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Effective quantum observables

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Il Nuovo Cimento B (1971-1996)

Summary

We construct a quantum-theoretic formalism which is meaningful also in the absence of the axiom of choice. In terms of the standard formalism the observables correspond to the intrinsically effective Hamiltonians. Here a self-adjoint operator is intrinsically effective iff the Schrödinger equation of its generated semigroup is soluble by means of eigenfunction series expansions. As an application we investigate quantum theory in models of set theory, where the axiom of choice is violated. We explain the failure of the axiom of choice in terms of symmetry properties of the perceivable concepts of an external observer who applies these concepts in the description of quantum-theoretic experimental configurations.

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Authors and Affiliations

  1. Institut für Mathematik, Universität für Bodenkultur Wien, Gregor Mendel-Straße 33, A-1180, Wien, Austria

    N. Brunner

  2. Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040, Wien, Austria

    K. Svozil

  3. Abteilung für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040, Wien, Austria

    M. Baaz

Authors
  1. N. Brunner
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  2. K. Svozil
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  3. M. Baaz
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Brunner, N., Svozil, K. & Baaz, M. Effective quantum observables. Il Nuovo Cimento B 110, 1397–1413 (1995). https://doi.org/10.1007/BF02849839

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  • DOI: https://doi.org/10.1007/BF02849839

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