A poynting theorem for moving bodies and the relativistic mechanics of extended objects

Abstract

Maxwell's macroscopic field equations have long been regarded as the correct formulation of electrodynamic behavior even in the presence of moving materials. However, they do not lead to a Poynting theorem which can be given a reasonable physical interpretation with moving media present. The power converted to mechanical form, for example, is lost somewhere in the usual Poynting theorem. This fact among others has led recent workers in classical macroscopic electrodynamics to the conclusion that Maxwell's equations are not sufficiently general.However, the special theory of relativity seems to require that they hold in all inertial reference frames since they agree with experiment in a proper or rest frame.This idea is an abuse of the special theory of relativity.It is pointed out in this paper that a law of physics can only be regarded as invariant in form and meaning for all inertial observers if it agrees with experiment in a non-proper or moving frame of reference. The physical laws take on degenerate forms in a proper frame since there is something unique about a proper frame which makes it different relativistically from all other frames. Thus, Maxwell's equations must represent a degenerate form of more basic relationships which are valid in all inertial frames. Lan J. Chu has postulated a modified set of electrodynamic relationships which reduce to Maxwell's equations in a proper or rest coordinate system. It is shown that Chu's self-consistent re-formulation of macroscopic electrodynamics leads to a Poynting-type theorem which is easy to interpret physically even in the presence of moving media. The thorough interpretation of this Poynting theorem for moving bodies requires a study of the meaning of force and power from a macroscopic point of view and the relativistic laws of transformation which they obey. An approach to the relativistic mechanics of extended objects is postulated. It is assumed that there exists for every object at a particular instant some inertial coordinate system in which the net momentum of the object is zero.Various parts of the object move relative to this rest coordinate system but the net momentum of all the parts vanishes.The total energy of the object in its rest frame is the rest energy. The rest energy or rest mass of the object may vary with time. The total energy and net linear momentum of the object in some moving inertial coordinate system are related to the rest frame quantities in exactly the same way as for a point mass. The variation with time of the body's rest mass does not destroy the covariance of the formulation. Furthermore, the approach developed is consistent with macroscopic electrodynamics. As an electromagnetic field heats or polarizes a body, its rest mass increases. Relativistic particle mechanics does not allow such an effect since the rest mass is regarded as an invariant property of the particle.