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A Quantum Informational Approach to the Problem of Time

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Abstract

Several novel approaches have been proposed to resolve the problem of time by relating it to change. We argue using quantum information theory that the Hamiltonian constraint in quantum gravity cannot probe change, so it cannot be used to obtain a meaningful notion of time. This is due to the absence of quantum Fisher information with respect to the quantum Hamiltonian of a time-reparametization invariant system. We also observe that the inability of this Hamiltonian to probe change can be related to its inability to discriminate between states of such a system. However, if the time-reparametization symmetry is spontaneously broken due to the formation of quantum cosmological time crystals, these problems can be resolved, and it is possible for time to emerge in quantum gravity.

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Acknowledgements

S.B. was supported by the Estonian Research Council grants PRG356 “Gauge Gravity” and by the European Regional Development Fund through the Center of Excellence TK133 “The Dark Side of the Universe”. J.Q.Q. acknowledges the nancial support of the Ramsay Fellowship. S.B. also acknowledges JSPS Postdoctoral Fellowships for Research in Japan and KAKENHI Grant-in-Aid for Scientific Research No. JP21F21789.

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Authors and Affiliations

  1. Department of Physics Engineering, Istanbul Technical University, 34469, Istanbul, Turkey

    Salman Sajad Wani

  2. Canadian Quantum Research Center, 204-3002 32 Ave, Vernon , BC, V1T 2L7, Canada

    Salman Sajad Wani, Mir Faizal & Behnam Pourhassan

  3. Institute for Photonics and Advanced Sensing and School of Physical Science, The University of Adelaide, Adelaide , SA, 5005, Australia

    James Q. Quach

  4. Irving K. Barber School of Arts and Sciences, University of British Columbia - Okanagan, Kelowna, BC, V1V 1V7, Canada

    Mir Faizal

  5. Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB, T1K 3M4, Canada

    Mir Faizal

  6. Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411, Tartu, Estonia

    Sebastian Bahamonde

  7. Department of Physics, Tokyo Institute of Technology, 1-12-1 Ookayama, Meguro-ku, Tokyo, 152-8551, Japan

    Sebastian Bahamonde

  8. Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050, Tomsk, Russia

    Sebastian Bahamonde

  9. School of Physics, Damghan University, Damghan, 3671641167, Iran

    Behnam Pourhassan

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  1. Salman Sajad Wani
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  2. James Q. Quach
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  3. Mir Faizal
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Correspondence to Mir Faizal.

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Wani, S.S., Quach, J.Q., Faizal, M. et al. A Quantum Informational Approach to the Problem of Time. Found Phys 52, 25 (2022). https://doi.org/10.1007/s10701-022-00540-6

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