扭不扭？！用4D几何量解Trouton-Noble实验佯谬
Torque or no torque?! The resolution of the paradox using 4D geometric quantities with the explanation of the Trouton-Noble experiment
摘要：
本文解决了带电粒子在不同惯性系中运动的力和力矩的力学方程不同的明显矛盾。同样的悖论出现在所有通常的“解释”的特劳顿-诺布尔实验。证明了悖论的真正起因是- \emph{the use of three dimensional (3D) quantities}，例如，$\mathbf{E}$，$\mathbf{B}$，$\mathbf{F}$，$\mathbf{L}$，$% \mathbf{N}$，\emph{their transformations and equations with them.}我们处理的是\emph{4D geometric quantities, their Lorentz transformations and equations with them}而不是3D量。在这样的处理中，悖论不会出现。用\emph{4D geometric quantities} %的解释与相对性原理和特劳顿-诺布尔实验完全一致。
英文摘要：
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 - \emph{the use of three dimensional (3D) quantities}, e.g., $\mathbf{E}$, $\mathbf{B}$, $\mathbf{F}$, $\mathbf{L}$, $% \mathbf{N}$, \emph{their transformations and equations with them.} Instead of using 3D quantities we deal with \emph{4D geometric quantities, their Lorentz transformations and equations with them}. In such treatment the paradoxes do not appear. The explanation with \emph{4D geometric quantities}% is in a complete agreement with the principle of relativity and with the Trouton-Noble experiment.
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