"Tracking rule" and generalization of special relativity

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 and T. Yarman. Eur. Phys. J. Plus 132, 400 (2017); A.L. Kholmetskii, O.V. Missevitch, T. Yarman, and M. Arik. Europhys. Lett. 129, 3006 (2020)). The purely phenomenological origin of this rule in the framework of STR allows assuming the 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. (author)