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European Journal of Physics

The change of velocity of a moving magnet when it enters or leaves a strong electric field

Gordon R. Freeman, Norman Henry March

Published Jul 1, 1997• 4 citations
Publisher

Abstract

When a moving magnetic dipole enters a strong electric field the velocity of the magnet changes by a tiny amount. When a polarized, coherent beam of magnetic particles is split, the two parts passed through strong electric fields of opposite sign, then rejoined, interference patterns are observed due to the phase shift between the de Broglie waves of the two branches. Two recent, extremely delicate experiments, one using neutron interferometry and the second using F nuclei in TlF molecules, are reviewed and interpreted in this way. The fractional velocity change was 1 part in for the neutrons and 1 in for the TlF molecules. This explains the phase shift discussed by Aharonov and Casher and, contrary to their statement, is not equivalent to an Aharonov - Bohm effect. The latter requires that a de Broglie wave phase shift be produced by a vector potential in the absence of a field.

DOI
10.1088/0143-0807/18/4/009

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Motivated by the theoretical work of Boyer [J. Phys. A: Math. Gen. 39 (2006) 3455] plus the quite recent interferometric experiment of Shinohara, Aoki and Morinaga [Phys. Rev. A66 (2002) 042106] in which the scalar Aharonov-Bohm effect was studied, we re-open the extension to neutral particles carrying a magnetic moment and passing through a region of intense electric field, treated theoretically by Aharonov and Casher (AC) and independently by Anandan. An alternative interpretation of results on (a) neutrons and (b) TlF molecules to that afforded by AC is shown to involve only (i) the de Broglie wavelength of matter waves and (ii) the prediction from Maxwell’s equations for the change in velocity of a neutral moving magnet as it enters or leaves an electric field. The exquisite sensitivity of experiment (b) allows a fractional change in velocity of order 10 15 to be quantitatively determined.

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When a moving magnetic dipole enters a strong electric field the velocity of the magnet changes by a tiny amount. When a polarized, coherent beam of magnetic particles is split, the two parts passed through strong electric fields of opposite sign, then rejoined, interference patterns are observed due to the phase shift between the de Broglie waves of the two branches. Two recent, extremely delicate experiments, one using neutron interferometry and the second using F nuclei in TlF molecules, are reviewed and interpreted in this way. The fractional velocity change was 1 part in for the neutrons and 1 in for the TlF molecules. This explains the phase shift discussed by Aharonov and Casher and, contrary to their statement, is not equivalent to an Aharonov - Bohm effect. The latter requires that a de Broglie wave phase shift be produced by a vector potential in the absence of a field.
Motivated by the theoretical work of Boyer [J. Phys. A: Math. Gen. 39 (2006) 3455] plus the quite recent interferometric experiment of Shinohara, Aoki and Morinaga [Phys. Rev. A66 (2002) 042106] in which the scalar Aharonov-Bohm effect was studied, we re-open the extension to neutral particles carrying a magnetic moment and passing through a region of intense electric field, treated theoretically by Aharonov and Casher (AC) and independently by Anandan. An alternative interpretation of results on (a) neutrons and (b) TlF molecules to that afforded by AC is shown to involve only (i) the de Broglie wavelength of matter waves and (ii) the prediction from Maxwell’s equations for the change in velocity of a neutral moving magnet as it enters or leaves an electric field. The exquisite sensitivity of experiment (b) allows a fractional change in velocity of order 10 15 to be quantitatively determined.
When an electron beam passes outside a confined magnetic flux, the motional magnetic field of the electrons overlaps the confined flux. The potential energy of the magnetic dipolar interaction of the motional magnetic field with the confined magnetic flux causes the velocity of the electrons to change slightly, which shifts the phase of the electron de Broglie wave. When portions of an electron beam pass on different sides of a confined flux and are then mixed, they produce an interference pattern. There is a similar magnetic dipolar interaction, with resulting velocity and phase changes, when a beam of magnetic particles interacts with the motional magnetic flux produced by their crossing a strong electric field. These are classical electromagnetic dipolar (not Lorentz) interactions that causes changes in Berry's geometrical phase, but are not ESAB or AC effects. Data that were suggested to demonstrate the ESAB and AC effects have been quantitatively interpreted in terms of motional magnetic fields and velocity changes.
The scalar version of the Aharonov-Bohm effect predicts a phase shift for de Broglie waves due to the action of a scalar potential in an otherwise field-free (i.e., force-free) region of space. Unlike the more familiar effect due to the magnetic vector potential, the scalar effect has hitherto remained unverified due, presumably, to technical difficulties in electron interferometry. Rather than using electrons acted on by electrostatic potentials, we have performed an analogous interferometry experiment with thermal neutorns subject to pulsed magnetic fields. The expected phase shifts have been observed to a high degree of accuracy.
A phase shift for de Broglie waves due to the action of a scalar potential in an otherwise field-free (i.e., force-free) region of space is known as the scalar Aharonov-Bohm (AB) effect. Unlike the more familiar AB effect due to the magnetic vector potential, the scalar effect has hitherto remained unverified due, presumably, to technical difficulties in electron interferometry. We have performed an analogous interferometric experiment with thermal neutrons subject to pulsed magnetic fields. The observations were carried out at the University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. The expected phase shifts have been observed to a high degree of accuracy. A detailed description of the experiment and its interpretation is given in this paper.
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.
The AB (Aharonov-Bohm) effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle's wave function, even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect, an electron beam is split into two paths, with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams, the vector potential A associated with the magnetic flux  through the solenoid induces a phase shift in the electron's wave function.This phase shift, quantified by qc     , manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED (quantum electrodynamics), where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems, beyond its classical role.This article outlines the AB effect, including its theoretical framework, experimental observations, and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.