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Preface
Introduction. The Stern-Gerlach Experiment
PART I THE STRUCTURE OF QUANTUM THEORY
1. Vector Spaces
Vectors
Operators
Eigenvectors and Eigenvalues
Inner Products of Vectors in R2
Complex Numbers
The Space C2
The Pauli Spin Matrices
Mathematical Generalization
Vector Spaces
Linear Operators
Inner Products on V
Subspaces and Projection Operators
Orthonormal Bases
Operators with a Discrete Spectrum
Operators with a Continuous Spectrum
Hilbert Spaces
2. States and Observables in Quantum Mechanics
Classical Mechanics: Systems and Their States
Observables and Experimental Questions
States and Observables in Quantum Theory
Probabilities and Expectation Values
The Evolution of States in Classical Mechanics
Determinism
The Evolution of States in Quantum Mechanics
Theories and Models
3. Physical Theory and Hilbert Spaces
Minimal Assumptions for Physical Theory
The Representation of Outcomes and Events
The Representation of States
Determinism, Indeterminism, and the Principle of Superposition
Mixed States
Observables and Operators
Relations between Observables: Functional Dependence and Compatibility
Incompatible Observables
The Representational Capacity of Hilbert Spaces
The Schrodinger Equation
4. Spin and ItsRepresentation
Symmetry Conditions and Spin States
A Partial Representation of Spin in R2
The Representation of (Sa) in C2
Conclusion
5. Density Operators and Tensor-Product Spaces
Operators of the Trace Class
Density Operators
Density Operators on C2
Pure and Mixed States
The Dynamical Evolution of States
Gleason\'s Theorem
Composite Systems and Tensor-Product Spaces
The Reduction of States of Composite Systems
Part II The Interpretation of Quantum Theory
6. The Problem of Properties
Properties, Experimental Questions, and the Dispersion Principle
The EPR Argument
Bohm\'s Version of the EPR Experiment
The Statistical Interpretation
Kochen and Specker\'s Example
Generalizing the Problem
The Bell-Wigner Inequality
Hidden Variables
Interpreting Quantum Theory: Statistical States and Value States
7. Quantum Logic
The Algebra of Properties of a Simple Classical System
Boolean Algebras
Posets and Lattices
The Structure of S(H)
The Algebra of Events
A Formal Approach to Quantum Logic
An Unexceptionable Interpretation of Quantum Logic
Putnam on Quantum Logic
Properties and Deviant Logic
8. Probability, Causality, and Explanation
Probability Generalized
Two Uniqueness Results
The Two-Slit Experiment: Waves and Particles
The Two-Slit Experiment: Conditional Probabilities
The Bell-Wigner Inequality and Classical Probability
Bell Inequalities and Einstein-Locality
Bell Inequalities and Causality
Coupled Systems and Conditional Probabilities
Probability, Causality, and Explanation
9. Measurement
Three Principles of Limitation
Indeterminacy and Measurement
Projection Postulates
Measurement and Conditionalization
The Measurement Problem and Schrodinger\'s Cat
Jauch\'s Model of the Measurement Process
A Problem for Internal Accounts of Measurement
Three Accounts of Measurement
10. An Interpretation of Quantum Theory
Abstraction and Interpretation
Properties and Latencies: The Quantum Event Interpretation
The Copenhagen Interpretation
The Priority of the Classical World
Quantum Theory and the Classical Horizon
Appendix A. Gleason\'s Theorem
Appendix B. The Lyders Rule
Appendix C. Coupled Systems and Conditionalization
References
Index