On Some Novel Consequences of Clifford Space Relativity Theory

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.

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

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)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  2. 2

    Amelino-Camelia G.: Doubly-special relativity: first results and key open problems. Int. J. Mod. Phys D 11, 1643 (2002)

    ADS  MathSciNet  Article  MATH  Google 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)

    ADS  Article  Google Scholar 

  5. 5

    Castro C., Pavsic M.: Higher derivative gravity and torsion from the geometry of C-spaces. Phys. Lett. B 539, 133 (2002)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  6. 6

    Castro C., Pavsic M.: On Clifford algebras of spacetime and the conformal group. Int. J. Theor. Phys 42, 1693 (2003)

    MathSciNet  Article  MATH  Google Scholar 

  7. 7

    Castro C., Pavsic M.: The extended relativity theory in Clifford-spaces. Prog. Phys. 1, 31 (2005)

    MathSciNet  MATH  Google Scholar 

  8. 8

    Castro C.: Superluminal particles and the extended relativity theories. Found. Phys. 42(9), 1135 (2012)

    ADS  MathSciNet  Article  MATH  Google 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)

    MathSciNet  Article  MATH  Google Scholar 

  10. 10

    Castro C.: Novel physical consequences of the extended relativity in Clifford spaces. Adv. Appl. Clifford Algebras 25, 65–79 (2015)

    MathSciNet  Article  MATH  Google 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)

    Article  MATH  Google Scholar 

  12. 12

    Gross D., Mende P.: The high-energy behavior of string scattering amplitudes. Phys. Lett. B 197, 129–134 (1987)

    ADS  MathSciNet  Article  Google Scholar 

  13. 13

    Kempf A., Mangano G.: Minimal length uncertainty relation and ultraviolet regularisation. Phys. Rev. D 55, 7909–7920 (1997)

    ADS  Article  Google Scholar 

  14. 14

    Lukierski J., Nowicki A., Ruegg H., Tolstoy V.: q-deformation of Poincare algebra. Phys. Lett. B 264, 331–338 (1991)

    ADS  MathSciNet  Article  Google Scholar 

  15. 15

    Majid S., Ruegg H.: Bicrossproduct structure of \({\kappa}\) -Poincare group and non-commutative geometry. Phys. Lett. B 334, 348–354 (1994)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  16. 16

    Magueijo J., Smolin L.: Gravity’s rainbow. Class. Quant. Grav. 21, 1725–1736 (2004)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  17. 17

    Nottale, L.: Fractal Space-time and Micro-physics. World Scientific, Singapore (1993)

  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)

  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)

  20. 20

    Pavsic M.: A novel view on the physical origin of \({{\rm E}_8}\). J. Phys. A 41, 332001 (2008)

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Carlos Castro.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Castro, C. On Some Novel Consequences of Clifford Space Relativity Theory. Adv. Appl. Clifford Algebras 27, 255–266 (2017). https://doi.org/10.1007/s00006-015-0553-x

Download citation

Keywords

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