Quantum Logic in Algebraic Approach

1. Front Matter

   Pages i-x

   PDF

2. Introduction

   • Miklós Rédei

   Pages 1-9

3. Observables and states in the Hilbert space formalism of quantum mechanics

   • Miklós Rédei

   Pages 11-28

4. Lattice theoretic notions

   • Miklós Rédei

   Pages 29-43

5. Hilbert lattice

   • Miklós Rédei

   Pages 45-60

6. Physical theory in semantic approach

   • Miklós Rédei

   Pages 61-75

7. Von Neumann lattices

   • Miklós Rédei

   Pages 77-101

8. The Birkhoff-von Neumann concept of quantum logic

   • Miklós Rédei

   Pages 103-117

9. Quantum conditional and quantum conditional probability

   • Miklós Rédei

   Pages 119-137

10. The problem of hidden variables

    • Miklós Rédei

    Pages 139-169

11. Violation of Bell’s inequality in quantum field theory

    • Miklós Rédei

    Pages 171-190

12. Independence in quantum logic approach

    • Miklós Rédei

    Pages 191-213

13. Reichenbach’s common cause principle and quantum field theory

    • Miklós Rédei

    Pages 215-225

14. Back Matter

    Pages 227-243

    PDF

This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic. The seminars were delivered during the first semester of the 1993/1994 academic year in the Unit for Foundations of Science of the Department of History and Foundations of Mathematics and Science, Faculty of Physics, Utrecht University, The Netherlands, while I was staying in that Unit on a European Community Research Grant, and in the Center for Philosophy of Science, University of Pittsburgh, U. S. A. , where I was staying during the 1994/1995 academic year as a Visiting Fellow on a Fulbright Research Grant, and where I also was supported by the Istvan Szechenyi Scholarship Foundation. The financial support provided by these foundations, by the Center for Philosophy of Science and by the European Community is greatly acknowledged, and I wish to thank D. Dieks, the professor of the Foundations Group in Utrecht and G. Massey, the director of the Center for Philosophy of Science in Pittsburgh for making my stay at the respective institutions possible. I also wish to thank both the members of the Foundations Group in Utrecht, especially D. Dieks, C. Lutz, F. Muller, J. Uffink and P. Vermaas and the participants in the seminars at the Center for Philosophy of Science in Pittsburgh, especially N. Belnap, J. Earman, A. Janis, J. Norton, and J.

• Hilbert space
• algebra
• mechanics
• probability
• quantum field theory
• quantum mechanics
• science

`As an extraordinarily readable monograph with a well-chosen topic, the book can be highly recommended to students and researchers in quantum physics as well as in mathematical fields related to quantum mechanics.'
Zentralblatt MATH, 910 (1999)

• Faculty of Natural Sciences, Loránd Eötvös University, Budapest, Hungary

  Miklós Rédei

Policies and ethics