Universality of quantum time dilation

TL;DR

This paper explores how quantum superpositions of spatial states lead to novel quantum time dilation effects, revealing both universal and non-universal behaviors and identifying a unique quantum correction without classical analog.

Contribution

It demonstrates the universality of kinematic quantum time dilation and the non-universality of gravitational quantum time dilation, along with identifying a new quantum effect beyond classical analogs.

Findings

Kinematic quantum time dilation is universal for any clock mechanism.

Gravitational quantum time dilation is not universal.

A new quantum time dilation effect with no classical counterpart was identified.

Abstract

Time dilation is a difference in measured time between two clocks that either move with different velocities or experience different gravitational potentials. Both of these effects stem from the theory of relativity and are usually associated with classically defined trajectories, characterized by position, momentum, and acceleration. However, when spatial degrees of freedom are treated in a quantum way and a clock is allowed to be in a coherent superposition of either two momenta or two heights, additional quantum corrections to classical time dilation appear, called kinematic and gravitational quantum time dilations, respectively. We show that similarly to its classical counterpart, kinematic quantum time dilation is universal for any clock mechanism, while gravitational quantum time dilation is not. We also show that although both of these effects reduce to incoherent averaging of different classical time dilation contributions, there exists an additional quantum time dilation effect that has no classical analog and can be extracted from higher-order corrections to the system's Hamiltonian.