Generalized boosts with shell structure of the parameter space

TL;DR

This paper proposes a modified boost transformation in pseudo-Euclidean space, introducing a shell structure in velocity space that leads to a new group of inertial reference frames with bounded velocities.

Contribution

It introduces a novel shell-based structure in velocity space and a corresponding group of transformations, extending the classical boost concept in Minkowski space.

Findings

Velocity space partitioned into shells with distinct inertial frames

Group of transformations is isomorphic to permutation or integer groups

Bounded velocity intervals allow new inertial frame classifications

Abstract

A modification of boost transformation in arbitrary pseudo-Euclidean space is suggested, which in the case of the Minkowski space admits the existence of inertial reference frames moving with velocities taking values in a certain bounded interval. The velocity space may be partitioned by hypersurfaces \beta^2=\beta^2_k=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 in the case of finite number of shells, or the group of integers in the case of countable number of shells in the velocity space