Aharonov-Bohm Effects for Electromagnetism and Gravity in Four-Dimensional Spacetime

TL;DR

This paper develops a geometric framework for the gravitational Aharonov-Bohm effect in four-dimensional spacetime, showing how curvature causes nonlocal quantum phase shifts, and suggests experimental tests using atom interferometry.

Contribution

It introduces a geometric approach to gravitational Aharonov-Bohm effects, linking spacetime curvature to quantum phase shifts and demonstrating their isomorphism with electromagnetic effects.

Findings

Spacetime curvature induces nonlocal quantum phase shifts.

Gravitational phase shifts are mathematically equivalent to electromagnetic ones.

Theoretical support for experimental detection via atom interferometry.

Abstract

This paper investigates a geometric framework for the gravitational Aharonov-Bohm effect in four-dimensional spacetime, demonstrating how spacetime curvature induces nonlocal quantum phase shifts within field-free regions. By constructing vector bundles on spacetime manifolds equipped with Levi-Civita connections, we derive the holonomy transformations for parallel-transported quantum states. Under the Newtonian approximation, metric decomposition into Minkowski background plus scalar potential perturbations reveals through the linearized Einstein field equations that the gravitationally induced phase shift is mathematically isomorphic to its electromagnetic counterpart. These results establish the quantum observability of gravitational gauge structures and provide theoretical support for experimental verification via atom interferometry.