Abstract
After the attempts at unifying the electromagnetic and gravitational fields by H. Weyl and A. S. Eddington, A. Einstein quickly became a central and driving figure in this research. His concept of unifying fields via geometry (affine or metric-affine) was taken up by others like E. Schrödinger in Dublin, M.-A. Tonnelat in Paris, B. Finzi in Milano, V. Hlavatý, Bloomington, Indiana, and their collaborators. Larger groups also existed in Japan and India. Worldwide, not many more than 170 physicists and mathematicians took part in this research. After a sketch of the geometrical and physical concepts involved, I briefly describe some scientific relations among various persons/groups and the changing interest in research concerning classsical unified field theory during the period investigated (ca. 1930 to the 1960s).
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Notes
- 1.
The Italian groups around Bruno Finzi (1899–1974) and Maria Pastori (1895–1975) will be taken into account in Section 14.4.2.
- 2.
This 2nd part will, hopefully, be ready during 2010.
- 3.
The skew-symmetrical part appears in the “angle” and leads to an unwanted property: The angle between X und Y is different from the angle between Y and X: \(cos(\angle (X,Y)) - cos(\angle (Y,X )) = 2 \frac {k_{ij} X^i Y^j}{|X||Y|} \neq 0\).
- 4.
Note that the symmetric and skew-symmetric parts have their own inverses.
- 5.
For an arbitrary curved surface there is no a priori rule when to call vectors in different points as being parallel.
- 6.
The name used in the Paris group for Equation (14.8), i.e., “equation de liaison” does not carry a physical interpretation.
- 7.
The gauge idea was successfully resurrected in 1928, however, within quantum mechanics. It later played a big role within non-abelian gauge theories.
- 8.
Note that alternative curvature tensors could and have been defined.
- 9.
We cannot discuss here the many different possibilities for building symmetric rank 2 tensors from the curvature tensor.
- 10.
Thus 84 field equations hold for the 80 variables.
- 11.
\( A_{,~j} := \frac {\partial A}{\partial x^j}\).
- 12.
Note that another possibility would have been \(\frac {1}{2}g^{kr} (g_{ri,~j} + g_{jr,~i} - g_{ji,~r})\equiv \{.. \}_{Hattori}+ 2 k^{kl}h_{lm}\{{ }_{ij}^m \}_{h} + \theta ^{~~k}_{ij}\) with \(\theta ^{~~k}_{ij}= \frac {1}{2}k^{kr}(k_{ri,j} + k_{jr,i} - k_{ji,r})~.\)
- 13.
It is the “Bose” from Bose-Einstein statistics.
- 14.
Maurer-Tison introduced
$$\displaystyle \begin{aligned} g_{\alpha \beta} &= h_{\alpha \beta} + k_{\alpha \beta}, \\ g^{\alpha \beta} &= l^{\alpha \beta} + m^{\alpha \beta}. \end{aligned} $$ - 15.
q is another constant.
- 16.
At present, my databank contains 632 papers from 1930–1965.
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Goenner, H. (2018). Unified Field Theory up to the 1960s: Its Development and Some Interactions Among Research Groups. In: Rowe, D., Sauer, T., Walter, S. (eds) Beyond Einstein. Einstein Studies, vol 14. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-7708-6_14
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