"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

20 Concluding Comment

A leafing through the pages of this review of the history of classical unified field theory in the years between the mid 1930s and mid 1960s will suggest that some historians of physics, and almost all journalists writing about the evolution of classical unified field theories or “Theories of Everything” adjust their published views: their focus on Einstein’s work in this field is not only excessive but unrealistic. This is due to at least two counts:
  1. Others like Schrödinger, Hlavatý and the totally neglected French groups (Tonnelat, Lichnerowicz) – not to point to the many further names given in this review – have contributed equal shares;
  2. In this field, Einstein has not produced novel ideas from which physics and mathematics could have benefited conceptually (cf. Section 18.1.2). Certainly, he was the most prominent player; it is fair to say that without the influence of the three eminent Nobel prize winners Einstein, Schrödinger and de Broglie (who backed M.-A. Tonnelat), the active period of research in classical UFT would have been shorter-lived, and its history much easier to write.

It remains a riddle why the signs pointing to a dead end of the Einstein–Schrödinger research-line of unified field theory, already highly visible before the 1950s, were overlooked or pushed aside by Einstein and others for so long: the flood of geometrical structures drowning a small number of physical concepts, the ambiguity in the dynamics for the “total field” (Lagrange density), the almost total lack of empirically testable output. Kaluza–Klein theory as the other type of unitary field theory fared much better. In combination with Weyl’s second attempt toward a gauge principle, it paved the way to Yang–Mills theory able to describe the fundamental interactions with the exception of the gravitational. The final form of a generally accepted gauge theory of gravitation is still being discussed. Unfortunately, since the late 1930s, Einstein had written off Kaluza–Klein theory (cf. Section 3.2) and thus cannot be held in esteem for the successes of gauge theory.

In the wording of this review, the avowal, encountered occasionally, that Einstein’s papers were read “sympathetically”, will not be found. Like the papers of all other researchers, I tried to read his publications as neutrally as possible. While valuating research according to its place inside the body of unified field theory, I strove to judge past research from the physics at the time, not from the angle of the up-to-date state of the art. I am aware of the limits to this: the increase of knowledge since the period looked at, cannot be blanked out completely. Vice versa, no lesson from failed classical unified field theories is drawn here with regard to actual speculative theories with their claim to unify all four fundamental interactions. We just hope that current scientific practitioners are prepared to learn from the history of physics.

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