# Time Dilation of Quantum Clocks in a Relativistic Gravitational Potential

## TL;DR

This paper explores how quantum clocks experience time dilation in a relativistic gravitational field, aligning with predictions from general relativity.

## Contribution

The study introduces a novel application of the Page and Wootters formalism to analyze quantum clocks in entangled states under gravitational effects.

## Key findings

- Quantum clocks exhibit gravitational time dilation consistent with Schwarzschild predictions.
- Gravitational redshift emerges naturally from the quantum-time formalism used.
- Entangled clock states show distinct dynamical behavior compared to product states.

## 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.