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Clock Time in Quantum Cosmology

Department of Physics, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602, Japan
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Universe 2019, 5(2), 66; https://doi.org/10.3390/universe5020066
Received: 9 January 2019 / Revised: 18 February 2019 / Accepted: 19 February 2019 / Published: 22 February 2019
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Abstract

We consider the conditioning of the timeless solution to the Wheeler–DeWitt equation by a predefined matter clock state in the simple scenario of an FLRW universe. The resulting evolution of the geometrodynamical degree of freedom with respect to clock time is characterized by the “Berry connection” of the reduced geometrodynamical space, which relies on the coupling of the clock with the geometry. When the connection vanishes, the standard Schrödinger equation is obtained for the geometry with respect to clock time. When one considers environment-induced decoherence in the semiclassical limit, this condition is satisfied, and clock time coincides with cosmic time. Explicit results for the conditioned wave functions for minimal clocks made up of two quantum harmonic oscillator eigenstates are shown. View Full-Text
Keywords: quantum time; quantum clock; quantum cosmology; FLRW universe; Berry phase quantum time; quantum clock; quantum cosmology; FLRW universe; Berry phase
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Rotondo, M.; Nambu, Y. Clock Time in Quantum Cosmology. Universe 2019, 5, 66.

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