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On 336 kissing spheres in 10 dimensions, 528 P-Brane states in 11 dimensions and the 60 elementary particles of the standard model

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  • El Naschie, M.S.

Abstract

The paper gives a short outline of some interesting relations between sphere packing in higher dimensional spaces, the theory of P-Brane and the number of elementary particles in the standard model. In particular we show that the 336 independent components of the Riemann curvature tensor may be represented by the contact points of 336 nine-dimensional spheres with a single central sphere embedded in 10 dimensions. Subsequently we show that the number of states in the 11-dimensional P-Brane super gravity, namely 528 may be found from the number of the contact points by scale transformation involving the seven-dimensional sphere and 11-dimensional M theory. Finally by eliminating shadow particles and using Kappa-like invariance, the theoretical number of elementary particles to be expected at an energy scale close to that of electro weak unification is found to beN(SM)=[(336)(11/7)]/8=66.Considering that there are at present only 60 experimentally confirmed particles, the result implies that there are some 6 particles still missing.

Suggested Citation

  • El Naschie, M.S., 2005. "On 336 kissing spheres in 10 dimensions, 528 P-Brane states in 11 dimensions and the 60 elementary particles of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 447-457.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:2:p:447-457
    DOI: 10.1016/j.chaos.2004.09.071
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    1. El Naschie, M.S., 2005. "Determining the number of Higgs particles starting from general relativity and various other field theories," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 711-726.
    2. El Naschie, M.S., 2005. "Einstein’s dream and fractal geometry," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 1-5.
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    1. El Naschie, M.S., 2007. "The Fibonacci code behind super strings and P-Branes. An answer to M. Kaku’s fundamental question," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 537-547.
    2. He, Ji-Huan, 2007. "The number of elementary particles in a fractal M-theory of 11.2360667977 dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 346-351.
    3. Chen, Qingjiang & Huo, Ailian, 2009. "The research of a class of biorthogonal compactly supported vector-valued wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 951-961.
    4. He, Ji-Huan, 2007. "On the number of elementary particles in a resolution dependent fractal spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1645-1648.
    5. El Naschie, M.S., 2007. "Estimating the experimental value of the electromagnetic fine structure constant α¯0=1/137.036 using the Leech lattice in conjunction with the monster group and Spher’s kissing number in 24 dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 383-387.
    6. El Naschie, M.S., 2005. "Spinorial content of the standard model, a different look at super-symmetry and fuzzy E-infinity hyper Kähler," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 303-311.
    7. El Naschie, M.S., 2008. "Deriving the largest expected number of elementary particles in the standard model from the maximal compact subgroup H of the exceptional Lie group E7(-5)," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 956-961.
    8. El Naschie, M.S., 2005. "An elementary model based method for determining the number of possible Higg bosons in the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 701-706.
    9. Marek-Crnjac, L., 2006. "Different Higgs models and the number of Higgs particles," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 575-579.
    10. El Naschie, M.S., 2008. "Conjectures regarding kissing spheres hierarchy and quantum gravity unification," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 346-350.
    11. He, Ji-Huan & Xu, Lan, 2009. "Number of elementary particles using exceptional Lie symmetry groups hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2119-2124.
    12. Iovane, G. & Giordano, P., 2005. "Hypersingular integral equations, waveguiding effects in Cantorian Universe and genesis of large scale structures," Chaos, Solitons & Fractals, Elsevier, vol. 25(4), pages 879-896.
    13. El Naschie, M.S., 2005. "From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 969-977.
    14. El Naschie, M.S., 2007. "From symmetry to particles," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 427-430.
    15. El-Okaby, Ayman A., 2008. "Exceptional Lie groups, E-infinity theory and Higgs Boson," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1305-1317.
    16. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    17. El Naschie, M.S., 2009. "Kac–Moody exceptional E12 from simplictic tiling," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1569-1571.
    18. El Naschie, M.S., 2006. "Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 297-330.
    19. El Naschie, M.S., 2005. "Tadpoles, anomaly cancellation and the expectation value of the number of the Higgs particles in the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 659-663.

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