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Foundations of Physics

, Volume 45, Issue 10, pp 1166–1178 | Cite as

Bootstrapping Time Dilation Decoherence

  • Cisco Gooding
  • William G. Unruh
Article

Abstract

We present a general relativistic model of a spherical shell of matter with a perfect fluid on its surface coupled to an internal oscillator, which generalizes a model recently introduced by the authors to construct a self-gravitating interferometer (Gooding and Unruh in Phys Rev D 90:044071, 2014). The internal oscillator evolution is defined with respect to the local proper time of the shell, allowing the oscillator to serve as a local clock that ticks differently depending on the shell’s position and momentum. A Hamiltonian reduction is performed on the system, and an approximate quantum description is given to the reduced phase space. If we focus only on the external dynamics, we must trace out the clock degree of freedom, and this results in a form of intrinsic decoherence that shares some features with a proposed “universal” decoherence mechanism attributed to gravitational time dilation (Pikovski et al in Nat Phys, 2015). We note that the proposed decoherence remains present in the (gravity-free) limit of flat spacetime, emphasizing that the effect can be attributed entirely to proper time differences, and thus is not necessarily related to gravity. Whereas the effect described in (Pikovski et al in Nat Phys, 2015) vanishes in the absence of an external gravitational field, our approach bootstraps the gravitational contribution to the time dilation decoherence by including self-interaction, yielding a fundamentally gravitational intrinsic decoherence effect.

Keywords

General relativity Intrinsic decoherence Time dilation 

Notes

Acknowledgments

The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Templeton Foundation (Grant No. JTF 36838) for financial support. Also, we are grateful to the Aspelmeyer and Brukner groups at the University of Vienna, as well as Friedemann Queisser, Dan Carney, Philip Stamp, and Bob Wald, for stimulating discussions.

References

  1. 1.
    Gooding, C., Unruh, W.G.: Self-gravitating interferometry and intrinsic decoherence. Phys. Rev. D 90, 044071 (2014)CrossRefADSGoogle Scholar
  2. 2.
    Pikovski, I., Zych, M., Costa, F., Brukner, C̆.: Universal decoherence due to gravitational time dilation. Accepted for publication in Nature Physics, (2015). doi: 10.1038/nphys3366. arXiv:1311.1095
  3. 3.
    Zych, M., Costa, F., Pikovski, I., Brukner, C̆.: Quantum interferometric visibility as a witness of general relativistic proper time. Nat. Commun. 2, 505 (2011). arXiv:1105.4531v2
  4. 4.
    Zych, M., Costa, F., Pikovski, I., Ralph, T.C., Brukner, C̆.: General relativistic effects in quantum interference of photons. Class. Quantum Grav. 29, 224010 (2012). arXiv:1206.0965v2
  5. 5.
    Stamp, P.C.E.: The decoherence puzzle. Stud. Hist. Philos. Mod. Phys. 37, 467 (2006)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Arnowitt, R.L., Deser, S., Misner, C.W.: Canonical variables for general relativity. Phys. Rev. 117, 1595 (1960). arXiv:gr-qc/0405109
  7. 7.
    Kraus, P., Wilczek, F.: Self-interaction correction to black hole radiance. Nucl. Phys. B 433, 403 (1995). arXiv:gr-qc/9408003v1
  8. 8.
    Walls, D., Milburn, G.: Quantum Optics. Springer, Berlin (1994)zbMATHCrossRefGoogle Scholar
  9. 9.
    Penrose, R.: On gravity’s role in quantum state reduction. Gen. Relativ. Gravit. 28, 581–600 (1996)zbMATHMathSciNetCrossRefADSGoogle Scholar
  10. 10.
    Diósi, L.: Models for universal reduction of macroscopic quantum fluctuations. Phys. Rev. A 40, 1165–1174 (1989)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of British ColumbiaVancouverCanada

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