Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment.

*(English)*Zbl 1082.81502Summary: 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.

##### MSC:

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 |

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\textit{M. S. El Naschie}, Chaos Solitons Fractals 27, No. 1, 39--42 (2006; Zbl 1082.81502)

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##### References:

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