Conceptual Foundations of Quantum Mechanics provides a detailed view of the conceptual foundations and problems of quantum physics, and a clear and comprehensive account of the fundamental physical implications of the quantum formalism. This book deals with nonseparability, hidden variable theories, measurement theories and several related problems. Mathematical arguments are presented with an emphasis on simple but adequately representative cases. The conclusion incorporates a description of a set of relationships and concepts that could compose a legitimate view of the world.
Author(s): Bernard d'Espagnat
Series: Advanced Book Classics
Edition: 2
Publisher: Westview Press
Year: 1999
Language: English
Pages: 352
Contents
PEDRO'S DEBATE (PREFACE TO SECOND EDITION)
Mathematics and Physics
Physics and Existing World Views
Own Guesses
PREFACE TO FIRST EDITION
Part One: ELEMENTS OF QUANTUM MECHANICS
1. Matter Waves
2. Superposition and Linearity
2.1 Superposition of Waves
2.2 The Evolution in Time
23 The Correspondence Principle
2.4 The Necessity for a More General Formalism
References
3. Statement of the Rules
References
4. Comments
4.1 On the Description of Ensembles by Kets
4.2 Assumption Q
4.3 Indeterminism
4.4 Miscellaneous Remarks
5. Alternative Formulations
5.1 The Mean Value Rule
5.2 The Heisenberg Picture for Time Evolution
Part Two: DENSITY MATRICES AND MIXTURES
6. The Density Matrix Formalism
6.1 The Density Matrix
6.2 Pure Cases and Mixtures
6.3 Time Dependence of Density Matrices
6.4 Alternative Formulation of Quantum Rules
6.5 Mixtures Defined by One and the Same Density Matrix
6.6 A Proposition Bearing on Correlations
References
7. Mixtures
7.1 Operators and Observables
7.2 Proper and Improper Mixtures
7.3 The Homogeneity of Ensembles
7.4 Observable Having a Value on a System
7.5 Quantum Ensembles and Supplementary Variables
References
Exercises of Part Two
Part Three: QUANTUM NONSEPARABILITY
8. The Einstein-Podolosky-Rosen Problem
8.1 The Formal Aspects
8.2 Conceptual Aspects
8.3 Relativistic Aspects
References
9. Possible Views on Nonseparability
References
10. Individuals, Ensembles, States
10.1 Quantum Mechanics of Individual Systems
10.2 The Quantum States
References
11. The "Hidden Variables" Approach
11.1 The Existence Problem
11.2 Hidden Variables and the Separability Problem
11.3 Nonseparability in Hidden Variables Theories
11.4 Another Proof
11.5 Search for Possible Violations of Quantum Mechanics
11.6 Further Discussion and Comments
References
12. Direct Study of Some Principles
12.1 Some Aspects of the Calculus of Propositions
12.2 A Set of "Natural" Assumptions Centered on Separability
12.3 Consequences
12.4 Inequalities
12.5 Discussion: Experimental
12.6 Discussion: Theoretical
12.7 Conclusions
References
13. Aspects of the Problem of Retrodiction
13.1 "Independent Time Evolution" and the Retrodiction Problem
13.2 Connected Problems
References
Exercises of Part Three
Part Four: MEASUREMENT THEORIES
14. Elements of Measurement Theory
14.1 Some Introductory Remarks
14.2 Survey of Ideal Measurement Theory
14.3 An Explicit Example
14.4 Measurement and the Density Matrix Formalism
14.5 An Erroneous Argument
References
15. Classical Properties
15.1 Classical Measurements
15.2 A Proposition Bearing on Classical Observables
15.3 Scope and Criticism of the Theory
References
16. Macroscopic Instruments
16.1 Irreversibility: Dualislic Approach
16.2 The One-Principle Approach: Statistical Phase Cancellation
16.3 More Refined Considerations
References
17. Of Cats and Pointers
17.1 An application of the Conventional Formalism
17.2 Two Generations
References
18. Nonideal Measurements: Small Influence of Outside World
18.1 Preliminaries
18.2 Generality of Nonideal Measurements
18.3 Nonideal Measurements with Initial Slate as Mixture
18.4 A Generalization
18.5 Discussion of the Green Model for Measurement
18.6 Generalizations
18.7 Conclusion
References
Exercises of Part Four
Part Five: KNOWLEDGE AND THE PHYSICAL WORLD
19. Reality and Objects
19.1 Realism
19.2 Micro-Objectivism
19.3 Macro-Objectivism
19.4 Macro-Objectivism and Long-Range Correlations
19.5 Other Versions of Scientific Realism
References
20. Positivism
20.1 Structures; Weak and Strong Objectivity
20.2 The Positivistic Standpoint
20.3 Objections to Positivism Viewed as a Basic Philosophy
References
21. Bohr and Heisenberg
21.1 Summary of Bohr's Thesis
21.2 Discussion
21.3 Some Aspects of Heisenberg's Philosophy
21.4 Conclusion
References
22. Wigner's Friend
References
23. The Relativity of States
23.1 Outline of the Theory
23.2 Discussion
References
Part Six: SUMMARY AND OUTLOOK
24. Summary
References
25. Outlook
References
AUTHOR INDEX
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SUBJECT INDEX
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