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Hilbert space, the number of Higgs particles and the quantum two-slit experiment. (English) Zbl 1082.81501
Summary: Rigorous mathematical formulation of quantum mechanics requires the introduction of a Hilbert space. By contrast, the Cantorian E-infinity approach to quantum physics was developed largely without any direct reference to the afore mentioned mathematical spaces. In the present work we present a novel reinterpretation of basic $$\varepsilon^{(\infty)}$$ Cantorian spacetime relations in terms of the Hilbert space of quantum mechanics. In this way, we gain a better understanding of the physical and mathematical structure of quantum spacetime. In particular we show that the two-slit experiment required a definite topology which is consistent with a certain fuzzy Kähler manifold or more generally a Cantorian spacetime manifold. Finally by determining the Euler class of this manifold, we can estimate the most likely number of Higgs particles which may be discovered.

##### MSC:
 81P99 Foundations, quantum information and its processing, quantum axioms, and philosophy
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##### References:
 [1] El Naschie, M.S., On a fuzzy Kähler-like manifold which is consistent with the two-slit experiment, Int J nonl sci num simul, 6, 2, 95-98, (2005) [2] El Naschie MS. Nonlinear dynamics of the two-slit experiment with quantum particles. Int J “Problems of nonlinear analysis in engineering systems”. Russia: Kazan University (in press). [3] El Naschie, M.S., From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold, Chaos, solitons & fractals, 25, 969-977, (2005) · Zbl 1070.81118 [4] El Naschie, M.S., Non-Euclidean spacetime structure and the two-slit experiment, Chaos, solitons & fractals, 26, 1-6, (2005) · Zbl 1122.81338 [5] El Naschie, M.S., A new solution for the two-slit experiment, Chaos, solitons & fractals, 25, 935-939, (2005) · Zbl 1071.81502 [6] El Naschie, M.S., A review of E-infinity theory and the mass spectrum of high energy particle physics, Chaos, solitons & fractals, 19, 209-236, (2004) · Zbl 1071.81501 [7] El Naschie MS. Emerging research fronts. Comments by Mohamed El Naschie ISI Essential Science Indicators. Available from: http://esi-topics.com/erf/2004/October04.MohamedElNaschie.html. [8] Kaku M. Quantum field theory. Oxford: 1993. [9] Dirac PAM. The principles of quantum mechanics. Oxford: 1987. [10] Young N. An introduction to Hilbert space. Cambridge: 2004. [11] Debnath, L.; Mikusinski, P., Hilbert spaces with applications, (1999), Academic Press London [12] Tanaka Y. The mass spectrum and E-infinity theory. Chaos, Solitons & Fractals (in press). · Zbl 1082.81532 [13] El Naschie, M.S., Iterated function systems, information and the two-slit experiment of quantum mechanics, (), 185-189 [14] Donaldson SK, Kronheimer PB. The geometry of four-manifolds. Oxford: 1990. [15] He, Ji-Huan, In search of 9 hidden particles, Int J nonl sci simul, 6, 2, 95-98, (2005)
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