Quantum features in statistical observations of “timeless” classical systems

We pursue the view that quantum theory may be an emergent structure at large space–time scales. 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.