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Mie’s Electromagnetic Theory of Matter and the Background to Hilbert’s Unified Foundations of Physics

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Foundations of Mathematics and Physics One Century After Hilbert

Abstract

On November 20, 1915, David Hilbert delivered a talk in Göttingen, presenting his new axiomatic derivation of the “basic equations of physics”. This talk is often remembered because, allegedly, Hilbert presented in them, five days prior to Einstein, the correct, generally-covariant equations of gravitation that lie at the heart of the general theory of relativity (GTR).

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Notes

  1. 1.

    Unless otherwise stated, all translations from German are mine.

  2. 2.

    For an historical account of light bending as a test for relativity, see [5]. For a parallel account of red shift, see [6].

  3. 3.

    Readers interested in an updated, thorough account of the research on the history of general relativity, including the topics discussed here, should consult the collection [27].

  4. 4.

    Letter from Mie to Hilbert, February 13, 1916. The letter is preserved in the Hilbert Nachlass, NSUB Göttingen, Cod Ms David Hilbert 254/2.

  5. 5.

    See the announcement in Jahresbericht der DMV 22 (1913), 27. We have no direct evidence of the contents of Born’s lecture at this time.

  6. 6.

    See the announcement in Jahresbericht der DMV 22 (1913), 207.

  7. 7.

    Sauer [30, 553] points out that “this assumption distinguishes Mie’s theory from the usual Maxwell theory with charges and currents as external sources are given by the usual Lorentz electron theory. This theory can formally be included into the general framework by letting \(\Phi \) depend on external sources, however, then \(\Phi \) would explicitly depend on the space-time variables.”

  8. 8.

    Mie’s letter is in Hilbert’s Nachlass, Staats- und Universitäts Bibliothek, Göttingen Göttingen - Cod Ms David Hilbert 254/1.

  9. 9.

    Actually, I made some efforts to gather documents related to this visit, unfortunately without much success. Nevertheless, I did find in Hilbert’s Nachlass in Göttingen the handwritten notes taken by an unidentified person at the first of Einstein’s lectures (Staats- und Universitäts Bibliothek, Göttingen, Cod Ms D Hilbert 724). These notes have now been published in [10, 586–90].

  10. 10.

    In present-day terms, this function would be more properly called a Lagrangian function, while the term “Hamiltonian” usually refers to functions involving momenta and representing the total energy of the system considered. For the purposes of the present article and for the sake of historical precision, however, it seems more convenient to abide by the original terminology.

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  1. Tel Aviv University, Tel Aviv, Israel

    Leo Corry

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  1. Leo Corry
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  1. Nice and Sophia Antipolis University, Nice, France

    Joseph Kouneiher

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Corry, L. (2018). Mie’s Electromagnetic Theory of Matter and the Background to Hilbert’s Unified Foundations of Physics. In: Kouneiher, J. (eds) Foundations of Mathematics and Physics One Century After Hilbert. Springer, Cham. https://doi.org/10.1007/978-3-319-64813-2_2

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