gravity from 1962 – 1964. Thereafter, she went into cosmology and astrophysics.

All four leading figures summed up their research in books or, as was the case with Einstein and Schrödinger, in sections of their books on special and general relativity.

Referee reports and citations

It is interesting to find out who reviewed papers on UFT for the Mathematical Reviews.313 Principal group leaders like Einstein (but his co-workers as well), Schrödinger, and Tonnelat are not among them except for Hlavatý. In Paris, only Yvonne Fourès/Choquet-Bruhat and Mme. J. Charles-Renaudie wrote reports. I checked only 128 papers; they were reviewed by 14 people, half of which were direct scientific contributors to UFT. Among the reviewers were six mathematicians.314 The theoretical physicist A. H. Taub is the one who wrote most reviews (31), followed by V. Hlavatý with 23 and M. Wyman with 20 reports.315 None of the papers by the Italian groups is in this sample. We note, however, that quite a few of such reviews are a mere description of the contents.

As to citations, the Italian group around Finzi, Pastori and Udeschini mostly referred to work inside the group. From the research done in other places, Princeton (Einstein, AE & Straus) is quoted most often (23 times); next in frequency are Schrödinger’s and Papapetrou’s research in Dublin (quoted 11 times) and Hlavatý’s papers (referred to 10 times). English authors (Bonnor, Stephenson) and French scientists (Lichnerowicz, Tonnelat) follow (4 times each). And vice-versa, by looking at the bibliographies in Tonnelat’s books [632, 641*], Italian authors stand for 7% of the entries, at best.

Citation of authors in Germany after the second world war (P. Jordan, E. Schücking, K. Just), occurred in research on scalar-tensor theory – as an outgrowth of Kaluza–Klein unitary theory – mainly by the Paris group.

18.2.4 International conferences and summer schools

During the time-span considered, due to the external circumstances only a handful of international conferences took place at which the subject of gravitation and unified field theory could have been discussed. Most famous are the Volta Conference, in 1927 in Como, and the fifth Solvay Conference on Electrons and Photons in the same year in Brussels. The first conference, held at Lake Como, led to the public introduction of the uncertainty principle by Niels Bohr and Werner Heisenberg. In the 5th Solvay conference, the leading figures were Albert Einstein and Niels Bohr. Einstein, disenchanted with Heisenberg’s “Uncertainty Principle”, unceasingly fought the statistical interpretation of quantum mechanics. In both conferences, the discussion was not about UFT, specifically, but on classical theory versus quantum theory. The second Volta conference did not take place until 1932; its topic was “Europe”. All further Volta conferences did not touch unified field theory. The same is true for the subsequent Solvay conferences: During the 11th Solvay Congress on “The structure and Evolution of the Universe” in 1958 the main topic discussed was “steady state” theory versus general relativistic cosmology; unified field theory remained untouched.

Since the 1960s, several international conferences on gravitation, as described by general relativity, were organized on a regular basis like the CNRS-colloquia and proceedings of the meetings by the International Society on Relativity and Gravitation. Three months after Einstein’s death, a “Jubilee Conference” took place in Bern, Switzerland, commemorating fifty years of relativity since the publication of Einstein’s famous 1905 paper on the electrodynamics of moving bodies. Two of its eight principal topics were aimed at Unified field theory; in fact, two plenary talks and three short communications concerning UFT out of the 36 spoken contributions by 32 scientists were then given. This conference was the starting one of a series organized by the “Committee on General Relativity and Gravitation”, later to be absorbed by the “International Society on General Relativity and Gravitation”. Follow-ups were GR-1: “Conference on the Role of Gravitation in Physics” in Chapel Hill, NC (Jan. 18 – 23, 1957), GR-2: Les théories relativistes de la gravitation. Colloques in Royaumont, France (21 – 27 June 1959), GR-3: “Conférence internationale sur les théories relativistes de la gravitation” in Warszawa and Jablonna (25 – 31 July 1962),316 GR-4 “International Conference on Relativistic Theories of Gravitation” in London (1965), GR-5 “Conference on Gravity” in Tbilisi (USSR) (1968). During the conference in Chapel-Hill, only one paper on unified field theory was given (by KursunĊglu), and, in a subsection of another one, by Lichnerowicz, “the Cauchy problem for the asymmetric theory” was dealt with. M.-A. Tonnelat and Y. Thiry as well as Ph. Droz-Vincent reported about their research in the GR-2 proceedings. In the subsequent GR-3 conference UFT was represented only marginally. In 1958, L. de Broglie and M.-A. Tonnelat organized a meeting in Paris on “Actual problems in the theory of relativity”. All but one of the articles were concerned with general relativity or astrophysics. By this, the move away from UFT is clearly seen [374]. Also, in April 1960, the first conference on the topic of gravitation in Japan, a “Symposium on Gravity”, was held at the Research Institute for Fundamental Physics. Unified field theory was not discussed [662*].

Summer schools sprang up like the Brandeis Summer Institute or the Summer Seminars on Applied Mathematics in Boulder and Ithaca, NY, since the 1960s. They reflected progress in the study of general relativity and relativistic astrophysics, but did not include any discussion of classical unified field theory. This can also be seen in the reports of a conference celebrating the 50th anniversary of general relativity in Berlin in 1965. J. A. Wheeler talked about “How is it today with Einstein’s idea to comprehend everything as geometry?” His comment on Einstein’s UFT was that none to Einstein’s attempts had been successful, some even had led to unphysical results. The main thrust of his talk was an obvious effort to establish the Princeton school as the modern successor of Einstein’s ideas (geons, wormholes, E-geometry) [697]. Thus, when communication in the form of conferences and summer schools finally was rapidly growing, since the mid 1960s, UFT was doomed: at best it came to be viewed as an old-fashioned pastime.317

The unfortunate parallelism C. Lanczos saw between the political changes caused by the dictatorships, “whether of the Russian, Italian or German variety”, and the development of theoretical physics toward theories with high predictability catering to the needs of “industry and technology”, after World War II, must be rejected. It was to serve a barely cloaked downgrading of quantum field theory in comparison with Einstein’s “refined abstract thinking, armed with the mighty tools of advanced mathematics […]” ([349], pp. 57–59).

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