Lorentz Transformations of the Electric and Magnetic Fields According to Minkowski

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 $\Phi$ and magnetic $\Psi$ fields and discovered that, e.g., $\Phi$ correctly transforms by the LT again to ${\Phi }^{\prime }$. 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.

Section 4. and also a new paragraph at the end of Sec. 3 are added. Some small changes in the Abstract and the text are made and new references are added as well.

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Cited by in corpus (4)

• The Constitutive Relations and the Magnetoelectric Effect for Moving Media
• The Lorentz transformations of the vectors E, B, P, M and the external electric fields from a stationary superconducting wire with a steady current and from a stationary permanent magnet
• The manifestly covariant Aharonov-Bohm effect in terms of the 4D fields
• Electric and magnetic fields as explicitly observer dependent four-dimensional vectors and their Lorentz transformations according to Minkowski-Ivezić