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

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.

References in corpus (2)

• Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity
• Nonlocality of a single particle

Cited by in corpus (25)

• Quantum field theory for spin operator of the photon
• Geometric phases and the Sagnac effect: Foundational aspects and sensing applications
• Local description of the Aharonov-Bohm effect with a quantum electromagnetic field
• Coherence and realism in the Aharonov-Bohm effect
• Inference of gravitational field superposition from quantum measurements
• The Quantum Totalitarian Property and Exact Symmetries
• Aharonov-Casher and shielded Aharonov-Bohm effects with a quantum electromagnetic field
• Gauge independent description of Aharonov-Bohm Effect
• Electrodynamic Aharonov-Bohm effect
• Probing quantum coherence at a distance and Aharonov-Bohm non-locality
• Schrödinger operators with multiple Aharonov-Bohm fluxes
• Gauge invariance of the local phase in the Aharonov-Bohm interference: quantum electrodynamic approach
• The Aharonov-Bohm effect in a closed flux line
• Aharonov-Bohm effect with an effective complex-valued vector potential
• Quadratic forms for Aharonov-Bohm Hamiltonians
• Gauge invariance of the Aharonov-Bohm effect in a quantum electrodynamics framework
• Aharonov-Bohm effect mediated by massive photons
• Comment on "Aharonov-Bohm Phase is Locally Generated Like All Other Quantum Phases"
• Topological schemes in spacetime for the electrodynamic Aharonov-Bohm effect
• Explaining Bell Locally
• Time-symmetry and topology of the Aharonov-Bohm effect
• Gauge dependence of the Aharonov-Bohm phase in a quantum electrodynamics framework
• Interference in the Heisenberg Picture of Quantum Field Theory, Local Elements of Reality and Fermions
• The Aharonov Bohm effect as a material phenomenon
• Topology of the Aharonov-Bohm effect in different reference frames