Particles, Fields and Forces (eBook)

Contents 7
1 Introduction 12
2 Particles or Waves? 14
2.1 How to Describe a Wave 17
2.1.1 Wavelength Represents Momentum 17
2.1.2 Frequency Represents Energy 19
2.1.3 Superposition and Interference of Waves 21
2.2 Probability Amplitude 24
2.3 What Is Waving? 26
3 Fields and Waves Making up Reality 28
3.1 What Is a Field? 28
3.2 All We Are Is Waves in a Field 29
3.2.1 Objection 1: How Can a Billiard Ball Be a Wave? 30
3.2.2 Objection 2: But Things Do not Look like Waves 30
3.2.3 Objection 3: How Can Waves Make a Table Seem Massive? 31
3.2.4 Objection 4: But Waves Die Out, Don’t They? 31
3.2.5 Objection 5: What, Then, Is Empty Space Through Which I Can Throw a Ball? 32
3.2.6 Objection 6: Oh-no, Not the Ether Again… 33
3.3 Conclusion 35
4 What Is a Particle if It Is a Wave? 36
4.1 Where Is a Particle? 36
4.2 Waves in Space 37
4.3 Waves in Space and the Double Slit Experiment 40
4.4 Waves in Time 42
4.5 A Particle Is a Bunch of Waves 43
4.6 Velocity of Particles and Waves 44
5 The Potential of a Field’s Elasticity 47
5.1 Exchanging Energy in a Field 48
5.2 Waves in a Medium 50
6 A Wave of Relativity 54
6.1 Wave Velocity 54
6.2 How Does a Wave Become Massive? 55
6.2.1 A Game of Rope and Springs 55
6.2.2 Example: Photons in a Plasma 65
6.2.3 Conclusion and Summary 66
6.3 The Elasticity of the Minkowski Metric 67
6.4 Length Contraction and Time Dilation of Waves 70
6.5 About Higgs 72
7 Quantization of Fields 73
7.1 First Quantization 73
7.2 Second Quantization 75
7.3 Phonons 78
7.4 Conclusion 79
8 Energy in Waves and Fields 80
8.1 Conservation Laws 81
8.1.1 Energy—Momentum Tensor 82
8.2 To Envision a Field Quantum 86
8.2.1 Coupled Oscillators 87
8.3 Collapse of the Wave Function 90
8.4 Describing a Field Quantum 91
9 Symmetry and the Origin of Force 93
9.1 The Symmetry of Rotations 93
9.1.1 Rotations in a Plane 93
9.1.2 Rotations in Three Dimensions 95
9.1.3 Rotations in Eight Dimensions 97
9.2 The Electromagnetic Field 98
9.2.1 QED 102
9.2.2 The Electromagnetic Field 103
9.3 Path Integral 106
9.4 How Does Symmetry Create a Force? 110
9.4.1 A Constant Field and The Refractive Index 116
9.4.2 Conclusion on the Electromagnetic Force 117
10 Propagators and Virtual Particles 119
10.1 Time Order of Events and Feynman Diagrams 123
10.2 Propagator 127
10.3 Relation Between Virtual and Real Particle 132
10.3.1 Summarizing 133
10.4 What Is an Electron Really? 134
10.5 How Do Virtual Particles Create a Force? 136
10.5.1 Electrons of Equal Charge 137
10.5.2 An Electron and a Positron 139
10.5.3 Conclusion 141
10.6 Path Integral Revisited 142
10.7 Fluctuating Fields 144
10.7.1 Casimir Effect 145
10.8 The Arrow of Time 146
11 Renormalisation of Fearful Infinities 150
11.1 Renormalizing Mass 152
11.2 Renormalizing Charge 153
11.3 Renormalisation Group 155
11.4 Quantum De-Coherence and “Collapse of the Wave Function” Revisited 157
12 Spin Makes up Bosons and Fermions 160
12.1 What Is Spin? 160
12.1.1 Orbital Momentum in the Atom 161
12.1.2 The Origin of Spin 166
12.1.3 Spin as a Wave 170
12.2 Fermions and Bosons 173
12.2.1 Wave Phase 174
12.2.2 Fermions 174
12.2.3 Bosons 176
12.2.4 Spinor Fields 177
12.2.5 Fermions in Opposite Spin 182
12.3 Helicity 182
12.4 Chirality 183
12.4.1 Fermions Come in Two Chiralities, Called Left and Right. Bosons Do Not 184
12.4.2 Under Parity, the Chirality of a Fermion Is Swapped to the Opposite Chirality 185
12.4.3 Low Velocity Fermions Flip Chirality at the Frequency of Their Mass 185
12.4.4 Chirality Is Not the Same as Spin 187
12.4.5 Fermions of Different Chirality are Different Particles 188
12.4.6 At Very High Velocity the Chirality of Fermions Becomes Fixed and Related to Their Helicity 189
12.5 Fermions Becoming Bosons 192
12.6 Conclusions on Spin, Helicity and Chirality 192
13 Conservation of Charge and Particle Number 194
13.1 Particle Number Conservation 194
13.2 Charge Conservation 195
14 Particle Zoo 197
14.1 A Visit to the Particle Zoo 197
14.2 Introducing the Fundamental Particle Overview 202
14.3 The Rabbit Hole 203
15 Electroweak Force in the Early Universe 205
15.1 The First 10?12 s 206
15.1.1 Electron and Neutrino Waves 207
15.1.2 Introducing the Original U(1) Gauge Field 208
15.2 Symmetry Amongst the Waves 209
15.2.1 Introducing the SU(2) Gauge Field 211
15.2.2 Including Isosping Symmetry in the Overview of Waves 214
15.3 Introducing the Higgs Field 216
15.3.1 Fields Overview First 10?12 s 219
15.4 Fundamental Particle Overview 2 220
16 Symmetry Breaking and the World Will Never Be the Same 222
16.1 Mixing Fields 223
16.1.1 What Condensates in the Vacuum? 224
16.2 Breaking the Symmetry of the Higgs Field 226
16.2.1 Consequences for the U(1) and SU(2) Gauge Bosons 228
16.2.2 Mass of the W?, W+ and Z° 231
16.2.3 Consequences for the Fermion Interaction Potentials 232
16.3 Interactions 234
16.3.1 Photon Interactions 234
16.3.2 W-Interactions 235
16.3.3 Z-Interactions 238
16.3.4 Z-W Self-interactions 240
16.3.5 Neutron Decay 240
16.3.6 Radioactive Decay 242
16.3.7 Cabibbo Rotation 244
16.3.8 Concluding 246
16.4 Fermions Gaining Mass 246
16.5 Parity Violation and CPT Symmetry 248
16.6 Family Business 254
16.7 Fundamental Particle Overview 3 256
17 The Strong Force: Quantum Chromo Dynamics 258
17.1 The Big Why 258
17.2 The Colour Symmetry 261
17.3 QCD Fields Overview 270
17.3.1 Colour Confinement 271
17.3.2 Quark Jets 274
17.3.3 Asymptotic Freedom 276
17.4 Composite Particles 278
17.5 Interactions 280
17.5.1 Quark-Quark Colour Interactions 281
17.5.2 Annihilation and Creation 283
17.5.3 Gluon-Gluon Interactions 284
17.5.4 Proton—Anti-proton Collisions 284
17.5.5 Residual Strong Force or Nuclear Force 286
17.6 Mass of Quarks, Mesons and Baryons 288
17.7 Fundamental Particle Overview 4 290
18 Gravity as a Field 293
18.1 A Field Theory of Gravity 293
18.2 Background Independence 298
18.3 Other Problems 299
Further Reading 302
Pop Science 302
The Internet 303
References and Sources 305
Index 311