Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Introduction -- 1.1 Scope of this book -- 1.2 Quantum states and variables -- 1.3 Quantum dynamics -- 1.4 Mathematics I. Linear algebra -- 1.5 Mathematics II. Calculus, probability theory -- 1.6 Quantum reasoning -- 1.7 Quantum measurements -- 1.8 Quantum paradoxes -- 2 Wave functions -- 2.1 Classical and quantum particles -- 2.2 Physical interpretation of the wave function -- 2.3 Wave functions and position -- 2.4 Wave functions and momentum -- 2.5 Toy model -- 3 Linear algebra in Dirac notation -- 3.1 Hilbert space and inner product -- 3.2 Linear functionals and the dual space -- 3.3 Operators, dyads -- 3.4 Projectors and subspaces -- 3.5 Orthogonal projectors and orthonormal bases -- 3.6 Column vectors, row vectors, and matrices -- 3.7 Diagonalization of Hermitian operators -- 3.8 Trace -- 3.9 Positive operators and density matrices -- 3.10 Functions of operators -- 4 Physical properties -- 4.1 Classical and quantum properties -- 4.2 Toy model and spin half -- 4.3 Continuous quantum systems -- 4.4 Negation of properties (NOT) -- 4.5 Conjunction and disjunction (AND, OR) -- 4.6 Incompatible properties -- 5 Probabilities and physical variables -- 5.1 Classical sample space and event algebra -- 5.2 Quantum sample space and event algebra -- 5.3 Refinement, coarsening, and compatibility -- 5.4 Probabilities and ensembles -- 5.5 Random variables and physical variables -- 5.6 Averages -- 6 Composite systems and tensor products -- 6.1 Introduction -- 6.2 Definition of tensor products -- 6.3 Examples of composite quantum systems -- 6.4 Product operators -- 6.5 General operators, matrix elements, partial traces -- 6.6 Product properties and product of sample spaces -- 7 Unitary dynamics -- 7.1 The Schrödinger equation -- 7.2 Unitary operators.

7.3 Time development operators -- 7.4 Toy models -- 8 Stochastic histories -- 8.1 Introduction -- 8.2 Classical histories -- 8.3 Quantum histories -- 8.4 Extensions and logical operations on histories -- 8.5 Sample spaces and families of histories -- 8.6 Refinements of histories -- 8.7 Unitary histories -- 9 The Born rule -- 9.1 Classical random walk -- 9.2 Single-time probabilities -- 9.3 The Born rule -- 9.4 Wave function as a pre-probability -- 9.5 Application: Alpha decay -- 9.6 Schrödinger's cat -- 10 Consistent histories -- 10.1 Chain operators and weights -- 10.2 Consistency conditions and consistent families -- 10.3 Examples of consistent and inconsistent families -- 10.4 Refinement and compatibility -- 11 Checking consistency -- 11.1 Introduction -- 11.2 Support of a consistent family -- 11.3 Initial and final projectors -- 11.4 Heisenberg representation -- 11.5 Fixed initial state -- 11.6 Initial pure state. Chain kets -- 11.7 Unitary extensions -- 11.8 Intrinsically inconsistent histories -- 12 Examples of consistent families -- 12.1 Toy beam splitter -- 12.2 Beam splitter with detector -- 12.3 Time-elapse detector -- 12.4 Toy alpha decay -- 13 Quantum interference -- 13.1 Two-slit and Mach-Zehnder interferometers -- 13.2 Toy Mach-Zehnder interferometer -- 13.3 Detector in output of interferometer -- 13.4 Detector in internal arm of interferometer -- 13.5 Weak detectors in internal arms -- 14 Dependent (contextual) events -- 14.1 An example -- 14.2 Classical analogy -- 14.3 Contextual properties and conditional probabilities -- 14.4 Dependent events in histories -- 15 Density matrices -- 15.1 Introduction -- 15.2 Density matrix as a pre-probability -- 15.3 Reduced density matrix for subsystem -- 15.4 Time dependence of reduced density matrix -- 15.5 Reduced density matrix as initial condition -- 15.6 Density matrix for isolated system.

15.7 Conditional density matrices -- 16 Quantum reasoning -- 16.1 Some general principles -- 16.2 Example: Toy beam splitter -- 16.3 Internal consistency of quantum reasoning -- 16.4 Interpretation of multiple frameworks -- 17 Measurements I -- 17.1 Introduction -- 17.2 Microscopic measurement -- 17.3 Macroscopic measurement, first version -- 17.4 Macroscopic measurement, second version -- 17.5 General destructive measurements -- 18 Measurements II -- 18.1 Beam splitter and successive measurements -- 18.2 Wave function collapse -- 18.3 Nondestructive Stern-Gerlach measurements -- 18.4 Measurements and incompatible families -- 18.5 General nondestructive measurements -- 19 Coins and counterfactuals -- 19.1 Quantum paradoxes -- 19.2 Quantum coins -- 19.3 Stochastic counterfactuals -- 19.4 Quantum counterfactuals -- 20 Delayed choice paradox -- 20.1 Statement of the paradox -- 20.2 Unitary dynamics -- 20.3 Some consistent families -- 20.4 Quantum coin toss and counterfactual paradox -- 20.5 Conclusion -- 21 Indirect measurement paradox -- 21.1 Statement of the paradox -- 21.2 Unitary dynamics -- 21.3 Comparing M and M -- 21.4 Delayed choice version -- 21.5 Interaction-free measurement? -- 21.6 Conclusion -- 22 Incompatibility paradoxes -- 22.1 Simultaneous values -- 22.2 Value functionals -- 22.3 Paradox of two spins -- 22.4 Truth functionals -- 22.5 Paradox of three boxes -- 22.6 Truth functionals for histories -- 23 Singlet state correlations -- 23.1 Introduction -- 23.2 Spin correlations -- 23.3 Histories for three times -- 23.4 Measurements of one spin -- 23.5 Measurements of two spins -- 24 EPR paradox and Bell inequalities -- 24.1 Bohm version of the EPR paradox -- 24.2 Counterfactuals and the EPR paradox -- 24.3 EPR and hidden variables -- 24.4 Bell inequalities -- 25 Hardy's paradox -- 25.1 Introduction -- 25.2 The first paradox.

25.3 Analysis of the first paradox -- 25.4 The second paradox -- 25.5 Analysis of the second paradox -- 26 Decoherence and the classical limit -- 26.1 Introduction -- 26.2 Particle in an interferometer -- 26.3 Density matrix -- 26.4 Random environment -- 26.5 Consistency of histories -- 26.6 Decoherence and classical physics -- 27 Quantum theory and reality -- 27.1 Introduction -- 27.2 Quantum vs. classical reality -- 27.3 Multiple incompatible descriptions -- 27.4 The macroscopic world -- 27.5 Conclusion -- Bibliography -- Ch. 1. Introduction -- Ch. 2. Wave functions -- Ch. 3. Linear algebra in Dirac notation -- Ch. 4. Physical properties -- Ch. 5. Probabilities and physical variables -- Ch. 6. Composite systems and tensor products -- Ch. 7. Unitary dynamics -- Ch. 8. Stochastic histories -- Ch. 9. The Born rule -- Ch. 10. Consistent histories -- Ch. 12. Examples of consistent families -- Ch. 13. Quantum interference -- Ch. 14. Dependent (contextual) events -- Ch. 16. Quantum reasoning -- Chs. 17 and 18. Measurements -- Ch. 19. Coins and counterfactuals -- Ch. 20. Delayed choice paradox -- Ch. 21. Indirect measurement paradox -- Ch. 22. Incompatibility paradoxes -- Ch. 23. Singlet state correlations -- Ch. 24. EPR paradox and Bell inequalities -- Ch. 25. Hardy's paradox -- Ch. 26. Decoherence and the classical limit -- Ch. 27. Quantum theory and reality -- References -- Index.