AN AXIOMATIC APPROACH TO RELATIVITY THEORY

Abstract

General Relativity Theory is presented in an axiomatic form. Attention is focussed on the axiom of Landau, which concerns the spatial structure of bodies and the speed of light. It is shown that there is no compelling support for Landau's axiom in General Relativity Theory. In Special Relativity Theory, the axiom is more interesting: Rephrasing Landau's axiom in geometric terms, the complete theory of rigid bodies m Special Relativity is obtained. Direct physical consequences of this theory include the effects of Michelson-Morley, Sagnac, and Thomas. It is argued that the global isotropy of our universe should be regarded as a fundamental axiom of physics. Using this axiom, we present a new axiomatization of Special Relativity which ties this theory to the expansion of our universe and to the existence of rigid bodies. It follows as a theorem that the speed of light must be nearly constant. It also follows that the global structure of our universe is that of a uniformly expanding hyperbolic Robertson-Walker universe. It is shown that such a universe is compatible with the theory of General Relativity, despite generally received opinion that it is not. Furthermore, in such e. universe there are no particle horizons and no missing matter problems. The observed values of both the Hubble constant and the deceleration parameter are correctly predicted. Finally, we combine the above results in a new bi-metric theory of spacetime, in which we have both the Minkowski metric and Einstein's familiar metric. The Minkowski metric describes the global structure of spacetime as well as the spatial structure of bodies. Einstein's metric describes the physics of freely falling particles. The theoretical difference with General Relativity is that we reject Landau's assumption. The experimental consequence of this is that we predict small but measurable variations in the speed of light.