由延迟量同时推导Jefimenko方程和Maxwell方程
Simultaneous inference of Jefimenko's and Maxwell's equations from retardation
摘要:
假设延迟的想法作为一个基本的公理,我们调查如何Jefimenko和麦克斯韦方程可以推断。在推论中,我们从库仑和毕奥-萨伐尔的场表达式的延迟版本开始,作为一个不完整的,开始的例子。通过计算和比较它们的散度、旋度和时间导数,我们改进了计算方法。因此,通过相同的过程进一步改进改进的仿射,并且最终的仿射场与Jefimenko的场识别。我们对麦克斯韦方程组的推论,与从库仑场和毕奥-萨伐尔场推导静态微分方程(发散和旋度)的精神大致相同,而这些场是在不知道发散和旋度方程的控制律的情况下通过实验已知的。
英文摘要:
Assuming the idea of retardation as an underlying axiom, we investigate how Jefimenko's and Maxwell's equations can be inferred. In the inference, we begin with the retarded versions of Coulomb's and Biot-Savart's field expression as an incomplete, starting ansatz. By calculating and comparing their divergences, curls, and time derivatives, we improve the ansatz. Thus improved ansatz is further improved through the same procedure and the final ansatz fields are identified with Jefimenko's fields. Our inference of Maxwell's equations is in much the same spirit as the derivation of static differential equations (divergences and curls) from the Coulomb's and Biot-Savart's fields known experimentally without knowing their governing laws of the divergence and curl equations.
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