Foundations of Physics

, Volume 33, Issue 9, pp 1339–1347 | Cite as

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

  • Tomislav Ivezić


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.

standard transformations of E and B special relativity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Einstein, Ann. Physik. 17, 891(1905), translated by W. Perrett and G. B. Jeffery, in The Principle of Relativity (Dover, New York).Google Scholar
  2. 2.
    J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1977), 2nd edn.Google Scholar
  3. 3.
    L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1979), 4th edn.Google Scholar
  4. 4.
    T. Ivezić, Found. Phys. 31, 1139(2001).Google Scholar
  5. 5.
    T. Ivezić, Ann. Fondation Louis de Broglie 27, 287(2002).Google Scholar
  6. 6.
    T. Ivezić, hep-th/0207250; hep-ph/0205277.Google Scholar
  7. 7.
    R. M. Wald, General Relativity (The University of Chicago Press, Chicago, 1984).Google Scholar
  8. 8.
    T. Ivezić, Found. Phys. Lett. 15, 27(2002); physics/0103026; physics/0101091.Google Scholar
  9. 9.
    F. Rohrlich, Nuovo Cimento B 45, 76(1966).Google Scholar
  10. 10.
    A. Gamba, Amer. J. Phys. 35, 83(1967).Google Scholar
  11. 11.
    C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1970).Google Scholar
  12. 12.
    T. Ivezić, Found. Phys. Lett. 12, 105(1999); T. Ivezić, Found. Phys. Lett. 12, 507 (1999).Google Scholar
  13. 13.
    H. N. Núñez Yépez, A. L. Salas Brito, and C. A. Vargas, Revista Mexicana de Física 34, 636(1988).Google Scholar
  14. 14.
    S. Esposito, Found. Phys. 28, 231(1998).Google Scholar
  15. 15.
    D. Hestenes, Space-Time Algebra (Gordon & Breach, New York, 1966).Google Scholar
  16. 16.
    B. Jancewicz, Multivectors and Clifford Algebra in Electrodynamics (World Scientific, Singapore, 1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Tomislav Ivezić
    • 1
  1. 1.Ruder Bošković InstituteZagrebCroatia

Personalised recommendations