Towards Formalising Schutz' Axioms for Minkowski Spacetime in Isabelle/HOL

Abstract

Special Relativity is a cornerstone of modern physical theory. While a standard coordinate model is well-known and widely taught today, several alternative systems of axioms exist. This paper reports on the formalisation of one such system which is closer in spirit to Hilbert's axiomatic approach to Euclidean geometry than to the vector space approach employed by Minkowski. We present a mechanisation in Isabelle/HOL of the system of axioms as well as theorems relating to temporal order. Proofs and excerpts of Isabelle/Isar scripts are discussed, particularly where the formal work required additional steps, alternative approaches, or corrections to Schutz' prose.

Formalising Geometric Axioms for Minkowski Spacetime and Without-Loss-of-Generality Theorems

“…9-17]. Brevity precludes a reproduction of our mechanisation here, and we refer to a prior contribution [17] and our recent, detailed description [19] for details.…”