 Derivation of the Euler characteristic and the curvature of Cantorian-fractal spacetime using Nash Euclidean embedding and the universal Menger spongeM.S. El Naschie Chaos, Solitons & Fractals, 2009, vol. 41, issue 5, 2394-2398 Abstract: The present work gives an analytical derivation of the curvature K of fractal spacetime at the point of total unification of all fundamental forces which is marked by an inverse coupling constant equal α¯gs=26.18033989. To do this we need to first find the exact dimensionality of spacetime. This turned out to be n=4 for the topological dimension and ∼〈n〉=4+ϕ3=4.236067977 for the intrinsic Hausdorff dimension. Second we need to find the Euler characteristic of our fractal spacetime manifold. Since E-infinity Cantorian spacetime is accurately modelled by a fuzzy K3 Kähler manifold, we just need to extend the well known value χ=24 of a crisp K3 to the case of a fuzzy K3. This leads then to χ(fuzzy)=26+k=α¯gs. The final quite surprising result is that at the point of unification of our resolution dependent fractal-Cantorian spacetime manifold we encounter a Coincidencia Egregreium, namelyK=χ=D=α¯gs=26+k=26.18033989.Finally we look for some indirect experimental evidence for the correctness of our result using the COBE measurement in conjunction with Nash embedding of the universal Menger sponge. Date: 2009 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:41:y:2009:i:5:p:2394-2398 DOI: 10.1016/j.chaos.2008.09.021 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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