Quantum Physics, Fuzzy Sets and Logic

Steps Towards a Many-Valued Interpretation of Quantum Mechanics
2015
ISBN: 978-3-319-19383-0
Verlag: Springer International Publishing

Buch, Englisch, 70 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1299 g

Reihe: SpringerBriefs in Physics

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.

Zielgruppe

Research

Autoren/Hrsg.

Pykacz, Jaros¿aw

Pykacz, Jaroslaw

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Fuzzy-Set-Theorie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

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.

Über Autor(innen)

Jaroslaw Pykacz, born 1952, studied physics and mathematics at the University of Gdansk 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.