Christoph Schiller DUMMY TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEXT TEX Motion Mountain The Adventure of Physics www.motionmountain.net Christoph Schiller Motion Mountain The Adventure of Physics available at www.motionmountain.net Editio decima octava Proprietas scriptoris Christophori Schiller secundo anno Olympiadis vicesimae sextae secundo anno Olympiadis vicesimae octavae Omnia proprietatis iura reservantur et vindicantur Imitatio prohibita sine auctoris permissione Non licet pecuniam expetere pro aliquo, quod partem horum verborum continet; liber pro omnibus semper gratuitus erat et manet Eighteenth revision, September Copyright © – by Christoph Schiller, between the second year of the th olympiad and the second year of the th olympiad All rights reserved Commercial reproduction, distribution or use, in whole or in part, is not allowed without the written consent of the copyright owner You are not allowed to charge money for anything containing any part of this text; it was and remains free for everybody About the cover photograph, see page To T τῷ ἐµοὶ δαὶµονι Die Menschen stärken, die Sachen klären Contents Preface 20 An appetizer First Part : 23 Cl assical Physics – How Do Things and Images Move? Chapter II Special R el ativity Maximum speed, observers at rest, and motion of light 249 249 Chapter III Gravitation and R el ativity Maximum force: general relativity in one statement The new ideas on space, time and gravity Motion in general relativity – bent light and wobbling vacuum 10 Why can we see the stars? – Motion in the universe 11 Black holes – falling forever 12 Does space differ from time? 13 General relativity in ten points – a summary for the layman 319 319 344 362 402 440 454 460 Chapter IV Cl assical Electrodynamics 14 Liquid electricity, invisible fields and maximum speed 15 What is light? 16 Charges are discrete – the limits of classical electrodynamics 17 Electromagnetic effects and challenges 18 Classical physics in a nutshell – one and a half steps out of three 478 478 516 545 547 568 Intermezzo The Brain, L anguage and the Human Condition 584 Second Part : tions? Quantum Theory – What Is Matter? What Are Interac- 656 656 668 685 702 Chapter VI Permu tation of Particles 23 Are particles like gloves? 24 Rotations and statistics – visualizing spin 719 719 727 Chapter VII Details of Quantum Theory and Electromagnetism 25 Superpositions and probabilities – quantum theory without ideology 26 Applied quantum mechanics – life, pleasure and the means to achieve them 27 Quantum electrodynamics – the origin of virtual reality 739 739 761 796 Copyright © Christoph Schiller November 1997–September 2005 Chapter V Quanta of Light and Matter 19 Minimum action – quantum theory for poets and lawyers 20 Light – the strange consequences of the quantum of action 21 Motion of matter – beyond classical physics 22 Colours and other interactions between light and matter www.motionmountain.net 28 28 40 158 239 Motion Mountain Chapter I Galilean Motion Why should we care about motion? Galilean physics – motion in everyday life Global descriptions of motion: the simplicity of complexity From the limitations of physics to the limits of motion 28 Quantum mechanics with gravitation – the first approach 809 Chapter VIII Inside the Nucleus 29 The structure of the nucleus – the densest clouds 30 The strong nuclear interaction and the birth of matter 31 The weak nuclear interaction and the handedness of nature 32 The standard model of elementary particle physics – as seen on television 33 Grand unification – a simple dream 836 836 857 868 872 873 Chapter IX Advanced Quantum Theory (Not yet Avail able) 879 Chapter X Quantum Physics in a Nu tshell 880 Intermezzo Bacteria, Flies and Knots 896 Third Part : Particles? Motion Withou t Motion – What Are Space, Time and 918 920 952 975 985 1016 Chapter Extension and Unification (Not yet Avail able) 1046 Chapter XIII The Top of the Mountain (Not yet Avail able) 1047 Fourth Part : Appendices Appendix A Notation and Conventions 1049 Appendix B Units, Measurements and Constants 1060 Appendix C Particle Properties 1078 Appendix D Numbers and Spaces 1098 Appendix E Information Sources on Motion 1128 Appendix F Challenge Hints & Solu tions 1134 Appendix G List of Illustrations 1178 Appendix H List of Tables 1190 Appendix I Name Index 1193 Appendix J Subject Index 1216 XII Motion Mountain Chapter XI General R el ativity Versus Quantum Mechanics 34 Does matter differ from vacuum? 35 Nature at large scales – is the universe something or nothing? 36 The physics of love – a summary of the first two and a half parts 37 Maximum force and minimum distance: physics in limit statements 38 The shape of points – extension in nature www.motionmountain.net Copyright © Christoph Schiller November 1997–September 2005 Detailed Contents Preface 20 An appetizer 23 First Part : Cl assical Physics How Do Things and Images Move? 28 28 40 61 70 145 158 161 173 Copyright © Christoph Schiller November 1997–September 2005 133 www.motionmountain.net 108 Motion Mountain Chapter I Galilean Motion Why should we care about motion? Does motion exist? 29 • How should we talk about motion? 31 • What are the types of motion? 32 • Perception, permanence and change 36 • Does the world need states? 38 • Curiosities and fun challenges about motion 39 • Galilean physics – motion in everyday life What is velocity? 41 • What is time? 42 • Why clocks go clockwise? 47 • Does time flow? 47 • What is space? 48 • Are space and time absolute or relative? 50 • Size: why area exists, but volume does not 51 • What is straight? 54 • A hollow Earth? 55 • Curiosities and fun challenges about everyday space and time 56 • How to describe motion: kinematics What is rest? 63 • Objects and point particles 66 • Legs and wheels 69 • Objects and images Motion and contact 72 • What is mass? 72 • Is motion eternal? 77 • More on conservation – energy 79 • Is velocity absolute? – The theory of everyday relativity 81 • Rotation 83 • Rolling wheels 87 • How we walk? 87 • Is the Earth rotating? 89 • How does the Earth rotate? 94 • Does the Earth move? 96 • Is rotation relative? 99 • Curiosities and fun challenges about everyday motion 100 • Legs or wheels? – Again 106 • Dynamics due to gravitation Properties of gravitation 111 • Dynamics: how things move in various dimensions? 115 • Gravitation in the sky 116 • The Moon 117 • Orbits 118 • Tides 120 • Can light fall? 123 • What is mass? – Again 124 • Curiosities and fun challenges about gravitation 125 • What is classical mechanics? Should one use force? 134 • Complete states: initial conditions 139 • Do surprises exist? Is the future determined? 141 • A strange summary about motion 144 • Bibliography Global descriptions of motion: the simplicity of complexity Measuring change with action The principle of least action 164 • Why is motion so often bounded? 168 • Curiosities and fun challenges about Lagrangians 170 • Motion and symmetry Why can we think and talk? 174 • Viewpoints 174 • Symmetries and groups 176 • Representations 177 • Symmetries, motion and Galilean contents 201 212 214 232 239 242 249 249 www.motionmountain.net 269 282 Copyright © Christoph Schiller November 1997–September 2005 Chapter II Special Relativity Maximum speed, observers at rest, and motion of light Can one play tennis using a laser pulse as the ball and mirrors as rackets? 254 • Special relativity in a few lines 256 • Acceleration of light and the Doppler effect 257 • The difference between light and sound 260 • Can one shoot faster than one’s shadow? 261 • The addition of velocities 263 • Observers and the principle of special relativity 263 • What is space-time? 266 • Can we travel to the past? – Time and causality 268 • Curiosities of special relativity Faster than light: how far can we travel? 269 • Synchronization and aging: can a mother stay younger than her own daughter? – Time travel to the future 270 • Length contraction 272 • Relativistic movies – aberration and Doppler effect 275 • Which is the best seat in a bus? 277 • How fast can one walk? 278 • Is the speed of shadow greater than the speed of light? 278 • Parallel to parallel is not parallel – Thomas rotation 282 • A never-ending story: temperature and relativity 282 • Relativistic mechanics Mass in relativity 283 • Why relativistic snooker is more difficult 284 • Mass is concentrated energy 285 • Collisions, virtual objects and tachyons 287 • Systems of particles: no centre of mass 289 • Why is most motion so slow? 290 • The history of the mass–energy equivalence formula by de Pretto and Einstein 290 • Four-vectors 291 • Four-momentum 294 187 Motion Mountain physics 179 • Reproducibility, conservation and Noether’s theorem 182 • Curiosities and fun challenges about motion symmetry 187 • Simple motions of extended bodies – oscillations and waves Waves and their motion 189 • Why can we talk to each other? – Huygens’ principle 193 • Signals 194 • Solitary waves and solitons 195 • Curiosities and fun challenges about waves and extended bodies 197 • Do extended bodies exist? Mountains and fractals 201 • Can a chocolate bar last forever? 202 • How high can animals jump? 203 • Felling trees 204 • The sound of silence 205 • Little hard balls 205 • Curiosities and fun challenges about fluids and solids 208 • What can move in nature? Why are objects warm? Entropy 217 • Flow of entropy 218 • Do isolated systems exist? 219 • Why balloons take up space? – The end of continuity 220 • Brownian motion 221 • Entropy and particles 223 • The minimum entropy of nature: the quantum of information 224 • Why can’t we remember the future? 226 • Is everything made of particles? 226 • Why stones can be neither smooth nor fractal, nor made of little hard balls 227 • Curiosities and fun challenges about heat 228 • Self-organization and chaos Curiosities and fun challenges about self-organization 237 • From the limitations of physics to the limits of motion Research topics in classical dynamics 239 • What is contact? 240 • Precision and accuracy 240 • Can all of nature be described in a book? 241 • Why is measurement possible? 241 • Is motion unlimited? 242 • Bibliography ... particular between the various examples of motion This is a guide to the top of what I have called Motion Mountain The hike is one of the most beautiful adventures of the human mind Clearly, the first... fire, the warmth of a human body, the waves of the sea and the mood changes of people are all variations of motion of particles This story is told in more detail in the second part of the text,... limitations of physics to the limits of motion 28 Quantum mechanics with gravitation – the first approach 809 Chapter VIII Inside the Nucleus 29 The structure of the nucleus – the densest clouds 30 The