Emergent discrete time and quantization: relativistic particle with extradimensions

TL;DR

This paper investigates a relativistic particle in higher dimensions with compactified internal spaces, constructing a discrete physical time linked to ergodic properties, leading to a quantum-like evolution in external space.

Contribution

It introduces a method to define discrete physical time in a reparametrization invariant system with extra dimensions, connecting classical ergodic behavior to quantum evolution.

Findings

Discrete physical time can be constructed from invariant observables.

External motion exhibits quantum-like unitary evolution.

Ergodicity relates physical time to proper time on average.

Abstract

We study the reparametrization invariant system of a classical relativistic particle moving in (5+1) dimensions, of which two internal ones are compactified to form a torus. A discrete physical time is constructed based on a quasi-local invariant observable. Due to ergodicity, it is simply related to the proper time on average. The external motion in Minkowski space can then be described as a unitary quantum mechanical evolution.