The classical counterpart of the Aharonov-Bohm phase

Abstract

The existence of the Aharonov-Bohm phase shows that the magnetic field may produce nonlocal effects in quantum mechanics. It is generally believed that such a nonlocal behavior of the magnetic field is not possible in classical physics and that this represents a clear difference between classical and quantum mechanics. Contrary to these beliefs, we argue that the classical counterpart of the Aharonov-Bohm phase, which is identified here with the electromagnetic angular momentum of the configuration formed by an electric charge moving around an infinitely-long solenoid enclosing a uniform magnetic flux, shows that the magnetic field may produce nonlocal effects in classical mechanics. We discuss this momentum in detail by putting special emphasis on its topological and nonlocal features. The momentum is topological because it depends on the number of windings the electric charge carries out around the solenoid and is nonlocal because the magnetic flux has no local consequences at any point on the charge trajectory. The topological feature allows us to introduce the concept of accumulated electromagnetic angular momentum and the nonlocal feature allows us to speak of a dynamical nonlocality attributable to the equations of classical electrodynamics.