On the interpretation of time-reparametrization-invariant quantum mechanics

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.

13 pages, set in REVTeX. One figure available by FAX from [email protected]

References in corpus (3)

• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• An algebraic extension of Dirac quantization: Examples
• Holomorphic quantum mechanics with a quadratic Hamiltonian constraint

Cited by in corpus (8)

• The Rest-Frame Instant Form of Metric Gravity
• Emergent discrete time and quantization: relativistic particle with extradimensions
• Time without time: a stochastic clock model
• Reparametrization Invariance and Some of the Key Properties of Physical Systems
• Coherent State Approach to Time Reparameterization Invariant Systems
• Time evolution in quantum cosmology
• Internal time, test clocks and singularity resolution in dust-filled quantum cosmology
• Coherent State Approach to Quantum Clocks