  It is shown that electromagnetic potentials convey physical information
beyond that supplied by electric and magnetic fields alone, and are thus more
fundamental. Observable physical properties can impose conditions on the
selection of electromagnetic gauge (i.e. sets of potentials) that are explicit
and restrictive. This is true both classically and quantum mechanically. The
implication that the choice of gauge carries physical information is confirmed
by exhibiting a set of potentials that describes fields correctly, but that
violates physical constraints. The basic conclusions are that physical
requirements place limits on acceptable gauges; and that potentials are more
fundamental than fields in both classical and quantum physics, representing a
major generalization of the quantum-only Aharonov-Bohm effect. These important
properties are obscured if the dipole approximation is employed. The properties
demonstrated here relate directly to conditions that exist in strong-field
laser applications.
