# The Aharonov-Bohm phase is locally generated (like all other quantum phases)

## TL;DR

This paper demonstrates that the Aharonov-Bohm phase arises from local entanglement between charge and photons, challenging non-local explanations and proposing a way to measure the phase locally.

## Contribution

It provides a quantum field theory model showing the AB phase is locally generated via entanglement, resolving non-locality issues in previous explanations.

## Key findings

- The AB phase is mediated by local photon entanglement.
- A gauge-invariant phase difference can be measured locally.
- The model predicts a specific phase difference along the charge's path.

## Abstract

In the Aharonov-Bohm (AB) effect, a superposed charge acquires a detectable phase by enclosing an infinite solenoid, in a region where the solenoid's electric and magnetic fields are zero. Its generation seems therefore explainable only by the local action of gauge-dependent potentials, not of gauge-independent fields. This was recently challenged by Vaidman, who explained the phase by the solenoid's current interacting with the electron's field (at the solenoid). Still, his model has a residual non-locality: it does not explain how the phase, generated at the solenoid, is detectable on the charge. In this paper we solve this non-locality explicitly, by quantising the field. We show that the AB phase is mediated locally by the entanglement between the charge and the photons, like all electromagnetic phases. We also predict a gauge-invariant value for the phase difference at each point along the charge's path. We propose a realistic experiment to measure this phase difference locally, by partial quantum state tomography on the charge, without closing the interference loop.