  Electromagnetic quantities at a spacetime point have tensor Lorentz
transformations between relatively-moving inertial frames. However, since the
Lorentz transformation of time between inertial frames depends upon both the
time and space coordinates, averages of electrodynamic quantities at a single
time will in general depend upon the inertial frame, and will differ between
inertial frames. Here we illustrate how the use of continuous charge and
current distributions rather than point-charge distributions can lead to
physically mystifying and even inaccurate results for electromagnetic
quantities and physical phenomena. The discrepancy noted between the average
electric field values in different inertial frames is particularly striking
because it is first order in the relative velocity between the frames.
