The Instability of a Quantum Superposition of Time Dilations

TL;DR

This paper explores how quantum superpositions of gravitational time dilations cause nonunitary evolution and dephasing, proposing an experiment to observe the quantum-classical transition using microwave interferometry.

Contribution

It introduces the concept that superpositions of gravitational potentials lead to observable dephasing effects and proposes a feasible experiment to study quantum to classical transition.

Findings

Dephasing timescale is experimentally accessible.

Superpositions of gravitational fields cause nonunitary evolution.

Proposed microwave interferometer experiment to test quantum gravity effects.

Abstract

Using the relativistic concept of time dilation we show that a superposition of gravitational potentials can lead to nonunitary time evolution. For sufficiently weak gravitational potentials one can still define, for all intents and purposes, a global coordinate system. A probe particle in a superposition of weak gravitational fields will, however, experience dephasing due to the different time dilations. The corresponding instability timescale is accessible to experiments, and can be used as a degree of macroscopicity. Finally, we suggest an experiment with smoothly tunable amplification in a microwave interferometer that allows a quantitative study of the quantum to classical boundary.