Some Rare Peripheral Implications of Electromagnetism

Abstract

This essay is essentially a plea for recognizing the Aharonov–Bohm (AB) integral as part of a quantum superstructure of Maxwell theory counting units of flux. The Gauss–Ampère (GA) integral then is added as a counter of net charge as well as an exterior product of the two, suggested by Kiehn, as counter of units of action. De facto, the AB integral already has this status, yet how its prestatistical nature relates to standard statistics-based quantum mechanics needs delineation. For electromagnetism to claim this quantum superstructure as a legitimate member of its family it is unavoidable to take issue with the Copenhagen view of quantum mechanics as stated in the introductory paragraph of this article. The limiting mathematical traditions that have been standing in the way of such developments are briefly reviewed here. They pertain to the relations between local and global procedures as delineated in de Rham theory as well as recognizing certain metric-free aspects of electromagnetism as a requirement sine qua non for counting in the micro-domain. For extended discussions, references, and proofs pertaining to the ensuing Quantum Reprogramming of the Copenhagen interpretation, readers are invited to consult the monograph of that title, by the present author.