# Universal quantum modifications to general relativistic time dilation in delocalised clocks

## TL;DR

This paper explores how quantum superpositions of clock states can cause deviations from classical time dilation effects predicted by general relativity, revealing quantum modifications to proper time and measurement uncertainties.

## Contribution

It introduces a framework for quantum clocks, demonstrating universal quantum effects on time dilation and quantifying the impact of delocalisation and entanglement on clock precision.

## Key findings

- Quantum interference causes deviations in time dilation for nonclassical states.
- Delocalisation increases uncertainty in time measurement due to entanglement.
- Measurement of motion state can recover lost time measurement precision.

## Abstract

The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we demonstrate that, in the weak-field, low-velocity limit, all "good" quantum clocks experience time dilation as dictated by general relativity when their state of motion is classical (i.e. Gaussian). For nonclassical states of motion, on the other hand, we find that quantum interference effects may give rise to a significant discrepancy between the proper time and the time measured by the clock. The universality of this discrepancy implies that it is not simply a systematic error, but rather a quantum modification to the proper time itself. We also show how the clock's delocalisation leads to a larger uncertainty in the time it measures -- a consequence of the unavoidable entanglement between the clock time and its center-of-mass degrees of freedom. We demonstrate how this lost precision can be recovered by performing a measurement of the clock's state of motion alongside its time reading.