The Proof That the Standard Transformations of E and B Are Not the Lorentz Transformations

Abstract

In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not well-defined quantities in the 4D space-time and, contrary to the general belief, the usual Maxwell equations with the 3D E and B are not in agreement with the special relativity. The 4-vectors E a and B a, as well-defined 4D quantities, are introduced instead of ill-defined 3D E and B. The proof is given in the tensor and the Clifford algebra formalisms.

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Ivezić, T. The Proof That the Standard Transformations of E and B Are Not the Lorentz Transformations. Foundations of Physics 33, 1339–1347 (2003). https://doi.org/10.1023/A:1025645428575

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  • standard transformations of E and B
  • special relativity