# Interference of Clocks: A Quantum Twin Paradox

## TL;DR

This paper investigates how matter wave phases in atom interferometers relate to relativistic effects, revealing conditions under which they can or cannot measure gravitational time dilation and proposing a quantum-clock interferometer setup.

## Contribution

It demonstrates that certain light-pulse interferometers are insensitive to gravitational time dilation and introduces a novel quantum-clock interferometer geometry to isolate relativistic effects.

## Key findings

- Closed light-pulse interferometers without clock transitions are not sensitive to gravitational time dilation.
- They can serve as a quantum twin paradox setup.
- A proposed experimental geometry isolates the relativistic effect.

## Abstract

The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show: (i.) Closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential. (ii.) They can constitute a quantum version of the special-relativistic twin paradox. (iii.) Our proposed experimental geometry for a quantum-clock interferometer isolates this effect.