  Electrodynamics is usually written with a polarization vector field to
describe the response of matter to electric fields, or more specifically, to
describe changes in distribution of charge as an electric field is changed.
This approach does not allow unique specification of a polarization field from
measurements of electric and magnetic fields. Many polarization fields produce
the same electric and magnetic fields, because only the divergence of the
polarization enters Maxwell's first equation, relating charge and electric
field. The curl of any function can be added to a polarization field without
changing the electric field at all. The divergence of the curl is always zero.
Models of structures that produce polarization cannot be uniquely determined
from electrical measurements for the same reason. Models must describe charge
distribution not just distribution of polarization to be unique. I propose a
different paradigm to describe field dependent charge, i.e., to describe the
phenomena of polarization. I propose an operational definition of polarization
that has worked well in biophysics where a field dependent, time dependent
polarization provides the gating current that makes neuronal sodium and
potassium channels respond to voltage. The operational definition has been
applied successfully to experiments for nearly fifty years. Estimates of
polarization have been computed from simulations, models, and theories using
this definition and they fit experimental data quite well. I propose that the
same operational definition be used to define polarization charge in
experiments, models, computations, theories, and simulations of other systems.
Charge movement needs to be computed from a combination of electrodynamics and
mechanics because 'everything interacts with everything else'. The classical
polarization field need not enter into that treatment at all.
