  The basic physics disciplines of Maxwell's electrodynamics and Newton's
mechanics have been thoroughly tested in the laboratory, but they can
nevertheless also support nonphysical solutions. The unphysical nature of some
dynamical predictions is demonstrated by the violation of symmetry principles.
Symmetries are fundamental in physics since they establish conservation
principles. The procedures explored here involve gauge transformations that
alter basic symmetries, and these alterations are possible because gauge
transformations are not necessarily unitary despite the widespread assumption
that they are. That gauge transformations can change the fundamental physical
meaning of a problem despite the preservation of electric and magnetic fields
is a universal proof that potentials are more basic than fields. These
conclusions go to the heart of physics. Problems are not evident when fields
are perturbatively weak, but the properties demonstrated here can be critical
in strong-field physics where the electromagnetic potential becomes the
dominant influence in interactions with matter.
