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

• URL: http://arxiv.org/abs/2301.06502v2
• Date: Thu, 16 Oct 2025 03:06:50 GMT
• Title: Electromagnetic momentum in the Aharonov-Bohm quantum interference experiment from a physical perspective
• Authors: Ashok K. Singal,
• Abstract summary: In the Aharonov-Bohm setup, when a long but thin solenoid of current is introduced between the two coherent beams of electrons, an extra phase difference between the interfering beams appears.<n>This mysterious effect, purportedly arises owing to an electromagnetic momentum, attributed to the presence of a vector potential at the location of either beam.<n>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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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