Violation of Local Lorentz Invariance by Atomic Clocks

Abstract

Several authors have shown [9,10] that one can derive a precise functional form for the transformations between all inertial space-time reference frames S and S’ out of the infinite continuous class {S, S’} of inertial reference frames by relying on a succession of simple physical assumptions. The crux of the matter is the requirement of a group structure for the set of transformations, and hence relations of physical quantities like time e.g., between all inertial systems. Then the theory of relativity can be constructed by constraining the transformations through four successive hypotheses: homogeneity of space-time, isotropy of space, group structure and causality condition. Only the Lorentz transformations and their degenerate Galilean limit obey these constraints. It is the aim of Sec. II to demonstrate, that the first three hypotheses are violated in principle if the physical equivalence of relative velocities v and -v is violated in principle. Exactly that follows from experimental evidence.