A Proposed Electromagnetic Momentum-Energy 4-Vector for Charged Bodies Available to Purchase

The conventional electromagnetic momentum- and energy-density expressions $(E × H/c)$ and $[12(E2+H2)]$⁠, respectively (Heaviside-Lorentz units in free space), are known not to lead to a momentum-energy 4-vector for the fields of charged bodies. Yet the rest of classical electrodynamics is a covariant theory. This is a most remarkable anomaly. The reason for this anomaly is shown herein to lie in the procedure used to derive Poynting's theorem, which is shown not to be covariant in the presence of sources. A 4-vector is derived to represent the 4-momentum $dGμ$ contained within a volume element $dV$ of the electromagnetic field of a charged body with a 4-velocity $uμ ≡ (γv, iγc)$⁠: , where $γ ≡ (1 − v2/c2)−1/2$⁠. This proposed 4-vector is shown to remove several paradoxes associated with the predictions of the conventional momentum and energy density expressions. And the proposed 4-vector is also shown to be in agreement with the results of several experiments.