Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Quantum non-locality vs. quasi-local measurements in the conditions of the Aharonov-Bohm effect

ARMEN M. GULIAN

Published May 12, 2014• 0 citations
Publisher

Abstract

Theoretical explanation of the Meissner effect involves proportionality between current density and vector potential, which has many deep consequences. As noticed by de Gennes, superconductors in a magnetic field "find an equilibrium state where the sum of kinetic and magnetic energies is minimum" and this state "corresponds to the expulsion of the magnetic field". This statement still leaves an open question: from which source is the superconducting current acquiring its kinetic energy? A naïve answer, perhaps, is from the energy of the magnetic field. However, one can consider situations (Aharonov-Bohm effect), where the classical magnetic field is locally absent in the area occupied by the current. Experiments demonstrate that despite the local absence of the magnetic field, current is, nevertheless, building up. From what source is it acquiring its energy then? Locally, only a vector potential is present. How does the vector potential facilitate the formation of the current? Is the current formation a result of a truly non-local quantum action, or does the local action of the vector potential have experimental consequences? We discuss possible experiments with a hybrid normal-metal superconductor circuitry, which can clarify this puzzling situation. Experimental answers will be important for further developments.

DOI
10.1088/1742-6596/507/4/042012

Related papers

Meissner response of superconductors: Quantum non-locality vs. quasi-local measurements in the conditions of the Aharonov-Bohm effect

ARMEN M. GULIAN

Theoretical explanation of the Meissner effect involves proportionality between current density and vector potential [1], which has many deep consequences. Amongst them, one can speculate that superconductors in a magnetic field "find an equilibrium state where the sum of kinetic and magnetic energies is minimum" and this state "corresponds to the expulsion of the magnetic field" [2]. This statement still leaves an open question: from which source is superconducting current acquiring its kinetic energy? A naïve answer, perhaps, is from the energy of the magnetic field. However, one can consider situations (Aharonov-Bohm effect), where the classical magnetic field is absent in the space area where the current is being set up. Experiments demonstrate [3] that despite the local absence of magnetic field, current is, nevertheless, building up. From what source is it acquiring its energy then? Locally, only a vector potential is present. How does the vector potential facilitate the formation of the current? Is the current formation a result of truly non-local quantum action, or does the local action of the vector potential have experimental consequences, which are measurable quasi-locally? We discuss possible experiments with a hybrid normal-metal superconductor circuitry, which can clarify this puzzling situation. Experimental answers would be important for further theoretical developments.

arXiv:1208.1079•Aug 6, 2012•0 citations

Shielded, local Aharonov-Bohm effects: how quantum phases cannot be stopped

Pablo L. Saldanha, Chiara Marletto, Vlatko Vedral

Both classical and quantum wave interference phenomena rely on the notion of phase. In both classical as well as quantum electrodynamics the phases are acquired locally; however, the quantum phases have the additional property that they can be transmitted even when the classical value of the degree of freedom relevant for the transfer (such as the value of the electric field at one point) are zero. Here we use a covariant formalism that is capable of explaining the electric and magnetic versions of the Aharonov-Bohm effect, as well as the Aharonov-Casher effect, through local interactions of charges and currents with the quantum electromagnetic field. We show that Aharonov-Bohm effect, which is just another instance of interference based on a quantum phase, is present even if the solenoid generating the magnetic field is shielded by a superconductor. This is because even though the classical value of the magnetic field is zero in the superconductor (the Meissner effect), the quantum operators pertaining to the magnetic field are non-zero and are furthermore responsible for transmitting the phase information between the solenoid and the electron. The conclusion of our work is that quantum phases cannot be shielded and we believe that this, among other consequences, finally resolves the last outstanding mystery in the Aharonov-Bohm effect.

•Nov 17, 2020•2 citations

Against a proposed alternative explanation of the Aharonov–Bohm effect

Murray Peshkin

The Aharonov–Bohm (AB) effect is understood to demonstrate that the Maxwell fields can act nonlocally in some situations. However it has been suggested from time to time that the AB effect is somehow a consequence of a local classical electromagnetic field phenomenon involving energy that is temporarily stored in the overlap between the external field and the field of which the beam particle is the source. That idea was shown in the past not to work for some models of the source of the external field. Here a more general proof is presented for the magnetic AB effect to show that the overlap energy is always compensated by another contribution to the energy of the magnetic field in such a way that the sum of the two is independent of the external flux. Therefore no such mechanism can underlie the AB effect.

arXiv:1009.1613•Journal of Physics A Mathematical and Theoretical•Aug 12, 2010•1 citation

Unveiling the Role of Vector Potential in the Aharonov–Bohm Effect

M. Wakamatsu

The most popular interpretation of the Aharonov–Bohm (AB) effect is that the electromagnetic potential locally affects the complex phase of a charged particle’s wave function in the magnetic field free region. However, since the vector potential is a gauge-variant quantity, multiple researchers suspect that it is just a convenient tool for calculating the force field. This motivates them to explain the AB effect without using the vector potential, which inevitably leads to some sort of non-locality. This frustrating situation is shortly summarized by the statement by Aharonov et al. that the AB effect may be due to a local gauge potential or due to non-local gauge-invariant fields. In the present paper, we shall give several convincing arguments which support the viewpoint that the vector potential is not just a convenient mathematical tool with little physical entity. Despite its gauge arbitrariness, the vector potential certainly contains a gauge-invariant piece, which solely explains the observed AB phase shift. Importantly, this component has a property such that it is basically unique and cannot be eliminated by any regular gauge transformations. To complete the discussion, we also discuss the role of remaining gauge arbitrariness still contained in the entire vector potential.

arXiv:2506.07018•Symmetry•Jun 12, 2025•0 citations

The Aharonov Bohm effect as a material phenomenon

V. Rubaev, Leonid Evgenevich Fedichkin

An experiment to observe the Aharonov-Bohm effect is discussed. A solenoid which consists of a large number of point magnetic dipoles is considered as the source of a vector potential, which acts on a charged particle, and such potential has an electromagnetic field of zero strength in the region of a nonzero vector potential. A detailed microscopic analysis of the change in the quantum state phase of the entire system, namely, a particle and a set of dipoles, reveals the origin of the apparent nonlocality of the action of the vector potential, and shows the locality of the phase change mechanism. An analysis of an experiment with a solenoid shielded by a superconducting shell is given.

arXiv:2109.12438•Sep 25, 2021•0 citations

Magnetic flux and its topological effects in Aharonov-Bohm effect

Manvendra Somvanshi, D. Jaffino Stargen

The Aharonov-Bohm effect is a physical phenomenon in which the quantum state of a charged particle acquires a phase shift that is directly proportional to the magnetic flux, $Φ$, due to a (classical) magnetic field, ${\mathbf B}$, which is confined in a spatial region from which the magnetic field cannot escape. Even though the charged particle is not allowed to interact with the magnetic field, it accumulates a phase shift that affects the interference pattern produced. Not surprisingly, this apparent nonlocality is puzzling and counter intuitive. In this work, we provide an explanation that explains the physics underlying this apparent nonlocality. We find that the role of the confined magnetic field is to impart a puncture in the configuration space, $\mathbb{R}^2$, of the charge. Therefore, the quantum state corresponding to the charged quantum particle acquires the phase shift due to its response to the modified topology of the configuration space, $\mathbb{R}^2-\{0\}$, corresponding to the charge.

quant-pharXiv:2511.11120•Nov 17, 2025•0 citations
Theoretical explanation of the Meissner effect involves proportionality between current density and vector potential, which has many deep consequences. As noticed by de Gennes, superconductors in a magnetic field "find an equilibrium state where the sum of kinetic and magnetic energies is minimum" and this state "corresponds to the expulsion of the magnetic field". This statement still leaves an open question: from which source is the superconducting current acquiring its kinetic energy? A naïve answer, perhaps, is from the energy of the magnetic field. However, one can consider situations (Aharonov-Bohm effect), where the classical magnetic field is locally absent in the area occupied by the current. Experiments demonstrate that despite the local absence of the magnetic field, current is, nevertheless, building up. From what source is it acquiring its energy then? Locally, only a vector potential is present. How does the vector potential facilitate the formation of the current? Is the current formation a result of a truly non-local quantum action, or does the local action of the vector potential have experimental consequences? We discuss possible experiments with a hybrid normal-metal superconductor circuitry, which can clarify this puzzling situation. Experimental answers will be important for further developments.
Theoretical explanation of the Meissner effect involves proportionality between current density and vector potential [1], which has many deep consequences. Amongst them, one can speculate that superconductors in a magnetic field "find an equilibrium state where the sum of kinetic and magnetic energies is minimum" and this state "corresponds to the expulsion of the magnetic field" [2]. This statement still leaves an open question: from which source is superconducting current acquiring its kinetic energy? A naïve answer, perhaps, is from the energy of the magnetic field. However, one can consider situations (Aharonov-Bohm effect), where the classical magnetic field is absent in the space area where the current is being set up. Experiments demonstrate [3] that despite the local absence of magnetic field, current is, nevertheless, building up. From what source is it acquiring its energy then? Locally, only a vector potential is present. How does the vector potential facilitate the formation of the current? Is the current formation a result of truly non-local quantum action, or does the local action of the vector potential have experimental consequences, which are measurable quasi-locally? We discuss possible experiments with a hybrid normal-metal superconductor circuitry, which can clarify this puzzling situation. Experimental answers would be important for further theoretical developments.
Both classical and quantum wave interference phenomena rely on the notion of phase. In both classical as well as quantum electrodynamics the phases are acquired locally; however, the quantum phases have the additional property that they can be transmitted even when the classical value of the degree of freedom relevant for the transfer (such as the value of the electric field at one point) are zero. Here we use a covariant formalism that is capable of explaining the electric and magnetic versions of the Aharonov-Bohm effect, as well as the Aharonov-Casher effect, through local interactions of charges and currents with the quantum electromagnetic field. We show that Aharonov-Bohm effect, which is just another instance of interference based on a quantum phase, is present even if the solenoid generating the magnetic field is shielded by a superconductor. This is because even though the classical value of the magnetic field is zero in the superconductor (the Meissner effect), the quantum operators pertaining to the magnetic field are non-zero and are furthermore responsible for transmitting the phase information between the solenoid and the electron. The conclusion of our work is that quantum phases cannot be shielded and we believe that this, among other consequences, finally resolves the last outstanding mystery in the Aharonov-Bohm effect.
The Aharonov–Bohm (AB) effect is understood to demonstrate that the Maxwell fields can act nonlocally in some situations. However it has been suggested from time to time that the AB effect is somehow a consequence of a local classical electromagnetic field phenomenon involving energy that is temporarily stored in the overlap between the external field and the field of which the beam particle is the source. That idea was shown in the past not to work for some models of the source of the external field. Here a more general proof is presented for the magnetic AB effect to show that the overlap energy is always compensated by another contribution to the energy of the magnetic field in such a way that the sum of the two is independent of the external flux. Therefore no such mechanism can underlie the AB effect.
The most popular interpretation of the Aharonov–Bohm (AB) effect is that the electromagnetic potential locally affects the complex phase of a charged particle’s wave function in the magnetic field free region. However, since the vector potential is a gauge-variant quantity, multiple researchers suspect that it is just a convenient tool for calculating the force field. This motivates them to explain the AB effect without using the vector potential, which inevitably leads to some sort of non-locality. This frustrating situation is shortly summarized by the statement by Aharonov et al. that the AB effect may be due to a local gauge potential or due to non-local gauge-invariant fields. In the present paper, we shall give several convincing arguments which support the viewpoint that the vector potential is not just a convenient mathematical tool with little physical entity. Despite its gauge arbitrariness, the vector potential certainly contains a gauge-invariant piece, which solely explains the observed AB phase shift. Importantly, this component has a property such that it is basically unique and cannot be eliminated by any regular gauge transformations. To complete the discussion, we also discuss the role of remaining gauge arbitrariness still contained in the entire vector potential.
An experiment to observe the Aharonov-Bohm effect is discussed. A solenoid which consists of a large number of point magnetic dipoles is considered as the source of a vector potential, which acts on a charged particle, and such potential has an electromagnetic field of zero strength in the region of a nonzero vector potential. A detailed microscopic analysis of the change in the quantum state phase of the entire system, namely, a particle and a set of dipoles, reveals the origin of the apparent nonlocality of the action of the vector potential, and shows the locality of the phase change mechanism. An analysis of an experiment with a solenoid shielded by a superconducting shell is given.
The Aharonov-Bohm effect is a physical phenomenon in which the quantum state of a charged particle acquires a phase shift that is directly proportional to the magnetic flux, ΦΦΦ, due to a (classical) magnetic field, B{\mathbf B}B, which is confined in a spatial region from which the magnetic field cannot escape. Even though the charged particle is not allowed to interact with the magnetic field, it accumulates a phase shift that affects the interference pattern produced. Not surprisingly, this apparent nonlocality is puzzling and counter intuitive. In this work, we provide an explanation that explains the physics underlying this apparent nonlocality. We find that the role of the confined magnetic field is to impart a puncture in the configuration space, R2\mathbb{R}^2R2, of the charge. Therefore, the quantum state corresponding to the charged quantum particle acquires the phase shift due to its response to the modified topology of the configuration space, R2−{0}\mathbb{R}^2-\{0\}R2−{0}, corresponding to the charge.