On some Symmetry Axioms in Relativity Theories

TL;DR

This paper reviews symmetry axioms in special and general relativity, exploring their role in key predictions and proposing that these axioms are essential for the full characterization of relativistic spacetimes.

Contribution

It analyzes the connection between symmetry axioms in special relativity and their counterparts in general relativity, proposing a conjecture about their importance.

Findings

Symmetry axioms underpin key relativity predictions like time dilation and length contraction.

Counterparts of these axioms in general relativity are discussed.

A conjecture links the absence of these axioms to conformal equivalence of spacetimes.

Abstract

In this paper we review two symmetry axioms of special relativity and their connections to each other together with their role in some famous predictions of relativity theory, such as time dilation, length contraction, and the twin paradox. We also discuss briefly counterparts of these symmetry axioms in general relativity and formulate a conjecture, namely that without them the axioms of general relativity would capture general relativistic spacetimes only up to conformal equivalence.