Axiomatizing relativistic dynamics using formal thought experiments

Attila Molnár

Gergely Szekely

pp. 2183-2222

in: Gergely Szekely (ed), Logic and relativity theory, Synthese 192 (7), 2015.

Abstract

Thought experiments are widely used in informal explanations of Relativity Theories; however, they are not present explicitly in formalized versions of Relativity Theory. In this paper, we present an axiom system of Special Relativity which is able to express thought experiments formally and explicitly. Moreover, using these thought experiments, we can provide an explicit definition of relativistic mass based merely on kinematical concepts and thought experiments on collisions. Using this definition, we can geometrically prove the Mass Increase Formula (m_0 = m mathrel {cdot }sqrt{1-v^2}) in a natural way, without postulates of conservation of mass and momentum.