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

Physical Review A

Proposed Aharonov-Casher effect: Another example of an Aharonov-Bohm effect arising from a classical lag

Timothy H. Boyer

Published Nov 1, 1987• 110 citations
Publisher

Abstract

In 1984 Aharonov and Casher proposed that a beam of neutral particles with magnetic dipole moments passing around opposite sides of a line charge will undergo a relative quantum phase shift. This is currently under experimental investigation. Aharonov and Casher claimed that the magnetic dipole particles should undergo the phase shift despite experiencing no classical force. They suggested that this new effect has a ``duality'' with the solenoid Aharonov-Bohm effect where charged particles passing around a magnetic solenoid experience a phase shift despite, it is claimed, experiencing no classical force. Here it is pointed out that a magnetic dipole particle passing a line charge does indeed experience a classical electromagnetic force in the usual electric-current model for a magnetic dipole. This force will produce a relative lag between dipoles passing on opposite sides of the line charge, and the classical lag then leads to a quantum phase shift in exact agreement with that calculated by Aharonov and Casher. Thus actually the proposed Aharonov-Casher effect has a transparent explanation as a classical lag effect. It is emphasized that the solenoid Aharonov-Bohm effect is currently the only phase-shift effect which cannot be explained in an obvious fashion as arising from a classical lag and it is again proposed that also this shift may actually involve a classical electromagnetic lag effect. A natural experimental consequence suggested by the lag point of view is the breakdown of the interference pattern when the lag becomes comparable to the wave-packet coherence length.

DOI
10.1103/physreva.36.5083

Related papers

Classical Interaction of a Magnet and a Point Charge: The Classical Electromagnetic Forces Responsible for the Aharonov-Bohm Phase Shift

Timothy H. Boyer

A new classical electromagnetic analysis is presented suggesting that the Aharonov-Bohm phase shift is overwhelmingly likely to arise from a classical lag effect based upon classical electromagnetic forces. The analysis makes use of several aspects of classical electromagnetic theory which are unfamiliar to most physicists, including the Darwin Lagrangian, acceleration-based electric fields, internal electromagnetic momentum in a magnet, and a magnet model involving at least three mutually-interacting particles. Only when the acceleration-based electric forces acting on the passing charge are included do we find consistency with all the relativistic conservation laws: energy, linear momentum, angular momentum, and constant center-of-mass velocity. The electric forces on the passing charge lead to a lag effect which accounts quantitatively for the Aharonov-Bohm phase shift. Thus the classical analysis strongly suggests that the Aharonov-Bohm phase shift (observed when electrons pass a long solenoid which corresponds to a line of magnetic dipoles) is the analogue of the Matteucci-Pozzi phase shift (observed when electrons pass a line of electric dipoles). The classical electromagnetic analysis suggests experiments to distinguish the proposed classical-based lag effect from the presently accepted view that the Aharonov-Bohm phase shift is a quantum topological effect arising from magnetic fluxes in the absence of classical electromagnetic forces.

arXiv:1408.3745•Aug 16, 2014•4 citations

Classical Electromagnetic Deflections and Lag Effects Associated with Quantum Interference Pattern Shifts: Considerations Related to the Aharonov-Bohm Effect

Timothy H. Boyer

Classical electromagnetic lag effects can give rise to quantum interference pattern shifts such as that observed experimentally in the Aharonov-Bohm effect involving electrons passing a solenoid. This paper presents an extensive comparison between interference pattern shifts based upon classical electromagnetic fields, and based upon classical electromagnetic potentials as suggested by Aharonov and Bohm. Stress is placed upon the difference between two types of interference pattern shifts: those involving deflection of the entire interference pattern and those involving a deflection of only the double-slit pattern while leaving the single-slit envelope undisplaced. The first type of shift is produced by a classical deflecting force. The second type of shift can be produced by classical electromagnetic lag effects, and is also the type of shift associated with the Aharonov-Bohm effect. The two types are confused in the literature. A new experiment is proposed which shows the relationship between a classical lag effect, due to electrostatic fields on electrons passing along different paths, and the associated quantum interference pattern shifts. The experiment is analyzed in detail using the WKB approximation in the Schr\"odinger equation and also semiclassical ideas. The classical limit for the situation illustrates the Bohr correspondence principle, showing the relative lag between the electron wave packets becoming a measurable classical lag with a disappearance of the interference pattern as the lag becomes large compared to the wave-packet dimensions. For small shifts, the phase change predicted for the new experiment is identical with the scalar potential effect proposed by Aharonov and Bohm for a slightly different, time-varying experimental arrangement. The theoretical and experimental differences for large phase shifts are noted. The possibility is raised that a new classical electromagnetic lag effect may occur for electrons passing a small solenoid. Using a particular model for energy conservation, the predicted lag effect can be calculated and is associated with a quantum interference pattern shift of the same magnitude as predicted by Aharonov and Bohm based upon the electromagnetic vector potential. Thus the possibility exists that the experiments of Chambers and of M\"ollenstedt and Bayh may not confirm the ideas of Aharonov and Bohm on the vector potential in quantum theory. Several experiments are suggested which allow confirmation that the Aharonov-Bohm effect indeed involves local effects of the classical electromagnetic potential, rather than local electromagnetic fields leading to a new classical lag effect and hence to the observed quantum interference pattern shift.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Sep 15, 1973•100 citations

Derivation of the Aharanov Bohm phase shift using classical forces

H. Fearn, Nguyen, Khai

In 1959 Aharonov and Bohm suggested that an electron passing around a long solenoid would pick up a phase shift dependent on the magnetic field of the solenoid, even though the electrons themselves pass through a region of space which has a zero magnetic field. It has long been held that this result is purely quantum and is derived in many well known quantum mechanics text books using the Schrodinger equation and vector potential. Here the same phase shift is derived from a purely classical force, but relativistic transformations are taken into account. The force is in the direction of motion of the electron (or opposite) leading to a phase advance (or lag) and we obtain precisely the phase shift thought previously to be purely quantum. The only quantum result used here is the de Broglie wavelength of the particle, in order to get two slit like interference and the phase shift. We employ a stack of dipoles as the solenoid and note the same force on the electron in two different frames of reference. We shall consider the solenoid stationary and the electron moving, and then consider the electron rest frame and consider the solenoid moving in the opposite direction.

arXiv:1104.1449•Apr 7, 2011•0 citations

Interpretation of the Aharonov-Bohm and the Aharonov-Casher Effects in Terms of Classical Electromagnetic Fields

Gianfranco Spavieri, G. Cavalleri

When an electric charge passes past a stationary current loop the time-varying fields induce changes of the internal energy of the loop. The magnetic flux of the loop also changes and, by Faraday's law, creates a radiation electric field which acts back on the particle. This interaction produces a classical electromagnetic lag which generates the phase shifts of the wave function foreseen by these effects. A possible experimental test is proposed.

Europhysics Letters (EPL)•Feb 21, 1992•14 citations

ANALYSIS KUANTUM DAN VERIFIKASI EFEK AHARONOV-CASHER (QUANTUM ANALYSIS AND VERIFICATION OF THE AHAROVO V-CA SHER EFFECT)

Muslim Juliasih Partini

ABSTRACT\nThe interaction of charged and uncharged particles with intrinsic magnetic moment for the latter with an electromagnetic field in the microworld brings out the actual role of the electromagnetic potentials as emphasized in quantum theory which generate electromagnetic interaction via gauge invariance requirement.\nIn the Aharonov-Bohm (A-B) effect (dealing with two electron coherent beams passing a double slit system), the resulting interference pattern is shifted by the insertion of a very long solenoid between the two electron beams with an influence described by the magnetic vector\npotential A on the electron wave functions. Aharonov and Casher presented the complement of the Aharonov-Bohm effect involving the role of the electric scalar potential co on a beam of neutrons each carrying an internal magnetic dipole moment. A similar shift in the interference pattern is found involving two coherent neutron beam interference, where the solenoid in the A-B arrangement is replaced by an electric line charge, and the electrons by polarized neutrons. The effective Hamiltonian describing the two effects is used to determine the interference pattern.\nThe experiment to verify the existence of the Aharonov-Bohm effect which have been performed using an electron holography with a small toroidal ferromagnetic substance confining a magnetic flux by Tonomura in 1982 is discussed. The Aharonov-Casher effect, which was conducted using a Bonse-Hart single-crystal neutron interferometer by A. Cirnmino in 1989, is also discussed. Both experimental results lead to the same phenomenon: a phase shift in the observed pattern interference quantitatively explained as caused by the influence of the proper component of the electrodynamic potentials.\n\nKey Word: Kuantum, Aharonov- cahser

Teknosains•Jan 1, 2001•0 citations

New Mechanism of Aharonov Bohm Effect

Jiaqing Yan

The traditional Aharonov Bohm effect (AB effect) attributes the light and dark fringes on screen to phase interference of electron matter wave. It presumes that the magnetic field outside the solenoid equals zero and particles receive no force. This system has long served as key support for wave particle duality. This paper completely abandons the hypothesis of wave interference and quantum phase. It establishes the model of electron vibrating point particle to reveal the real physical mechanism of AB effect. Fringes are not superposition product of waves. They are formed by differential deflection of charged electrons under magnetic force and Coulomb repulsion, followed by regular superposition of two upper and lower particle beams. Both magnetic force and Coulomb repulsion are long range forces. They only differ in effective action range and variation rule of force with distance. Comparative experiments using direct current solenoid and direct current long straight wire can falsify the unrealistic assumption that magnetic field outside coil cancels out to zero. Supporting single side shielding verification experiment can directly test the correctness of orthodox quantum interpretation. Electrons have no wave property. As long as point particles with inherent vibration are modulated by field, they can form fringe similar to interference fringe. Photons are also point particles with inherent vibration. When photons pass through slits, they interact with slit wall and produce deflection, so as to form photon diffraction and interference fringes. The hypothesis of wave particle duality is invalid.

•Oct 2, 2026•0 citations
In 1984 Aharonov and Casher proposed that a beam of neutral particles with magnetic dipole moments passing around opposite sides of a line charge will undergo a relative quantum phase shift. This is currently under experimental investigation. Aharonov and Casher claimed that the magnetic dipole particles should undergo the phase shift despite experiencing no classical force. They suggested that this new effect has a ``duality'' with the solenoid Aharonov-Bohm effect where charged particles passing around a magnetic solenoid experience a phase shift despite, it is claimed, experiencing no classical force. Here it is pointed out that a magnetic dipole particle passing a line charge does indeed experience a classical electromagnetic force in the usual electric-current model for a magnetic dipole. This force will produce a relative lag between dipoles passing on opposite sides of the line charge, and the classical lag then leads to a quantum phase shift in exact agreement with that calculated by Aharonov and Casher. Thus actually the proposed Aharonov-Casher effect has a transparent explanation as a classical lag effect. It is emphasized that the solenoid Aharonov-Bohm effect is currently the only phase-shift effect which cannot be explained in an obvious fashion as arising from a classical lag and it is again proposed that also this shift may actually involve a classical electromagnetic lag effect. A natural experimental consequence suggested by the lag point of view is the breakdown of the interference pattern when the lag becomes comparable to the wave-packet coherence length.
A new classical electromagnetic analysis is presented suggesting that the Aharonov-Bohm phase shift is overwhelmingly likely to arise from a classical lag effect based upon classical electromagnetic forces. The analysis makes use of several aspects of classical electromagnetic theory which are unfamiliar to most physicists, including the Darwin Lagrangian, acceleration-based electric fields, internal electromagnetic momentum in a magnet, and a magnet model involving at least three mutually-interacting particles. Only when the acceleration-based electric forces acting on the passing charge are included do we find consistency with all the relativistic conservation laws: energy, linear momentum, angular momentum, and constant center-of-mass velocity. The electric forces on the passing charge lead to a lag effect which accounts quantitatively for the Aharonov-Bohm phase shift. Thus the classical analysis strongly suggests that the Aharonov-Bohm phase shift (observed when electrons pass a long solenoid which corresponds to a line of magnetic dipoles) is the analogue of the Matteucci-Pozzi phase shift (observed when electrons pass a line of electric dipoles). The classical electromagnetic analysis suggests experiments to distinguish the proposed classical-based lag effect from the presently accepted view that the Aharonov-Bohm phase shift is a quantum topological effect arising from magnetic fluxes in the absence of classical electromagnetic forces.
Classical electromagnetic lag effects can give rise to quantum interference pattern shifts such as that observed experimentally in the Aharonov-Bohm effect involving electrons passing a solenoid. This paper presents an extensive comparison between interference pattern shifts based upon classical electromagnetic fields, and based upon classical electromagnetic potentials as suggested by Aharonov and Bohm. Stress is placed upon the difference between two types of interference pattern shifts: those involving deflection of the entire interference pattern and those involving a deflection of only the double-slit pattern while leaving the single-slit envelope undisplaced. The first type of shift is produced by a classical deflecting force. The second type of shift can be produced by classical electromagnetic lag effects, and is also the type of shift associated with the Aharonov-Bohm effect. The two types are confused in the literature. A new experiment is proposed which shows the relationship between a classical lag effect, due to electrostatic fields on electrons passing along different paths, and the associated quantum interference pattern shifts. The experiment is analyzed in detail using the WKB approximation in the Schr\"odinger equation and also semiclassical ideas. The classical limit for the situation illustrates the Bohr correspondence principle, showing the relative lag between the electron wave packets becoming a measurable classical lag with a disappearance of the interference pattern as the lag becomes large compared to the wave-packet dimensions. For small shifts, the phase change predicted for the new experiment is identical with the scalar potential effect proposed by Aharonov and Bohm for a slightly different, time-varying experimental arrangement. The theoretical and experimental differences for large phase shifts are noted. The possibility is raised that a new classical electromagnetic lag effect may occur for electrons passing a small solenoid. Using a particular model for energy conservation, the predicted lag effect can be calculated and is associated with a quantum interference pattern shift of the same magnitude as predicted by Aharonov and Bohm based upon the electromagnetic vector potential. Thus the possibility exists that the experiments of Chambers and of M\"ollenstedt and Bayh may not confirm the ideas of Aharonov and Bohm on the vector potential in quantum theory. Several experiments are suggested which allow confirmation that the Aharonov-Bohm effect indeed involves local effects of the classical electromagnetic potential, rather than local electromagnetic fields leading to a new classical lag effect and hence to the observed quantum interference pattern shift.
In 1959 Aharonov and Bohm suggested that an electron passing around a long solenoid would pick up a phase shift dependent on the magnetic field of the solenoid, even though the electrons themselves pass through a region of space which has a zero magnetic field. It has long been held that this result is purely quantum and is derived in many well known quantum mechanics text books using the Schrodinger equation and vector potential. Here the same phase shift is derived from a purely classical force, but relativistic transformations are taken into account. The force is in the direction of motion of the electron (or opposite) leading to a phase advance (or lag) and we obtain precisely the phase shift thought previously to be purely quantum. The only quantum result used here is the de Broglie wavelength of the particle, in order to get two slit like interference and the phase shift. We employ a stack of dipoles as the solenoid and note the same force on the electron in two different frames of reference. We shall consider the solenoid stationary and the electron moving, and then consider the electron rest frame and consider the solenoid moving in the opposite direction.
ABSTRACT\nThe interaction of charged and uncharged particles with intrinsic magnetic moment for the latter with an electromagnetic field in the microworld brings out the actual role of the electromagnetic potentials as emphasized in quantum theory which generate electromagnetic interaction via gauge invariance requirement.\nIn the Aharonov-Bohm (A-B) effect (dealing with two electron coherent beams passing a double slit system), the resulting interference pattern is shifted by the insertion of a very long solenoid between the two electron beams with an influence described by the magnetic vector\npotential A on the electron wave functions. Aharonov and Casher presented the complement of the Aharonov-Bohm effect involving the role of the electric scalar potential co on a beam of neutrons each carrying an internal magnetic dipole moment. A similar shift in the interference pattern is found involving two coherent neutron beam interference, where the solenoid in the A-B arrangement is replaced by an electric line charge, and the electrons by polarized neutrons. The effective Hamiltonian describing the two effects is used to determine the interference pattern.\nThe experiment to verify the existence of the Aharonov-Bohm effect which have been performed using an electron holography with a small toroidal ferromagnetic substance confining a magnetic flux by Tonomura in 1982 is discussed. The Aharonov-Casher effect, which was conducted using a Bonse-Hart single-crystal neutron interferometer by A. Cirnmino in 1989, is also discussed. Both experimental results lead to the same phenomenon: a phase shift in the observed pattern interference quantitatively explained as caused by the influence of the proper component of the electrodynamic potentials.\n\nKey Word: Kuantum, Aharonov- cahser
The traditional Aharonov Bohm effect (AB effect) attributes the light and dark fringes on screen to phase interference of electron matter wave. It presumes that the magnetic field outside the solenoid equals zero and particles receive no force. This system has long served as key support for wave particle duality. This paper completely abandons the hypothesis of wave interference and quantum phase. It establishes the model of electron vibrating point particle to reveal the real physical mechanism of AB effect. Fringes are not superposition product of waves. They are formed by differential deflection of charged electrons under magnetic force and Coulomb repulsion, followed by regular superposition of two upper and lower particle beams. Both magnetic force and Coulomb repulsion are long range forces. They only differ in effective action range and variation rule of force with distance. Comparative experiments using direct current solenoid and direct current long straight wire can falsify the unrealistic assumption that magnetic field outside coil cancels out to zero. Supporting single side shielding verification experiment can directly test the correctness of orthodox quantum interpretation. Electrons have no wave property. As long as point particles with inherent vibration are modulated by field, they can form fringe similar to interference fringe. Photons are also point particles with inherent vibration. When photons pass through slits, they interact with slit wall and produce deflection, so as to form photon diffraction and interference fringes. The hypothesis of wave particle duality is invalid.