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Quantum Logic

  • Peter Mittelstaedt

Part of the Synthese Library book series (SYLI, volume 126)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Peter Mittelstaedt
    Pages 1-5
  3. Peter Mittelstaedt
    Pages 6-26
  4. Peter Mittelstaedt
    Pages 27-47
  5. Peter Mittelstaedt
    Pages 48-71
  6. Peter Mittelstaedt
    Pages 72-98
  7. Peter Mittelstaedt
    Pages 99-118
  8. Peter Mittelstaedt
    Pages 119-139
  9. Back Matter
    Pages 144-160

About this book

Introduction

In 1936, G. Birkhoff and J. v. Neumann published an article with the title The logic of quantum mechanics'. In this paper, the authors demonstrated that in quantum mechanics the most simple observables which correspond to yes-no propositions about a quantum physical system constitute an algebraic structure, the most important proper­ ties of which are given by an orthocomplemented and quasimodular lattice Lq. Furthermore, this lattice of quantum mechanical proposi­ tions has, from a formal point of view, many similarities with a Boolean lattice L8 which is known to be the lattice of classical propositional logic. Therefore, one could conjecture that due to the algebraic structure of quantum mechanical observables a logical calculus Q of quantum mechanical propositions is established, which is slightly different from the calculus L of classical propositional logic but which is applicable to all quantum mechanical propositions (C. F. v. Weizsacker, 1955). This calculus has sometimes been called 'quan­ tum logic'. However, the statement that propositions about quantum physical systems are governed by the laws of quantum logic, which differ from ordinary classical logic and which are based on the empirically well-established quantum theory, is exposed to two serious objec­ tions: (a) Logic is a theory which deals with those relationships between various propositions that are valid independent of the content of the respective propositions. Thus, the validity of logical relationships is not restricted to a special type of proposition, e. g. to propositions about classical physical systems.

Keywords

Interpretation logic proposition quantum mechanics

Authors and affiliations

  • Peter Mittelstaedt
    • 1
  1. 1.University of CologneGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-9871-1
  • Copyright Information Springer Science+Business Media B.V. 1978
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-009-9873-5
  • Online ISBN 978-94-009-9871-1
  • Buy this book on publisher's site