An Upper Bound for the Mass of Microscopic Clocks

TL;DR

This paper establishes an upper limit on the mass of microscopic clocks based on gravitational effects and quantum mechanics, ensuring minimal disturbance and self-interaction for precise time measurement.

Contribution

It introduces a novel upper bound on microscopic clock mass considering gravitational disturbance and self-interaction using semiclassical gravity.

Findings

Derived upper bounds on clock mass for specified time resolution.

Quantified gravitational self-interaction effects on clock accuracy.

Provided theoretical limits relevant for quantum gravity and precision measurement.

Abstract

According to general relativity, clocks are the basic measuring devices needed to probe spacetime geometry. However, it is generally accepted that the mass of clocks capable of measuring small time intervals must be bounded from below. In this article, we consider two gravitationally induced phenomena: first, the extent to which such a mass disturbs the geometry that the clocks intended to probe; second, the magnitude of the gravitational self-interaction. We adopt the semiclassical coupling between gravity and quantum matter in the non-relativistic regime to obtain upper bounds on the mass of the clocks for a given time resolution and running time.