The Aharonov-Bohm Effect and the Non-Locality Debate

Yakir Aharonov

Kicheon Kang

Abstract In the Aharonov-Bohm (AB) effect, interference fringes are observed for a charged particle in the absence of the local overlap with the external electromagnetic field. This notion of the apparent “nonlocality” of the interaction or the significant role of the potential have recently been challenged and are under debate. The quantum electrodynamic approach provides a microscopic picture of the characteristics of the interaction between a charge and an external field. We explicitly show the gauge invariance of the local phase shift in the magnetic AB effect, which is in contrast to the results obtained using the usual semiclassical vector potential. Our study can resolve the issue of the locality in the magnetic AB effect. However, the problem is not solved in the same way in the electric counterpart wherein virtual scalar photons play an essential role.

Peter Holland

Moreno Nourizadeh

The Aharonov-Bohm effect has generated a sixty-year debate between two interpretive camps: one holding that electromagnetic potentials are physically real, the other that electromagnetic fields act non-locally. This paper argues that the debate is structurally analogous to the paradigmatic seams identified across ten cases in the philosophy of physics and mathematics, where a framework generates phenomena it cannot accommodate because its enabling conditions have been excluded from its ontology. The enabling condition of electromagnetism, on the analysis presented here, is neither the potential nor the field but the connection on the electromagnetic fibre bundle, a relational structure from which both potential and field are derived as partial, regime-dependent articulations. The potential is the connection expressed in coordinates (hence non-unique). The field is the connection's curvature (hence informationally incomplete: it loses the holonomy). The Aharonov-Bohm effect is the diagnostic seam where this incompleteness forces itself into experimental visibility. The connection's withdrawal from local determination, manifested as gauge freedom, is not a defect of the formalism but the formal signature of an enabling condition that must remain operative but non-thematic for the framework to function. This diagnosis dissolves the binary between the two camps by identifying their shared presupposition: that the fundamental entity must be a locally determined quantity. It does not propose new physics. It applies a structural diagnostic, developed and tested across independent domains, to an experimentally confirmed quantum phenomenon whose interpretation remains contested.

Mostafa E. El Demery

The Aharonov-Bohm effect is a quantum mechanical effect, that is, has no classical counterpart. The effect was predicted in 1959 in a seminal paper of Y. Aharonov and D. Bohm [AB59] in which they demonstrated that a beam of electrons is affected by the existence of the electric/magnetic field even though electrons travel through field-free regions. Aharonov and Bohm carried out two hypothetical experiments to support their claim that potentials are more fundamental than fields and they are respon-sible of the effect. Since then, the debate has arisen around whether potentials are mathematical tools or fundamental entities in physics. Different arguments have been set to explain the results predicted by Aharonov and Bohm and experimentally confirmed. Amongst these arguments, the first argument adopted by Aharonov and Bohm was that potentials are physically significant. Many have claimed that fields do have non-local features, i.e. action at a distance. Others have claimed that topological effects may interpret the effect in which potentials are modeled as connections in higher-dimensional fiber bun-dle geometries. The most recent argument has been proposed by Vaidman [Vai12] who claimed that the the composite system is represented by one state, an entangled state, and due to the electromagnetic interactions part of this state is changed, hence, the total state. In the present essay, I will discuss the latter argument as well as reviewing some other arguments. i

Donald H. Kobe