# Quantum and classical effects in a light-clock falling in Schwarzschild geometry

## TL;DR

This paper investigates how quantum effects influence a light-clock's behavior in a gravitational field, revealing that quantum contributions increase with gravity and differ from classical predictions, highlighting a conflict between quantum theory and relativity.

## Contribution

It introduces a semiclassical quantum light-clock model in Schwarzschild geometry and analyzes quantum effects on time measurement discrepancies.

## Key findings

- Quantum contribution to clock discrepancy increases with gravitational strength.
- Quantum effects cause qualitative differences from classical light-clock predictions.
- Clock time is independent of initial Gaussian state.

## Abstract

Quantum theory and relativity offer different conceptions of time. To explore the conflict between them, we study a quantum version of the light-clock commonly used to illustrate relativistic time dilation. This semiclassical model combines elements of both theories. We show for Gaussian states of the light field that the clock time is independent of the initial state. We calculate the discrepancy between two such clocks when one is held in a gravitational field and the other is left to fall a certain distance. Contrasting our results with the case of pointlike observers in general relativity, as well as classical light-clocks, we find both quantitative and qualitative differences. We find that the quantum contribution to the discrepancy between the two clocks increases with the gravitational field strength, and results in a minimum resolution of the dropped clock (distinct from the quantum uncertainty in its measurement).