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  • Open Access

Measuring time in a timeless universe

Sam Kuypers1,* and Simone Rijavec2,†

  • *Contact author: samuelkuypers@gmail.com
  • †Contact author: simone.rijavec@physics.ox.ac.uk
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Phys. Rev. D 112, 063544 – Published 22 September, 2025

DOI: https://doi.org/10.1103/qfns-48vq

Abstract

Physical systems are usually assumed to evolve relative to an external time parameter, which is problematic because in quantum theory that parameter is not a physical observable. Page and Wootters (1984) solved this by proposing that the Universe is in a stationary state, eliminating the need for the external time parameter. Instead, their model contains an isolated subsystem, a clock, with which other subsystems are entangled, making the latter appear to evolve relative to different states of the clock. While this resolves the problem of the time parameter, the assumption that the clock is isolated prevents it from being measured, as this requires an interaction with another system. We prove that the clock can be measured while preserving the core features of the Page-Wootters construction. We also discuss clock synchronization.

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Phys. Rev. D 112, 063544– Published 22 September, 2025
  • Received 11 November 2024
  • Accepted 24 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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