The Aharonov-Bohm (AB) effect is now largely considered to be a manifestation of geometric phase. However, by decomposing the vector-potential gradient tensor into divergence, curl, and shear components, we isolate a field/charged-particle interaction that is not dependent on local electric and magnetic fields. We show that a local shear field provides a velocity-dependent, dynamic-phase interaction in the AB effect whose predictions are consistent with all known classes of AB experiments, including interference fringe shifts, the absence of time delays along the direction of propagation, and the possibility of lateral forces.
We address the question of locality versus nonlocality in the Aharonov-Bohm and the Aharonov-Casher effects. For this purpose, we investigate all possible configurations of ideal shielding of the overlap between the electromagnetic fields generated by a charge and by a magnetic flux and analyze their consequences on the Aharonov-Bohm-Casher interference. In a classical treatment of shielding, the Aharonov-Bohm-Casher effect vanishes regardless of the geometry of shielding when the local overlap of electromagnetic fields is completely eliminated. On the other hand, the result depends on the configuration of shielding if the charge quantization in the superconducting shield is taken into account. It is shown that our results are fully understood in terms of the fluctuating local-field interaction. Our analysis strongly supports the alternative view on the Aharonov-Bohm-Casher interference that the effects originate from the local action of electromagnetic fields.
Marletto and Vedral [Phys. Rev. Lett. 125, 040401 (2020)] propose that the Aharonov-Bohm (AB) phase is locally mediated by entanglement between a charged particle and the quantized electromagnetic field, asserting gauge independence for non-closed paths. In this Comment, we critically analyze their model and demonstrate that the AB phase arises from the interaction with the vector potential
A, not from entanglement, which is a byproduct of the quantum electrodynamics (QED) framework. We show that their field-based energy formulation, intended to reflect local electromagnetic interactions, is mathematically flawed due to an incorrect prefactor and yields
+qv⋅As in the Coulomb gauge, conflicting with QED's
−qv⋅As. This equivalence to
qv⋅As holds only approximately in the Coulomb gauge under static conditions, failing for time-dependent fields and other gauges, undermining their claim of a gauge-independent local mechanism. Furthermore, we confirm that the AB phase is gauge-dependent for non-closed paths, contradicting their assertion. Our analysis reaffirms the conventional explanation in the semi-classical picture, where the AB phase is driven by the vector potential
A, with entanglement playing no causal role in its generation.