Version 1
: Received: 17 January 2023 / Approved: 18 January 2023 / Online: 18 January 2023 (04:03:09 CET)
How to cite:
Singal, A. Wherein Lies the Momentum in Aharonov-Bohm Quantum Interference Experiment - A Classical Physics Perspective. Preprints2023, 2023010319. https://doi.org/10.20944/preprints202301.0319.v1
Singal, A. Wherein Lies the Momentum in Aharonov-Bohm Quantum Interference Experiment - A Classical Physics Perspective. Preprints 2023, 2023010319. https://doi.org/10.20944/preprints202301.0319.v1
Singal, A. Wherein Lies the Momentum in Aharonov-Bohm Quantum Interference Experiment - A Classical Physics Perspective. Preprints2023, 2023010319. https://doi.org/10.20944/preprints202301.0319.v1
APA Style
Singal, A. (2023). Wherein Lies the Momentum in Aharonov-Bohm Quantum Interference Experiment - A Classical Physics Perspective. Preprints. https://doi.org/10.20944/preprints202301.0319.v1
Chicago/Turabian Style
Singal, A. 2023 "Wherein Lies the Momentum in Aharonov-Bohm Quantum Interference Experiment - A Classical Physics Perspective" Preprints. https://doi.org/10.20944/preprints202301.0319.v1
Abstract
In the Aharonov-Bohm setup, a double-slit experiment, coherent beams of electrons passing through two slits form an interference pattern on the observing screen. However, when a long but thin solenoid of current is introduced behind the slits between the two electron beams, an extra phase difference between them appears, as shown by a shift in the interference pattern. This happens even though there is no magnetic field outside the solenoid, at the location of the beams. This is known as Aharonov-Bohm effect, though the idea was mooted apparently a decade earlier, and the effect sometimes is called Ehrenberg-Siday-Aharonov-Bohm effect. This mysterious effect, purportedly arises owing to an electromagnetic momentum, attributed to the presence at the location of either beam, a vector potential due to the solenoid of current even when there exists no magnetic field outside the solenoid. The first experimental confirmation came soon and It has since been amply verified using clever experimental setups, leaving hardly any doubts that the observed effect is real.However, on the theoretical side the picture is not so clear and 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. It has remained a puzzle, how just potential, thought to be a mere mathematical tools for calculating electromagnetic field, can give rise to an electromagnetic momentum in a system, in lieu of field itself. We here show that a subtle momentum can be seen to lie in the product of the drift velocities of the current carrying charges and the mass equivalent of their non-localized potential energies in the electric field of the interfering electrons, which manifests, from a classical point of view, a linear momentum in the system. It is this hard-to-pinpoint, additional momentum, reflected through an extra phase difference between the interfering beams of electrons, which exhibits from a classical physics perspective, the presence of an elusive, long sought-after electromagnetic momentum in the system.
Copyright:
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