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Knot wormholes and the dimensional invariant of exceptional Lie groups and Stein space hierarchies

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  • Elokaby, Ayman

Abstract

The present short note points out a most interesting and quite unexpected connection between the number of distinct knot as a function of their crossing number and exceptional Lie groups and Stein space hierarchies. It is found that the crossing number 7 plays the role of threshold similar to 4 and 5 in E-infinity theory and for the 11 crossing the number of distinct knots is very close to4α¯0+1=548+1=549,where α¯0=137 is the inverse integer electromagnetic fine structure constant. This is particularly intriguing in view of a similar relation pertinent to the 17 two and three Stein spaces where the total dimension is∑117Stein=5α¯0+1=685+1=686,as well as the sum of the eight exceptional Lie symmetry groups∑i=18|Ei|=4α¯0=548.The slight discrepancy of one is explained in both cases by the inclusion of El Naschie’s transfinite corrections leading to∑i=18|Ei|=(4)(137+k0)=548.328157and∑i=117Stein=(5)(137+k0)=685.41097,where ko=ϕ5(1−φ5) and φ=5-1/2.

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  • Elokaby, Ayman, 2009. "Knot wormholes and the dimensional invariant of exceptional Lie groups and Stein space hierarchies," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1616-1618.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1616-1618
    DOI: 10.1016/j.chaos.2008.07.003
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    1. El Naschie, M.S., 2008. "On a major exceptional Lie symmetry groups hierarchy and quantum gravity," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 42-44.
    2. El Naschie, M.S., 2008. "High energy physics and the standard model from the exceptional Lie groups," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 1-17.
    3. El Naschie, M.S., 2008. "The Exceptional Lie symmetry groups hierarchy and the expected number of Higgs bosons," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 268-273.
    4. 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.
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    1. El Naschie, M.S., 2009. "Derivation of the Euler characteristic and the curvature of Cantorian-fractal spacetime using Nash Euclidean embedding and the universal Menger sponge," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2394-2398.
    2. El Naschie, M.S., 2009. "Knots and exceptional Lie groups as building blocks of high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1799-1803.
    3. El Naschie, M.S., 2009. "On the Witten–Duff five Branes model together with knots theory and E8E8 super strings in a single fractal spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2018-2021.

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