A SPACE--PROPER TIME FORMULATION OF RELATIVISTIC GEOMETRY
Physical sciences research papers
AIR FORCE CAMBRIDGE RESEARCH LABS HANSCOM AFB MA
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Any formulation of the theory of relativity specifies implicitly or explicitly the exactness or inexactness of the temporal and spatial differentials that occur. The Minkowski formulation implicitly assumes the exactness of coordinate common time and the inexactness of proper time. In this paper we examine several other possibilities. The assumption of the exactness of proper time and inexactness of common time leads to a space-proper time SPT representation of events that a yields the customary formal results of the theory including the differential aging prediction of the twin paradox, b allows an analog of Fermats principle to describe both particles and light, and c leads to a many-proper time formulation of the relativistic many-body problem essentially equivalent to the Minkowski space formulation. Analogies between the SPT geometry and the geometric approach to thermodynamics, especially as formulated by Caratheodory, suggest the gamma function of relativity is an integrating factor with physical meaning for the many-body problem and also provides insight into the concept of virtual photons.
- Theoretical Mathematics
- Quantum Theory and Relativity