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"Christoph Schiller MOTION MOUNTAIN the adventure of physics light, charges and brains www.motionmountain.eu Christoph Schiller Motion Mountain The Adventure of Physics Light, Charges and Brains 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. The story of electricity reaches from measuring the weight of electric current to understanding the working of the human brain. This is the story of the adventures one encounters when exploring everything electric. In the map of physics, it corresponds to the most recent aspect of the lowest point in Figure 1. 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 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 * ‘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 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 pages, challenge solutions or URLs of other websites. Solutions and hints for challenges are given at the end of each part. Challenges are clas- preface 9 sified 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. Challenge 1 s Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.eu Copyright © Christoph Schiller November 1997–January 2009 Light, Charges and Brains In our quest to learn how things move, the experience of hiking and other motion leads us to discover that images are produced by charges, that charges move, accumulate and interact, and that there is a smallest charge in nature. We understand what love has to do with magnets and amber, why the brain is such an interesting device, and what distinguishes a good from a bad lie. Contents 15 1 L iquid electricit y, invisible fields and maximum speed Amber, lodestone and mobile phones 15 • How can one make lightning? 17 • Electric charge and electric fields 21 • Can we detect the inertia of electricity? 26 • Feeling electric fields 28 • Magnets 30 • Can humans feel magnetic fields? 30 • How can one make a motor? 31 • Magnetic fields 33 • Electromagnetic fields and Lagrangians 37 • How motors prove relativity to be right 38 • Curiosities and fun challenges about things electric and magnetic 40 • A summary: three basic facts about electricity 51 The description of electromagnetic field evolu tion Colliding charged particles 55 • The gauge field – the electromagnetic vector potential 56 • Energy and linear and angular momentum of the electromagnetic field 60 • The Lagrangian of electromagnetism 60 • The energy–momentum tensor and its symmetries of motion 61 • What is a mirror? 63 • What is the difference between electric and magnetic fields? 64 • Could electrodynamics be different? 65 • The brain: the toughest challenge for electrodynamics 66 • Challenges and fun curiosities about electrodynamics 67 What is light? Polarization and electromagnetism 74 • The slowness of progress in physics 81 • Another look at electromagnetic radiation 81 • How does the world look when riding on a light beam? 83 • Does light always travel in a straight line? 83 • The concentration of light 89 • Can one touch light? 90 • War, light and lies 94 • What is colour? 94 • Fun with rainbows 97 • What is the speed of light? – Again 97 • 200 years too late – negative refraction indices 101 • Metamaterials 102 • Signals and predictions 103 • Does the aether exist? 103 • Challenges and fun curiosities about light 104 Images and the eye – optics How to prove you’re holy 106 • Do we see what exists? 106 • How does one make pictures of the inside of the eye? 109 • How does one make holograms and other threedimensional images? 110 • Optical imaging 112 • Why can we see each other? 114 • Light as weapon? 116 • Challenges and fun curiosities about the eye and images 116 Charges are discrete – the limits of cl assical electrodynamics How fast do charges move? 119 • Challenges and curiosities about charge discreteness 120 Electromagnetic effects Is lightning a discharge? – Electricity in the atmosphere 122 • Does ball lightning exist? 124 • Does gravity make charges radiate? 126 • Research questions 126 • Levitation 128 • Matter, levitation and electromagnetic effects 132 • Challenges and fun curiosities about electromagnetic effects 139 • A summary of classical electrodynamics and of its limits 142 Cl assical physics in a nu tshell The future of planet Earth 145 • The essence of classical physics – the infinitely small and the lack of surprises 147 • Why have we not yet reached the top of the mountain? 148 52 2 69 3 106 4 119 5 122 6 144 7 contents 150 8 13 The story of the brain Evolution 151 • Children, laws and physics 151 • Polymer electronics 154 • Why a brain? 154 • What is information? 156 • What is memory? 157 • The capacity of the brain 159 • Curiosities about the brain 161 Thought and l anguage What is language? 163 • What is a concept? 167 • What are sets? What are relations? 168 • Infinity 171 • Functions and structures 172 • Numbers 173 • Why use mathematics? 178 • Is mathematics a language? 179 • Curiosities and fun challenges about mathematics 180 163 9 182 195 200 10 Concepts, lies and pat terns of nature Are physical concepts discovered or created? 183 • How do we find physical patterns and rules? 185 • What is a lie? 186 • Is this statement true? – A bit about nonsense 190 • Curiosities and fun challenges about lies and nonsense 192 Observations Have enough observations been recorded? 195 • Are all physical observables known? 196 • Do observations take time? 198 • Is induction a problem in physics? 198 The quest for precision and its implications What are interactions? – No emergence 201 • What is existence? 202 • Do things exist? 203 • Does the void exist? 204 • Is nature infinite? 205 • Is the universe a set? 206 • Does the universe exist? 207 • What is creation? 208 • Is nature designed? 210 • What is a description? 211 • Reason, purpose and explanation 212 • Unification and demarcation 213 • Pigs, apes and the anthropic principle 214 • Does one need cause and effect in explanations? 215 • Is consciousness required? 216 • Curiosity 217 • Courage 219 a Numbers and spaces Numbers as mathematical structures Complex numbers 223 • Quaternions 224 • Octonions 229 • Other types of numbers 231 • Grassmann numbers 232 Vector spaces Algebras Lie algebras 237 • Classification of Lie algebras 238 • Lie superalgebras 239 • The Virasoro algebra 240 • Kac–Moody algebras 240 Topology – what shapes exist? Topological spaces 241 • Manifolds 243 • Holes, homotopy and homology 245 Types and classification of groups Lie groups 247 • Connectedness 248 • Compactness 248 Mathematical curiosities and fun challenges b Units, measurements and constants Planck’s natural units 258 • Other unit systems 259 • Curiosities and fun challenges about units 261 • Precision and accuracy of measurements 266 • Basic physical constants 267 • Useful numbers 272 c S ources of information on motion Biblio graphy Challenge hints and solu tions Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.eu 221 221 232 234 241 246 253 255 Copyright © Christoph Schiller November 1997–January 2009 273 279 301 Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.eu Copyright © Christoph Schiller November 1997–January 2009 contents 316 14 Credits Film credits 316 • Image credits 316 Chapter 1 L IQUI D E L ECTRIC IT Y, INVISI BLE FIELDS AND MA XIMUM SPEED W Page ?? Challenge 2 e Ref. 1 hat is light? The study of relativity left us completely in the dark, even though e had embarked in it precisely to find an answer to that question. True, e have learned how the motion of light compares with that of objects. We also learned that light is a moving entity that cannot be stopped; but we haven’t learned anything about its nature. And what is contact? We still do not know. The answer to these long-standing questions emerges only from the study of those types of motion that are not related to gravitation, such as the ways magicians levitate objects. Revisiting the list of motors found in this world, we remark that gravitation hardly describes any of them. Neither the motion of sea waves, fire and earthquakes, nor that of a gentle breeze is caused by gravity. The same applies to the motion of muscles.* Have you ever listened to your own heart beat with a stethoscope? Without having done so, you cannot claim to have experienced the mystery of motion. Your heart has about 3000 million beats in your lifetime. Then it stops. It was one of the most astonishing discoveries of science that heart beats, sea waves and most other cases of everyday motion, as well as the nature of light itself, are connected to observations made thousands of years ago using two strange stones. These stones show that all those examples of motion that are called mechanical in everyday life are, without exception, of electrical origin. In particular, the solidity, the softness and the impenetrability of matter are due to internal electricity; also the emission of light is an electrical process. As these aspects are part of everyday life, we will leave aside all complications due to gravity and curved space-time. The most productive way to study electrical motion is to start, as in the case of gravity, with those types of motion which are generated without any contact between the bodies involved. Amber, lodestone and mobile phones Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.eu Copyright © Christoph Schiller November 1997–January 2009 The story of electricity starts with trees. Trees have a special relation to electricity. When a tree is cut, a viscous resin appears. With time it solidifies and, after millions of years, it forms amber. When amber is rubbed with a cat fur, it acquires the ability to attract small objects, such as saw dust or pieces of paper. This was already known to Thales of Miletus, one of the original seven sages, in the sixth century bce. The same observation can be made with many other polymer combinations, for example with combs and hair, * The photograph of a circular rainbow on page 11 was taken in 2006 from the Telstra Tower in Canberra (© Oat Vaiyaboon). 16 1 electricit y and fields F I G U R E 2 Objects surrounded by ﬁelds: amber (c. 1 cm), lodestone (c. 1 cm) and mobile phone (c. 10 cm) (© Philips) Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.eu water pipe comb rubbed on wool F I G U R E 3 How to amaze kids, especially in dry weather (photo © Robert Fritzius) Challenge 3 ny with soles of the shoe on carpets, and with a TV screen and dust. Children are always surprised by the effect, shown in Figure 3, that a comb rubbed on wool has on running tap water. The same effect can be produced with an air-filled rubber balloon rubbed on wool. Another interesting effect can be observed when a rubbed comb is put near a burning candle. (Can you imagine what happens?) Another part of the story of electricity involves an iron mineral found in certain caves around the world, e.g. in a region (still) called Magnesia in the Greek province of Thessalia, and in some regions in central Asia. When two stones of this mineral are put near each other, they attract or repel each other, depending on their relative orientation. In addition, these stones attract objects made of cobalt, nickel or iron. Today we also find various small objects in nature with more sophisticated properties, as shown in Figure 2. Some objects enable you to switch on a television, others unlock car doors, still others allow you to talk with far away friends. All these observations show that in nature there are situations where bodies exert influence on others at a distance. The space surrounding a body exerting such an influence is said to contain a field. A (physical) field is thus an entity that manifests itself by accelerating other bodies in its region of space. A field is some ‘stuff ’ taking up space. Experiments show that fields have no mass. The field surrounding the mineral found in Magne- Copyright © Christoph Schiller November 1997–January 2009 liquid electricit y, invisible fields and maximum speed TA B L E 1 Searches for magnetic monopoles, i.e., for magnetic charges 17 Search Smallest magnetic charge suggested by quantum theory Search in minerals Search in meteorites Search in cosmic rays Search with particle accelerators Magnetic charge Z д = h = e2α0 = 4.1 pWb e none, only dipoles Ref. 2 none, only dipoles Ref. 2 none, only dipoles Ref. 2 none, only dipoles Ref. 2 sia is called a magnetic field and the stones are called magnets.* The field around amber – called ἤλεκτρον in Greek, from a root meaning ‘brilliant, shining’ – is called an electric field. The name is due to a proposal by the famous English part-time physicist William Gilbert (1544–1603) who was physician to Queen Elizabeth I. Objects surrounded by a permanent electric field are called electrets. They are much less common than magnets; among others, they are used in certain loudspeaker systems.** The field around a mobile phone is called a radio field or, as we will see later, an electromagnetic field. In contrast to the previous fields, it oscillates over time. We will..."

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