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- At its core, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic. More specifically, in quantum mechanics each probability-bearing proposition of the form “the value of physical quantity A lies in the range B ” is represented by a projection operator on a Hilbert space H.
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Feb 4, 2002 · 1. Quantum Mechanics as a Probability Calculus. 1.1 Quantum Probability in a Nutshell. 1.2 The “Logic” of Projections. 1.3 Probability Measures and Gleason’s Theorem. 1.4 The Reconstruction of QM. 2. Interpretations of Quantum Logic. 2.1 Realist Quantum Logic. 2.2 Operational Quantum Logic. 3. Generalized Probability Theory.
- Quantum Theory and Mathematical Rigor
A brief explanation for this shift is provided below. See...
- The Basic Theory of Ordering Relations
Supplement to Quantum Logic and Probability Theory. The...
- Bell's Theorem
Bell’s Theorem is the collective name for a family of...
- Quantum Theory and Mathematical Rigor
QUANTUM LOGIC AND GENERALIZED PROBABILITY THEORY 1. INTRODUCTION The probabilitistic interpretation of quantum mechanics (QM) is in full agreement with the physical experience as long as one pays strict attention to the restriction that the probabilistic predictions are related to properties
Feb 4, 2002 · 1. Quantum Mechanics as a Probability Calculus. Supplement 1: The Basic Theory of Hilbert Spaces [Not yet available] Supplement 2: The Basic Theory of Ordering Relations. 2. Interpretations of Quantum Logic. 3. Generalized Probability Theory. 4. Logics Associated to Probabilistic Models. 5. Piron's Theorem. 6. Classical Representations. 7.
Abstract. The mathematics of classical probability theory was subsumed into classical measure theory by Kolmogorov in 1933. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von Neumann in the early thirties, as well.
Quantum, Probability, Logic: The Work and Influence of Itamar Pitowsky | SpringerLink. Book. © 2020. Quantum, Probability, Logic. The Work and Influence of Itamar Pitowsky. Home. Book. Editors: Meir Hemmo, Orly Shenker. Explores the state of art the in philosophy of physics. Details the work and ongoing influence of Itamar Pitowsky.
Back to Top. Notes to Quantum Logic and Probability Theory. 1. A few qualifications are in order already: In a more general formulation, one considers the lattice of projections of a von Neumann algebra. Only in the context of non-relativistic quantum mechanics, and then only absent superselection rules, is this algebra a type I factor.
Nov 1, 2018 · Quantum probability in decision making from quantum information representation of neuronal states. Andrei Khrennikov, Irina Basieva, Emmanuel M. Pothos & Ichiro Yamato. Scientific Reports 8,...