On the peculiarity of the Coulomb gauge

TL;DR

This paper critiques the Coulomb gauge in electromagnetism, proposing an alternative approach that simplifies the formalism, clarifies physics, and resolves inconsistencies inherent in the standard gauge method.

Contribution

It introduces a new perspective on the Coulomb gauge, addressing fundamental inconsistencies and offering a simplified, clearer formulation of electromagnetic wave equations.

Findings

Identifies major inconsistencies in the Coulomb gauge

Proposes an alternative formalism that clarifies basic physics

Removes inherent inconsistencies of the standard gauge approach

Abstract

In an earlier paper we provided an alternative to the standard gauge concept for deriving the classical electromagnetic wave equations. This alternative involves recognition of two previously overlooked basic equations and represents a simplification of the formalism and a clarification of some basic physics that is obscured in the standard method. It also removes inconsistencies inherent in the gauge approach. The present paper relates to the Coulomb gauge and addresses another example of a major inconsistency that derives directly from the gauge concept