Axiomatizing relativistic dynamics without conservation postulates

TL;DR

This paper axiomatizes relativistic dynamics using simple geometric axioms in first-order logic, providing a geometric proof of mass relations and explaining Einstein's $E=mc^2$ without relying on conservation postulates.

Contribution

It introduces a purely geometrical axiomatization of relativistic mechanics that derives key mass-energy relations without conservation assumptions.

Findings

Geometric proof of mass relation formula

Explanation of Einstein's $E=mc^2$ from axioms

Connection to traditional conservation axioms

Abstract

A part of relativistic dynamics (or mechanics) is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein's famous $E=mc^2$. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.