On the interpretation of time-reparametrization-invariant quantum mechanics

Details On the interpretation of time-reparametrization-invariant quantum mechanics On the interpretation of time-reparametrization-invariant quantum mechanics

1995-09-25

arxiv.org/abs/gr-qc/9509047v1

Phys.Rev. D53 (1996) 7336-7344

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, set in REVTeX. One figure available by FAX from i.d.lawrie@leeds.ac.uk

Scientific paper

10.1103/PhysRevD.53.7336

The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description of time evolution for the remaining variable which is essentially equivalent to the standard quantum mechanics of an unconstrained system. In contrast to a similar proposal of Rovelli, evolution is with respect to the geometrical proper time, and the Heisenberg equation of motion is exact. The possibility of a ``test clock'', which would reveal time evolution while contributing negligibly to the Hamiltonian constraint is examined, and found to be viable in the semiclassical limit of large quantum numbers.

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