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.
Зміст
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 Łukasiewicz logic.- Perspectives.- The many-valued interpretation of quantum mechanics.
Про автора
Jarosław Pykacz, born 1952, studied physics and mathematics at the University of Gdańsk and received his Ph D 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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