The Structure and Interpretation of Quantum Mechanics Book

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 Its Representation

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 Lÿders Rule

Appendix C. Coupled Systems and Conditionalization

References

Index