Jackson's paradox and its resolution by the four-dimensional geometric quantities

Abstract

In this paper it is shown that the real cause of Jackson's paradox is the use of three-dimensional (3D) quantities, e.g., $\mathbf{E}$, $% \mathbf{B}$, $\mathbf{F}$, $\mathbf{L}$, $\mathbf{T}$, their transformations and equations with them. The principle of relativity is naturally satisfied and there is no paradox when the physical reality is attributed to the 4D geometric quantities, e.g., to the 4D torque $N$ (bivector) or, equivalently, to the 4D torques $N_{s}$ and $N_{t}$ (1-vectors), which together contain the same physical information as the bivector $N$.