Quantum Physics, Fuzzy Sets and Logic

Steps Towards a Many-Valued Interpretation of Quantum Mechanics

Jarosław Pykacz (Autor)

Buch | Softcover

VI, 70 Seiten

2015 | 2015
Springer International Publishing (Verlag)
978-3-319-19383-0 (ISBN)

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This Brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of Lukasiewicz 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 Lukasiewicz infinite-valued logic endowed with partially defined conjunctions and disjunctions.

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.

Introduction.- A brief survey of main interpretations of quantum mechanics.- A brief survey of many-valued logics.- Fuzzy sets and many-valued logics.- Many-valued logics in quantum mechanics.- Birkhoff-von Neumann quantum logic.- Birkhoff-von Neumann quantum logic as infinite-valued Lukasiewicz logic.- Perspectives.- The many-valued interpretation of quantum mechanics.

"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)

Erscheint lt. Verlag	30.6.2015
Reihe/Serie	SpringerBriefs in Physics
Zusatzinfo	VI, 70 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	141 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Birkhoff-von Neumann Quantum Logic • Birkhoff–von Neumann Quantum Logic • Fuzzy Interpretation of Quantum Mechanics • Infinite-valued Logic • Interpretation of quantum mechanics • Lukasiewicz Infinite-valued Logic • Łukasiewicz Infinite-valued Logic • Many-valued Interpretation of Quantum Mechanics • Many-valued Logic • Quantum Logic
ISBN-10	3-319-19383-X / 331919383X
ISBN-13	978-3-319-19383-0 / 9783319193830
Zustand	Neuware