On the Chu-Haus-Penfield principle of virtual power

Abstract

This principle has been obtained by CHU, HAUS and PENFIELD (1) as a generalization for nonstatie system of the principle of vir tual work used in static cases (3). However the generalization has been performed considering as variable the Lorentz matrix connecting physical quantities relative to the laboratory frame with the same quantities measured in local rest frames. This procedure is not allowable in special relativity, where the connection is given between two inertial rest frames, therefore having a constant relative velocity. I t is therefore surprising that by a wrong procedure the mentioned authors (1) succeed in finding the correct energy-momentum tensor for the electromagnetic field in vacuum. One could think (although hardly) that the Chu-Haus-Penfield principle is a convenient trick starting from a wrong basis but justified (~ a posteriori ~> (s). Nevertheless one is not allowed to extend the above wrong (( principle >> where there is no sure check, as in the case of the dielectric media. Here there is not, at present, a sound criterion in order to choose between the Minkowsky and the Abraham's tensor. Consequently CHU, HAus and PENFIELD (1) are not allowed in stating that the Minkowsky tensor is physically unacceptable since they obtain the Abraham's one (4). Hence the (~principle >> of vir tual power, by which one can obtain only energy-momentum tensors, is of no use. Actually in the vacuum one has already the conventional, sure expression obtained by a correct procedure starting from the Maxwell equation. In dielectric media there is the ambiguity as to which energy tensor (whether Minkowsky or Abraham or somebody else's) is the correct one and one cannot use a wrong procedure, as the above (~ principle >>, to support a choice. A more exhaustive criticism against the principle of vir tual power has been raised by Lo SURDO (5), who has emphasized that, when differentiations are involved, the