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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

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  • El Naschie, M.S.

Abstract

We start with various observations regarding the kissing number in the 24-dimensional Leech lattice Nτ(24)=196560 as well as the j-function coefficient b=196884 and the minimal dimension in which the monster group can act Dm=196883. Subsequently based on the previous results and earlier numerical experiments, we use a quibic potential to derive a quadratic equationx2+12820x-(Nτ(24)/10)=0where 128=spin 7=(2)7, 10=D(10) and Nτ(24)=196560 are the spin representation, the super string dimension and the Leech kissing number, respectively. It is found that the only positive solution of this equation isx1=137.036=α¯0which is the accurate experimental value of inverse of the electromagnetic fine structure constant. This remarkable result is interpreted in terms of the connection between the Moonshine conjecture and string theory as well as the E-infinity relation between the kissing number in 10 dimensions Kτ(10)=336 and the degrees of freedom of Klein’s modular space dim Γ(7)=336.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:383-387
    DOI: 10.1016/j.chaos.2006.09.014
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    References listed on IDEAS

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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. 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.
    3. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    4. El Naschie, M.S., 2006. "Holographic dimensional reduction: Center manifold theorem and E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 816-822.
    5. El Naschie, M.S., 2007. "Feigenbaum scenario for turbulence and Cantorian E-infinity theory of high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 911-915.
    6. Naschie, M.S. El, 2006. "Holographic correspondence and quantum gravity in E-infinity spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 871-875.
    7. El Naschie, M.S., 2007. "Hilbert space, Poincaré dodecahedron and golden mean transfiniteness," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 787-793.
    8. 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.
    9. El Naschie, M.S., 2007. "On the topological ground state of E-infinity spacetime and the super string connection," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 468-470.
    10. El Naschie, M.S., 2006. "On two new fuzzy Kähler manifolds, Klein modular space and ’t Hooft holographic principles," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 876-881.
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    Cited by:

    1. Marek-Crnjac, L., 2008. "The connection between the electromagnetic fine structure constant α¯0 and the monster Lie algebra," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 257-262.
    2. Marek-Crnjac, L., 2008. "Exceptional Lie groups hierarchy, orthogonal and unitary groups in connection with symmetries of E-infinity space-time," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 517-520.
    3. Gottlieb, I. & Agop, M. & Enache, V., 2009. "Games with Cantor’s dust," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 940-945.
    4. Agop, M. & Paun, V. & Harabagiu, Anca, 2008. "El Naschie’s ε(∞) theory and effects of nanoparticle clustering on the heat transport in nanofluids," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1269-1278.
    5. El Naschie, M.S., 2008. "On a transfinite symmetry group with 10 to the power of 19 dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 539-541.
    6. El Naschie, M.S., 2007. "From pointillism to E-infinity electromagnetism," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1377-1381.
    7. El Naschie, M.S., 2007. "From symmetry to particles," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 427-430.
    8. He, Ji-Huan & Xu, Lan & Zhang, Li-Na & Wu, Xu-Hong, 2007. "Twenty-six dimensional polytope and high energy spacetime physics," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 5-13.
    9. Marek-Crnjac, L., 2007. "The fundamental coupling constants of physics in connection with the dimension of the special orthogonal and unitary groups," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1382-1386.
    10. Akbulak, Mehmet & Bozkurt, Durmuş, 2009. "On the order-m generalized Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1347-1355.
    11. Agop, M. & Chicos, Liliana & Nica, P., 2009. "Transport phenomena in nanostructures and non-differentiable space–time," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 803-814.

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