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Lorentz transformations of the electric and magnetic fields according to Minkowski

The usual transformations (UT) of the 3-vectors E and B that were found by Lorentz and by Poincare and independently by Einstein in 1905 are generally considered to be the Lorentz transformations (LT) (boosts) 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 section 11.6 of Minkowski (1908 Nachr. Ges. Wiss. Gottingen 53), he defined the vectors (4-vectors in the usual notation) of the electric Phi and magnetic Psi fields and discovered that, for example, Phi correctly transforms to Phi' by the LT. His correct LT are reinvented and generalized in Ivezic (2005 Found. Phys. Lett. 18 301). In this study, we show the essential similarity and some differences between Minkowski's relations in section 11.6 (1908) and the results obtained in Ivezic (2005). The general expressions for the LT (boosts) and UT of vectors E and B are presented. They are not contained either in Minkowski (1908) or in Ivezic (2005). The low-velocity limit of the UT and LT is briefly examined.

Galilean electromagnetism; standard transformations; low velocities; moving bodies; electrodynamics

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