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In the first part of this paper we review the fundamental difference betweenthe usual transformations of the three-dimensional (3D) vectors of the electricfield $\mathbf{E}$, the magnetic field $\mathbf{B}$, the polarization$\mathbf{P}$, the magnetization $\mathbf{M}$ and the Lorentz transformations ofthe 4D geometric quantities, vectors E, B, P, M, with many additionalexplanations and several new results. In the second part, we have discussed theexistence of the electric field vector E outside a stationary superconductingwire with a steady current and also different experiments for the detection ofsuch electric fields. Furthermore, a fundamental prediction of the existence ofthe external electric field vector E from a stationary permanent magnet isconsidered. These electric fields are used for the resolution of the"charge-magnet paradox" with 4D geometric quantities for a qualitativeexplanation of the Aharonov-Bohm effect in terms of fields and not, as usual,in terms of the vector potential and for a qualitative explanation that theparticle interference is not a test of a Lorentz-violating model ofelectrodynamics according to which a magnetic solenoid generates not only astatic magnetic field but also a static electric field.

journal of physics. conference series

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