Conceptual Foundations of Quantum Mechanics

Description

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. 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 A B C D E F G H J K L M N O P R S T V W Y Z SUBJECT INDEX A B C D E F G H I J K L M N O P Q R S T U V W