Electromagnetic momentum in the Aharonov-Bohm quantum interference experiment from a physical perspective

TL;DR

This paper provides a physical explanation for the electromagnetic momentum observed in the Aharonov-Bohm effect, linking it to the velocities of charges in the solenoid and their potential energy, clarifying a long-standing puzzle.

Contribution

It offers a novel physical interpretation of electromagnetic momentum in the Aharonov-Bohm experiment within classical electromagnetism, connecting it to charge velocities and potential energy.

Findings

Electromagnetic momentum arises from charge velocities and potential energy.

The effect is explained without invoking non-classical concepts.

The explanation aligns with experimental observations.

Abstract

In the Aharonov-Bohm setup, a double-slit experiment, when a long but thin solenoid of current is introduced between the two coherent beams of electrons behind the slits, an extra phase difference between the interfering beams appears, as shown by a shift in the interference pattern. This mysterious effect, purportedly arises owing to an electromagnetic momentum, attributed to the presence of a vector potential at the location of either beam, due to the solenoid of current even when the magnetic field is zero outside the solenoid. It has remained a puzzle, how mere potential, thought to be just a mathematical tool for calculating electromagnetic field, can give rise to electromagnetic momentum in a system. Experimentally the effect has been amply verified, with hardly any doubts that the observed effect is real. A satisfactory physical explanation of the existence of momentum, at least under the aegis of classical electromagnetism, is still missing since inception of the idea more than half a century back. We show here the presence of electromagnetic momentum in the product of the drift velocities of the current-carrying charges within the solenoid and the mass equivalent of their potential energies in the electric field of the external charges.