Skip to main content

Quantum Logic

  • Book
  • © 1978

Overview

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

eBook USD 9.99 USD 84.99
Discount applied Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

About this book

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.

Similar content being viewed by others

Keywords

Table of contents (8 chapters)

Authors and Affiliations

  • University of Cologne, Germany

    Peter Mittelstaedt

Bibliographic Information

  • Book Title: Quantum Logic

  • Authors: Peter Mittelstaedt

  • Series Title: Synthese Library

  • DOI: https://doi.org/10.1007/978-94-009-9871-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1978

  • Hardcover ISBN: 978-90-277-0925-7Published: 30 November 1978

  • Softcover ISBN: 978-94-009-9873-5Published: 19 October 2011

  • eBook ISBN: 978-94-009-9871-1Published: 06 December 2012

  • Series ISSN: 0166-6991

  • Series E-ISSN: 2542-8292

  • Edition Number: 1

  • Number of Pages: VIII, 160

  • Topics: Philosophy of Science, Logic

Publish with us