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Acta Physica Sinica

The dynamical mechanism of A-B effect and its testing scheme

Ruifeng Wang, 北京交通大学物理系,北京 100044

Published Jan 1, 2005• 1 citation
Publisher

Abstract

The dynamical mechanism of A-B effect is discussed in detail. It is found that A-B effect is due to the superposition of the magnetic field produced by the moving charges with that in the solenoid, rathor than the existence of vector potential A. If such a magnetic field superposition can be prevented, the A-B effect will disappear, even though the vector potential A still exists in space. To verify this conclusion, a new experimental scheme is suggested.

DOI
10.7498/aps.54.4532

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The dynamical mechanism of A-B effect is discussed in detail. It is found that A-B effect is due to the superposition of the magnetic field produced by the moving charges with that in the solenoid, rathor than the existence of vector potential A. If such a magnetic field superposition can be prevented, the A-B effect will disappear, even though the vector potential A still exists in space. To verify this conclusion, a new experimental scheme is suggested.
There are two interpretations of the Aharonov-Bohm (A-B) effect. One interpretation asserts that the A-B effect demonstrates that the vector potential is a physical reality that can result in the phase shift of a moving charge in quantum mechanics. The other interpretation asserts that the phase shift of the moving charge results from the interaction energy between the electromagnetic field of the moving charge and external electromagnetic fields. This paper briefly reviews these two interpretations and analyzes their differences. In addition, a new experimental scheme is proposed to determine which interpretation is correct.
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 magnetic Aharonov-Bohm effect shows that charged particles may be affected by the vector potential in regions without any electric or magnetic fields [1]. The Aharonov-Bohm effect was experimentally confirmed [2-3] and has been found in many situations [4-6]. A common explanation is based on quantum mechanics, which states that the wavefunctions associated with the charges will accumulate a phase shift due to the vector potential. However, consensus about its nature and interpretation has not been achieved [7-14]. We here propose a simple but reasonable interpretation based on the theory for electromagnetic radiation and couplings [15]. The energy associated with a pulse radiator is divided into a Coulomb-velocity energy and a radiative energy, together with a macroscopic Schott energy accounting for the energy exchange between them. All these energies are expressed with terms including the potentials, so are the mutual coupling energies. There exists a force acting on the moving charges even though the fields completely vanish. This force makes the charges pass through the magnetic solenoid in different velocity with different path length, causing a phase shift the same as that obtained with quantum mechanics. The theory is originally aimed for providing an interpretation for electromagnetic radiation and mutual coupling. It is derived directly from the Maxwell theory with no modification but only substitution and reorganization.
We present a review and discussion of the physical meaning of the vector potential in electromagnetism by means of a classical experiment in which a long solenoid, connected to a sinusoidal voltage supply, produces an electric field and a vector potential in a circuit exterior to the solenoid itself. Some basic considerations are recalled concerning the meaning of action-at-a-distance and local description, in terms of 'real fields' of the induced electromotive force on the circuit outside the solenoid. From this viewpoint the roles played by the magnetic field, the electric field and the vector potential to account for the physical effects are reviewed. Finally, the connections between these considerations and the magnetic Aharonov–Bohm effect are recalled in the light of recent theoretical work aimed at explaining the Aharonov–Bohm phase shift in terms of the magnetic field without resorting to the vector potential.