从牛顿定律开始，通过狭义相对论的协方差要求推导麦克斯韦方程组
Derivation of Maxwell's equations via the covariance requirements of the special theory of relativity, starting with Newton's laws
摘要：
麦克斯韦方程组、牛顿定律和狭义相对论之间的联系是从牛顿口头阐述他的前两个定律开始的推导建立起来的。导出的方程需要是协变的，并且简单性准则要求带电粒子上的四矢量力与四矢量速度线性相关。连接张量具有可导出的对称性，并包含电场和磁场矢量。洛伦兹力定律出现了，麦克斯韦方程组的自由空间出现的假设，张量和它的对偶必须都满足一阶偏微分方程。非均匀扩展产生电荷密度和电流密度作为场的源，并且产生电荷的电荷守恒定律。牛顿第三定律被重新解释为一个互易性陈述，它要求源项中的电荷可以被视为与测试粒子相同的物理实体，并且两者可以被分配相同的单位。无论是空间反演还是时间反演都需要协方差，这就排除了磁荷是对电荷施加力的电磁场源。
英文摘要：
A connection between Maxwell's equations, Newton's laws, and the special theory of relativity is established with a derivation that begins with Newton's verbal enunciation of his first two laws. Derived equations are required to be covariant, and a simplicity criterion requires that the four-vector force on a charged particle be linearly related to the four-vector velocity. The connecting tensor has derivable symmetry properties and contains the electric and magnetic field vectors. The Lorentz force law emerges, and Maxwell's equations for free space emerge with the assumption that the tensor and its dual must both satisfy first order partial differential equations. The inhomogeneous extension yields a charge density and a current density as being the source of the field, and yields the law of conservation of charge. Newton's third law is reinterpreted as a reciprocity statement, which requires that the charge in the source term can be taken as the same physical entity as that of the test particle and that both can be assigned the same units. Requiring covariance under either spatial inversions or time reversals precludes magnetic charge being a source of electromagnetic fields that exert forces on electric charges.
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