欧几里德几何中运动电荷有限速度传播电相互作用的协变公式
Covariant formulation of at finite speed propagating electric interaction of moving charges in Euclidean geometry
摘要：
麦克斯韦电动力学假定了电磁作用的有限传播速度和电磁场的概念，但它只满足闵可夫斯基度规中的协变性（洛伦兹不变性）。源自麦克斯韦场论的达尔文运动电荷力定律也符合洛伦兹不变性。庞加莱原理指出，物理定律可以在不同的几何形状下用相同的意义来表述，这表明运动电荷的延迟电磁相互作用甚至在欧几里得几何中也可能是协变的（伽利略不变性）。在保持传播速度有限的情况下，打破麦克斯韦场论，试图找到伽利略不变力定律。通过改变Liénard-Wiechert势（LWP），引入了一种新的两运动电荷的阻滞势--公共阻滞电势（CREP），它依赖于两相互作用电荷的速度。所寻求的力定律是通过CREP的二阶近似确定的。令人惊讶的是，得到的定律是伽利略不变量韦伯力定律。从延迟电势的二级近似中重新发现了韦伯力定律，证实了韦伯力定律的意义，并证明了它是一个延迟的近似定律。韦伯力定律甚至包含了磁力，这一事实告诉我们，磁现象仅仅是推迟的电相互作用的一种表现。CREP的三阶近似开启了EM波的可能性，并创造了一个完整的欧几里得电动力学。
英文摘要：
Maxwell's electrodynamics postulates the finite propagation speed of electromagnetic (EM) action and the notion of EM fields, but it only satisfies the requirement of the covariance in Minkowski metric (Lorentz invariance). Darwin's force law of moving charges, which originates from Maxwell's field theory complies the Lorentz invariance as well. Poincaré's principle stating that physical laws can be formulated with identical meaning on different geometries suggest, that the retarded EM interaction of moving charges might be covariant even in Euclidean geometry (Galilean invariance). Keeping the propagation speed finite, but breaking with Maxwell's field theory in this study an attempt is made to find a Galilean invariant force law. Through the altering of the Liénard-Wiechert potential (LWP) a new retarded potential of two moving charges, the Common Retarded Electric Potential (CREP) is introduced which depends on the velocities of both interacting charges. The sought after force law is determined by means of the second order approximation of CREP. The law obtained is the Galilean invariant Weber's force law, surprisingly. Its rediscovery from the second order approximation of a retarded electric potential confirms the significance of Weber's force law and proves it to be a retarded and approximative law. The fact that Weber's force law implies even the magnetic forces tells us that magnetic phenomena are a manifestation of the retarded electric interaction exclusively. The third order approximation of the CREP opens the possibility of EM waves, and the creation of a complete, Euclidean electrodynamics.
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