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.
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.
The Aharonov-Bohm (AB) effect highlights the fundamental role of electromagnetic potentials in quantum mechanics, manifesting as a phase shift for a charged particle in field-free regions. While well-established for static magnetic fluxes, the effect's behavior under time-varying fluxes remains an open and debated question. Employing the WKB method, we derive the AB phase shift for a time-dependent magnetic vector potential, demonstrating that for circular paths in the quasistatic regime, it is proportional to the time-averaged enclosed magnetic flux,
ΔφAB=T1∫0TeΦ(t)dt, with the total phase shift, including kinetic contributions, equaling
eΦ(0). For non-circular paths, the phase shift depends on both the flux history and path geometry, revealing the effect's hybrid nature involving gauge potentials and induced electric fields. We verify the consistency of our gauge choice with Maxwell's equations and discuss the implications for local versus nonlocal interpretations of the AB effect. We also generalize the results to scenarios with nonzero external magnetic fields, where the enclosed flux is through the actual electron paths, and for circular paths of radius
R, the AB phase shift is also proportional to the time average of the enclosed flux
Φenc(R,t), with the total phase shift depending only on the initial enclosed flux
eΦenc(R,0); for general non-circular paths, the external magnetic field affects trajectories and phase accumulation through the Lorentz force, leading to additional path dependence. These findings clarify the role of gauge-dependent potentials and induced fields in the generalized AB effect, offering new theoretical insights and potential applications in quantum technologies.
We analyze the quantum phase effects for point-like charges and electric (magnetic) dipoles under a natural assumption that the observed phase for a dipole represents the sum of corresponding phases for charges composing this dipole. This way we disclose two novel quantum phases for charged particles, which we named as complementary electric Aharonov-Bohm (A-B) phase and complementary magnetic A-B phase, respectively. We reveal that these phases are derived from the Schrödinger equation only in the case, where the operator of momentum is re-defined via the replacement of the canonical momentum of particle by the sum of its mechanical momentum and interactional field momentum for a system of charged particles. The related alteration should be introduced to Klein-Gordon and Dirac equations, too, and implications of this modification are discussed.
Abstract We analyze the physical meaning of quantum phases for moving electric/magnetic dipoles through a superposition of quantum phases for point-like charges of the dipole, and in this way we disclose two new quantum phases for moving charges, next to the well-known magnetic and electric Aharonov-Bohm phases. We find that a consistent description of the full set of quantum phase effects for charged particles requires to modify the standard definition of the momentum operator via the canonical momentum of a particle towards a more inclusive definition, where this operator is associated with the vector sum of mechanical and interactional electromagnetic (EM) momenta for a charged particle in the EM field. Some principal implications of this result are discussed.
We analyse the physical meaning of quantum phase effects for point-like charges and electric (magnetic) dipoles in an electromagnetic (EM) field. At present, there are known eight effects of such a kind: four of them (the magnetic and electric Aharonov – Bohm phases for electrons, the Aharonov – Casher phase for a moving magnetic dipole and the He – McKellar – Wilkens phase for a moving electric dipole) had been disclosed in 20th century, while four new quantum phases had recently been found by our team (A. L. Kholmetskii, O. V. Missevitch, T. Yarman). In our analysis of physical meaning of these phases, we adopt that a quantum phase for a dipole represents a superposition of quantum phases for each charge, composing the dipole. In this way, we demonstrate the failure of the Schrödinger equation for a charged particle in an EM field to describe new quantum phase effects, when the standard definition of the momentum operator is used. We further show that a consistent description of quantum phase effects for moving particles is achieved under appropriate re-definition of this operator, where the canonical momentum of particle in EM field is replaced by the interactional EM field momentum. Some implications of this result are discussed.