Comment on "Aharonov-Bohm Phase is Locally Generated Like All Other Quantum Phases"

TL;DR

This Comment scrutinizes Marletto and Vedral’s claim that the Aharonov-Bohm (AB) phase is locally mediated by entanglement with the quantized electromagnetic field. It shows the AB phase fundamentally arises from coupling to the vector potential $\mathbf{A}$ within QED, not from entanglement, and that their proposed gauge-independent local field energy $\mathcal{E}_{\text{field}}$ is flawed: it carries a problematic $\tfrac{1}{2}$ prefactor, yields a sign mismatch with the QED interaction energy in the Coulomb gauge, and implies gauge-invariant phases for non-closed paths contrary to standard QED. The critique demonstrates that the equivalence between $\mathcal{E}_{\text{field}}$ and the magnetic interaction $q\mathbf{v}\cdot\mathbf{A}$ is gauge-specific (valid only in the Coulomb gauge under static conditions) and does not hold for time-dependent fields. It further argues that the AB phase is gauge-dependent for non-closed paths, and that entanglement plays at most an incidental role, with the AB phase remaining fully accounted for by the classical vector potential in a semi-classical picture. Collectively, the paper reinforces the conventional interpretation of the AB effect and clarifies the misattributions in MV2020.

Abstract

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 \(\mathbf{A}\), 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 \( +q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}} \) in the Coulomb gauge, conflicting with QED's \( -q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}} \). This equivalence to \( q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}} \) 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 \(\mathbf{A}\), with entanglement playing no causal role in its generation.