IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i4p1616-1618.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908003056
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.07.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. El Naschie, M.S., 2008. "Eliminating gauge anomalies via a “point-less” fractal Yang–Mills theory," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1332-1335.
    2. El Naschie, M.S., 2008. "Bounds on the number of possible Higgs particles using grand unification and exceptional Lie groups," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 633-637.
    3. Iovane, Gerardo, 2009. "The set of prime numbers: Multiscale analysis and numeric accelerators," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1953-1965.
    4. El Naschie, M.S., 2009. "On zero-dimensional points curvature in the dynamics of Cantorian-fractal spacetime setting and high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2725-2732.
    5. El Naschie, M.S., 2009. "Curvature, Lagrangian and holonomy of Cantorian-fractal spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2163-2167.
    6. El Naschie, M.S., 2008. "Removing spurious non-linearity in the structure of micro-spacetime and quantum field renormalization," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 60-64.
    7. Elokaby, A., 2009. "On the deep connection between instantons and string states encoder in Klein’s modular space," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 303-305.
    8. Iovane, Gerardo, 2009. "The set of prime numbers: Multifractals and multiscale analysis," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1945-1958.
    9. El Naschie, M.S., 2008. "Deriving quarks confinement from the topology of quantum spacetime and heterotic string theory," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 193-195.
    10. El Naschie, M.S., 2009. "Arguments for the compactness and multiple connectivity of our cosmic spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2787-2789.
    11. 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.
    12. El Naschie, M.S., 2008. "Towards a quantum field theory without Gribov copies and similar problems," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 936-938.
    13. 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.
    14. Marek-Crnjac, L., 2008. "From Arthur Cayley via Felix Klein, Sophus Lie, Wilhelm Killing, Elie Cartan, Emmy Noether and superstrings to Cantorian space–time," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1279-1288.
    15. 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.
    16. El Naschie, M.S., 2009. "BPS states, dualities and determining the mass of elementary particles," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1263-1265.
    17. Chen, Qingjiang & Liu, Baocang & Cao, Huaixin, 2009. "Construction of a sort of multiple pseudoframes for subspaces with filter banks," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 801-808.
    18. El Naschie, M.S., 2008. "Anomalies free E-infinity from von Neumann’s continuous geometry," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1318-1322.
    19. El Naschie, M.S., 2008. "Mathematical foundation of E-Infinity via Coxeter and reflection groups," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1267-1268.
    20. El Naschie, M.S., 2008. "An energy balance Eigenvalue equation for determining super strings dimensional hierarchy and coupling constants," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1283-1285.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1616-1618. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.