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"Christoph Schiller MOTION MOUNTAIN the adventure of physics fall, flow and heat www.motionmountain.eu Christoph Schiller Motion Mountain The Adventure of Physics Fall, Flow and Heat available free of charge at www.motionmountain.eu Editio vicesima secunda. Proprietas scriptoris © Christophori Schiller secundo anno Olympiadis vicesimae nonae. 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. Twenty-second edition, second printing, ISBN 978-300-021946-7. Copyright © 2009 by Christoph Schiller, the second year of the 29th Olympiad. This pdf file is licensed under the Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Germany Licence, whose full text can be found on the website creativecommons.org/licenses/by-nc-nd/3.0/de, with the additional restriction that reproduction, distribution and use, in whole or in part, in any product or service, be it commercial or not, is not allowed without the written consent of the copyright owner. The pdf file was and remains free for everybody to read, store and print for personal use, and to distribute electronically, but only in unmodified form and at no charge. To Esther and Britta τῷ ἐμοὶ δαὶμονι Die Menschen stärken, die Sachen klären. Preface The present overview of everyday physics is the result of a threefold aim I have pursued since 1990: to present the basics of motion in a way that is simple, up to date and vivid. In order to be simple, the text focuses on concepts, while keeping mathematics to the necessary minimum. Understanding the concepts of physics is given precedence over using formulae in calculations. The whole text is within the reach of an undergraduate. Observation of the world around us allows us to deduce six essential statements: everyday motion is continuous, conserved, relative, reversible, mirror-invariant – and nature is lazy. Nature is indeed lazy: it minimizes change. This text explores how these results are deduced and how they fit with all those observations that seem to contradict them. In the structure of modern physics, shown in Figure 1, the results on everyday motion form the major part of the starting point. In order to be up to date, the text is enriched by the many gems – both theoretical and empirical – that are scattered throughout the scientific literature. In order to be vivid, the text tries to startle the reader as much as possible. Reading a book on general physics should be like going to a magic show. We watch, we are astonished, we do not believe our eyes, we think, and finally – maybe – we understand the trick. When we look at nature, we often have the same experience. The text tries to intensify this by following a simple rule: on each page, there should be at least one surprise or provocation for the reader to think about. Numerous interesting challenges are proposed. Hints or answers to these are given in an appendix. Giving full rein to one’s curiosity and thought leads to the development of a strong and dependable character. The motto of the text, die Menschen stärken, die Sachen klären, a famous statement by Hartmut von Hentig on pedagogy, translates as: ‘To clarify things, to fortify people.’ Exploring any limit requires courage; and courage is also needed to abandon space and time as tools for the description of the world. Changing habits of thought produces fear, often hidden by anger; but we grow by overcoming our fears. The great adventures in life allow this: exploring love is one, exploring physics is another. Eindhoven and other places, 8 January 2009 “ Primum movere, deinde docere.* Antiquity ” Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.eu Copyright © Christoph Schiller November 1997–January 2009 Advice for learners In my experience as a teacher, there was one learning method that never failed to transform unsuccessful pupils into successful ones: if you read a book for study, summarize every section you read, in your own words, aloud. If you are unable to do so, read the * ‘First move, then teach.’ In modern languages, the mentioned type of moving (the heart) is often called motivating; both terms go back to the same Latin root. 8 preface PHYSICS: Describing motion with action. (Unified) theory of motion Adventures: understanding everything, intense fun with thinking, catching a glimpse of bliss What are space, time and quantum particles? General relativity Adventures: the night sky, measuring curved space, exploring black holes and the universe, space and time How do everyday, fast and large things move? Quantum theory with gravity Adventures: bouncing neutrons, understanding tree growth Quantum field theory Adventures: building accelerators, understanding quarks, stars, bombs and the basis of life, matter, radiation How do small things move? What are things? Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.eu Classical gravity Adventures: climbing, skiing, space travel, the wonders of astronomy and geology Special relativity Adventures: understanding time dilation, length contraction and E=mc2 c h, e, k Quantum theory Adventures: death, sexuality, biology, enjoying art, colours in nature, all high-tech business, medicine, chemistry, evolution G Galilean physics, electricity and heat Adventures: sport, music, sailing, cooking, using electricity and computers, understanding the brain and people F I G U R E 1 A complete map of physics: the connections are deﬁned by the speed of light c, the gravitational constant G, the Planck constant h, the Boltzmann constant k and the elementary charge e. Copyright © Christoph Schiller November 1997–January 2009 section again. Repeat this until you can clearly summarize what you read in your own words, aloud. You can do this alone in a room, or with friends, or while walking. If you do this with everything you read, you will reduce your learning and reading time significantly. In addition, you will enjoy learning from good texts much more and hate bad texts much less. Masters of the method can use it even while listening to a lecture, in a low voice, thus avoiding to ever take notes. Using this book Text in green, as found in many marginal notes, is a link that can be clicked in a pdf reader. Green links can be bibliographic references, footnotes, cross references to other preface 9 pages, challenge solutions or URLs of other websites. Solutions and hints for challenges are given at the end of each part. Challenges are classified as research level (r), difficult (d), standard student level (s) and easy (e). Challenges of type r, d or s for which no solution has yet been included in the book are marked (ny). A request The text is and will remain free to download from the internet. In exchange, please send me a short email on the following issues: — What was unclear? — What story, topic, riddle, picture or movie did you miss? — What should be improved or corrected? Feedback on the specific points listed on the www.motionmountain.eu/help.html web page is most welcome of all. You can also add feedback directly to www.motionmountain. eu/wiki. On behalf of all other readers, thank you in advance for your input. For a particularly useful contribution you will be mentioned – if you want – in the acknowledgements, receive a reward, or both. But above all, enjoy the reading. Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.eu Challenge 1 s Copyright © Christoph Schiller November 1997–January 2009 Fall, Flow and Heat In our quest to learn how things move, the experience of hiking and other motion leads us to introduce the concepts of velocity, time, length, mass and temperature, and to use them to measure change. We discover how to float in free space, why we have legs instead of wheels, why disorder can never be eliminated, and why one of the most difficult open issues in science is the flow of water through a tube. Contents 14 1 Why should we care abou t motion? Does motion exist? 15 • How should we talk about motion? 17 • What are the types of motion? 19 • Perception, permanence and change 23 • Does the world need states? 25 • Galilean physics in six interesting statements 26 • Curiosities and fun challenges about motion 27 • Summary on motion 30 From motion measurement to continuit y What is velocity? 32 • What is time? 37 • Clocks 40 • Why do clocks go clockwise? 41 • Does time flow? 43 • What is space? 44 • Are space and time absolute or relative? 48 • Size – why area exists, but volume does not 49 • What is straight? 53 • A hollow Earth? 53 • Curiosities and fun challenges about everyday space and time 54 • Summary about everyday space and time 64 How to describe motion – kinematics Throwing, jumping and shooting 67 • Enjoying vectors 69 • What is rest? What is velocity? 70 • Acceleration 72 • Objects and point particles 75 • Legs and wheels 77 • Curiosities and fun challenges about kinematics 79 • Summary of kinematics 80 From objects and images to conservation Motion and contact 82 • What is mass? 83 • Momentum and mass 85 • Is motion eternal? – Conservation of momentum 90 • More conservation – energy 91 • Rotation 94 • Rolling wheels 99 • How do we walk? 100 • Curiosities and fun challenges about conservation 101 • Summary on conservation 107 From the rotation of the earth to the rel ativit y of motion How does the Earth rotate? 115 • Does the Earth move? 118 • Is velocity absolute? – The theory of everyday relativity 124 • Is rotation relative? 125 • Curiosities and fun challenges about relativity 126 • Legs or wheels? – Again 131 • Summary on Galilean relativity 133 Motion due to gravitation Properties of gravitation 138 • Dynamics – how do things move in various dimensions? 142 • Gravitation in the sky 143 • The Moon 145 • Orbits 147 • Tides 150 • Can light fall? 153 • What is mass? – Again 154 • Curiosities and fun challenges about gravitation 156 • Summary on gravitation 169 Cl assical mechanics and the predictabilit y of motion Should one use force? Power? 170 • Friction and motion 173 • Friction, sport, machines and predictability 173 • Complete states – initial conditions 177 • Do surprises exist? Is the future determined? 178 • Free will 180 • Summary on predictability 181 • Global descriptions of motion 182 Measuring change with action The principle of least action 190 • Lagrangians and motion 192 • Why is motion so often bounded? 194 • Curiosities and fun challenges about Lagrangians 197 • Summary on action 200 Motion and symmetry Why can we think and talk about the world? 201 • Viewpoints 203 • Symmetries and groups 204 • Representations 205 • Symmetries, motion and Galilean 31 2 65 3 81 4 108 5 134 6 170 7 186 8 201 9 contents 13 physics 208 • Reproducibility, conservation and Noether’s theorem 211 • Curiosities and fun challenges about symmetry 215 • Parity and time invariance 216 • Summary on symmetry 216 218 10 Simple motions of extended bodies – oscill ations and waves Waves and their motion 220 • Why can we talk to each other? – Huygens’ principle 226 • Why is music so beautiful? 228 • Signals 230 • Solitary waves and solitons 232 • Curiosities and fun challenges about waves and extended bodies 235 • Summary on waves and oscillations 241 11 D o extended bodies exist? – L imits of continuit y Mountains and fractals 242 • Can a chocolate bar last forever? 242 • The case of Galileo Galilei 244 • How high can animals jump? 246 • Felling trees 246 • The sound of silence 248 • Little hard balls 248 • The motion of fluids 252 • Curiosities and fun challenges about fluids 255 • Curiosities and fun challenges about solids 263 • Summary on extension 268 • What can move in nature? – Flows 268 Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.eu 242 270 12 From heat to time-invariance Temperature 270 • Thermal energy 273 • Entropy 274 • Flow of entropy 276 • Do isolated systems exist? 276 • Why do balloons take up space? – The end of continuity 277 • Brownian motion 279 • Entropy and particles 281 • The minimum entropy of nature – the quantum of information 282 • Why can’t we remember the future? 283 • Is everything made of particles? 284 • Why stones can be neither smooth nor fractal, nor made of little hard balls 285 • Curiosities and fun challenges about heat and reversibility 286 • Summary on heat and time-invariance 293 13 Self-organization and chaos – the simplicit y of complexit y Curiosities and fun challenges about self-organization 302 • Summary on selforganization and chaos 305 14 From the limitations of physics to the limits of motion Research topics in classical dynamics 306 • What is contact? 306 • Precision and accuracy 307 • Can all of nature be described in a book? 308 • Something is wrong about our description of motion 309 • Why is measurement possible? 309 • Is motion unlimited? 310 a Notation and conventions The Latin alphabet 311 • The Greek alphabet 313 • The Hebrew alphabet and other scripts 315 • Digits and numbers 315 • The symbols used in the text 316 • Calendars 318 • People Names 320 • Abbreviations and eponyms or concepts? 320 Biblio graphy Challenge hints and solu tions Credits Acknowledgements 383 • Film credits 384 • Image credits 384 294 306 311 Copyright © Christoph Schiller November 1997–January 2009 322 347 383 Chapter 1 W HY SHOULD W E C AR E AB OUT MOTION? W Ref. 1 Ref. 2 ham! The lightning striking the tree nearby violently disrupts our quiet forest alk and causes our hearts to suddenly beat faster. In the top of the tree e see the fire start and fade again. The gentle wind moving the leaves around us helps to restore the calmness of the place. Nearby, the water in a small river follows its complicated way down the valley, reflecting on its surface the ever-changing shapes of the clouds. Motion is everywhere: friendly and threatening, terrible and beautiful. It is fundamental to our human existence. We need motion for growing, for learning, for thinking and for enjoying life. We use motion for walking through a forest, for listening to its noises and for talking about all this. Like all animals, we rely on motion to get food and to survive dangers. Like all living beings, we need motion to reproduce, to breathe and to digest. Like all objects, motion keeps us warm. Motion is the most fundamental observation about nature at large. It turns out that everything that happens in the world is some type of motion. There are no exceptions. Motion is such a basic part of our observations that even the origin of the word is lost in the darkness of Indo-European linguistic history. The fascination of motion has always made it a favourite object of curiosity. By the fifth century bce in ancient Greece, its study had been given a name: physics. Motion is also important to the human condition. What can we know? Where does the world come from? Who are we? Where do we come from? What will we do? What should we do? What will the future bring? What is death? Where does life lead? All these questions are about motion. The study of motion provides answers that are both deep and surprising. Motion is mysterious. Though found everywhere – in the stars, in the tides, in our eyelids – neither the ancient thinkers nor myriads of others in the 25 centuries since then have been able to shed light on the central mystery: what is motion? We shall discover that the standard reply, ‘motion is the change of place in time’, is inadequate. Just recently an answer has finally been found. This is the story of the way to find it. Motion is a part of human experience. If we imagine human experience as an island, then destiny, symbolized by the waves of the sea, carried us to its shore. Near the centre of * Zeno of Elea (c. 450 bce), one of the main exponents of the Eleatic school of philosophy. “ All motion is an illusion. Zeno of Elea* ” Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.eu Copyright © Christoph Schiller November 1997–January 2009 why should we care abou t motion? 15 Astronomy theory of motion quantum field theory Material sciences Chemistry Medicine Biology relativity thermodynamics Geosciences quantum theory electromagnetism Motion Mountain Engineering Physics mechanics Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.eu Emotion bay Mathematics The humanities Social sea F I G U R E 2 Experience Island, with Motion Mountain and the trail to be followed the island an especially high mountain stands out. From its top we can see over the whole landscape and get an impression of the relationships between all human experiences, in particular between the various examples of motion. This is a guide to the top of what I have called Motion Mountain (see Figure 2; a less artistic but more exact version is given in Figure 1). The hike is one of the most beautiful adventures of the human mind. The first question to ask is: Does motion exist? “ Ref. 3 Ref. 4 Challenge 2 s Ref. 5 Das Rätsel gibt es nicht. Wenn sich eine Frage überhaupt stellen läßt, so kann sie beantwortet werden.* Ludwig Wittgenstein, Tractatus, 6.5 Copyright © Christoph Schiller November 1997–January 2009 To sharpen the mind for the issue of motion’s existence, have a look at Figure 3 or at Figure 4 and follow the instructions. In all cases the figures seem to rotate. One can experience similar effects if one walks over Italian cobblestone that is laid down in wave patterns or with the many motion illusions by Kitaoka Akiyoshi shown at www.ritsumei. ac.jp/~akitaoka. How can we make sure that real motion is different from these or other similar illusions? Many scholars simply argued that motion does not exist at all. Their arguments deeply influenced the investigation of motion. For example, the Greek philosopher Parmenides * ‘The riddle does not exist. If a question can be put at all, it can also be answered.’ ” 16 1 why should we care abou t motion? F I G U R E 3 Illusions of motion: look at the ﬁgure on the left and slightly move the page, or look at the white dot at the centre of the ﬁgure on the right and move your head back and forward Ref. 6 Challenge 3 s Ref. 7 (born c. 515 bce in Elea, a small town near Naples) argued that since nothing comes from nothing, change cannot exist. He underscored the permanence of nature and thus consistently maintained that all change and thus all motion is an illusion. Heraclitus (c. 540 to c. 480 bce ) held the opposite view. He expressed it in his famous statement πάντα ῥεῖ ‘panta rhei’ or ‘everything flows’.* He saw change as the essence of nature, in contrast to Parmenides. These two equally famous opinions induced many scholars to investigate in more detail whether in nature there are conserved quantities or whether creation is possible. We will uncover the answer later on; until then, you might ponder which option you prefer. Parmenides’ collaborator Zeno of Elea (born c. 500 bce) argued so intensely against motion that some people still worry about it today. In one of his arguments he claims – in simple language – that it is impossible to slap somebody, since the hand first has to travel halfway to the face, then travel through half the distance that remains, then again so, and so on; the hand therefore should never reach the ..."

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