  The fundamental difference between the true transformations (TT) and the
apparent transformations (AT) is explained. The TT refer to the same quantity,
while the AT refer, e.g., to the same measurement in different inertial frames
of reference. It is shown that the usual transformations of the three-vectors E
and B are - the AT. The covariant electrodynamics with the four-vectors E(sup
alpha) and B(sup alpha) of the electric and magnetic field is constructed. It
is also shown that the conventional synchronous definitions of the
electromagnetic energy and momentum contain both, the AT of the volume,
i.e.,the Lorentz contraction, and the AT of E and B, while Rohrlich's
expressions contain only the AT of E and B. A manifestly covariant expression
for the energy-momentum density tensor and the electromagnetic 4-momentum is
constructed using E(sup alpha) and B(sup alpha). The "4/3" problem is discussed
and it is shown that all previous treatments either contain the AT of the
volume, or the AT of E and B, or both of them. In our approach all quantities
are four-dimensional spacetime tensors whose transformations are the TT.
