The Proof that the Standard Transformations of E and B are not the Lorentz Transformations. Clifford Algebra Formalism

In this paper it is exactly proved by using the Clifford algebra formalism that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not the Lorentz transformations of well-defined quantities from the 4D spacetime but the 'apparent' transformations of the 3D quantities. Thence the usual Maxwell equations with the 3D E and B are not in agreement with special relativity. The 1-vectors E and B, as well-defined 4D quantities, are introduced instead of ill-defined 3D E and B.Comment: 16 pages, section 3.3. is added and it contains the same proof for Hestenes' and Jancewicz's E and