The mathematical role of time and space-time in classical physics

TL;DR

This paper examines the fundamental role of time and space-time in classical physics, demonstrating their eliminability in several key theories through axiomatic analysis.

Contribution

It applies Padoa's principle to show that time and space-time are not essential primitives in various classical physical theories.

Findings

Time is eliminable in Newtonian mechanics.

Space-time is dispensable in Hamiltonian mechanics, Maxwell's theory, Dirac electron, gauge fields, and general relativity.

Abstract

We use Padoa's principle of independence of primitive symbols in axiomatic systems in order to discuss the mathematical role of time and space-time in some classical physical theories. We show that time is eliminable in Newtonian mechanics and that space-time is also dispensable in Hamiltonian mechanics, Maxwell's electromagnetic theory, the Dirac electron, classical gauge fields, and general relativity.