It is shown that the total electric charge, as determined from the Gauss law, is a quantum object. The argument is based on elementary considerations concerning the number of photons, which should be large in a classical situation.
@article{bwmeta1.element.bwnjournal-article-bcpv41z2p257bwm, author = {Staruszkiewicz, Andrzej}, title = {On the quantal nature of the Coulomb field}, journal = {Banach Center Publications}, volume = {38}, year = {1997}, pages = {257-262}, zbl = {0900.81005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv41z2p257bwm} }
Staruszkiewicz, Andrzej. On the quantal nature of the Coulomb field. Banach Center Publications, Tome 38 (1997) pp. 257-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv41z2p257bwm/
[000] [1] R.P. Feynman, QED, Princeton University Press, 1985.
[001] [2] René Descartes, Regulae Ad Directionem Ingenii, I quote from the Polish translation, published by PWN, Warsaw 1958, page 9.
[002] [3] W.B. Berestetsky, E.M. Lifshitz, and L.P. Pitaevsky, Relativistic Quantum Theory, Moscow 1968, in Russian.
[003] [4] M. Alexander and P.G. Bergmann, Foundations of Physics 14, 925 (1984).
[004] [5] A. Staruszkiewicz, an essay in honour of Yakir Aharonov, published in Quantum Coherence and Reality, ed. by J.S. Anandan and J.L. Safko, World Scientific, Singapore 1994, page 90.
[005] [6] A. Staruszkiewicz, Ann. Phys. (N.Y.) 190, 354 (1989).