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Foundations of Physics

, Volume 19, Issue 3, pp 269–291 | Cite as

Electrodynamics of the Maxwell-Lorentz type in the ten-dimensional space of the testing of special relativity: A case for Finsler type connections

  • Jose G. Vargas
  • Douglas G. Torr
Article

Abstract

It has recently been shown by Vargas, (4) that the passive coordinate transformations that enter the Robertson test theory of special relativity have to be considered as coordinate transformations in a seven-dimensional space with degenerate metric. It has also been shown by Vargas that the corresponding active coordinate transformations are not equal in general to the passive ones and that the composite active-passive transformations act on a space whose number of dimensions is ten (one-particle case) or larger (more than one particle).

In this paper, two different (families of) electrodynamics are constructed in ten-dimensional space upon the coordinate free form of the Maxwell and Lorentz equations. The two possibilities arise from the two different assumptions that one can naturally make with respect to the acceleration fields of charges, when these fields are related to their relativistic counterparts. Both theories present unattractive features, which indicates that the Maxwell-Lorentz framework is unsuitable for the construction of an electrodynamics for the Robertson test theory of the Lorentz transformations. It is argued that this construction would first require the formulation of Maxwell-Lorentz electrodynamics in the form of a connection in Finsler space. If such formulation is possible, the sought generalization would consist in simply changing bases in the tangent spaces of the manifold that supports the connection. In addition, the number of dimensions of the space of the Robertson transformations would be ten, but not greater than ten.

Keywords

Manifold Tangent Space Coordinate Transformation Special Relativity Free Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J. G. Vargas,Found. Phys. 14, 625, 1984.Google Scholar
  2. 2.
    J. G. Vargas and D. G. Torr,Found. Phys. 16, 1089 (1986).Google Scholar
  3. 3.
    H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949).Google Scholar
  4. 4.
    J. G. Vargas,Found. Phys. 16, 1231 (1986).Google Scholar
  5. 5.
    R. Mansouri and R. V. Sexl,Gen. Rel. Grav. 8, 497 (1977).Google Scholar
  6. 6.
    R. Mansouri and R. V. Sexl,Gen. Rel. Grav. 8, 515 (1977).Google Scholar
  7. 7.
    R. Mansouri and R. V. Sexl,Gen. Rel. Grav. 8, 809 (1977).Google Scholar
  8. 8.
    D. W. MacArthur,Phys. Rev. A33, 1 (1986).Google Scholar
  9. 9.
    T. Chang,Phys. Lett. 70A, 1 (1979).Google Scholar
  10. 10.
    J. Rembielinski,Phys. Lett. 78A, 33 (1980).Google Scholar
  11. 11.
    E. Cartan,Bull. Math. Soc. Roum. Sci. 35, 69 (1933), reprinted inOeuvres Completes (Gauthier-Villars, Paris, 1955), Vol. 111/2, p. 1239.Google Scholar
  12. 12.
    J. G. Vargas,Found. Phys. 12, 765 (1982).Google Scholar
  13. 13.
    L. D. Landau and E. M. Lifshitz,Classical Theory of Fields (Addison-Wesley, Reading, Massachussets, 1951).Google Scholar
  14. 14.
    J. G. Vargas,Lett. Nuovo Cimento 28, 289 (1980).Google Scholar
  15. 15.
    D. Lovelock and H. Rund,Tensors, Differential Forms and Variational Principles (Wiley, New York, 1975).Google Scholar
  16. 16.
    A. Lichnerowicz,Eléments de calcul tensoriel (Librairie Armand Colin, Paris, 1950).Google Scholar
  17. 17.
    R. Adler, M. Bazin, and M. Schriffer,Introduction to General Relativity (McGraw-Hill, New York, 1975).Google Scholar
  18. 18.
    D. Hestenes,Space-Time Algebra (Gordon & Breach, New York, 1966).Google Scholar
  19. 19.
    E. Cartan,Exposés de géométrie (Hermann, Paris, 1971).Google Scholar
  20. 20.
    G. S. Asanov,Finsler Geometry, Relativity and Gauge Theories (Reidel, Dordrecht, 1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Jose G. Vargas
    • 1
  • Douglas G. Torr
    • 1
  1. 1.Department of PhysicsUniversity of Alabama in HuntsvilleHuntsville

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