"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
