论Felix Klein的电磁学几何模型
On Felix Klein's Geometric Model of Electromagnetism
摘要：
1917年F.克莱因提出了他的工作射影几何A。爱因斯坦进一步发展了广义相对论。克莱因有一个特殊的方式来考虑数学和物理之间的关系，根据他的厄兰格定理和几何建模的物理现象。他的目标是建立非欧几里德几何的物理基础。然而，他写给爱因斯坦的信没有续集。我们认为F.克莱因的想法仍然值得关注，因为它们可以用一种与诉诸场论完全不同的方法来建模麦克斯韦方程。寻找替代方案的一个原因是，目前的场论只使用几何作为一种形式技术，从而抑制了人类的直觉，从把握物理世界。本文收集了我们认为与电磁接收信号模型相关的线索。在前两章中，我们强调了经典物理学的一些特征，即质点的轨迹，以及静力学和动力学在处理旋转方面的差异。在第三章中，我们最后回顾了F。克莱因对电磁学和狭义相对论的几何建模方法。
英文摘要：
In 1917 F. Klein proposed his work on projective geometry to A. Einstein for further developments of general relativity. Klein had a peculiar way to consider the relationship between mathematics and physics, based on his Erlanger Programm and geometrical modeling of physical phenomena. He was aiming at a physical foundation for non Euclidean geometry. However, the letters he wrote to Einstein had no sequel. We think that F. Klein's ideas still deserve some attention, as they can be useful for modeling Maxwell's equations with a radically different approach than resorting to field theories. One reason for looking for alternatives is that current field theories use geometry exclusively as a formal technique thereby inhibiting human intuition from grasping the physical world. This article collects cues that we deem relevant for a model of electromagnetic received signals. In the first two chapters we highlight a few features of classical physics, namely the trajectories of mass points, and the differences in treating rotations between statics and dynamics. In the third chapter, we finally review F. Klein's approach toward geometrical modeling of electromagnetism and special relativity.
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