Interpreting quantum mechanics: modern foundations
"This text has a general, non-mathematical discussion of common misconceptions around quantum mechanics, followed by a detailed mathematical discussion of how quantum field theory affects Important philosophical problems. It will be a valuable resource for students and researchers interested in...
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge ; New York ; Port Melbourne ; New Delhi ; Singapore
Cambridge University Press
2024
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "This text has a general, non-mathematical discussion of common misconceptions around quantum mechanics, followed by a detailed mathematical discussion of how quantum field theory affects Important philosophical problems. It will be a valuable resource for students and researchers interested in the foundations and philosophy of quantum mechanics"-- |
| Physical Description: | xiii, 325 Seiten Illustrationen, Diagramme |
| ISBN: | 9781009261555 100926155X |
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Contents page xii Preface Part I A Nonmathematical Exposition of Quantum Mechanics and Quantum Field Theory 1 It's All Fields and Waves 1.1 1.2 1.3 1.4 2 How Fields Generate Particles 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3 vii Field Resonances Two Types of Quantization Resonances as Particles Bosons and Fermions A Wave Can Be a Very Solid Thing . And a Solid Can Be a Very Wavy Thing Dirac’s Beautiful Theory Are Particles Real? Jumpy Detectors 3.1 3.2 3.3 3.4 3.5 4 Fields Waves Basic Wave Effects The Return of the Ether Atoms and Natural Length Scales Electron Jumps The Photoelectric Effect Avalanche Detectors, Measurement, and Randomness The Uncertainty Principle 1 3 3 9 11 16 18 18 20 23 25 27 28 30 32 35 35 37 42 43 45 Nonlocality 48 4.1 4.2 4.3 48 51 Correlation Experiments Why Physicists Want to Preserve Relativity One Explanation That Won’t Work: The Local Hidden-Variables Hypothesis 52
viii Contents 4.4 4.5 5 Alternative Interpretations of Quantum Mechanics 5.1 5.2 5.3 5.4 6 Unitary Theories Will Not Work Decoherence Environmentally Induced Selection Quantum Trajectories and Spontaneous Collapse Quantifying Spontaneous Collapse Living with Nonlocality Quantum Mechanics and Our View of Reality 7.1 7.2 7.3 7.4 7.5 8 The Many-Worlds Hypothesis Bohmian Pilot Waves Variants of Positivism Spontaneous Collapse Decoherence and Collapse 6.1 6.2 6.3 6.4 6.5 6.6 7 The Copenhagen Interpretation Are Fields Real? The Tao of Copenhagen Free Will and Quantum Mechanics Can Quantum Fluctuations Create Something from Nothing? Spontaneous Symmetry Breaking Did We Create Ourselves? Quantum Mechanics and Technology 8.1 8.2 8.3 8.4 8.5 Quantum Mechanics in Your Pocket: Computer Chips and Nanotechnology 111 Tunneling, Radioactivity, and Quantum Biology Quantum Cryptography Quantum Information Processing Lasers, Superfluids, and Superconductors Part II Basic Results of Quantum Mechanics Schrödinger Equation Calculations 9.1 9.2 9.3 9.4 9.5 9.6 62 62 67 69 71 75 75 77 80 82 85 88 93 93 98 101 104 108 111 115 117 120 123 128 Key Points 9 55 58 Wave Equations Quantum Confinement Energy: Why Nanometers are Important Fermi Pressure in Solids: Why are Solids Solid? Vibration of Atoms: The Simple Harmonic Oscillator Model Unit Analysis of Atomic States Universal Conductance in Quantum Wires 131 133 133 136 137 139 141 144
Contents ix 10 Comparing Classical and Quantum Systems 10.1 10.2 10.3 Derivation of the Planck Spectrum 10.1.1 Planck’s Derivation in Terms of Particle Statistics 10.1.2 Derivation Using Quantum Field Theory Classical Chaos Theory Quantum and Classical Entanglement Part III A Short Course in Quantum Field Theory 11 Preliminary Mathematics 11.1 11.2 11.3 11.4 11.5 12 155 157 157 159 163 165 167 167 170 Boson Quantization 173 12.1 173 173 175 176 176 179 180 183 185 185 187 188 188 190 12.2 12.3 12.4 12.5 13 Dirac Wave Notation General Properties of Operators Operators and Measurements The Schrödinger Equation The Uncertainty Principle 11.5.1 Fourier Analysis 11.5.2 Derivation of the Uncertainty Relationship 147 147 148 149 150 152 The Harmonic Oscillator 12.1.1 Derivation of Harmonic Oscillator States 12.1.2 Basic Rules for Particle Operators Phonon Quantization 12.2.1 Derivation of Phonon Properties 12.2.2 Basic Rules for Phonons 12.2.3 Spatial Field Operators The Thermodynamic Limit in Quantum Field Theory Photon Quantization 12.4.1 Derivation of Photon Properties 12.4.2 Basic Rules for Photons Coherent States of Bosons 12.5.1 Time Dependence of a Coherent State 12.5.2 Number-Phase Uncertainty and Coherent States Fermion Quantization 13.1 13.2 Fermion Field Operators 13.1.1 Quantum Field Hamiltonians 13.1.2 Visualizing the Fermion Field 13.1.3 Fermion Spatial Field Operators The Dirac Fermion Field 13.2.1 Derivation of the Dirac Equation 13.2.2 The Dirac Equation and Spin 192 192 192 193 196 197 197 199
Contents 14 14.1 14.2 14.3 14.4 14.5 15 201 Fermi’s Golden Rule 201 14.1.1 Derivation of Fermi ’s Golden Rule 201 14.1.2 Fermi’s Golden Rule and Quantum Statistics 204 Interaction Terms 205 14.2.1 Electron-Phonon Interactions 205 14.2.2 Electron-Photon Interactions 207 14.2.3 Other Interactions 209 Optical Transitions 210 14.3.1 Derivation of the Bloch Equations for a Two-Level System 210 14.3.2 The Bloch Vector Representation 212 Single-Photon Transitions and Fermi’s Golden Rule 214 Nonlinear Optics and Nonunitarity 216 Transition Rules Feynman Diagrams 15.1 15.2 15.3 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 Diagram Rules for Feynman Theory 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 16.2 16.3 16.4 The Local Hidden-Variables Hypothesis 16.1.1 Quantum Wave States of the EPR Experiment 16.1.2 Bell’s Inequality 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 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 250 The Transactional Interpretation 16.4.1 Are There Advanced Waves in Quantum Field Theory? 16.4.2 Is There Nonunitarity in
Quantum Field Theory? 219 219 221 222 223 226 229 229 230 232 235 237 237 237 240 242 243 245 247 248 249 251 251 253
Contents xi 17 Entanglement in a Classical System 17.1 17.2 17.3 An Optical System with Second Quantization Entangled States of a Resonator Bell Inequality for the Classical Resonator Part V Decoherence, Spontaneous Coherence, and Spontaneous Collapse 18 Irreversibility in Unitary Quantum Field Theory 18.1 18.2 18.3 18.4 19 Decoherence in Quantum Field Theory 19.1 19.2 19.3 19.4 20 Density Matrix Formalism Correlation Functions in Quantum Field Theory Time-Evolution Equations for Correlation Functions of a Many-Particle System Quantum Trajectories 19.4.1 Derivation of the Time-Evolution Equations for the Density Matrix 19.4.2 The Quantum Trajectories Recipe Proposed Model for Spontaneous Collapse of Fermion States 20.1 20.2 20.3 20.4 20.5 21 The Poincaré Recurrence Theorem 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 Experimental Verification of the Quantum Boltzmann Equation Proof of the Quantum H-Theorem Hypothesis of Nonunitary Behavior of Quantum Fields Action on Superposition States Implementation in Quantum Field Theory Comparison to Weak Measurement Theory Relativistic Considerations Spontaneous Coherence: Lasers, Superfluids, and Superconductors 21.1 21.2 21.3 21.4 Appendix A Index Spontaneous Coherence Why Phase Coherence Leads to “Super” Behavior Superconductors and Superfluids are the Same Thing Lasers Also Involve Spontaneous Symmetry Breaking Summary of quantum interpretations 255 255 259 260 265 267 267 269 269 272 273 275 278 278 280 281
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| isbn | 9781009261555 100926155X |
| language | English |
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| physical | xiii, 325 Seiten Illustrationen, Diagramme |
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| spelling | Snoke, David W. Verfasser (DE-588)1139127810 aut Interpreting quantum mechanics modern foundations David W. Snoke (University of Pittsburgh) Cambridge ; New York ; Port Melbourne ; New Delhi ; Singapore Cambridge University Press 2024 xiii, 325 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier "This text has a general, non-mathematical discussion of common misconceptions around quantum mechanics, followed by a detailed mathematical discussion of how quantum field theory affects Important philosophical problems. It will be a valuable resource for students and researchers interested in the foundations and philosophy of quantum mechanics"-- Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantum theory Quantentheorie (DE-588)4047992-4 s DE-604 Quantenfeldtheorie (DE-588)4047984-5 s Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035027899&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Snoke, David W. Interpreting quantum mechanics modern foundations Quantenfeldtheorie (DE-588)4047984-5 gnd Quantentheorie (DE-588)4047992-4 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4047992-4 |
| title | Interpreting quantum mechanics modern foundations |
| title_auth | Interpreting quantum mechanics modern foundations |
| title_exact_search | Interpreting quantum mechanics modern foundations |
| title_full | Interpreting quantum mechanics modern foundations David W. Snoke (University of Pittsburgh) |
| title_fullStr | Interpreting quantum mechanics modern foundations David W. Snoke (University of Pittsburgh) |
| title_full_unstemmed | Interpreting quantum mechanics modern foundations David W. Snoke (University of Pittsburgh) |
| title_short | Interpreting quantum mechanics |
| title_sort | interpreting quantum mechanics modern foundations |
| title_sub | modern foundations |
| topic | Quantenfeldtheorie (DE-588)4047984-5 gnd Quantentheorie (DE-588)4047992-4 gnd |
| topic_facet | Quantenfeldtheorie Quantentheorie |
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