Generalized boosts with shell structure of the parameter space

Abstract

A modification of boost transformation in arbitrary pseudo-Euclidean space is suggested, which in the case of the Minkowsky space admits an existing of inertial reference frames moving with velocities taking values in a certain bounded interval. The velocity space may be partitioned by hypersurfaces β2 = βk2 = const, k = 1, 2, 3, ..., into a finite or countable number of domains (shells), each of which has own class of inertial ‘reference frames’ and the velocity composition law. These shells are in one-to-one correspondence. A set of mappings of shells to each other forms the group, isomorphic to permutation group ZN in the case of finite (N + 1) number of shells, or the group of integers Z in the case of countable number of shells in the velocity space.