Interpreting Quantum Mechanics: Modern Foundations

This novel text directly addresses common claims and misconceptions around quantum mechanics and presents a fresh and modern understanding of this fundamental and essential physical theory. It begins with a non-mathematical introduction to some of the more controversial topics in the foundations of quantum mechanics. For those more familiar with the theoretical framework of quantum mechanics, the text moves on to a general introduction to quantum field theory, followed by a detailed discussion of cutting-edge topics in this area such as decoherence and spontaneous coherence. Several important philosophical problems in quantum mechanics are considered, and their interpretations are compared, notably the Copenhagen and many-worlds interpretations. The inclusion of frequent real-world examples, such as superconductors and superfluids, ensures the book remains grounded in modern research. This book will be a valuable resource for students and researchers in both physics and the philosophy of science interested in the foundations of quantum mechanics. Contents Preface Part I A Nonmathematical Exposition of Quantum Mechanics and Quantum Field Theory 1 It’s All Fields and Waves 1.1 Fields 1.2 Waves 1.3 Basic Wave Effects 1.4 The Return of the Ether 2 How Fields Generate Particles 2.1 Field Resonances 2.2 Two Types of Quantization 2.3 Resonances as Particles 2.4 Bosons and Fermions 2.5 A Wave Can Be a Very Solid Thing 2.6 And a Solid Can Be a Very Wavy Thing 2.7 Dirac’s Beautiful Theory 2.8 Are Particles Real? 3 Jumpy Detectors 3.1 Atoms and Natural Length Scales 3.2 Electron Jumps 3.3 The Photoelectric Effect 3.4 Avalanche Detectors, Measurement, and Randomness 3.5 The Uncertainty Principle 4 Nonlocality 4.1 Correlation Experiments 4.2 Why Physicists Want to Preserve Relativity 4.3 One Explanation That Won’t Work: The Local Hidden-Variables Hypothesis 4.4 The Copenhagen Interpretation 4.5 Are Fields Real? 5 Alternative Interpretations of Quantum Mechanics 5.1 The Many-Worlds Hypothesis 5.2 Bohmian Pilot Waves 5.3 Variants of Positivism 5.4 Spontaneous Collapse 6 Decoherence and Collapse 6.1 Unitary Theories Will Not Work 6.2 Decoherence 6.3 Environmentally Induced Selection 6.4 Quantum Trajectories and Spontaneous Collapse 6.5 Quantifying Spontaneous Collapse 6.6 Living with Nonlocality 7 Quantum Mechanics and Our View of Reality 7.1 The Tao of Copenhagen 7.2 Free Will and Quantum Mechanics 7.3 Can Quantum Fluctuations Create Something from Nothing? 7.4 Spontaneous Symmetry Breaking 7.5 Did We Create Ourselves? 8 Quantum Mechanics and Technology 8.1 Quantum Mechanics in Your Pocket: Computer Chips and Nanotechnology 8.2 Tunneling, Radioactivity, and Quantum Biology 8.3 Quantum Cryptography 8.4 Quantum Information Processing 8.5 Lasers, Superfluids, and Superconductors Key Points Part II Basic Results of Quantum Mechanics 9 Schrodinger Equation Calculations ̈ 9.1 Wave Equations 9.2 Quantum Confinement Energy: Why Nanometers are Important 9.3 Fermi Pressure in Solids: Why are Solids Solid? 9.4 Vibration of Atoms: The Simple Harmonic Oscillator Model 9.5 Unit Analysis of Atomic States 9.6 Universal Conductance in Quantum Wires 10 Comparing Classical and Quantum Systems 10.1 Derivation of the Planck Spectrum 10.1.1 Planck’s Derivation in Terms of Particle Statistics 10.1.2 Derivation Using Quantum Field Theory 10.2 Classical Chaos Theory 10.3 Quantum and Classical Entanglement Part III A Short Course in Quantum Field Theory 11 Preliminary Mathematics 11.1 Dirac Wave Notation 11.2 General Properties of Operators 11.3 Operators and Measurements 11.4 The Schrodinger Equation 165 ̈ 11.5 The Uncertainty Principle 11.5.1 Fourier Analysis 11.5.2 Derivation of the Uncertainty Relationship 12 Boson Quantization 12.1 The Harmonic Oscillator 12.1.1 Derivation of Harmonic Oscillator States 12.1.2 Basic Rules for Particle Operators 12.2 Phonon Quantization 12.2.1 Derivation of Phonon Properties 12.2.2 Basic Rules for Phonons 12.2.3 Spatial Field Operators 12.3 The Thermodynamic Limit in Quantum Field Theory 12.4 Photon Quantization 12.4.1 Derivation of Photon Properties 12.4.2 Basic Rules for Photons 12.5 Coherent States of Bosons 12.5.1 Time Dependence of a Coherent State 12.5.2 Number-Phase Uncertainty and Coherent States 13 Fermion Quantization 13.1 Fermion Field Operators 13.1.1 Quantum Field Hamiltonians 13.1.2 Visualizing the Fermion Field 13.1.3 Fermion Spatial Field Operators 13.2 The Dirac Fermion Field 13.2.1 Derivation of the Dirac Equation 13.2.2 The Dirac Equation and Spin 14 Transition Rules 14.1 Fermi’s Golden Rule 14.1.1 Derivation of Fermi’s Golden Rule 14.1.2 Fermi’s Golden Rule and Quantum Statistics 14.2 Interaction Terms 14.2.1 Electron–Phonon Interactions 14.2.2 Electron–Photon Interactions 14.2.3 Other Interactions 14.3 Optical Transitions 14.3.1 Derivation of the Bloch Equations for a Two-Level System 14.3.2 The Bloch Vector Representation 14.4 Single-Photon Transitions and Fermi’s Golden Rule 14.5 Nonlinear Optics and Nonunitarity 15 Feynman Diagrams 15.1 The Expansion of the S-Matrix 15.1.1 Justification of Wick’s Theorem 15.1.2 Green’s Functions 15.1.3 Example: S-Matrix for a Boson-Mediated Interaction 15.2 Diagram Rules for Feynman Theory 15.3 How to Interpret Feynman Diagrams 15.3.1 Example: Vacuum Energy 15.3.2 Example: Self-Energy 15.3.3 Example: Nonlinear Optics in Vacuum Part IV Mathematical Considerations of Philosophy of Quantum Mechanics 16 Mathematical Considerations of Quantum Interpretations 16.1 The Local Hidden-Variables Hypothesis 16.1.1 Quantum Wave States of the EPR Experiment 16.1.2 Bell’s Inequality 16.2 The Many-Worlds Hypothesis 16.2.1 The Spectral Weight Problem 16.2.2 The Many-Worlds Hypothesis and Nonlocality 16.2.3 Many-Worlds and Spontaneous Symmetry Breaking 16.3 Bohmian Hydrodynamics 16.3.1 Derivation of the Bohmian Flow Equations 16.3.2 Comparison of Quantum Field Theory and Bohmian Particles in a Standing Wave 16.4 The Transactional Interpretation 16.4.1 Are There Advanced Waves in Quantum Field Theory? 16.4.2 Is There Nonunitarity in Quantum Field Theory? 17 Entanglement in a Classical System 17.1 An Optical System with Second Quantization 17.2 Entangled States of a Resonator 17.3 Bell Inequality for the Classical Resonator Part V Decoherence, Spontaneous Coherence, and Spontaneous Collapse 18 Irreversibility in Unitary Quantum Field Theory 18.1 The Poincare Recurrence Theorem 267 ́ 18.2 The Quantum Boltzmann Equation 18.2.1 Derivation of the Quantum Boltzmann Equation for a Many-Particle System 18.2.2 Quantum Boltzmann Equation for an Interacting Gas 18.3 Experimental Verification of the Quantum Boltzmann Equation 18.4 Proof of the Quantum H-Theorem 19 Decoherence in Quantum Field Theory 19.1 Density Matrix Formalism 19.2 Correlation Functions in Quantum Field Theory 19.3 Time-Evolution Equations for Correlation Functions of a Many-Particle System 19.4 Quantum Trajectories 19.4.1 Derivation of the Time-Evolution Equations for the Density Matrix 19.4.2 The Quantum Trajectories Recipe 20 Proposed Model for Spontaneous Collapse of Fermion States 20.1 Hypothesis of Nonunitary Behavior of Quantum Fields 20.2 Action on Superposition States 20.3 Implementation in Quantum Field Theory 20.4 Comparison to Weak Measurement Theory 20.5 Relativistic Considerations 21 Spontaneous Coherence: Lasers, Superfluids, and Superconductors 21.1 Spontaneous Coherence 21.2 Why Phase Coherence Leads to “Super” Behavior 21.3 Superconductors and Superfluids are the Same Thing 21.4 Lasers Also Involve Spontaneous Symmetry Breaking Appendix A Summary of quantum interpretations Index