The Conceptual Foundations of Quantum Mechanics

Description

In this book Jeffrey A. Barrett provides an introduction to the history and conceptual foundations of quantum mechanics. He begins with a description of classical mechanics and a discussion of the quantum phenomena that radically undermine our common-sense classical intuitions about how the physical world works. He then considers the physical and conceptual arguments that led to the standard von Neumann-Dirac formulation of quantum mechanics and how the standard theory explains quantum phenomena. This includes a discussion of how the theory's two dynamical laws work with the standard interpretation of states to explain determinate measurement records, quantum statistics, interference effects, entanglement, decoherence, and quantum nonlocality. A careful understanding of how the standard theory works ultimately leads to the quantum measurement problem. Barrett considers how this problem threatens the logical consistency of the standard theory and then turns to a discussion of the main proposals for resolving it. This includes collapse formulations of quantum mechanics, the various many-worlds theories, and Bohmian mechanics. In discussing alternative formulations he pays particular attention to the explanatory role played by each theory's empirical ontology and associated metaphysical commitments, and the conceptual trade-offs between theoretical options. The book is well-suited to those interested in physics and the history and philosophy of quantum mechanics. The Conceptual Foundations of Quantum Mechanics Contents Preface List of Figures 1. Classical Mechanics 1.1 Quantum Mechanics and Philosophical Intuition 1.2 Newtonian Mechanics 1.3 Problems with Classical Mechanics 1.4 The Stability of Matter 2. Quantum Phenomena 2.1 Spin Properties 2.2 Basic Properties of the Boxes 2.3 Quantum-Mechanical Interference 2.4 How Electrons Move 2.5 Superpositions, Property Attribution, and the Total-of-Nothing Box 2.6 Random, Nonlocal, and Indeterminate 3. The Mathematics of Quantum Mechanics 3.1 Hilbert Space 3.2 Spin Space 4. The Standard Formulation of Quantum Mechanics 4.1 The von Neumann–Dirac Theory 4.2 Spin Boxes and the Linear Dynamics 4.3 Quantum Statistics 4.4 Combining Boxes 4.5 Physical Properties more Generally: K Mesons and Qubits 5. Quantum Interference 5.1 The Simple Two-Path Experiment 5.2 Measurement 5.3 Barriers 5.4 Decoherence 5.5 Quantum Records 5.6 Total-of-Nothing 5.7 The Wave Function 6. Real and/or Local 6.1 The EPR Argument 6.2 Quantum Mechanics and Relativity 6.3 Bell’s Theorem 6.4 Bell-Type Theorems 6.5 Quantum Property Attribution Redux 6.6 EPR Morals 7. The Quantum Measurement Problem 7.1 Wigner’s Friend 7.2 The Measurement Problem 7.3 Why A-Type Measurements are Difficult 8. The Collapse of the Quantum State 8.1 Wigner’s Solution 8.2 GRW. 8.3 GRW 8.4 GRWr, GRWm, and GRWf 8.5 Empirical Ontology and Experience 9. Pure Wave Mechanics 9.1 Everett’s Solution to the Measurement Problem 9.2 The Bare Theory 9.3 Pure Wave Mechanics with just the Standard Interpretation of States 9.4 The Relative-State Formulation of Pure Wave Mechanics 9.5 Everett’s Empiricism 10. Many Worlds and Such 10.1 Extending Pure Wave Mechanics 10.2 Splitting-Worlds 10.3 Probability and Typical Worlds 10.4 Decohering Worlds 10.5 Single-Mind and Many-Minds Theories 10.6 Many Threads and Many Maps 10.7 Epistemological, Pragmatic, and Information-Theoretic Interpretations 11. Bohmian Mechanics 11.1 Bohm’s Theory 11.2 Basic Spin Experiments 11.3 Interference and the Two-Path Experiment 11.4 Measurements and Records 11.5 Surreal Trajectories and Decoherence 11.6 How the Theory Explains Experience 11.7 EPR and Relativity 11.8 Virtues and Vices 12. Empirical Ontology and Explanation 12.1 The Explanatory Work of Metaphysics 12.2 Beables and Experience 12.3 Metaphysics and Empirical Adequacy 12.4 Empirical Ontology and Experience 12.5 Philosophical Morals Appendix A: A Formal Characterization of Hilbert Space Bibliography Index