The Interpretation of Quantum Mechanics

Preface
How To Read This Book
1  Elementary Quantum Mechanics
     THE BEGINNINGS OF QUANTUM MECHANICS
          1. The Mechanics of Waves, Matrices and Quanta
     MATHEMATICAL FORMALISM
          2. Quantum Mechanics in a Hilbert Space
          3. The Spectral Theorem
     FEYNMAN HISTORIES
          4. Feynman\'s Formulation of Quantum Dynamics
     PROBABILITIES AND STATES
          5. Quantum Probabilities
          6. The Density Operator
          7. Dynamics
          8. How to Describe a Complex System
     REFERENCE FRAMES
          9. How to Construct the Physical Hilbert Space
          10. Relativistic Invariance
     APPENDIX: THE UNCERTAINTY RELATION FOR ENERGY
     PROBLEMS
2  The Problems of Measurement Theory
     EXPERIMENTAL DEVICES
          1. What Is a Measurement?
          2. Some Examples of Measurements
          3. The Stern-Gerlach Experiment
     ELEMENTARY MEASUREMENT THEORY
          4. Von Neumann\'s Formal Theory of Measurements
          5. The Problem of Macroscopic Interferences
     THE COPENHAGEN INTERPRETATION
          6. The Prescriptions of Measurement Theory
          7. The Copenhagen Epistemology
          8. Schrodinger\'s Cat and Wigner\'s Friend
     WHAT AN INTERPRETATION SHOULD BE
          9. Why Does Physics Need an Interpretation?
          10. The Criteria of an Interpretation. Consistency and Completeness
          PROBLEMS
     Interlude  
     FIVE IDEAS FOR CONSTRUCTING A CONSISTENT INTERPRETATION. PROPERTIES, HISTORIES, 
     LOGIC CLASSICAL APPROXIMATIONS AND DECOHERENCE
3  Foundations and Properties
     THE BASIC PRINCIPLES
          1. The Mathematical Framework
          2. Dynamics
     THE PROPERTIES OF A SYSTEM
          3. Properties 1
          4. Probabilities and States
          5. Gleason\'s Theorem
          6. Taking Time into Account
     APPENDIX: GLEASON\'S THEOREM
4  Histories
     THE NOTION OF HISTORY
          1. Experiments and Histories
          2. Definition of Histories
     THE PROBABILITIES OF HISTORIES
          3. Logical Criteria for the Probabilities
          4. Connection with Feynman Histories*
     CONSISTENCY CONDITIONS
          5. The Consistency Conditions for Additive Probabilities
     APPENDIX A: GENERAL FORM OF THE CONSISTENCY CONDITIONS
          1. Notations
          2. The Main Results
          3. Sketch of the Proof
     APPENDIX B: THE UNIQUENESS OF PROBABILITIES
     PROBLEMS
5  The Logical Framework of Quantum Mechanics
     ABOUT LOGIC
          1. Why Does One Need Logic?
          2. What Is Logic?
     QUANTUM LOGIC
          3. Defining a Quantum Logic
          4. The Complementarity \"Principle\"
     A FOUNDATION FOR INTERPRETATION
          5. The Universal Rule of Interpretation
     APPLICATIONS
          6. Interferences
          7. The Straight-Line Motion of a Particle
          8. Decays
          9. Approximations in Logic
     APPENDIX A: FORMAL LOGIC
     APPENDIX B: FORMAL LOGIC AND CONSISTENCY
     APPENDIX C: THE NO-CONTRADICTION THEOREM
     APPENDIX D: LOGIC AND TIME REVERSAL
     PROBLEMS
6  Recovering Classical Physics
     OBJECTS
          1. Orientation
          2. Quantum Mechanics of Collective Observables
          3. Classical Variables
     CLASSICAL PROPERTIES
          4. A Return to Classical Logic
          5. The Quantum Form of a Classical Property
          6. The Construction of Quasi-Projectors
     DYNAMICS
          7. The Dynamical Correspondence
     JUSTIFYING COMMON SENSE
          8. Recovering Common Sense
     APPENDIX A: ELEMENTS OF MICROLOCAL ANALYSIS
          1. Operators and Symbols
          2. Operator Products
          3. Norm Estimates
          4. Estimates of Trace Norms
          5. More General Phase Spaces
          6. Summary
     APPENDIX B: SEMICLASSICAL THEOREMS
          1. Theorem A
          2. Dynamics: Theorem C
     APPENDIX C: CONSISTENCY OF CLASSICAL LOGIC
     APPENDIX D: A CRITERION FOR THE EXISTENCE OF COLLECTIVE OBSERVABLES
     PROBLEMS
7  Decoherence
     ORIENTATION
          1. An Intuitive Approach
     SOLVABLE MODELS
          2. A Simple Model
          3. Another Example: The Pendulum
     MORE GENERAL MODELS
          4. The General Theory
          5. Decoherence by the External Environment
          6. Back to Schrodinger\'s Cat
     CAN ONE CIRCUMVENT DECOHERENCE?
          7. A Criticism of Decoherence
          8. One Cannot Circumvent Decoherence
          9. Justifying the Assumptions*
          10. The Direction of Time
     APPENDIX: DECOHERENCE FROM AN EXTERNAL ENVIRONMENT
     PROBLEM
8  Measurement Theory
     1. Reality and Theory. Facts and Phenomena
     2. An Introduction to Measurement Theory
     MEASUREMENT OF A SINGLE OBSERVABLE
          3. What Is a Measurement?
          4. The Main Theorems
     WAVE FUNCTION REDUCTION
          5. Two Successive Measurements
     ACTUAL FACTS
          6. Actual Facts and the Present Time
          7. Everett\'s Answer
          8. A Law of Physics Different from All Others
     THE NOTION OF TRUTH
          9. The Criteria of Truth
          10. Up to What Point Can One Know the State?
          11. Explicit States
     APPENDIX A: THE THEOREMS OF MEASUREMENT THEORY
          1. Preliminary Notions
          2. The Proof of Theorem 5
          3. Data Imply Results
     APPENDIX B: THE DENSITY OPERATOR AND INFORMATION THEORY
9  Questioning Quantum Mechanics
     THE EINSTEIN-PODOLSKY-ROSEN EXPERIMENT
          1. The Background
          2. Analyzing the EPR Experiment
          3. Bohm\'s Version of the EPR Experiment
          4. Truth and Reliability in the EPR Experiment
          5. The Relativistic Case
          6. Separability
     HIDDEN VARIABLES
          7. Hidden Variable Theories
          8. Bell\'s Inequalities
     PROBLEM
10  Nonclassical Macroscopic Systems
     NONCLASSICAL SUPERCONDUCTORS
          1. Superconductors
          2. The Aharonov-Bohm Effect
          3. The Basis of Leggett\'s Experiments
     CHAOTIC SYSTEMS
          4. Classical and Quantum Statistics of Chaotic Systems
11  Experiments
     EXPERIMENTS SHOWING HISTORIES
          1. The Decay of a Particle
          2. Repeated Measurements
          3. The Zeno Effect
          4. Observing a Unique Atom
     INTERFERENCES
          5. The Badurek-Rauch-Tuppinger Experiment^12
          6. Delayed-Choice Experiments
     LEGGETT\'S EXPERIMENTS
          7. The Experiments with SQUIDs
12  Summary and Outlook
     THE RULES OF INTERPRETATION
          1. The Basic Principles
          2. Properties
          3. The Logical Framework
          4. The Foundations of Classical Physics
          5. Classical Logic
          6. Decoherence
          7. Can One Circumvent Decoherence?
          8. The Theory of Phenomena
          9. Measurement Theory
          10. Actual Facts
          11. Truth Criteria
          12. The State of a System
          13. The Relation with Bohr\'s Interpretation
          14. Geii-Mann and Hartle\'s Approach
          15. Perspectives
     PHILOSOPHICAL ASPECTS
          16. Twenty-one Theses
          17. Is the Theory Objective?
          18. Is the Theory Realistic?
          19. About the Foundations of Science
          20. Total Realism
Notes
     PREFACE
     CHAPTER 1
     CHAPTER 2
     INTERLUDE
     CHAPTER 3
     CHAPTER 4
     CHAPTER 5
     CHAPTER 6
     CHAPTER 7
     CHAPTER 8
     CHAPTER 9
     CHAPTER 10
     CHAPTER 11
     CHAPTER 12
Index