Foundations of Physics

, Volume 31, Issue 12, pp 1785–1806 | Cite as

Equivalence Principle and the Principle of Local Lorentz Invariance

  • W. A. RodriguesJr.
  • M. Sharif


In this paper we scrutinize the so called Principle of Local Lorentz Invariance (PLLI) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics, we introduce in the General Theory of Relativity two classes of reference frames (PIRFs and LLRFγs) which as natural generalizations of the concept of the inertial reference frames of the Special Relativity Theory. We show that it is the class of the LLRFγs that is associated with the PLLI. Next we give a definition of physically equivalent reference frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the PLLI is false. However our finding is not in contradiction with the many experimental claims vindicating the PLLI, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that PIRFs are not physically equivalent.


General Relativity Reference Frame General Theory Special Relativity Natural Generalization 
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  1. 1.
    W. A. Rodrigues, Jr., M. Scanavini, and L. P. de Alcantara, Found. Phys. Lett. 3, 59 (1990).Google Scholar
  2. 2.
    N. Bourbaki, Theorie des Ensembles (Hermann, Paris, 1957).Google Scholar
  3. 3.
    H. Reichenbach, The Philosophy of Space and Time (Dover, New York, 1958).Google Scholar
  4. 4.
    R. K. Sachs and H. Wu, General Relativity for Mathematicians (Springer, New York, 1977).Google Scholar
  5. 5.
    W. A. Rodrigues, Jr. and M. A. F. Rosa, Found. Phys. 19, 705 (1989).Google Scholar
  6. 6.
    W. A. Rodrigues, Jr. and E. Capelas de Oliveira, Phys. Lett. A 140, 479 (1989).Google Scholar
  7. 7.
    Y. Choquet-Bruhat, C. Dewitt-Morette, and M. Dillard-Bleick, Analysis, Manifolds and Physics, revised edn. (North-Holland, Amsterdam, 1982).Google Scholar
  8. 8.
    W. A. Rodrigues, Jr. and M. Sharif, “Rotating frames in SRT: Sagnac effect and related issues,” Found. Phys. 31(12) (2001).Google Scholar
  9. 9.
    S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 1 (Wiley, New York, 1963).Google Scholar
  10. 10.
    R. L. Bishop and S. I. Goldberg, Tensor Analysis on Manifolds (Dover, New York, 1980).Google Scholar
  11. 11.
    A. S. Eddington, The Mathematical Theory of Relativity, 3rd edn. (Chelsea, New York, 1975).Google Scholar
  12. 12.
    R. C. Tolman, Relativity, Thermodynamics and Cosmology (Dover, New York, 1987).Google Scholar
  13. 13.
    T. Matolsci, Spacetime Without Reference Frames (Akadémiai Kiadó, Budapest, 1993).Google Scholar
  14. 14.
    J. E. Maiorino and W. A. Rodrigues, Jr., “What is superluminal wave motion?,” Sci. Tech. Mag. 4(2) (1999); electronic book at∼stm.Google Scholar
  15. 15.
    J. L. Synge, Relativity: The General Theory (North-Holland, Amsterdam, 1960).Google Scholar
  16. 16.
    M. Friedman, Foundations of Spacetime Theories (University Press, Princeton, 1983).Google Scholar
  17. 17.
    C. M. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francesco, 1973).Google Scholar
  18. 18.
    I. Ciufuolini and J. A. Wheeler, Gravitation and Inertia (University Press, Princeton, New Jersey, 1995).Google Scholar
  19. 19.
    C. M. Will, Theory and Experiment in Gravitational Physics (University Press, Cambridge, 1980).Google Scholar
  20. 20.
    B. Bertotti and L. P. Grishchuk, Class. Quant. Grav. 7, 1733 (1990).Google Scholar
  21. 21.
    M. D. Gabriel and M. P. Haugan, Phys. Rev. D 141, 2943 (1990).Google Scholar
  22. 22.
    S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972).Google Scholar
  23. 23.
    E. Prugrovecki, Quantum Geometry: A Framework Quantum General Relativity (Kluwer Academic, Dordrecht, 1992).Google Scholar
  24. 24.
    J. Norton, Einstein and the History of General Relativity, D. Howard and J. Stachel, eds. (Birkhäuser, Boston, 1989).Google Scholar
  25. 25.
    N. Rosen, Proc. Israel Acad. Sci. Hum. 1, 12 (1968).Google Scholar

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • W. A. RodriguesJr.
    • 1
    • 2
  • M. Sharif
    • 3
  1. 1.Institute of Mathematics, Statistics and Scientific ComputationIMECC-UNICAMPCampinas, SPBrazil
  2. 2.Wernher von Braun Advanced Research Center, UNISALCampinas, SPBrazil
  3. 3.Institute of Mathematics, Statistics and Scientific ComputationIMECC-UNICAMPCampinas, SPBrazil

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