In 1995, Romer1 wrote an inquiry regarding the momentum and energy flow of electromagnetic systems with particular reference to hidden momentum. The responses2 to the inquiry, as well as earlier related work,3 touched on conservation of energy, linear momentum, and angular momentum. However, none discuss what I believe is the crux of the matter, the conservation law associated with the invariance of classical electrodynamics under proper Lorentz transformation, which implies the constant velocity of the system center of energy.
In this connection, it was pointed out recently4 that the application of external forces to the charged particles of classical electron theory leads to the relation
where is the total (mechanical and electromagnetic) system energy,
