# Quantum clocks observe classical and quantum time dilation

## TL;DR

This paper explores how quantum clocks in curved spacetime can exhibit classical and quantum time dilation effects, deriving probabilities and uncertainty relations, with potential for experimental observation of quantum corrections.

## Contribution

It introduces a framework for quantum clocks experiencing superpositions of proper times and derives quantum corrections to classical time dilation effects.

## Key findings

- Quantum clocks in localized states observe classical time dilation.
- Quantum superpositions lead to observable quantum corrections.
- Derived a proper time-energy/mass uncertainty relation.

## Abstract

At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through curved spacetime. The probability that one clock reads a given proper time conditioned on another clock reading a different proper time is derived. From this conditional probability distribution, it is shown that when the center-of-mass of these clocks move in localized momentum wave packets they observe classical time dilation. We then illustrate a quantum correction to the time dilation observed by a clock moving in a superposition of localized momentum wave packets that has the potential to be observed in experiment. The Helstrom-Holevo lower bound is used to derive a proper time-energy/mass uncertainty relation.