The quantum gravity Immirzi parameter - A general physical and topological interpretation

M.S.El Naschie1

Abstract

The paper argues that the Immirzi crucial free parameter of the spin networks theory of quantum gravity represents a definite quantum entanglement correction. In turn, this entanglement may be explained as a consequence of zero measure non-classical topology of the relevant geometrical-topological setting and the associated fiber bundle symmetry group. In particular, we show that the Immirzi parameter may be interpreted as a three-particle probability for quantum entanglement akin to Hardy's probability for two quantum particles. We give the exact limiting value of the Immirzi parameter to be γc = φ6 = 0.05572809, where φ = (51/2 - 1)/2. Thus, while Hardy's quantum entanglement was found exactly using Dirac's conventional quantum mechanics and confirmed experimentally to be P(Hardy) = φ5 = 0.090169943, we have a similar situation for the free parameter of loop quantum gravity, namely, that γ = log 2/(π 31/2) = 0.055322 ⇒ φ6 = 0.055728. This result will be shown to have far-reaching consequences for quantum physics and cosmology.

References

  1. R. Penrose, The Road to Reality. A Complete Guide to the Laws of the Universe (Jonathan Cape, London, 2004).
  2. C. Rovelli, Quantum Gravity (Cambridge Press, Cambridge, 2004).
  3. A. Vilenkin, Phys. Rev. D 41, 3038 (1990).
  4. C. Rovelli and T. Thiemann, The Immirzi parameter in quantum general relativity, gr-qc/9705059.
  5. T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, 2007).
  6. M. S. El Naschie, Chaos, Solitons and Fractals 27(2), 297 (2006).
  7. M. S. El Naschie, J. of Quantum Info. Sci., 1(2), 50 (2011). Free access online: Sept. 2011, (http://www.SCRIP.org/journal/jqis (Scientific Research).
  8. L. Hardy, Phys. Rev. Lett. 71(11), 1665 (1993).
  9. Ji-Huan He et al, Nonlinear Sci. Lett B 1(2), 45 (2011).
  10. L. Marek-Crnjac, Phys. Res. Int., Article ID 874302, doi: 10.1155/2011/874302 (2011).
  11. M.S. El Naschie, Chaos, Solitons and Fractals 41(5), 2635 (2009).
  12. M.S. El Naschie, Chaos, Solitons and Fractals 19(1), 209 (2004).
  13. T. Palmer, Proc. Roy. Soc. A. 465 (2009).
  14. G. Ord: Fractal space-time, J. Phys. A: Math. Gen. 16, 1869 (1983).
  15. L. Amendola and S. Tsujikawa, Dark energy: Theory and Observations (Cambridge University Press, Cambridge, 2010).
  16. L. Sigalotti and A. Mejias, Chaos, Solitons and Fractals 30(3), 521 (2006).
  17. S. Hendi and M. Sharif Zadeh, J. Theor. Phys. 1, 37 (2012) (IAU Publishing-ISSN 2251-855).
  18. M. S. El Naschie, Chaos, Solitons and Fractals 35(1), 202 (2008).
  19. M. S. El Naschie, Chaos, Solitons and Fractals 29(4), 871 (2006).
  20. M. S. El Naschie, Chaos, Solitons and Fractals 26(1), 13 (2005).
  21. L. Marek-Crnjac, Chaos, Solitons and Fractals 34(3), 677 (2007).
  22. M. S. El Naschie, Chaos, Solitons and Fractals 41(4), 1569 (2009).
  23. M. S. El Naschie, Chaos, Solitons and Fractals 36(1), 1 (2008).
  24. A. Elokaby, Chaos, Solitons and Fractals 42(1), 303 (2009).
  25. K. G. Schlesinger: Towards Quantum Mathematics. Part I: From Quantum Sets Theory to University Quantum Mechanics (Erwin Schodinger Ins for Math. Phys, 1998; Preprint Vienna, Austria ESI 537, available via http://www.esi.ac.at).
  26. D. R. Finkelstein, Quantum Relativity (Springer, Berlin, 1996).
  27. M. S. El Naschie, Chaos, Solitons and Fractals 29(4), 816 (2006).
  28. M. S. El Naschie, Chaos, Solitons and Fractals 29(4), 845 (2006).
  29. A. Connes: Noncommutative Geometry (Academic Press, San Diego, 1994).
  30. Yu. Gnedin, A. Grib, and V. Mastepanenko, in: Proc. of the Third Alexander Friedmann Int. Seminar on Gravitation and Cosmology (Friedmann Lab. Pub., St. Petersberg, 1995).
  31. A. Vilenkin and E. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, 2001).
For more information about this paper please visit Springer's Home Page of this paper.



Back to The Contents Page