Quantum Physics, Fuzzy Sets and Logic

1. Front Matter

   Pages i-vi

   PDF

2. Introduction

   • Jarosław Pykacz

   Pages 1-3

3. A Brief Survey of Main Interpretations of Quantum Mechanics

   • Jarosław Pykacz

   Pages 5-13

4. A Brief Survey of Many-Valued Logics

   • Jarosław Pykacz

   Pages 15-22

5. Fuzzy Sets and Many-Valued Logics

   • Jarosław Pykacz

   Pages 23-28

6. Many-Valued Logics in Quantum Mechanics

   • Jarosław Pykacz

   Pages 29-32

7. Birkhoff-von Neumann Quantum Logic

   • Jarosław Pykacz

   Pages 33-45

8. B-vN Quantum Logic as \(\infty \)-Valued Łukasiewicz Logic

   • Jarosław Pykacz

   Pages 47-57

9. Perspectives

   • Jarosław Pykacz

   Pages 59-63

10. The Many-Valued Interpretation of Quantum Mechanics

    • Jarosław Pykacz

    Pages 65-67

11. Back Matter

    Pages 69-70

    PDF

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.

• Birkhoff–von Neumann Quantum Logic
• Fuzzy Interpretation of Quantum Mechanics
• Infinite-valued Logic
• Interpretation of Quantum Mechanics
• Many-valued Interpretation of Quantum Mechanics
• Many-valued Logic
• Quantum Logic
• Łukasiewicz Infinite-valued Logic

“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)

• Institute of Mathematics, University of Gdańsk, Gdańsk, Poland

  Jarosław Pykacz

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.

Policies and ethics