三维E、B麦克斯韦方程组在洛伦兹变换上不协变而在标准变换上协变的证明新的洛伦兹不变场方程
The Proof that Maxwell Equations with the 3D E and B are not Covariant upon the Lorentz Transformations but upon the Standard Transformations. The New Lorentz Invariant Field Equations
摘要：
本文用几何代数和张量形式研究了通常的麦克斯韦方程组（ME）分别与三维电场和磁场矢量E和B的洛伦兹变换（LT）和标准变换（ST）。不同的4D代数对象被用来表示通常的观察者相关和新的观察者独立的电场和磁场。发现ME的ST不同于它们的LT，因此具有3D E和B的ME在LT上不是协变的，而是在ST上。所获得的结果不依赖于用于表示电场和磁场的4D代数对象的特征。用1-向量E和B、双向量E_{Hv}和B_{Hv}以及抽象张量4-向量E^{a}和B^{a}给出洛伦兹不变场方程。所有这些量都是在没有参考系的情况下定义的，即，绝对数量。当引入一些基时，它们被表示为包括分量和基的基于坐标的几何量。它明确表明，这种几何方法与实验，例如，法拉第盘，在所有相对运动的惯性参考系中，这不是用3D E和B及其ST的通常方法的情况。
英文摘要：
In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B respectively, are examined using both the geometric algebra and tensor formalisms. Different 4D algebric objects are used to represent the usual observer dependent and the new observer independent electric and magnetic fields. It is found that the ST of the ME differ from their LT and consequently that the ME with the 3D E and B are not covariant upon the LT but upon the ST. The obtained results do not depend on the character of the 4D algebric objects used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors E_{Hv} and B_{Hv} and the abstract tensors, the 4-vectors E^{a} and B^{a}. All these quantities are defined without reference frames, i.e., as absolute quantities. When some basis has been introduced, they are represented as coordinate-based geometric quantities comprising both components and a basis. It is explicitly shown that this geometric approach agrees with experiments, e.g., the Faraday disk, in all relatively moving inertial frames of reference, which is not the case with the usual approach with the 3D E and B and their ST.
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