Postulates and Experimental Features in Maxwell's Electromagnetic Equations

TL;DR

This paper critically examines the foundational assumptions and derivations of Maxwell's equations, highlighting physical approximations and mathematical misapplications, and discusses implications for experimental phenomena like the Aharonov-Bohm effect.

Contribution

It challenges the standard derivation of Maxwell's differential equations from integral forms, emphasizing the need to reconsider their equivalence and physical validity.

Findings

Maxwell's integral equations involve significant physical approximations

The common derivation of differential equations from integral forms often misuses Stokes theorem

Experimental comparisons suggest reconsidering the foundational assumptions of electromagnetic theory

Abstract

The Maxwell integral equations expressing Ampere's and Faraday's laws are shown to be affected by heavy physical approximations. The usual deduction from them, moreover, of the corresponding set of differential Maxwell equations is based, in general, on a wrong use of the Stokes theorem. The equivalence, therefore, between the two sets of equations must be reconsidered. Interesting conclusions may be drawn from the comparison between the experimental set-ups of the Faraday's law and of the Aharonov-Bohm effect.