4D几何量与通常的3D量。杰克逊悖论的解决
The 4D geometric quantities versus the usual 3D quantities. The resolution of Jackson's paradox
摘要：
在本文中，我们提出了不同的四维（4D）几何量（克利福德多向量）的定义。给出了力矩N和角动量M（双矢量）分别分解为1-矢量N_{s}，N_{t}和M_{s}，M_{t}的新方法.转矩N_{s}、N_{t}（角动量M_{s}、M_{t}）合在一起包含与双矢量N（双矢量M）相同的物理信息。从不变量狭义相对论（ISR）的观点出发，反对处理三维量$\mathbf{E}$、$\mathbf{B}$、$\mathbf{F}$、$\mathbf{L}$、$\mathbf{N}$等及其变换的常用方法。在ISR中，我们认为四维几何量在理论上和\emph{experimentally}在四维时空中都是定义良好的。这不是通常的3D数量的情况。结果表明，当用四维几何量代替三维几何量时，力矩不存在明显的电动力学佯谬，相对性原理自然满足。
英文摘要：
In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors N_{s}, N_{t} and M_{s}, M_{t} respectively are given. The torques N_{s}, N_{t} (the angular momentums M_{s}, M_{t}), taken together, contain the same physical information as the bivector N (the bivector M). The usual approaches that deal with the 3D quantities $\mathbf{E}$, $\mathbf{B}$, $\mathbf{F}$, $\mathbf{L}$, $\mathbf{N}$, etc. and their transformations are objected from the viewpoint of the invariant special relativity (ISR). In the ISR it is considered that 4D geometric quantities are well-defined both theoretically and \emph{experimentally} in the 4D spacetime. This is not the case with the usual 3D quantities. It is shown that there is no apparent electrodynamic paradox with the torque, and that the principle of relativity is naturally satisfied, when the 4D geometric quantities are used instead of the 3D quantities.
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