Axiomatizing relativistic dynamics without conservation postulates

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.