The gauge non-invariance of Classical

Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is de-scribed 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 vari-ables (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 to-wards enlarging the number of variables and introducing a more power-ful symmetry rather than conversely aiming at reducing the number of variables and eliminating the symmetry [1]. We claim that the poten-tials 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.