Abstract
Zeeman (1964) has shown that the group of automorphisms for the relation of causality on Minkowski space is that generated by the orthochronous Poincaré (Halpern, 1968) group and dilatations. Here we prove that the group of automorphisms that preserve the time-like vectors of Minkowski space normwise is the complete Poincaré group. We prove that the timelike structure within the null cone of a single event does define the whole structure of Minkowski space. Further, it is shown that only inertial observers can use Minkowski space to describe space-time.
Similar content being viewed by others
References
Blumenthal, Leonard M. (1953).Distance Geometry. Oxford.
Halpern, Francis R. (1968).Special Relativity and Quantum Mechanics. Prentice Hall, Inc., New York.
Landau, L. and Lifshitz, E. (1951).The Classical Theory of Fields. Addison-Wesley, p. 6.
Synge, J. L. (1956).Relativity-The Special Theory. North-Holland Publishing Company, Amsterdam, p. 69.
Zeeman, E. C. (1964). Causality Implies the Lorentz Group,Journal of Mathematical Physics,5(4).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Williams, G. A discussion of causality and the Lorentz group. Int J Theor Phys 7, 415–421 (1973). https://doi.org/10.1007/BF00713243
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00713243