Covariant Formulation of Electromagnetic 4-Momentum in Terms of 4-Vectors E^αand B^α

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.