  Conservation principles establish the primacy of potentials over fields in
electrodynamics, both classical and quantum. The contrary conclusion that
fields are primary is based on the Newtonian concept that forces completely
determine dynamics, and electromagnetic forces depend directly on fields.
However, physical conservation principles come from symmetries such as those
following from Noether's theorem, and these require potentials for their
statement. Examples are given of potentials that describe fields correctly but
that violate conservation principles, demonstrating that the correct statement
of potentials is necessary. An important consequence is that gauge
transformations are severely limited when conservation conditions must be
satisfied. When transverse and longitudinal fields are present concurrently,
the only practical gauge is the radiation gauge.
