Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-05-16
Phys.Rev. D66 (2002) 044020
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages; LaTeX. 4 (.ps) plus 2 (.gif) figure files
Scientific paper
10.1103/PhysRevD.66.044020
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 quasi-local 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 Schr\"odinger equation.
Elze H.-Th.
Schipper O.
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