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arXiv · 0906.3166

Lorentz Transformations of the Electric and Magnetic Fields According to Minkowski

Tomislav Ivezic
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Abstract

The usual transformations (UT) of the 3-vectors E and B that are found by Lorentz, Poincaré and independently by Einstein in 1905. are generally considered to be the Lorentz transformations (LT) of E and B. According to the UT E in one frame is 'seen' as E' and B' in a relatively moving frame. In Minkowski's last paper, in 1908. in section 11.6, he defined the vectors (with four components) of the electric $Φ$ and magnetic $Ψ$ fields and discovered that, e.g., $Φ$ correctly transforms by the LT again to $Φ^{\prime}$. His correct LT are reinvented in, e.g., [11] ([11] Ivezić T 2005 Found. Phys. Lett. 18 301). In this paper we show the essential similarity and some differences between Minkowski's relations in section 11.6 and the results obtained in [11]. The low-velocity limit of the UT and the LT is briefly examined. A short discussion of the comparison with the Trouton-Noble experiment is presented.

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Tomislav Ivezic. 2010-03-06. Lorentz Transformations of the Electric and Magnetic Fields According to Minkowski. https://doi.org/10.1088/0031-8949%2F82%2F05%2F055007

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