A cornerstone of quantum mechanics can be fully explained using old-fashioned classical physics if we allow a single number to be complex.
The Aharonov-Bohm effect is replicable through classical electromagnetism when the four-potential is treated as a complex value. This effect was previously considered a uniquely quantum phenomenon that proved the existence of hidden fields. This research suggests that what we thought was a quantum mystery is actually a general wave property found in classical theory. It bridges a major gap between the two most successful theories in physics. This rethink could change how we design sensors and quantum computers by using classical principles to control quantum states. It proves that the line between classical and quantum is thinner than we thought.
Deceptive Gauge: Quantum Nature of the Aharonov-Bohm Effect Revisited
SSRN · 6635959
The Aharonov-Bohm (AB) effect, often viewed as uniquely quantum, can emerge within classical electromagnetism if the four-potential is allowed to be complex under local U(1) gauge transformations. In a plane double-layer setup with superconducting plates, we show that wave modes in field-free regions acquire a path-dependent phase determined solely by the potential, independent of quantum wave functions or synthetic gauge fields. This classical phase shift arises from the gauge-invariant structu