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

Donald Marolf
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Abstract

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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Donald Marolf. 1994-12-06. Almost Ideal Clocks in Quantum Cosmology: A Brief Derivation of Time. https://doi.org/10.1088/0264-9381%2F12%2F10%2F007

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