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On the interpretation of time-reparametrization-invariant quantum mechanics

Ian D. Lawrie·Richard J. Epp
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Abstract

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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Ian D. Lawrie, Richard J. Epp. 1995-09-25. On the interpretation of time-reparametrization-invariant quantum mechanics. https://doi.org/10.1103/physrevd.53.7336

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