Gravitational time dilation in extended quantum systems: the case of light clocks in Schwarzschild spacetime

TL;DR

This paper models quantum light clocks in Schwarzschild spacetime to understand how their spatial extension affects measurements of gravitational time dilation, providing a step towards relativistic quantum clock descriptions.

Contribution

It introduces a quantum light clock model in Schwarzschild spacetime with fixed mirror separation, analyzing how spatial extension influences gravitational time dilation measurements.

Findings

Vertical clock measures proper time at its center.

Fundamental bounds on clock precision are derived.

Operational method to define clock time at small scales.

Abstract

The precision of optical atomic clocks is approaching a regime where they resolve gravitational time dilation on smaller scales than their own extensions. Hence, an accurate description of quantum clocks has to take their spatial extension into account. In this article, as a first step towards a fully relativistic description of extended quantum clocks, we investigate a quantized version of Einstein's light clock fixed at a constant distance from a large massive object like the Earth. The model consists of a quantum light field in a one-dimensional cavity in Schwarzschild spacetime, where the distance between the mirrors is fixed by a rigid rod. By comparing a vertical and a horizontal clock, we propose an operational way to define the clock time when the clock resolves gravitational time dilation on scales smaller than its extension. In particular, we show that the time measured by the vertical light clock is equivalent to the proper time defined at its center. We also derive fundamental bounds on the precision of these clocks for measurements of proper time and the Schwarzschild radius.