Proposal for locality test of Aharonov-Bohm effect via Andreev interferometer without a loop

TL;DR

This paper proposes a test to distinguish local and nonlocal models of the Aharonov-Bohm effect using an Andreev interferometer setup, potentially resolving fundamental questions about quantum nonlocality in electromagnetic interactions.

Contribution

It introduces a local gauge-invariant Lagrangian model for the Aharonov-Bohm effect and suggests an experimental setup to test its predictions against the standard nonlocal model.

Findings

Local model predicts a gauge-invariant phase shift in interference.

Standard nonlocal model does not predict a gauge-invariant phase shift.

Experimental observation can differentiate between local and nonlocal models.

Abstract

We propose a quantitative test of the quantum nonlocality in the electromagnetic interaction that generates the Aharonov-Bohm effect. For this purpose, we derive an interaction Lagrangian based on the local action of gauge-invariant quantities only, and compare it with the standard potential-based ("nonlocal") Lagrangian. It is shown that the two models provide identical results for any phenomena involving classical equations of motion or topological quantum phases. Interestingly, we find an example violating this equivalence, that is, the interference of single charges coproduced from two independent sources. Whereas a well-defined phase shift of the interference is predicted in the "local" model, the standard nonlocal Lagrangian does not provide a gauge-invariant phase shift. This implies that an observation of the interference in the proposed setup can rule out the gauge-dependent potential-based model. This result has profound implications as it can settle the issue of dynamical nonlocality in the quantum electromagnetic interaction.