Quantum features in statistical observations of "timeless" classical systems

TL;DR

This paper explores how quantum features can emerge from classical Hamiltonian systems with a probabilistic relation between proper time and physical time, suggesting a possible origin of quantum mechanics from classical dynamics.

Contribution

It introduces a framework where classical systems with a probabilistic time relation exhibit quantum-like behavior, bridging classical and quantum descriptions.

Findings

Classical systems can display quantum features under certain probabilistic time relations.

Path-integral formulation allows primordial states to evolve unitarily in specific limits.

Supports the idea that quantum mechanics may emerge from classical deterministic systems.

Abstract

We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the discrete physical time. This is motivated by studies of ``timeless'' reparametrization invariant models, where discrete physical time has recently been constructed based on coarse-graining local observables. Describing such deterministic classical systems with the help of path-integrals, primordial states can naturally be introduced which follow unitary quantum mechanical evolution in suitable limits.