Torque or no torque?! The resolution of the paradox using 4D geometric quantities with the explanation of the Trouton-Noble experiment

Original · EN

In this paper we have resolved the apparent paradox of different mechanical equations for force and torque governing the motion of a charged particle in different inertial frames. The same paradox arises in all usual ``explanations'' of the Trouton-Noble experiment. It is shown that the real cause of the paradoxes is - the use of three dimensional (3D) quantities, e.g., E, B, F, L, % N, their transformations and equations with them. Instead of using 3D quantities we deal with 4D geometric quantities, their Lorentz transformations and equations with them. In such treatment the paradoxes do not appear. The explanation with 4D geometric quantities% is in a complete agreement with the principle of relativity and with the Trouton-Noble experiment.