Measuring time in a timeless universe

TL;DR

This paper addresses the challenge of measuring time within a universe modeled as stationary, demonstrating that clocks can be measured without disrupting the core quantum entanglement structure, and discussing synchronization.

Contribution

It proves that clocks in the Page-Wootters model can be measured while maintaining their entangled state, resolving a key limitation of the original framework.

Findings

Clocks can be measured without destroying entanglement.

Measurement preserves the stationary state of the universe model.

Discusses methods for clock synchronization in quantum systems.

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 & 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 synchronisation.