Special Relativity over the Field of Rational Numbers

TL;DR

This paper explores the possibility of formulating special relativity over the rational numbers, showing that a consistent axiom system can be modeled even without real or complex numbers.

Contribution

It introduces an axiom system for special relativity that can be modeled over the field of rational numbers, expanding the mathematical foundations of the theory.

Findings

Special relativity can be modeled over the rational numbers.

The choice of number field depends on auxiliary assumptions.

A natural axiom system compatible with rational numbers is proposed.

Abstract

We investigate the question: what structures of numbers (as physical quantities) are suitable to be used in special relativity? The answer to this question depends strongly on the auxiliary assumptions we add to the basic assumptions of special relativity. We show that there is a natural axiom system of special relativity which can be modeled even over the field of rational numbers.