Related papers: Observers and Timekeepers: From the Page-Wootters Mechanism to the Gravitational Path Integral

Observers and Timekeepers: From the Page-Wootters Mechanism to the Gravitational Path Integral

URL: http://arxiv.org/abs/2506.21489v1
Date: Thu, 26 Jun 2025 17:18:50 GMT
Title: Observers and Timekeepers: From the Page-Wootters Mechanism to the Gravitational Path Integral
Authors: Zixia Wei,
Abstract summary: Quantum gravity in a closed universe faces two a priori distinct yet seemingly related issues: the problem of time and the fact that its Hilbert space dimension is one.<n>We argue that the two issues arise from two distinct non-perturbative effects: the former from summing over metrics and the latter from summing over topologies.<n>We propose a method for incorporating observers and timekeepers into the gravitational path integral and show that implementing a timekeeper in this way furnishes an observer-dependent generalization of holography.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Quantum gravity in a closed universe faces two a priori distinct yet seemingly related issues: the problem of time and the fact that its Hilbert space dimension is one. Both have been argued to be resolvable by formulating physics relative to an observer. Using a simple gravitational path integral model, we explain that the two issues arise from two distinct non-perturbative effects: the former from summing over metrics and the latter from summing over topologies. We then revisit the Page-Wootters mechanism, one of the earliest frameworks for formulating quantum mechanics relative to an observer, see how it applies to both issues, and introduce some new ingredients. In particular, we emphasize a hierarchy between an observer and a timekeeper. An observer is a subsystem of the universe whose specification results in a nontrivial Hilbert space, while a timekeeper is an observer with a specified history that can be used as a reference for the time of the environment and experiences a nontrivial time evolution. Finally, we propose a method for incorporating observers and timekeepers into the gravitational path integral and show that implementing a timekeeper in this way furnishes an observer-dependent generalization of holography.

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