Skip to main content
SpringerLink
Log in

Spatial Directions, Anisotropy and Special Relativity

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The concept of an objective spatial direction in special relativity is investigated and theories assuming light-speed isotropy while accepting the existence of a privileged spatial direction are classified, including so-called very special relativity. A natural generalization of the proper time principle is introduced which makes it possible to devise non-optical experimental tests of spatial isotropy. Several common misunderstandings in the relativistic literature concerning the role of spatial isotropy are clarified.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Allais, M.: L’anisotropie de l’Espace. La Nécessaire Révision de Certains Postulats des Théories Contemporaines. Clément Juglar, Paris (1997)

    Google Scholar 

  2. Arcidiacono, G.: A new ‘Projective Relativity’ based on the De Sitter universe. Gen. Relativ. Gravit. 7, 885–889 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  3. Bartocci, U., Mamone Capria, M.: Symmetries and asymmetries in classical and relativistic electrodynamics. Found. Phys. 21, 787–801 (1991)

    Article  ADS  Google Scholar 

  4. Berzi, V., Gorini, V.: Reciprocity principle and the Lorentz transformations. J. Math. Phys. 10, 1518–1524 (1969)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. Bogoslovsky, G.Yu.: A special-relativistic theory of the locally anisotropic space-time. I: the metric and group of motions of the anisotropic space of events. Nuovo Cimento Soc. Ital. Fis. B 40, 99–115 (1977)

    Article  ADS  Google Scholar 

  6. Bogoslovsky, G.Yu.: A special-relativistic theory of the locally anisotropic space-time. II: mechanics and electrodynamics in the anisotropic space. Nuovo Cimento Soc. Ital. Fis. B 40, 116–134 (1977)

    Article  ADS  Google Scholar 

  7. Bogoslovsky, G.Yu.: On the local anisotropy of space-time, inertia and force fields. Nuovo Cimento Soc. Ital. Fis. B 77, 181–190 (1983)

    Article  ADS  Google Scholar 

  8. Bogoslovsky, G.Yu.: From the Weyl theory to a theory of locally anisotropic spacetime. Class. Quantum Gravity 9, 569–575 (1992)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. Bogoslovsky, G.Yu.: Lorentz symmetry violation without violation of relativistic symmetry. Phys. Lett. A 350, 5–10 (2006)

    Article  ADS  MATH  Google Scholar 

  10. Bogoslovsky, G.Yu., Goenner, H.F.: Concerning the generalized Lorentz symmetry and the generalization of the Dirac equation. Phys. Lett. A 323, 40–47 (2004). arXiv:hep-th/0402172v1, 21 Feb. 2004

    Article  ADS  MATH  MathSciNet  Google Scholar 

  11. Bröcker, T., tom Dieck, T.: Representations of Compact Lie Groups. Springer, Berlin (1985)

    MATH  Google Scholar 

  12. Chupp, T.E., Hoare, R.J., Loveman, R.A., Oteiza, E.R., Richardson, J.M., Wagshul, M.E.: Results of a new test of local Lorentz invariance: a search for mass anisotropy in 21Ne. Phys. Rev. Lett. 63, 1541–1545 (1989)

    Article  ADS  Google Scholar 

  13. Cohen, A.G., Glashow, S.L.: Very special relativity. Phys. Rev. Lett. 97, 021601 (2006). arXiv:hep-ph/0601236v1, 27 Jan. 2006

    Article  ADS  MathSciNet  Google Scholar 

  14. Dingle, H.: Science at the Crossroads. Brian & O’Keeffe, London (1972)

    Google Scholar 

  15. Eddington, A.S.: Space Time and Gravitation. Cambridge University Press, Cambridge (1921)

    MATH  Google Scholar 

  16. Einstein, A.: Zur Elektrodynamik bewegter Körper. Ann. Phys. 17, 891–921 (1905)

    Article  MATH  Google Scholar 

  17. Fantappiè, L.: Su una nuova teoria di “relatività finale”. Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat. 17, 158–165 (1954)

    MATH  Google Scholar 

  18. Gibbons, G.W., Gomis, J., Pope, C.N.: General very special relativity is Finsler geometry. Phys. Rev. D 76, 081701 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  19. Goenner, H.F., Bogoslovsky, G.Yu.: A class of anisotropic (Finsler-)space-time geometries. Gen. Relativ. Gravit. 31, 1383–1394 (1999)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  20. Lamoreaux, S.K., Jacobs, J.P., Heckel, B.R., Raab, F.J., Fortson, E.N.: New limits on spatial anisotropy from optically pumped 201Hg and 199Hg. Phys. Rev. Lett. 25, 3125–3128 (1986)

    Article  ADS  Google Scholar 

  21. Levy-Nahas, M.: Deformation and contraction of Lie algebras. J. Math. Phys. 8, 1211–1222 (1967)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  22. Lucas, J.R., Hodgson, P.E.: Spacetime and Electromagnetism. Oxford University Press, London (1990)

    MATH  Google Scholar 

  23. Mamone Capria, M.: On the conventionality of simultaneity in special relativity. Found. Phys. 31, 775–818 (2001)

    Article  MathSciNet  Google Scholar 

  24. Mamone Capria, M., Pambianco, F.: On the Michelson–Morley experiment. Found. Phys. 24, 885–899 (1994)

    Article  ADS  Google Scholar 

  25. Moller, C.: The Theory of Relativity, 2nd edn. Oxford University Press, London (1972)

    Google Scholar 

  26. Noz, M.E., Kim, Y.S. (eds.): Special Relativity and Quantum Theory. Kluwer Academic, Dordrecht (1988)

    MATH  Google Scholar 

  27. Pais, A.: “Subtle is the Lord...”. The Science and the Life of Albert Einstein. Oxford University Press, London (1982)

    Google Scholar 

  28. Penrose, R.: The Road to Reality [2004]. Vintage, New York (2007)

    Google Scholar 

  29. Poincaré, H.: Sur la dynamique de l’électron. Rend. Circ. Mat. Palermo 21, 129–176 (1906)

    Article  MATH  Google Scholar 

  30. Wigner, E.P.: On unitary representations of the inhomogeneous Lorentz group. Ann. Math. 40, 149–204 (1939)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, via Vanvitelli, 1, 06123, Perugia, Italy

    Marco Mamone Capria

Authors
  1. Marco Mamone Capria
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marco Mamone Capria.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mamone Capria, M. Spatial Directions, Anisotropy and Special Relativity. Found Phys 41, 1375–1397 (2011). https://doi.org/10.1007/s10701-011-9554-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-011-9554-3

Keywords

Search

Navigation