Journal of Statistical Physics

, Volume 53, Issue 3–4, pp 893–932 | Cite as

Logical reformulation of quantum mechanics. I. Foundations

  • Roland Omnès
Articles

Abstract

The basic rules of quantum mechanics are reformulated. They deal primarily with individual systems and do not assume that every ket may represent a physical state. The customary kinematic and dynamic rules then allow to construct consistent Boolean logics describing the history of a system, following essentially Griffiths' proposal. Logical implication is defined within these logics, the multiplicity of which reflects the complementary principle. Only one interpretative rule of quantum mechanics is necessary in such a framework. It states that these logics providebona fide foundations for the description of a quantum system and for reasoning about it. One attempts to build up classical physics, including classical logic, on these quantum foundations. The resulting theory of measurement needs not to statea priori that the eigenvalues of an observable have to be the results of individual measurements nor to assume wave packet reduction. Both these properties can be obtained as consequences of the basic rules. One also needs not to postulate that every observable is measurable, even in principle. A proposition calculus is obtained, allowing in principle the replacement of the discussion of problems concerned with the practical interpretation of experiments by due calculations.

Key words

Quantum mechanics foundations logic classical limit wave packet reduction 

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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Roland Omnès
    • 1
  1. 1.Laboratoire de Physique Théorique et Hautes Energies (Laboratoire associé au Centre National de la Recherche Scientifique)Université de Paris-SudOrsayFrance

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