Time Fisher information associated with fluctuations in quantum geometry

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 Hami...

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Bibliographic Details
Published in:Europhysics letters 2022-09, Vol.139 (6), p.62002
Main Authors: Wani, Salman Sajad, Quach, James Q., Faizal, Mir
Format: Article
Language:English
Subjects:
Constraints
Fisher information
Quantum gravity
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Summary: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.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/ac8caf