Abstract
Classical electrodynamics is a local theory describing local interactions between charges and electromagnetic fields and therefore one would not expect that this theory could predict nonlocal effects. But this perception implicitly assumes that the electromagnetic configurations lie in simply connected regions. In this paper, we consider an electromagnetic configuration lying in a non-simply connected region, which consists of a charged particle encircling an infinitely long solenoid enclosing a uniform magnetic flux, and show that the electromagnetic angular momentum of this configuration describes a nonlocal interaction between the encircling charge outside the solenoid and the magnetic flux confined inside the solenoid. We argue that the nonlocality of this interaction is of topological nature by showing that the electromagnetic angular momentum of the configuration is proportional to a winding number. The magnitude of this electromagnetic angular momentum may be interpreted as the classical counterpart of the Aharonov–Bohm phase.
Highlights
Three years after the publication of the seminal paper by Aharonov and Bohm [1] on the prediction of the effect that bears their name, the Aharonov–Bohm (AB) effect, Tassie and Peshkin [2] claimed that “... the quantum mechanical effects of the inaccessible field can be understood, both mathematically and physically, through angular momentum considerations ...” They argued that in regions where electrons encircling inaccessible magnetic fields, classical physics predicts that, in addition to the mechanical angular momentum: Lm = (r × mv)z, there is an electromagnetic angular momentum along the z-axis whose magnitude is given by Lz = eΦ 2π c (1)where e is the electron charge and Φ is the inaccessible magnetic flux
We examine in detail the configuration formed by a charged particle encircling an infinitely long solenoid enclosing a uniform magnetic flux and show that this particle moves in a non- connected region where there is no magnetic field but there is a nonzero vector potential
We have shown that classical electrodynamics can predict nonlocal effects even though this theory is the prototype of a local theory
Summary
The quantum mechanical effects of the inaccessible field can be understood, both mathematically and physically, through angular momentum considerations ...”. They argued that in regions where electrons encircling inaccessible magnetic fields, classical physics predicts that, in addition to the mechanical angular momentum: Lm = (r × mv)z, there is an electromagnetic angular momentum along the z-axis whose magnitude is given by. We examine in detail the configuration formed by a charged particle encircling an infinitely long solenoid enclosing a uniform magnetic flux and show that this particle moves in a non- connected region where there is no magnetic field but there is a nonzero vector potential. Throughout our study we emphasise the topological and nonlocal features of (1)
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