  Although gauge invariance preserves the values of physical observables, a
gauge transformation can introduce important alterations of physical
interpretations. To understand this, it is first shown that a gauge
transformation is not, in general, a unitary transformation. Also, physical
interpretations are based on both kinetic energy and potential energy
expressions. While the kinetic energy is a measurable quantity, and hence
gauge-invariant, the potential energy is gauge-dependent. Two basic examples
are examined; one classical and the other quantum-mechanical. The aim is to
show that the use of the Coulomb (or radiation) gauge is always consistent with
the way that fields are generated in the laboratory. Upon transformation out of
the Coulomb gauge, this connection is lost, and physical interpretations can
give rise to misleading inferences.
