Quantum Untangling: An Intuitive Approach to Quant um Mechanics from Einstein to Higgs

ISBN-13: 9781394190577 / Angielski / Miękka / 2023 / 375 str.

USA) Sh UK; Harvard University Simon (Cambridge University

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Introduction xiiAcknowledgements xiiiModule I Special Relativity 11 Special Relativity 31.1 Special Relativity: Simple, Yet Baffling 31.2 The Speed of Light Is Constant: So What? 41.3 The Invariant Interval Equation 51.4 Time Distortion Quantified 61.5 Length Distortion 81.6 Leading Clocks Lag 91.7 Lorentz Transformations and Invariance 101.8 Summary: Are You Joking Mr Einstein? 112 Paradoxes of Special Relativity 132.1 Journey to a Distant Planet (1) 132.2 Journey to a Distant Planet (2) 142.3 The Twin Paradox 162.4 Experimental Proof 183 Einstein's Famous Equation 203.1 Mass, Energy, Momentum - and Particle Time 203.2 How Did Albert Figure It Out? 213.2.1 The Ingredients 213.2.2 The Calculation 213.2.3 The Intuition 223.3 Three Beautiful Equations 233.4 How Wrong Were We? 243.5 One Further Equation 253.6 Summary 26Module II Essential Quantum Mechanics 274 Wave-particle Duality 294.1 Classical Physics Cannot Explain... 294.2 Quanta of Light and the Photoelectric Effect 304.3 De Broglie's Crazy Idea 314.4 The Double-slit Experiment 324.5 Schrödinger's Mistreated Cat 344.6 Summary 355 Superpositions and Uncertainty 375.1 The Free Particle Wave Function 375.1.1 The Phase of the Wave 385.1.2 Derivatives of the Free Particle Wave Function 385.1.3 Linking Back to Special Relativity 395.1.4 Consider a Rocket 405.2 From Sinusoid to Uncertainty 415.3 Superposition 425.3.1 Superposition Saves the Day 425.3.2 Combining Eigenstates 435.4 Heisenberg's Uncertainty Principle 445.5 In Praise of Fuzziness 455.6 God Plays Dice: The Role of Probability 465.7 Summary 475.8 What Is This Wave Function? 475.9 The Role of Rest Mass 486 Everything Happens ... Kind of 496.1 The Feynman Path Integral 496.2 Change in Phase of the Wave Function 506.3 Simplified Path Integral Model 516.4 The Principle of Stationary Action 536.5 Action and the Lagrangian 546.6 From the Lagrangian to the Equations of Motion 556.7 The Uncertainty Relationship: A Different Perspective 566.8 Feynman Diagrams 576.9 Summary 587 Measurement and Interaction 607.1 What Can You Know about a Quantum System? 607.2 Collapse of the Wave Function 617.3 When a Body Meets a Body ... 637.4 An Electron in a Box 637.5 Collapse of the Wave Function - a Twist 657.6 Decoherence and the Measurement Problem 667.7 When a Body Leaves a Body - Entanglement at a Distance 677.8 Summary 688 Module Summary and Schrödinger 708.1 Module Summary 708.2 Adding up the Implications 738.3 The Path to Schrödinger's Equation 738.3.1 The Klein-Gordon Equation 748.3.2 A Taste of Schrödinger's Equation 758.3.3 Incorporating Potential Energy 768.4 Module Memory Jogger 78Module III Complex Quantum Mechanics 799 Introducing Complex Numbers 819.1 Welcome to Complex Numbers 819.1.1 We Have a Problem 829.1.2 Complex Notation for Phase 829.1.3 Interference Calculations 839.1.4 A Friend with Benefits 849.1.5 Not a Free Lunch 849.2 Representing the Wave Function with Complex Notation 859.3 Summary 8510 Superpositions and Fourier Transforms 8610.1 The Maths of Fourier Transforms 8710.1.1 Example 1: Fourier Transform of a Position Eigenstate 8810.1.2 Example 2: Fourier Transform of dPsi 8810.2 Heisenberg's Uncertainty Principle and the Gaussian Distribution 8910.3 The Quantum Footprint 9010.4 Time and Energy 9210.5 Summary 9311 Schrödinger's Equation 9511.1 Understanding Schrödinger's Equation 9511.1.1 Incorporating Potential Energy 9611.1.2 Superpositions 9611.1.3 Schrödinger's Equation in Words 9611.2 Operators, Eigenstates and Eigenvalues 9711.3 Commutation Relations 10011.4 Expectation Values and Dirac Notation 10111.5 Energy Eigenstates are Stationary 10211.6 Time-independent Schrödinger Equation 10212 Schrödinger's Equation in Action 10412.1 Free Particle Wave Function (E > V) 10412.2 Creeping into Forbidden Places (E12.3 The Finite Potential Well 10612.4 Quantum Tunnelling and the Sun 10612.5 Dodging Potential Obstacles (E > V) 10812.6 Quantum Biology 11012.7 Wave Packets: A Model for Localised Particles 11012.8 Summary 11313 Quantum Harmonic Oscillator 11413.1 Introduction 11413.1.1 The Simple Harmonic Oscillator 11413.1.2 The SHO and QHO: Why Do We Care? 11513.2 Penetration Model for the QHO 11613.3 Schrödinger's Equation for the QHO 11713.3.1 Ground State of the QHO 11813.3.2 A Trick to Find the Other Energy Eigenstates of the QHO 11913.3.3 The QHO Energy Eigenstate Ladder 12013.3.4 QHO Superpositions 12113.4 The QHO in Three Dimensions 12213.5 Formal Definition of the Creation and Annihilation Operators 12313.6 The Path to Quantum Field Theory (QFT) 12514 Angular Momentum 12614.1 A Primer on Classical Angular Momentum 12614.2 Quanta of Angular Momentum 12814.3 Angular Momentum's Intricate Dance 12814.4 Angular Kinetic Energy and Angular Momentum 12914.5 The Pattern of Angular Momentum Eigenstates 13014.5.1 Ground State: l = 0 13114.5.2 First Energy Level: l = 1 13114.5.3 Three Distinct First Level States: l = 1, m = .1, 0, + 1 13114.5.4 Resulting in the Pattern 13214.6 The Angular Momentum Creation Operator 13314.7 Summary 13415 Coulomb Potential 13615.1 The Hydrogen Emission Spectrum 13615.2 The Challenge of the Coulomb Potential 13715.3 A Primitive Model 13815.4 Schrödinger's Equation for Hydrogen 13915.4.1 Spherical Harmonics - merci Monsieur Laplace 13915.4.2 The Angular Equation 14115.4.3 The Shape of the Atomic Orbitals 14215.4.4 Radial Kinetic Energy 14315.4.5 The Radial Equation 14415.5 Discussion 14616 The Periodic Table 14916.1 Introduction 14916.2 Adding More Protons 15016.3 The Periodic Table 15016.4 Molecular Bonds 15216.4.1 Ionic Bonds 15216.4.2 Covalent Bonds 15316.5 Bonds in the Nucleus 15416.6 Virtual Particles 15416.7 Fusion and Fission 15516.8 Module Summary 15616.9 Module Memory Jogger 157Module IV Relativistic Quantum Mechanics 15917 Spin 16117.1 Intrinsic Angular Momentum: Spin 16117.2 Spin-half Particles and the Pauli Exclusion Principle 16217.2.1 The Stern-Gerlach Experiment 16217.2.2 Spin-half and Spinors 16317.2.3 The Pauli Exclusion Principle 16417.2.4 The Pauli Matrices 16517.3 Integer-spin: The Photon 16817.3.1 Photon Polarisation 16917.4 Bell's Inequality and the Aspect Experiment 17017.5 Summary 17218 The Dirac Equation 17318.1 Yet Another Equation? 17318.2 Bi-spinors and Four-component Wave Functions 17418.3 The Dirac Equation 17518.3.1 The Ingredients 17518.3.2 Dirac's Crazy Insight 17618.3.3 Dirac's Matrices 17718.3.4 We Are Finally There: Dirac's Equation 17918.4 Spin-half Is Built in 18018.5 Interpreting the Dirac Equation 18218.5.1 Zero Momentum: Distinct Spin and Antiparticles 18218.5.2 The Dirac Equation and Minkowski Spacetime 18218.5.3 Particle and Antiparticle States 18318.5.4 Moving Frame 18418.6 The Dirac Equation and Hydrogen 18518.7 Dirac Equation: Modern Formulation 18618.8 The Aftermath: Physics Falls Apart Again 18619 Quantum Field Theory 18919.1 Changing the Question 19019.2 Quantum Fields Win the Day 19019.2.1 The Quantum Field Structure 19119.2.2 Quantum Fields and Spin 19219.2.3 Creation and Annihilation 19219.2.4 Bosons Like to Party 19319.2.5 Conservation of Energy and Momentum 19419.3 Non-relativistic Path Integrals and Action 19519.4 QFT Path Integrals: A Relativistic Twist 19719.5 Energy and Time 19719.6 QFT Field Development Pathways 19819.7 The Klein-Gordon Lagrangian as a Model 19919.8 Global Gauge Invariance to Phase 20019.9 Summary 20120 Local Gauge Invariance 20220.1 Introduction to Local Gauge Invariance 20220.2 The Infinity Swimming Pool - an Analogy 20420.3 Refresher in Electromagnetics (EM) 20520.3.1 EM Refresher (1): The Basics 20520.3.2 EM Refresher (2): The Vector Potential 20620.4 The EM Quantum Field and Lagrangian 20820.5 EM Gauge Invariance 21020.6 U(1) Local Gauge Invariance: Putting Together the Pieces 21020.6.1 The Swimming Pool: The Electron Field 21020.6.2 The Balancing Tank: The EM Field 21120.6.3 The Connection 21120.6.4 The Interaction 21120.6.5 The Infinity Pool: Combined Electron and EM Fields 21120.7 The Dirac Lagrangian 21220.8 Interaction and the Pathway of Stationary Action 21320.9 The Photon Must Be Massless 21420.10 Summary 21421 QED and Feynman Diagrams 21621.1 Feynman Diagrams 21621.2 Example: Electron-positron Annihilation 21821.3 Off-shell Drift and the QED Interaction 21921.4 Feynman Rules 22121.4.1 The Vertex and the Coupling Constant 22121.4.2 The Propagator 22221.4.3 Illustrative QED Calculation (Simplified) 22321.4.4 From Amplitude to Cross Section 22421.5 Resonance and the Search for New Particles 22521.6 Do Virtual Particles Exist? 22522 Renormalisation and EFT 22722.1 Troublesome Loops 22722.2 The Dressed Electron 22822.3 Using Feynman Diagrams 22922.4 Renormalisation 23022.5 Ken Wilson's Effective Field Theory (EFT) 23222.6 Summary 23223 The Strong Force 23423.1 The Elementary Particles 23423.2 The Strong Force: An Overview 23523.2.1 Colour Charge 23623.2.2 QCD, Gluons and Confinement 23623.2.3 Strong Force Coupling Constant 23723.3 QCD Local Gauge Invariance 23823.3.1 SU(3) Symmetry and Colour 23823.3.2 A Short Detour into Group Theory 24023.3.3 The QCD Lagrangian 24123.3.4 Gluons and the Generators 24223.3.5 Summary: QCD As an Infinity Swimming Pool 24323.4 The Residual Strong Force 24423.5 Oh No! Here Comes Jill Again! 24524 The Weak Force and Higgs Field (1) 24624.1 Idealised Weak Force and SU(2) Symmetry 24624.2 The Real Weak Force 24824.2.1 Weak Isospin 24824.2.2 Weak Interactions 24924.2.3 Massive Weak Bosons 25024.2.4 Wu and the Weak Left-handed Bias 25024.3 What About SU(2) Gauge Symmetry? 25124.4 Mass, Chirality and the Higgs Field 25224.4.1 Mass as an Interaction 25224.4.2 Chirality Versus Helicity 25324.4.3 Chiral Dirac Equation 25424.5 The Story So Far 25525 The Weak Force and Higgs Field (2) 25725.1 The Higgs Interaction 25725.2 The Higgs Field and Mechanism 25825.3 The Maths of the Higgs Field 25925.4 Visualising the Higgs Field 25925.5 Spontaneous Symmetry Breaking 26025.6 The Maths of the Higgs Mechanism 26025.6.1 The Starting Point 26125.6.2 The Potential of the Higgs Field 26125.6.3 Rotational Fluctuations of the Higgs Field 26225.6.4 Putting It All Together 26225.7 The Discovery of the Higgs Boson 26425.8 Electroweak Unification 26425.8.1 The Z Boson 26525.8.2 The Photon 26625.9 Summary 26626 The Standard Model and Beyond 26926.1 The Standard Model Lagrangian 26926.2 From Einstein and de Broglie to Higgs 27126.3 Questions and Problems 27126.4 General Relativity and Quantum Mechanics 27226.5 Supersymmetry (SUSY) 27326.6 String Theory 27426.6.1 Gravity in String Theory 27426.6.2 Difficulties with String Theory 27526.7 Loop Quantum Gravity (LQG) 27626.7.1 LQG Space as a Quantum Entity 27726.7.2 LQG Background Independence: Spin Networks 27826.7.3 Difficulties with LQG 27926.8 That's All Folks! 28026.9 Module Memory Jogger 280Index 282

O autorze

Simon Sherwood studied Natural Sciences at Cambridge University and has an MBA from Harvard Business School. Following four years as a strategy consultant with the Boston Consulting Group he embarked on a career in the hospitality industry as CEO of Orient-Express Hotels and more recently, Chairman of Elegant Hotels PLC. Simon Sherwood lives in Oxfordshire with his wife and two daughters.