Can classical electrodynamics predict nonlocal effects?

TL;DR

This paper demonstrates that classical electrodynamics can predict nonlocal, topological effects, exemplified by electromagnetic angular momentum related to the Aharonov-Bohm phase in non-simply connected regions.

Contribution

It reveals that classical electrodynamics can account for nonlocal effects through topological electromagnetic angular momentum in complex configurations.

Findings

Electromagnetic angular momentum depends on the winding number.

Nonlocal interaction is topological in nature.

Classical angular momentum parallels the Aharonov-Bohm phase.

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.