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Foundations of Physics

, Volume 13, Issue 7, pp 731–743 | Cite as

A constructive-axiomatic approach to the Lie structure in general spacetime by the principle of approximative reproducibility

  • Dieter Mayr
Part I. Invited Papers Dedicated to Günther Ludwig

Abstract

The present article covers the first part of our constructive-axiomatic approach to general spacetime, guided by Ludwig's conception of an axiomatic base. The leading idea of axiomatization is a generalized version of the equivalence principle—the principle of approximative reproducibility. As fundamental concepts we use processes and reproductions of processes. On the universe of processes the point space of events is founded which carries the familiar properties of spacetime topology. A general contact relation for reproductions is the key structure to build up a group of tangential germs (pre-jets). Finally, using Yamabe's characterization we obtain the Lie structure.

Keywords

Present Article Generalize Version Fundamental Concept Equivalence Principle Point Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    H. Poincare, “Sur la dynamique de l'électron,”C. R. 140, 1504 (1905).Google Scholar
  2. 2.
    A. Einstein, “Zur Elektrodynamik bewegter Körper,”Ann. d. Phys. 17, 891 (1905).Google Scholar
  3. 3.
    H. Freudenthal, “Neuere Fassung des Riemann-Helmholtz-Lieschen Raumproblems,”Math. Zeitschr. 69, 374 (1956).Google Scholar
  4. 4.
    H.-J. Schmidt,Axiomatic Characterization of Physical Geometry (Lecture Notes in Physics Volume 111) (Springer, Berlin, 1979).Google Scholar
  5. 5.
    H. Freudenthal, “Das Helmholtz-Liesche Raumproblem bei indefiniter Metrik,”Math. Annalen 156, 263 (1964).Google Scholar
  6. 6.
    D. Mayr, “A Constructive-Axiomatic Approach to Physical Space and Spacetime Geometries of Constant Curvature by the Principle of Reproducibility,” inSpace, Time, and Mechanics D. Mayr and G. Süssmann, eds. (Reidel, Dordrecht, 1983).Google Scholar
  7. 7.
    G. Ludwig,Die Grundstrukturen einer physikalischen Theorie (Springer, Berlin, 1978).Google Scholar
  8. 8.
    Aristotle,Physics (Loeb's Classical Library, London, 1926).Google Scholar
  9. 9.
    J. Ehlers, “Survey of General Relativity Theory,” inRelativity, Astrophysics, and Cosmology, W. Israel, ed. (Reidel, Dordrecht, 1973).Google Scholar
  10. 10.
    W. Rindler,Essential Relativity (Springer, New York, 1977).Google Scholar
  11. 11.
    S. Kobayashi and K. Nomizu,Foundations of Differential Geometry I (Interscience, New York, 1963).Google Scholar
  12. 12.
    J. Ehlers, F. A. E. Pirani, and A. Schild, “The Geometry of Free Fall and Light Propagation,” inGeneral Relativity, L. O'Raifeartaigh, ed. (Clarendon Press, Oxford, 1972).Google Scholar
  13. 13.
    N. Bourbaki,Elements of Mathematics. General Topology (Hermann, Paris, 1966).Google Scholar
  14. 14.
    N. Bourbaki,Éléments de mathématique. Variétés différentielles et analytiques” (Hermann, Paris, 1971).Google Scholar
  15. 15.
    H. Yamabe, “A Generalization of a Theorem of Gleason,”Ann. Math. 58(2), 351 (1953).Google Scholar
  16. 16.
    D. Montgomery and L. Zippin,Topological Transformation Groups (Krieger, New York, 1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • Dieter Mayr
    • 1
  1. 1.Sektion Physik der Universität München, Theoretische PhysikMünchen 2BRD

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