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Advances in Applied Clifford Algebras

, Volume 27, Issue 1, pp 255–266 | Cite as

On Some Novel Consequences of Clifford Space Relativity Theory

  • Carlos Castro
Article
  • 66 Downloads

Abstract

Some of the novel physical consequences of the Extended Relativity Theory in C-spaces (Clifford spaces) are presented. In particular, generalized photon dispersion relations which allow for energy-dependent speeds of propagation while still retaining the Lorentz symmetry in ordinary spacetimes, while breaking the extended Lorentz symmetry in C-spaces. We analyze in further detail the extended Lorentz transformations in Clifford Space and their physical implications. Based on the notion of “extended events” one finds a very different physical explanation of the phenomenon of “relativity of locality” than the one described by the doubly special relativity framework. We finalize with a discussion of the modified dispersion relations, rainbow metrics and generalized uncertainty relations in C-spaces which are extensions of the stringy uncertainty relations.

Keywords

Clifford algebras and Extended relativity in Clifford spaces Modified dispersion relations Rainbow metrics Generalized uncertainty principle 

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References

  1. 1.
    Amelino-Camelia G.: Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale. Int. J. Mod. Phys D 11, 35 (2002)ADSMathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Amelino-Camelia G.: Doubly-special relativity: first results and key open problems. Int. J. Mod. Phys D 11, 1643 (2002)ADSMathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Amelino-Camelia, G.; Freidel, L.; Kowalski-Glikman, J.; Smolin, L.: The principle of relative locality. arXiv.org:1101.0931
  4. 4.
    Amati D., Ciafaloni M., Veneziano G.: Superstring collisions at planckian energies. Phys. Lett. B 197, 81–88 (1987)ADSCrossRefGoogle Scholar
  5. 5.
    Castro C., Pavsic M.: Higher derivative gravity and torsion from the geometry of C-spaces. Phys. Lett. B 539, 133 (2002)ADSMathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Castro C., Pavsic M.: On Clifford algebras of spacetime and the conformal group. Int. J. Theor. Phys 42, 1693 (2003)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Castro C., Pavsic M.: The extended relativity theory in Clifford-spaces. Prog. Phys. 1, 31 (2005)MathSciNetMATHGoogle Scholar
  8. 8.
    Castro C.: Superluminal particles and the extended relativity theories. Found. Phys. 42(9), 1135 (2012)ADSMathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Castro C.: The extended relativity theory in Clifford phase spaces and modifications of gravity at the planck/hubble scales. Adv. Appl. Clifford Algebras 24, 29–53 (2014)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Castro C.: Novel physical consequences of the extended relativity in Clifford spaces. Adv. Appl. Clifford Algebras 25, 65–79 (2015)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    da Rocha R., Bernardini A.E., Vaz J. Jr: \({\kappa}\) -deformed Poincare algebras and quantum Clifford–Hopf algebras int. J. Geom. Meth. Mod. Phys. 7, 821–836 (2010)CrossRefMATHGoogle Scholar
  12. 12.
    Gross D., Mende P.: The high-energy behavior of string scattering amplitudes. Phys. Lett. B 197, 129–134 (1987)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Kempf A., Mangano G.: Minimal length uncertainty relation and ultraviolet regularisation. Phys. Rev. D 55, 7909–7920 (1997)ADSCrossRefGoogle Scholar
  14. 14.
    Lukierski J., Nowicki A., Ruegg H., Tolstoy V.: q-deformation of Poincare algebra. Phys. Lett. B 264, 331–338 (1991)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Majid S., Ruegg H.: Bicrossproduct structure of \({\kappa}\) -Poincare group and non-commutative geometry. Phys. Lett. B 334, 348–354 (1994)ADSMathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Magueijo J., Smolin L.: Gravity’s rainbow. Class. Quant. Grav. 21, 1725–1736 (2004)ADSMathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Nottale, L.: Fractal Space-time and Micro-physics. World Scientific, Singapore (1993)Google Scholar
  18. 18.
    Nottale, L.: Scale Relativity and Fractal Space-time: a New Approach to Unifying Relativity and Quantum Mechanics. World Scientific Publishing Company, Singapore (2011)Google Scholar
  19. 19.
    Pavsic, M.: The landscape of theoretical physics: a global view, from point particles to the brane world and beyond, in search of a unifying principle. In: Fundamental Theories of Physics, vol. 19. Kluwer, Dordrecht (2001)Google Scholar
  20. 20.
    Pavsic M.: A novel view on the physical origin of \({{\rm E}_8}\). J. Phys. A 41, 332001 (2008)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Quantum Gravity Research GroupTopangaUSA
  2. 2.Center for Theoretical Studies of Physical SystemsClark Atlanta UniversityAtlantaUSA

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