Quantum Logic - Mittelstaedt, Peter
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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…mehr

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Produktbeschreibung
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.
Autorenporträt
Prof. Dr. Peter Mittelstaedt is emeritus professor at the University of Cologne. His main research fields are Foundations of Quantum Theory, Relativity Theory, Philosophy of Science and Logic. He has published various books with Springer: "Laws of Nature" (2005, together with P.A. Weingartner), "The Quantum Theory of Measurement" (1996, together with P. Busch and P.J. Lahti) and "Quantum Logic" (1978). Dr. Kristina Engelhard edited this 2nd enlarged edition of the book by Prof. P. Mittelstaedt. She obtained her PhD in Philosophy at the University of Cologne with a thesis entitled "The Simple and Matter. Inquiries into Kant's Antinomy of Division" and she is currently Research and Teaching Assistant at the Philosophy Department of the University of Cologne (Germany).