Almost Ideal Clocks in Quantum Cosmology: A Brief Derivation of Time

Details Almost Ideal Clocks in Quantum Cosmology: A Brief Derivation of Time Almost Ideal Clocks in Quantum Cosmology: A Brief Derivation of Time

1994-12-06

arxiv.org/abs/gr-qc/9412016v1

Class.Quant.Grav. 12 (1995) 2469-2486

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages ReVTeX (35 preprint pages)

Scientific paper

10.1088/0264-9381/12/10/007

A formalism for quantizing time reparametrization invariant dynamics is considered and applied to systems which contain an `almost ideal clock.' Previously, this formalism was successfully applied to the Bianchi models and, while it contains no fundamental notion of `time' or `evolution,' the approach does contain a notion of correlations. Using correlations with the almost ideal clock to introduce a notion of time, the work below derives the complete formalism of external time quantum mechanics. The limit of an ideal clock is found to be closely associated with the Klein-Gordon inner product and the Newton-Wigner formalism and, in addition, this limit is shown to fail for a clock that measures metric-defined proper time near a singularity in Bianchi models.

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