Quantum Clocks, Gravitational Time Dilation, and Quantum Interference

TL;DR

This paper introduces a quantum proper time observable, extends classical time dilation to quantum clocks in weak gravitational fields, and proposes an experiment to observe quantum gravitational time dilation effects via interference.

Contribution

It develops a quantum proper time concept, demonstrates quantum time dilation in weak gravity, and proposes a quantum interference experiment to observe gravitational effects.

Findings

Quantum time dilation obeys classical gravitational time dilation in weak fields.

Time dilation involves external coordinate time and proper times of quantum clocks.

Proposes an experimental setup to observe quantum gravitational time dilation via interference.

Abstract

A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order to investigate whether the weak equivalence principle holds for quantum matter. We find that for general quantum states the quantum time dilation in a weak gravitational field obeys a similar gravitational time dilation found in classical relativity. However, unlike the special relativistic case, the time dilation involves the external time (a background coordinate time at the observer on the Earth) as well as the proper times of two clocks. We also investigate a quantum time dilation effect induced by a clock in a superposition of wave packets localized in momentum space or in position space and propose the setup to observe the gravitational effect in the quantum interference effect in the time dilation.