Quantum Interference to Measure Spacetime Curvature: A Proposed Experiment at the Intersection of Quantum Mechanics and General Relativity

TL;DR

This paper proposes an experiment using atom interferometry in Low Earth Orbit to measure spacetime curvature by analyzing quantum phase differences, linking quantum mechanics and general relativity.

Contribution

It introduces a novel method to measure Riemann curvature components via quantum phase differences in atom interferometry, applicable to gravitational waves.

Findings

Quantum phase difference relates to spacetime volume and curvature tensor.

Method applicable to gravitational waves in long wavelength limit.

Proposes a feasible experiment in Low Earth Orbit.

Abstract

An experiment in Low Earth Orbit (LEO) is proposed to measure components of the Riemann curvature tensor using atom interferometry. We show that the difference in the quantum phase $\Delta\phi$ of an atom that can travel along two intersecting geodesics is given by $mR_{0i0j}/\hbar$ times the spacetime volume contained within the geodesics. Our expression for $\Delta\phi$ also holds for gravitational waves in the long wavelength limit.