Understanding Quantum Mechanics: The World According to Modern Quantum Foundations

Preface
Acknowledgements
Contents
1 Some Mathematical Foundations of Quantum Mechanics
	1.1 Ontology
	1.2 The Wave Function and Born\'s Statistical Hypothesis
	1.3 The Spreading of the Wave Packet
	1.4 No Mystery: The Double-Slit Experiment
	1.5 The Importance of Configuration Space
	1.6 The Classical Limit
		1.6.1 Motion of Concentrated Wave Packets
	1.7 Spin and the Stern–Gerlach Experiment
		1.7.1 The Pauli Equation and the Stern–Gerlach Experiment
	1.8 Why ``Spinors\'\'?
	1.9 Hilbert Space and Observables
2 The Measurement Problem
	2.1 The Orthodox Answer
	2.2 Solutions to the Measurement Problem
		2.2.1 The Negation of (1) Leads to Bohmian Mechanics
		2.2.2 The Negation of (2) Leads to Collapse Theories Such As GRW
		2.2.3 The Negation of (3) Leads to the Many Worlds Theory
	2.3 Other Alternatives?
	2.4 The Measurement Problem and Born\'s Statistical Hypothesis
	2.5 Decoherence
	2.6 The Ontology of Quantum Mechanics
3 Chance in Physics
	3.1 Typicality
	3.2 Small Causes, Large Effects
	3.3 Coarse Graining and Typicality Measures
	3.4 The Law of Large Numbers
	3.5 Typicality in the Continuum
		3.5.1 Newtonian Mechanics in Hamiltonian Form
		3.5.2 Continuity Equation and Typicality Measure
		3.5.3 Typicality and the Statistical Hypothesis
4 Bohmian Mechanics
	4.1 From the Universe to Subsystems
	4.2 Typicality Analysis and Born\'s Statistical Interpretation
	4.3 Heisenberg\'s Uncertainty
	4.4 Identical Particles and Topology
5 Collapse Theory
	5.1 GRW Theory
	5.2 Spontaneous Localization
	5.3 Remarks About Collapse Theories
6 The Many Worlds Theory
	6.1 Finding the World(s) in the Wave Function
		6.1.1 Everett Versus Bohm
	6.2 Probabilities in the Many Worlds Theory
		6.2.1 Everett\'s Typicality Argument
	6.3 Many Worlds: A Brief Assessment
7 The Measurement Process and Observables
	7.1 Ideal Measurements: PVMs
	7.2 PVMs and POVMs in General
	7.3 It Is Theory that Decides What Is Observable
8 Weak Measurements of Trajectories
	8.1 On the (Im)-Possibility of Measuring the Velocity
	8.2 Surrealistic Trajectories?
	8.3 Wheeler\'s Delayed-Choice Experiment
9 Hidden Variables
	9.1 Joint Measurements of Observables
	9.2 Two Assertions About Hidden Variables
		9.2.1 Von Neumann\'s Theorem
		9.2.2 The Kochen–Specker Theorem
	9.3 Contextuality
10 Nonlocality
	10.1 The EPR Argument
	10.2 Bell Inequality
	10.3 Implications and Misunderstandings
	10.4 CHSH Inequality and the Generalized Bell Theorem
		10.4.1 Derivation of the CHSH Inequality
	10.5 Nonlocality and Faster-than-Light Signaling
11 Relativistic Quantum Theory
	11.1 Difficulties of ``First\'\' and ``Second\'\' Class
		11.1.1 Infinite Mass
		11.1.2 Infinite Pair Creation
	11.2 Field Ontology: What Exactly Is It?
	11.3 Fermionic Fock Space
		11.3.1 Particles and Antiparticles
		11.3.2 Fock Space as the Dirac Sea
	11.4 Multi-Time Wave Function
		11.4.1 Time Evolution
12 Further Food for Thought
	12.1 Many Worlds Interpretation of Relativistic Quantum Mechanics
	12.2 Relativistic Bohm–Dirac Theory
	12.3 Nonlocality Through Retrocausality
	12.4 Bohmian ``Big Bang\'\' Model
	12.5 Relativistic GRW Theory
13 Epilogue
Index