Advertisement

Communications in Mathematical Physics

, Volume 28, Issue 3, pp 259–266 | Cite as

The structure of space-time transformations

  • H. J. Borchers
  • G. C. Hegerfeldt
Article

Abstract

LetT be a one-to-one mapping ofn-dimensional space-timeM onto itself. IfT maps light cones onto light cones and dimM≧3, it is shown thatT is, up to a scale factor, an inhomogeneous Lorentz transformation. Thus constancy of light velocity alone implies the Lorentz group (up to dilatations). The same holds ifT andT−1 preserve (xy)2>0. This generalizes Zeeman's Theorem. It is then shown that ifT maps lightlike lines onto (arbitrary) straight lines and if dimM≧3, thenT is linear. The last result can be applied to transformations connecting different reference frames in a relativistic or non-relativistic theory.

Keywords

Neural Network Statistical Physic Complex System Reference Frame Nonlinear Dynamics 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Zeeman, E. C.: Causality implies the Lorentz group. J. Math. Phys.5, 490 (1964).Google Scholar
  2. 2.
    Hegerfeldt, G. C.: The Lorentz transformations: Derivation of linearity and scale factor. Il Nuovo Cim. A10, 257 (1972).Google Scholar
  3. 3.
    Pickert, G.: Analytische Geometrie. 6. Aufl. (Sect. 26) Leipzig: Akad. Verlagsgesellschaft 1967.Google Scholar
  4. 4.
    Borchers, H. J., Hegerfeldt, G. C.: Über ein Problem der Relativitätstheorie: Wann sind Punktabbildungen desR n linear? Nachr. Gött. Akad. Wiss. (to be published).Google Scholar
  5. 5.
    Flato, M., Sternheimer, D.: Remarques sur les automorphismes causals de l'espace-temps. C. R. Acad. Sc. Paris, t. 263, 935 (1966).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • H. J. Borchers
    • 1
  • G. C. Hegerfeldt
    • 1
  1. 1.Institut für Theoretische PhysikUniversität GöttingenGöttingenGermany

Personalised recommendations