Overview

This Brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of Łukasiewicz infinite-valued logic. It begins with a short survey of main interpretations of quantum mechanics already proposed, as well as various models of many-valued logics and previous attempts to apply them for the description of quantum phenomena. The prospective many-valued interpretation of quantum mechanics is soundly based on a theorem concerning the isomorphic representation of Birkhoff-von Neumann quantum logic in the form of a special Łukasiewicz infinite-valued logic endowed with partially defined conjunctions and disjunctions.

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9783319193830

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The book summarizes decades of search of an adequate formulation of quantum mechanics using fuzzy set tools. ... The book is very easy to read; a feature rarely encountered in this field. The historical overview is rather detailed, the author found some forgotten sources and put them in context which is of separate interest. ... it is a good deal of advanced mathematical work which summarizes experience from one epoch of research. (Mirko Navara, zbMATH 1328.81020, 2016)

Author Information

Jarosław Pykacz, born 1952, studied physics and mathematics at the University of Gdańsk and received his PhD in theoretical physics in 1980. He was one of the founding fathers of the International Quantum Structures Association and served as its President in the years 2008 - 2010. He published about 50 papers on logico-philosophic foundations and application of fuzzy sets in quantum mechanics.

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