论文标题
根据Minkowski-ivezić的明确观察者和磁场作为明确观察者的四维矢量及其洛伦兹的变换
Electric and magnetic fields as explicitly observer dependent four-dimensional vectors and their Lorentz transformations according to Minkowski-Ivezić
论文作者
论文摘要
在本文中，使用了特殊相对论（SR）的几何方法，称为“不变的特殊相对论”（ISR）。在ISR中，认为在四维（4D）时期的物理定律中是4D几何，无坐标数量之间的几何，无坐标关系。数学证明，在ISR中，电气和磁场是4D时空上正确定义的向量。根据第一个证明，向量场的维度是由其域的维度确定的数学。由于在4D时空上定义了电场和磁场，它们是正确定义的4D向量的4D几何量（GQ）。如仅具有一个公理的公理几何公式所示，该公理是双向球场f的场方程[33]，[T。 Ivezić，发现。物理。 Lett。 18，401（2005），Arxiv：物理/0412167]，整个电磁作用的主要数量是双性体和磁场F。电气和磁场4D矢量E和B以数学正确的方式确定f和4D Velocity Velocity Velocity Velocity Velocity Velocity Velocity velocity velocity velocity velocity velocity velocity velerver who who who who e和b Fields e e e e e e e e e e e e e e e e e邦和b。此外，有证据表明，在数学正确的洛伦兹转换下，这是由Minkowski首先得出的，并根据4D GQ进行了重新发明和概括，例如在[23]中，[T。 Ivezić，物理。 scr。 82，055007（2010）]，当其他4D向量变换，即再次转到电场4D矢量时，电场4D向量会变换；与磁场4D向量B没有混合，如3D场的通常变换（UT）。使用4D GQS的该配方与电磁作用的实验（例如Motional EMF）具有真正的一致性。
In this paper a geometric approach to the special relativity (SR) is used that is called the "invariant special relativity" (ISR). In the ISR it is considered that in the four-dimensional (4D) spacetime physical laws are geometric, coordinate-free relationships between the 4D geometric, coordinate-free quantities. It is mathematicaly proved that in the ISR the electric and magnetic fields are properly defined vectors on the 4D spacetime. According to the first proof the dimension of a vector field is mathematicaly determined by the dimension of its domain. Since the electric and magnetic fields are defined on the 4D spacetime they are properly defined 4D vectors, the 4D geometric quantities (GQs). As shown in an axiomatic geometric formulation of electromagnetism with only one axiom, the field equation for the bivector field F [33], [T. Ivezić, Found. Phys. Lett. 18, 401 (2005), arXiv: physics/0412167], the primary quantity for the whole electromagnetism is the bivector field F. The electric and magnetic fields 4D vectors E and B are determined in a mathematically correct way in terms of F and the 4D velocity vector v of the observer who measures E and B fields. Furthermore, the proofs are presented that under the mathematicaly correct Lorentz transformations, which are first derived by Minkowski and reinvented and generalized in terms of 4D GQs, e.g., in [23], [T. Ivezić, Phys. Scr. 82, 055007 (2010)], the electric field 4D vector transforms as any other 4D vector transforms, i.e., again to the electric field 4D vector; there is no mixing with the magnetic field 4D vector B, as in the usual transformations (UT) of the 3D fields. This formulation with the 4D GQs is in a true agreement with experiments in electromagnetism, e.g., the motional emf.
