“Tracking rule” and generalization of special relativity

Abstract

We recall that a consistent description of the Thomas precession and Thomas-Wigner rotation is impossible without introducing a “tracking rule” into the structure of the special theory of relativity (STR), as we have shown in our publications (A.L. Kholmetskii, et al., Eur. Phys. J. Plus 132, 400 (2017); EPL 129, 3006 (2020)). The purely phenomenological origin of this rule in the framework of STR allows assuming an existence of a more general theory of empty space-time than STR where the “tracking rule” is intrinsically incorporated into its structure. We find a possible way of developing such a generalized theory of empty space-time, where the “tracking rule” naturally arises, and propose an experimental scheme for its verification.