Is there a "Charge - Magnet Paradox"

Abstract

In this paper it is shown that in the approach to special relativity which exclusively deals with the four-dimensional geometric quantities (4D GQs), the invariant special relativity (ISR), there is not recently posed paradox that in a static electric field a magnetic dipole moment (MDM) is subject to a torque in some frames and not in others. In the ISR, there is no need either for the change of the Lorentz force, but as a 4D GQ, or for the introduction of some "hidden" 3D quantities. Furthermore, in the ISR, contrary to all previous approaches, an electrically neutral current-loop in its rest frame possesses not only a MDM m, but also an electric dipole moment (EDM) p and a stationary permanent magnet possesses not only an intrinsic magnetization M but also an intrinsic electric polarization P. Hence, in a static electric field, both, a current-loop and a permanent magnet experience the Lorentz force K_{L} and the torque N in all relatively moving inertial frames. The quantities m, p, M, P, K_{L}, N are the 4D GQs.