General Relativity and Gravitation

, Volume 28, Issue 11, pp 1321–1334 | Cite as

Distinguishability of Weyl- from Lorentz-spacetimes by classical physical means

  • Udo Schelb
Research Articles


Axiomatic physical derivations of the mathematical picture of spacetime used in General Relativity, which are based on the primitive concepts of free fall and light propagation, have led in a direct, convincing manner only to a Weyl spacetime; a further reduction to the usual Lorentzian manifold required postulates which are much less convincing. In this paper we present a new postulate within a more recent spacetime axiomatics, by which there the Lorentzian spacetime is reached in a different way. The theory is based on similar basic notions with more emphasis on clock parametrizations; no quantumtheoretical reasonings are used. A very natural construction of the spacetime metric is the basis for the postulate which is essentially a compatibility condition for parametrizations of worldlines. The result motivates a renewed search for a better way of reduction in the mentioned theories and can guide it.

Key words

Axiomatic approach to General Relativity 


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  1. 1.
    Ehlers, J., Pirani, F. A. E., Schild, A. (1972). InGeneral Relativity. Papers in honour of J. L. Synge, L. O'Raifeartaigh, ed. (Clarendon Press, Oxford), p.63.Google Scholar
  2. 2.
    Meister, R. (1994).A structural analysis of the EPSspace-time theory. Enlarged English version of Diploma thesis,University of Paderborn.Google Scholar
  3. 3.
    Ehlers, J. (1973). InRelativity, Astrophysics, and Cosmology, W. Israel, ed. (Reidel, Dordrecht).Google Scholar
  4. 4.
    Audretsch, J. (1983).Phys. Rev. D 27, 2872.Google Scholar
  5. 5.
    Audretsch, J., Gähler, F., Straumann, N. (1984).Commun. Math. Phys. 95, 41.Google Scholar
  6. 6.
    Perlick, V. (1991).Class. Quantum Grav. 8, 1369.Google Scholar
  7. 7.
    Loinger, A. (1985).Nuovo Cimento B 88, 9.Google Scholar
  8. 8.
    Hochberg, D., Plunien, G. (1991).Phys. Rev. D 43, 3358.Google Scholar
  9. 9.
    Castro, C. (1992).Found. Phys. 22, 569.Google Scholar
  10. 10.
    Schröter, J. (1988).Rep. Math. Phys. 26, 303.Google Scholar
  11. 11.
    Schröter, J., Schelb, U. (1992).Rep. Math. Phys. 31, 5.Google Scholar
  12. 12.
    Schelb, U. (1992).Rep. Math. Phys. 31, 297.Google Scholar
  13. 13.
    Schelb, U. (1993). “An axiomatic theory of spacetime. Part IV.” Preprint, University of Paderborn.Google Scholar
  14. 14.
    Schröter, J., Schelb, U. (1993). “On the Relation between Space-time Theory and General Relativity.” Preprint 18/1993 of the Center for Interdisciplinary Research (ZIF), University of Bielefeld.Google Scholar
  15. 15.
    Ludwig, G. (1990).Die Grundstrukturen einer physikalischen Theorie (2nd ed., Springer-Verlag, Berlin/Heidelberg/New York).Google Scholar
  16. 16.
    Synge, J. L. (1971).Relativity: The general theory (North-Holland, Amsterdam).Google Scholar
  17. 17.
    Kronheimer, E. H., Penrose, R. (1967).Proc. Camb. Phil. Soc. 63, 481.Google Scholar
  18. 18.
    Schröter, J., Schelb, U. (1995).Gen. Rel. Grav. 27, 605.Google Scholar
  19. 19.
    Schelb, U. (1995). “On a condition distinguishing Weyl- and Lorentz-spacetimes.” Preprint University of Paderborn.Google Scholar
  20. 20.
    Perlick, V. (1987).Gen. Rel. Grav. 19, 1059.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Udo Schelb
    • 1
  1. 1.Department of PhysicsUniversity of PaderbornPaderbornGermany

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