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Foundations of Physics Letters

, Volume 10, Issue 3, pp 273–293 | Cite as

String theory, scale relativity and the generalized uncertainty principle

  • Carlos Castro
Article

Abstract

Extensions (modifications) of the Heisenberg uncertainty principle are derived within the framework of the theory of special scale-relativity proposed by Nottale. In particular, generalizations of the stringy uncertainty principle are obtained where the size of the strings is bounded by the Planck scale and the size of the universe. Based on the fractal structures inherent with two dimensional quantum gravity, which has attracted considerable interest recently, we conjecture that the underlying fundamental principle behind string theory should be based on an extension of the scale relativity principle whereboth dynamics as well as scales are incorporated in the same footing.

Key words

strings|scale relativity|uncertainty principle|fractals|quantum gravity|Planck length 

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References

  1. 1.
    P. Pfeif, J. Frohlich,Rev. Mod. Phys. 67 (40) (1995) 759–779.CrossRefADSGoogle Scholar
  2. 2.
    S. Weinberg,Ann. Phys. 194 (1989) 336–386.CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    C. Castro,Found. Phys. Lett. 4 (1) (1991) 91.CrossRefMathSciNetGoogle Scholar
  4. 4.
    A. Connes,Noncommutative Geomerty (Academic, New York, 1994).Google Scholar
  5. 5.
    D. Amati, M. Ciafaloni, and G. Veneziano,Phys. Lett. B 197 (1987) 91. D. Amati, M. Ciafaloni, and G. Veneziano,Phys. Lett. B 216 (1989) 41.ADSGoogle Scholar
  6. 6.
    M. Fabrichesi and G. Veneziano,Phys. Lett. B 233 (1989) 135.CrossRefADSGoogle Scholar
  7. 7.
    D. Gross and P. F. Mende,Phys. Lett. B 197 (1987) 129.CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    K. Konishi, G. Paffuti, and P. Provero,Phys. Lett. B 234 (1990) 276.CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    R. Guida, K. Konish, and P. Provero,Mod. Phys. Lett. A 6 (16) (1991) 1487.CrossRefADSGoogle Scholar
  10. 10.
    J. J. Atick and E. WittenNucl. Phys. B 310 (1988) 291.CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    M. Duff, R. R. Khuri, and J. X. Lu,Phys. Rev. 259 (1995) 213–326.MathSciNetGoogle Scholar
  12. 12.
    L. Susskind, “The world as a hologram,” hep-th/9409089.Google Scholar
  13. 13.
    L. Nottale,Int. J. Mod. Phys. A 4 (1989) 5047;A 7 (20) (1992) 4899.CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    L. Nottale,Fractal Spacetime and Microphysics: Towards the Theory of Scale Relativity (World Scientific, Singapore, 1993).Google Scholar
  15. 15.
    G. ’t Hooft,Phys. Lett. B 198 (1987) 61.CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    J. Ambjorn, Y. Watabiki,Nucl. Phys. B 455 (1995) 129.ADSMathSciNetGoogle Scholar
  17. 17.
    J. Ambjorn, J. Jurkiewicz and Y. Watabiki, “On the fractal structure of two-dimensional quantum gravity,” hep-lat/9507014. NBI-ITE-95-22 preprint.Google Scholar
  18. 18.
    S. Catterall, G. Thorleifsson, M. Bowick, and V. John, “Scaling and the fractal geometry of two-dimensional quantum gravity,” hep-lat/9504009.Google Scholar
  19. 19.
    J. Ambjorn, J. Jukiewicz, “Scaling in four-dimensional quantum gravity,” hep-th/9503006.Google Scholar
  20. 20.
    P. F. Mende, H. Ooguri,Nucl. Phys. B 339 (1990) 641.CrossRefADSMathSciNetGoogle Scholar
  21. 21.
    C. Castro,Found. Phys. 22 (4) (1992) 569.CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    E. Santamato,Phys. Rev. D 29 (1984) 216.CrossRefADSMathSciNetGoogle Scholar
  23. 23.
    J. P. Costella, “[p, q] ≠,’ Melbourne preprint, UM-P-95/51.Google Scholar
  24. 24.
    J. Borde, F. Lizzi,Mod. Phys. Lett. A 5 (10) (1990) 1911.Google Scholar
  25. 25.
    M. Karliner, I. Klebanov, and L. Susskind,Int. J. Mod. Phys. A 3 (1988) 1981.CrossRefADSGoogle Scholar
  26. 26.
    V. S. Vladimorov, I. V. Volovich, and E. I. Zelenov,P-adic Analysis and Mathematical Physics (World Scientific, Singapore, 1992).Google Scholar
  27. 27.
    L. Garay,Int. J. Mod. Phys. A 10 (1995) 145. A. Ashtekar, C. Rovelli, and L. Smolin,Phys. Rev. Lett. 69 (2) (1992) 237.CrossRefADSGoogle Scholar
  28. 28.
    E. Witten,Phys. Today April 1996, p. 24.Google Scholar
  29. 29.
    G. N. Ord,J. Phys. A. Math. Gen. 16 (1983) 1869.CrossRefADSMathSciNetGoogle Scholar
  30. 30.
    N. Itzhaki, “Time measurement in quantum gravity,” hep-th/9404123.Google Scholar
  31. 31.
    C. Castro, “Incorporating the scale-relativity principle in string theory and extended objects,” hep-th/9612003.Google Scholar
  32. 32.
    T. Yoneya,Mod. Phys. Lett. A 4 (1989) 1587.CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, and D. V. Nanopoulos, “On space-time uncertainty relations of Liouville strings and D branes,” hep-th/9701144.Google Scholar
  34. 34.
    A. Kempf, G. Mangano, “Minimal length uncertainty relation and ultraviolet regularization,” hep-th/9612084.Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Carlos Castro
    • 1
    • 2
    • 3
  1. 1.Center for Particle Theory, Physics DepartmentUniversity of TexasAustin
  2. 2.ICSC World LaboratoryLausanneSwitzerland
  3. 3.Center for Theoretical StudiesClark Atlanta UniversityAtlanta

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