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Indirect measurements and the mirror theorem: A liouville formulation of quantum mechanics

  • Irreversibility And Measurement In Quantum Mechanics
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Irreversibility and Causality Semigroups and Rigged Hilbert Spaces

Part of the book series: Lecture Notes in Physics ((LNP,volume 504-504))

Abstract

It is argued that the indirect measurement in Quantum Mechanics can be objectively formulated via the standard mirror property of noncommuting mappings. In this Liouville like formulation the primary, zero order step, regulates that the quantum probe and the measuring device entangle through objectively defined correlations uniquely prescribed from the mirror theorem. The secondary step of the indirect measurement process is then pictured as a resonance forming and decaying process which couples the phenomenon with the relevant time scales. It is suggested that these correlations lead to a description that guides our intuition towards a more satisfactory comprehension of quantum phenomena. The Liouville like formulation also assumes a stochastic component reminiscent of stochastic resonances in driven nonlinear dynamical systems. The possible relation to quantum aspects of chaos via existence of nonlocal hidden variables further promotes an ontological setting. We illustrate this in some concrete examples.

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Authors and Affiliations

  1. Department of Quantum Chemistry, Uppsala University, Box 518, S-751 20, Uppsala, Sweden

    E. Brändas & B. Hessmo

Authors
  1. E. Brändas
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  2. B. Hessmo
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Arno Bohm Heinz-Dietrich Doebner Piotr Kielanowski

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© 1998 Springer-Verlag

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Brändas, E., Hessmo, B. (1998). Indirect measurements and the mirror theorem: A liouville formulation of quantum mechanics. In: Bohm, A., Doebner, HD., Kielanowski, P. (eds) Irreversibility and Causality Semigroups and Rigged Hilbert Spaces. Lecture Notes in Physics, vol 504-504. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106793

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  • DOI: https://doi.org/10.1007/BFb0106793

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  • Print ISBN: 978-3-540-64305-0

  • Online ISBN: 978-3-540-69725-1

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