The gauge non-invariance of Classical Electromagnetism

TL;DR

This paper argues that the potentials in Classical Electromagnetism are not truly gauge-invariant and that the common gauge transformations introduce paradoxes, challenging traditional views on gauge symmetry in electromagnetism.

Contribution

It demonstrates that gauge transformations in Classical Electromagnetism lead to paradoxes and should be rejected, revising the understanding of potential indeterminacy.

Findings

Potentials are not fully gauge-invariant.

Gauge transformations introduce paradoxes.

Potentials are indeterminate only up to a constant.

Abstract

"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The physically meaningful degrees of freedom then reemerge as being those invariant under a transformation connecting the variables (gauge transformation). Thus, one introduces extra variables to make the description more transparent and brings in at the same time a gauge symmetry to extract the physically relevant content. It is a remarkable occurrence that the road to progress has invariably been towards enlarging the number of variables and introducing a more powerful symmetry rather than conversely aiming at reducing the number of variables and eliminating the symmetry" [1]. We claim that the potentials of Classical Electromagnetism are not indetermined with respect to the so-called gauge transformations. Indeed, these transformations raise paradoxes that imply their rejection. Nevertheless, the potentials are still indetermined up to a constant.