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., $\mathbf{E}$, , $\mathbf{F}$, $\mathbf{L}$, $\mathbf{T}$, 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 $N$.

10 pages

References in corpus (4)

• The Proof that the Standard Transformations of E and B are not the Lorentz Transformations. Clifford Algebra Formalism
• The Proof that Maxwell Equations with the 3D E and B are not Covariant upon the Lorentz Transformations but upon the Standard Transformations. The New Lorentz Invariant Field Equations
• Axiomatic geometric formulation of electromagnetism with only one axiom: the field equation for the bivector field F with an explanation of the Trouton-Noble experiment
• The 4D geometric quantities versus the usual 3D quantities. The resolution of Jackson's paradox