Advertisement

The mathematical origins of general relativity and of unified field theories

  • Elie G. Zahar
Workshop: Strucktur und Entwicklung Physikalischer Theorien
Part of the Lecture Notes in Physics book series (LNP, volume 100)

Abstract

In this paper I discuss the heuristic role which mathematics plays in physical discovery: first through the surplus structure which mathematics injects into physical principles which are given a mathematical formulation; secondly, through the realist interpretation of certain mathematical entities which appear at first sight to be devoid of any physical meaning. I then try to account for this dual role of mathematics in terms of a single philosophical principle, namely Meyerson's principle of identity. I finally apply these considerations to the study of two important questions; the questions namely of the continuity between STR and GTR (STR = Special Theory of Relativity, GTR = General Theory of Relativity) and of the emergence both of General Relativity and of the Unified Field Theories of Weyl, Eddington and Schrödinger-Einstein.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  1. 1.
    Cf. “Geometrie and Erfahrung” in: Einstein, Mein Weltbild, p. 119.Google Scholar
  2. 2.
    Cf. Oskar Becker, Grundlagen der Mathematik, pp. 144–167.Google Scholar
  3. 3.
    For the role which mathematical surplus structure plays in physics, cf. M. L. G. Redhead, “Symmetry in Intertheory Relations”, in: Synthese 32 (1975).Google Scholar
  4. 4.
    Cf. Bernhard Riemann, Collected Works, (Dover) pp. 272–273.Google Scholar
  5. 5.
    As above, p. 286.Google Scholar
  6. 6.
    Cf. Mach, Mechanics, Introduction. Also: Erkenntnis and Irrtum, pp. 164–182.Google Scholar
  7. 7.
    H. Weyl, Raum Zeit Materie, § 40.Google Scholar
  8. 8.
    Eddington, The mathematical Theory of Relativity, § 97.Google Scholar
  9. 9.
    Schrödinger, Space-Time Structure, Chapter XII.Google Scholar
  10. 10.
    Duhem, Aim and Structure of Physical Theory, Part 2,.Chapter 1.Google Scholar
  11. 11.
    For the important role which philosophical realism plays in the logic of discovery, cf. Popper, “Three Views Concerning Human Knowledge” in: ‘Conjectures and Refutations’ (Section 3).Google Scholar
  12. 12.
    For the fruitfulness of these equivalent reformulations, cf. Feynman, The Character of Physical Law, p. 168.Google Scholar
  13. 13.
    E. Meyerson, Identité et Réalité, Chapter I. Also: De L'Explication das Les Sciences, Chapter V.Google Scholar
  14. 14.
    Cf. Popper, “The Aim of Science”, in: Objective Knowledge, p. 191.Google Scholar
  15. 15.
    Identité et Réalité, Chapter III.Google Scholar
  16. 16.
    Weyl, Philosophy of Mathematics and Natural Science, p. 5.Google Scholar
  17. 17.
    Meyerson, La Déduction Relativiste, Chapter XX.Google Scholar
  18. 18.
    Weyl, Philosophy of Mathematics and Natural Science, pp. 87–88.Google Scholar
  19. 19.
    Mach, The History and the Root of the Principle of the Conservation of Energy, Notes.Google Scholar
  20. 20.
    Eddington, The Mathematical Theory of Relativity, p. 120.Google Scholar
  21. 21.
    “Prinzipielles zur allgemeinen Relativitätstheorie”, Annalen der Physik, Band 55, 1918. Also see Appendix 1.Google Scholar
  22. 22.
    For this point I am indebted to Professor J. Stachel.Google Scholar
  23. 23.
    Cf. above, see I.1.Google Scholar
  24. 24.
    Mathematical Theory of Relativity, p. 212.Google Scholar
  25. 25.
    Mathematical Theory of Relativity, p. 213.Google Scholar
  26. 26.
    Mathematical Theory of Relativity, p. 206.Google Scholar
  27. 27.
    Schrödinger, Space-Time Structure, p. 112.Google Scholar
  28. 28.
    Cf. my "Why did Einstein's programme supersede Lorentz's?, Brit. J. Phil. Sci. 24 (1973) pp 95–123 and 223–62.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Elie G. Zahar
    • 1
  1. 1.London School of EconomicsGreat Britain

Personalised recommendations