# Realistic Clocks for a Universe Without Time

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## Abstract

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.

## Notes

### Acknowledgements

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.

## References

- 1.DeWitt, B.S.: Quantum theory of gravity. I. The canonical theory. Phys. Rev.
**160**(5), 1113 (1967). https://doi.org/10.1103/PhysRev.160.1113 ADSCrossRefzbMATHGoogle Scholar - 2.Rovelli, C.: Time in quantum gravity: an hypotheis. Phys. Rev. D
**43**(2), 442 (1991). https://doi.org/10.1103/PhysRevD.43.442 ADSMathSciNetCrossRefGoogle Scholar - 3.Rovelli, C.: Quantum mechanics without time: a model. Phys. Rev. D
**42**(8), 2638 (1991). https://doi.org/10.1103/PhysRevD.42.2638 ADSCrossRefGoogle Scholar - 4.Page, D.N., Wootters, W.K.: Evolution without evolution: Dynamics described by stationary observables. Phys. Rev. D
**27**(12), 2885 (1983). https://doi.org/10.1103/PhysRevD.27.2885 ADSCrossRefGoogle Scholar - 5.Aharoniv, Y., Kaufherr, T.: Quantum frames of reference. Phys. Rev. D
**30**(2), 368 (1984). https://doi.org/10.1103/PhysRevD.30.368 ADSMathSciNetCrossRefGoogle Scholar - 6.Marletto, C., Vedral, V.: Evolution without evolution and without ambiguities. Phys. Rev. D
**95**(4), 043510 (2017). https://doi.org/10.1103/PhysRevD.95.043510. arXiv:1610.04773 [quant-ph] - 7.Giovannetti, V., Lloyd, S., Maccone, L.: Quantum time. Phys. Rev. D
**92**(4), 045033 (2015). https://doi.org/10.1103/PhysRevD.92.045033. arXiv:1504.04215 [quant-ph] - 8.Kuchar, K.V.: Time and interpretations of quantum gravity. In: Kunstatter G., Vincent D.E., Williams J.G. (eds.) Proceedings of 4th Canadian Conference on General Relativity and Relativistic Astrophysics (1992). https://doi.org/10.1142/S0218271811019347
- 9.Dolby, C.E.: The Conditional probability interpretation of the Hamiltonian constraint. arXiv:gr-qc/0406034
- 10.Corbin, V., Cornish, N.J.: Semi-classical limit and minimum decoherence in the conditional probability interpretation of quantum mechanics. Found. Phys.
**39**(5), 474 (2009). https://doi.org/10.1007/s10701-009-9298-5. arXiv:0811.2814 [gr-qc] - 11.Yeon, K.H., Um, C.I., George, T.F.: Coherent states for the damped harmonic oscillator. Phys. Rev. A
**36**(11), 5287 (1987)ADSCrossRefGoogle Scholar - 12.Um, C.I., Yeon, K.H., George, T.F.: The quantum damped harmonic oscillator. Phys. Rep.
**362**(2), 63 (2002). https://doi.org/10.1016/S0370-1573(01)00077-1 ADSMathSciNetCrossRefzbMATHGoogle Scholar - 13.Ng, Y .J., van Dam, H.: Limitation to quantum measurements of space-time distances. Ann. N. Y. Acad. Sci.
**755**(1), 579 (1995). https://doi.org/10.1111/j.1749-6632.1995.tb38998.x. arXiv:hep-th/9406110 - 14.Dirac, P.A.M.: Lectures on Quantum Mechanics. Yeshiva University, New York (1964)zbMATHGoogle Scholar
- 15.Prigogine, I., Stengers, I.: The End of Certainty. Simon and Schuster, New York (1997)Google Scholar
- 16.Bryan, K.L.H., Medved, A.J.M.: work in progressGoogle Scholar