Quantum and Quantum-like

Összefoglaló

During the last 20 years, the mathematical formalism of quantum theory, especially so-called quantum probability, has found an increasing number of applications within the social sciences, in particular in psychology, economics, sociology, etc. This field, which is sometimes referred to as 'quantum cognition', is not about models or theories which assume quantum effects to be relevant for cognitive processes; the main underlying assumption of quantum cognition is rather that the formalism of quantum theory can be applied to various cognitive phenomena.
This article emphasizes the similarities between phenomena in quantum theory and phenomena in psychology and sociology, thereby presenting arguments why the formalism developed in quantum theory may be of relevance to the cognitive sciences. It is also intended to be a very cursory introduction to the ideas of quantum theory.

Contents:

Abstract and Acknowledgements
Preface by Gábor Hofer-Szabó
1. Introduction
2. Similarities between Quantum Phenomena and Psychological Phenomena
3. Classical and Quantum Systems
4. Experiment and Theory
5. The Fundamental Concepts of Quantum Theory - A Brief Introduction
5.1. A Warning from John Bell
5.2. The Physics of Polarization
5.3. The Postulates of Quantum Theory
5.3.1. Postulate I: Representation of States
5.3.2. Postulate II: Representation of Observables
5.3.3. Postulate III: Born's Rule
5.3.4. Postulate IV: The Collapse of the Quantum State
5.3.5. Postulate V: Schrödinger's Equation
6. Superpositions and Decompositions of States
6.1. The Experimental Set-up
6.2. The First Mystery: Particle-Wave Duality
7. Clinton vs. Gore - An Application to the Social Sciences
8. Entanglement
8.1. Classical Correlations
8.2. Pure and Mixed States
8.3. Definitions for Entanglement
9. Einstein, Podolsky, and Rosen
9.1. Some History
9.2. EPR-States - Entangled Photons
9.3. The EPR-Argument - Why Quantum Theory May Not Be Complete
10. Bell-type Inequalities and Quantum Non-Locality
10.1. Non-Locality and Relativity
10.2. The CHS Inequality
10.3. Quantum Theory and Non-Locality
11. Contextuality
11.1. The Kochen-Specker Thorem
11.2. The 'Princess of Arbq'lu'
11.3. A Little Dictionary
11.4. Contextuality and Concept Combination - Case I
11.5. Contextuality and Concept Combination - Case II
11.6. Contextuality by Default and Signaling
12. 'Free Will' and an Open End
References