Lorentz-transformation properties for energy and momentum in electromagnetic systems, Timothy H. Boyer, Am. J. Phys. 53(2), February 1985
The Lorentz-transformation properties' of the energy and momentum in electromagnetic systems are illustrated in simple examples involving two point charges. For systems free of external forces the total energy and momentum consisting of mechanical and electromagnetic contributions are seem to transform as a Lorentz four-vector. The examples reveal the roles played by time nonsimultaneity between inertial frames and by the electromagnetic forces on one part of the system upon the other in maintaining the four-vector behavior in special relativity. For systems experiencing external forces the mechanical plus the plus electromagnetic energy and momentum do not transform as a Lorentz four-vector; the actual transformation properties can be understood from the descriptions for assembly of the system as viewed in two different inertial frames.