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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.

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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