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

TL;DR

This paper formalizes Schutz' axioms for Minkowski spacetime within Isabelle/HOL, providing a rigorous logical foundation closer to Hilbert's axiomatic style than traditional vector space models.

Contribution

It introduces a formal Isabelle/HOL mechanization of Schutz' axioms, including proofs and corrections, enhancing the logical rigor of special relativity foundations.

Findings

Successful formalization of Schutz' axioms in Isabelle/HOL

Identification of necessary proof steps and corrections

Enhanced understanding of temporal order in Minkowski spacetime

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.