zbMATH — the first resource for mathematics

Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment. (English) Zbl 1082.81502
Summary: On the one hand, a rigorous mathematical formulation of quantum mechanics requires the introduction of a Hilbert space and as we move to the second quantization, a Fock space. On the other hand, 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 utilize some novel reinterpretations of basic \(E^{(\infty)}\) Cantorian spacetime relations in terms of the Hilbert space of quantum mechanics. Proceeding in this way, we gain a better understanding of the physico-mathematical structure of quantum spacetime which is at the heart of the paradoxical and non-intuitive outcome of the famous quantum two-slit gedanken experiment.

81P99 Foundations, quantum information and its processing, quantum axioms, and philosophy
81R99 Groups and algebras in quantum theory
26A30 Singular functions, Cantor functions, functions with other special properties
Full Text: DOI
[1] El Naschie, M.S., On a fuzzy Kähler-like manifold which is consistent with the two-slit experiment, Int J nonlinear sci numer simulat, 6, 2, 95-98, (2005)
[2] El Naschie MS. Nonlinear dynamics of the two-slit experiment with quantum particles. International Journal, Problems of nonlinear analysis in engineering systems. Kazan University, Russia, 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:www/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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.