Time dilation of quantum clocks in a relativistic gravitational potential

TL;DR

This paper investigates how quantum clocks experience time dilation in a gravitational potential, aligning quantum dynamics with classical general relativity predictions using a quantum time formalism.

Contribution

It introduces a quantum framework for analyzing gravitational time dilation effects on clocks, including entangled states, connecting quantum mechanics with general relativity.

Findings

Quantum clocks exhibit time dilation consistent with Schwarzschild predictions.

Gravitational redshift emerges naturally from the quantum formalism.

Entanglement influences the dynamics of quantum clocks in gravitational fields.

Abstract

We study the dynamical evolution of two quantum clocks interacting with a relativistic gravitational potential. We find a time dilation effect for the clocks in agreement with the gravitational time dilation as obtained from the Schwarzschild solution in General Relativity. We perform our investigation via the Page and Wootters quantum time formalism, exploring the dynamics of clocks assuming them in both a product state and a more general (entangled) state. The gravitational redshift, as emerging from our framework, is also proposed and discussed.