Issue |
EPL
Volume 139, Number 6, September 2022
|
|
---|---|---|
Article Number | 62002 | |
Number of page(s) | 5 | |
Section | Mathematical and interdisciplinary physics | |
DOI | https://doi.org/10.1209/0295-5075/ac8caf | |
Published online | 22 September 2022 |
Time Fisher information associated with fluctuations in quantum geometry
1 Canadian Quantum Research Center - 204-3002, 32 Ave Vernon, BC V1T 2L7 Canada
2 School of Physics, Damghan University - P. O. Box 3671641167, Damghan, Iran
3 Institute for Photonics and Advanced Sensing and School of Physical Sciences, The University of Adelaide South Australia 5005, Australia
4 Commonwealth Scientific and Industrial Research Organisation (CSIRO) - Clayton, Victoria, 3168, Australia
5 Irving K. Barber School of Arts and Sciences, University of British Columbia - Okanagan, Kelowna, British Columbia V1V 1V7, Canada
6 Department of Physics and Astronomy, University of Lethbridge - Lethbridge, AB T1K 3M4, Canada
(a) E-mail: mirfaizalmir@gmail.com (corresponding author)
Received: 10 July 2022
Accepted: 25 August 2022
As time is not an observable, we use Fisher information (FI) to address the problem of time. We demonstrate that although the Hamiltonian operator is the generator of time, the Hamiltonian constraint operator cannot observe the change that arises through the passage of time. This is because the Hamiltonian constraint does not contain time FI. As we also identify an alternative operator on the world-sheet which does contain time FI, we argue that the timelessness of quantum gravity occurs due to the use of an inappropriate operator. We propose that a criterion for a physically meaningful operator in any quantum gravitational process is that it should contain non-vanishing time FI. Although we explicitly derive these results on the world-sheet of bosonic strings, we argue that it holds for any quantum geometry associated with time-reparametrization–invariant classical geometry.
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