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Quantum Reality


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Part I Our First Quantum Object: Light Some Opening Thoughts A Little Light Reading Lasers and Video Cameras Photons An Interference Experiment with Photons Interference as a Wave Effect Mach-Zehnder with Photons Delayed Choice Summary Endnotes Interlude 1: Another Interference Experiment Particles Electrons The Electron Gun The Stern-Gerlach Experiment Turning Things Round Things Get More Puzzling So, Where Did It Go? What Does It All Mean? Some Indications with Other Particles The Long and the Short of It Summary Endnotes Quantum States Where Are We Now? Describing Classical Systems Chaos Describing Quantum Systems Specific Example: Mach-Zehnder Again What's in a Number? Probability Amplitudes States in Stern-Gerlach Experiment General Stern-Gerlach States Some Further Thoughts What Are Quantum States? Endnotes Amplitudes More on Amplitudes Change of Basis Dirac Notation Orthogonal Bases New Light Through... Going the Other Way Endnotes Measurement Embracing Change Types of States Eigenstates Mixed States Expectation Values Operators How States Evolve Why Is State Reduction Necessary? Behind the Veil Determinism and Free Will Endnotes Interlude 2: The Complex Plane Magnitude and Phase Multiplying Complex Numbers Next Phase And Lastly... Apologies Endnotes Interference How Science Works The Double-Slit Experiment The Double Slit with Electrons Wave/Particle Duality Wave Nature of Electrons Double-Slit Amplitudes Phase and Physics An Experiment with Phase The Interference Term Last Thoughts Endnotes The Free Particle The Position Basis (And a Useful Abbreviation) Continuous Bases The Amplitude for a Free Particle Wavelength Frequency What Does the Amplitude Tell Us about the Motion of a Free Particle? Amplitudes, Energy, and Momentum Energy and Momentum Eigenstates Where Next? Endnotes Identical Particles Some Opening Thoughts Particle Dodgems Emphasizing the Weird The Moral of the Story States of More than One Particle Identical Particles States in Real World Final Thoughts Endnote Scattering Identical Bosons Scattering The Same, but Different: Identical Particles Using the Whole Detector And Another Way... Transitions Away from States What Does It All Mean? Lasers Bose-Einstein Condensates Einstein's Argument Endnotes Interlude 3: Matrix Operators Endnote Spin Fermions, Bosons, and Stern-Gerlach Magnets Angular Momentum Angular Momentum in Quantum Theory Magnetic Moments The Magnetic Moment of an Electron Intrinsic Angular Momentum Spin Operators Fermions and Bosons In Closing Endnotes Fermion States Exchange and Rotation Rotational Symmetry of States Reversing the Polarity of the Neutron Flow Coffee Mugs and Quantum States Spin, Symmetry, and Exchanges Time Spinning Things Round Time for Some Bullet Points Boson Spin States More on Time Reversal Time-Reversed Boson States What Just Happened? Endnotes Wave Functions Representations Infinite Expansions Wave Functions and State Functions Observables The Problem of Momentum Obtaining Momentum Operators and Representations So What Can We Do with p x? Position Operator Energy Operator The Equations of Quantum Theory E and H Stationary States Conclusions Endnotes Uncertainty Expectation Is Not Enough Heisenberg's Principle So What? I'm Not Sure What Uncertainty Means... Yet More Uncertainty Conjugation Time, Again... Energy/Time Uncertainty Final Musings Endnotes Interlude 4: Heisenberg's Equation Stationary States Energy-Time Uncertainty Endnote Part II Genealogy The Scientific Community "It Was the Best of Times, It Was the Worst of Times" Endnote Planck and Einstein Where to Start? Planck's Life Planck Enters Research Planck's Formula for Black Body Spectra Einstein Quantization of Light Photoelectric Effect Enter the Photon Bosons Final Thoughts Endnotes Niels Bohr The Godfather Early Life Atomic Theory Atomic Spectra Bohr's Atom Developments Complementarity Extensions Later Life Endnotes Werner Heisenberg Early Days The Development of Quantum Theory Cloud Chambers The Uncertainty Principle Quantum Concepts Later Life Endnotes Erwin Schroedinger Beginnings Electron Diffraction Enter the Wave Equation Matter Waves So What Is ? Nobel Prizes Schroedinger's Philosophy Endnotes Paul Dirac Dirac's Contributions to Quantum Physics Dirac the Person Dirac's Views on the Meaning of Quantum Theory Endnotes Conclusions Endnotes Part III Applications of Quantum Theory A Particle in a Box Another Brick in the Wall... Fixing the Momentum Energy Eigenstates Time Factor Normalization Two-Dimensional and Three-Dimensional Boxes Hydrogen Atom A Box Containing More than One Electron White Dwarf Stars Wave Packets That's All, Folks... Endnotes Entanglement Is Quantum Theory Complete? The EPR Argument Follow-Up by David Bohm Bohr's Reply to the EPR Argument Einstein and Bohr Schroedinger Introduces Entanglement Entanglement and Measurement That Damned Cat John Bell and Bohm's EPR Bell's Formula Aspect's Experiment Implications Endnotes Interlude 5: Density Operator Great Expectations Why Bother? Density Operator and EPR/Bohm Experiments Representing a State Density Operator and Entangled States The Density Matrix and the Measurement Problem Endnotes Interpretations What Is an Interpretation? A Collection of Problems The Nature of Probability State Reduction Entanglement Measurement Carnegie Hall Endnotes The Copenhagen Interpretation Bohr's Influence Bohr's View of Quantum Theory Heisenberg and Potentia Von Neumann and Measurement Mind of an Observer The Deep End... Conclusions Endnotes The Many Worlds Interpretation Criticisms of the Copenhagen Interpretation The Problem of the Cut Problem of Collapse The Many Worlds Interpretation Relative States Measurement Records And the Next One... The Ontological Step Many Worlds Arrives Many Worlds Matures The Nature of Probability State Reduction Entanglement Measurement Criticisms of the Many Worlds View Time Thoughts Endnotes Other Interpretations Being in Two Minds about Something... Mindless Hulks... The Advantages of Having More than One Mind The Ideas of David Bohm Ontological Interpretation Bohm's Version of Schroedinger Equation The Quantum Potential in Action Probability Quantum Potential and the Double-Slit Experiment Quantum Potential and the Particle in a Box Wave Function Collapse Reactions to Bohm's Theory Consistent Histories Projection Operators Histories Histories and Double Slits Environmental Imprint Histories in Cosmology What Have We Gained? Endnotes Quantum Field Theory Why Are We Doing This? Taking Identical Particles Seriously Particle Labels Substance Abuse States in Quantum Field Theory Fock States Up and Down We Go... Round and Round We Go... The Vacuum Operators Representing Observables The Story So Far Fermions and Bosons Change of Basis Basis for Progress So Why Is It Called Quantum Field Theory? Wave-Particle Duality Interactions in Quantum Field Theory Interaction Operators Interaction Potentials Vacuum Fluctuations Number Operators Again Fields and Numbers Endnotes Personal Conclusions Appendix A: List of Important Rules Appendix B: Glossary Appendix C: Useful Mathematics Appendix D: Bibliography Index

About the Author

The Royal Hospital School, Holbrook, Ipswich, UK


! a good and thorough presentation of the philosophical issues that have come so much to the fore in recent decades. This can in many ways stand among the best treatments of this side of the subject at the non-specialist level. ! --Contemporary Physics, Vol. 52, No. 1, January 2011

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