Realistic Clocks for a Universe Without Time
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There are a number of problematic features within the current treatment of time in physical theories, including the “timelessness” of the Universe as encapsulated by the Wheeler–DeWitt equation. This paper considers one particular investigation into resolving this issue; a conditional probability interpretation that was first proposed by Page and Wooters. Those authors addressed the apparent timelessness by subdividing a faux Universe into two entangled parts, “the clock” and “the remainder of the Universe”, and then synchronizing the effective dynamics of the two subsystems by way of conditional probabilities. The current treatment focuses on the possibility of using a (somewhat) realistic clock system; namely, a coherent-state description of a damped harmonic oscillator. This clock proves to be consistent with the conditional probability interpretation; in particular, a standard evolution operator is identified with the position of the clock playing the role of time for the rest of the Universe. Restrictions on the damping factor are determined and, perhaps contrary to expectations, the optimal choice of clock is not necessarily one of minimal damping.
The research of AJMM received support from an NRF Incentive Funding Grant 85353 and NRF Competitive Programme Grant 93595. KLHB is supported by an NRF bursary through Competitive Programme Grant 93595 and a Henderson Scholarship from Rhodes University. We acknowledge the contribution of an anonymous referee in pointing out a flaw in an earlier form of the manuscript.
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