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Cantorian spacetime and Hilbert space: Part I—Foundations

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  • Iovane, G.

Abstract

We are going to show the link between the ε(∞) Cantorian space and the Hilbert spaces H(∞). In particular, El Naschie’s ε(∞) is a physical spacetime, i.e. an infinite dimensional fractal space, where time is spacialized and the transfinite nature manifests itself. El Naschie’s Cantorian spacetime is an arena where the physics laws appear at each scale in a self-similar way linked to the resolution of the act of observation. By contrast the Hilbert space H(∞) is a mathematical support, which describes the interaction between the observer and the dynamical system under measurement.

Suggested Citation

  • Iovane, G., 2006. "Cantorian spacetime and Hilbert space: Part I—Foundations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 857-878.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:857-878
    DOI: 10.1016/j.chaos.2005.08.074
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    1. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
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    3. 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.
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    5. El Naschie, M.S., 2005. "Non-Euclidean spacetime structure and the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 1-6.
    6. 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.
    7. El Naschie, M.S., 2006. "Hilbert space, the number of Higgs particles and the quantum two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 9-13.
    8. El Naschie, M.S., 2005. "A guide to the mathematics of E-infinity Cantorian spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 955-964.
    9. Iovane, G. & Gargiulo, G. & Zappale, E., 2006. "A Cantorian potential theory for describing dynamical systems on El Naschie’s space–time," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 588-598.
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    14. Iovane, Gerardo, 2008. "The set of prime numbers: Symmetries and supersymmetries of selection rules and asymptotic behaviours," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 950-961.
    15. Marek-Crnjac, L., 2008. "Lie groups hierarchy in connection with the derivation of the inverse electromagnetic fine structure constant from the number of particle-like states 548, 576 and 672," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 332-336.
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