On the Fundamental Theorem of the Theory of Relativity

TL;DR

This paper introduces a new formulation and proof of the fundamental theorem of relativity in (3+1)-space-time, analyzing transformations, velocity laws, and axioms, including the role of the group axiom and light isotropy.

Contribution

It presents a novel formulation and proof of the fundamental theorem of relativity, exploring the classification of transformations and the impact of axioms like the group property and light isotropy.

Findings

Classification of special transformations and velocity addition laws.

Analysis of the role of the group axiom in relativity.

Clarification of issues previously misunderstood in the literature.

Abstract

A new formulation of what may be called the "fundamental theorem of the theory of relativity" is presented and proved in (3+1)-space-time, based on the full classification of special transformations and the corresponding velocity addition laws. A system of axioms is introduced and discussed leading to the result, and a study is made of several variants of that system. In particular the status of the group axiom is investigated with respect to the condition of the two-way isotropy of light. Several issues which are ignored or misunderstood in the literature are emphasized.