Time without time: A stochastic clock model

Hans-Thomas Elze and Otavio Schipper
Phys. Rev. D 66, 044020 – Published 28 August 2002
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Abstract

We study a classical reparametrization-invariant system, in which “time” is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a suitable potential, the internal motion is ergodic or more strongly irregular. We consider quasilocal observables which measure the system’s “change” in a coarse-grained way. Based on this, we construct a statistical timelike parameter, particularly with the help of maximum entropy method and Fisher-Rao information metric. The emergent reparametrization-invariant “time” does not run smoothly but is simply related to the proper time on the average. For sufficiently low energy, the external motion is then described by a unitary quantum mechanical evolution in accordance with the Schrödinger equation.

  • Received 21 May 2002

DOI:https://doi.org/10.1103/PhysRevD.66.044020

©2002 American Physical Society

Authors & Affiliations

Hans-Thomas Elze and Otavio Schipper

  • Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68.528, 21945-970 Rio de Janeiro, RJ, Brazil

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Issue

Vol. 66, Iss. 4 — 15 August 2002

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