Is there a "Charge - Magnet Paradox"

TL;DR

This paper demonstrates that using four-dimensional geometric quantities in invariant special relativity resolves the charge-magnet paradox by showing that electric and magnetic dipole moments coexist and experience forces consistently across all inertial frames.

Contribution

It introduces a 4D geometric quantity approach to special relativity that eliminates the paradox and reveals additional intrinsic dipole moments and polarizations in stationary objects.

Findings

No paradox in 4D GQ approach; magnetic dipole moments are frame-independent.

Electrically neutral current loops have intrinsic electric dipole moments.

Stationary magnets possess intrinsic electric polarization.

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.