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Transcript of PHYSICS FOR ALL.PDF
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Christoph Schiller
MOTION MOUNTAIN
the adventure of physics
www.motionmountain.net
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Christoph Schiller
Motion Mountain
eAdventure of Physics
available free of charge at
www.motionmountain.net
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Editio vicesima prima.
Proprietas scriptoris Christophori Schillersecundo anno Olympiadis vicesimae sextaequarto anno Olympiadis vicesimae octavae.
Omnia proprietatis iura reservantur et vindicantur.Imitatio prohibita sine auctoris permissione.Non licet pecuniam expetere pro aliquo, quodpartem horum verborum continet; liberpro omnibus semper gratuitus erat et manet.
Twenty-rst revision.
Copyright 19972007 by Christoph Schiller,between the second year of the 26th olympiadand the fourth year of the 28th olympiad.
All rights reserved. Commercial reproduction, commercialdistribution, and commercial use, in whole or in part, is notallowed without the written consent of the copyright owner.You are not allowed to charge money for anythingcontaining any part of this text; it was and remainsfree for everybody to read, to print for personal use,and to store and distribute electronically in unmodied form.
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To Esther
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Die Menschen strken, die Sachen klren.
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ContentsPreface 10An appetizer 12Advice for learners 16Using this book 16A request 16Acknowledgements 16
First Part : Fall , Flow and Heat
Chapter I Galilean Motion 221. Why should we care about motion? 222. Galilean physics motion in everyday life 373. Global descriptions of motion the simplicity of complexity 1804. From the limitations of physics to the limits of motion 291
Excursion A Notation and Conventions 318
Second Part : Relativity
Chapter II Special Relativity 3715. Maximum speed, observers at rest, and motion of light 371
Chapter III Gravitation and Relativity 4486. Maximum force general relativity in one statement 4487. e new ideas on space, time and gravity 4758. Motion in general relativity bent light and wobbling vacuum 4969. Why can we see the stars? Motion in the universe 53710. Black holes falling forever 57711. Does space dier from time? 59212. General relativity in ten points a summary for the layman 598
Third Part : L ight, Charges and Brains
Chapter IV Classical Electrodynamics 63313. Liquid electricity, invisible elds and maximum speed 63314. What is light? 68115. Charges are discrete the limits of classical electrodynamics 72816. Electromagnetic eects 73117. Classical physics in a nutshell one and a half steps out of three 750
Chapter V The Brain and Language 76918. Evolution and the brain 77019. ought and language 78020. Concepts, lies and patterns of nature 799
Excursion B Numbers and Spaces 843
Excursion C Sources of Information on Motion 877
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Excursion D Units , Measurements and Constants 883
Fourth Part : Quantum Theory : The Smallest Change
Chapter VI Quanta of L ight and Matter 92421. Minimum action quantum theory for poets 92422. Light the strange consequences of the quantum of action 94023. Motion of matter beyond classical physics 96224. Colours and other interactions between light and matter 984
Chapter VII Permutation of Particles 100225. Are particles like gloves? 100226. Rotations and statistics visualizing spin 1012
Chapter VIII Understanding Quantum Mechanics 102727. Superpositions and probabilities quantum theory without ideology 1027
Fifth Part : Pleasure , Technology and Stars
Chapter IX Advanced Quantum Theory 106328. Motion for enjoying life 106329. Quantum electrodynamics the origin of virtual reality 110830. Quantum mechanics with gravitation the rst approach 1122
Chapter X Inside the Nucleus 114931. e structure of the nucleus the densest clouds 114932. e strong nuclear interaction and the birth of matter 117433. e weak nuclear interaction and the handedness of nature 119034. e standard model of elementary particle physics as seen on television 119535. Grand unication a simple dream 119636. Extending quantum theory 1199
Chapter XI Quantum Physics in a Nutshell 1212
Chapter XII Bacteria , Flies and Knots 1229
Excursion E Particle Properties 1256
Sixth Part : Motion Without Motion What Are Space , Time and Par-ticles?
Chapter XIII General Relativity Versus Quantum Theory 128837. Does matter dier from vacuum? 129038. Nature at large scales is the universe something or nothing? 131639. e physics of love a summary of the rst two-and-a-half steps 133840. Maximum force and minimum distance physics in limit statements 134841. e shape of points extension in nature 137642. String theory a web of dualities 1403
Chapter XIV Unification (not yet available) 1420
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Chapter XV The Top of the Mountain (not yet available) 1421Postface 1425
Name index 1426
Subject index 1455
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Preface
Primum movere, deinde docere.
Antiquity
e intensity with which small children explore their environment suggests that there isa drive to grasp the way the world works, a physics instinct, built into each of us. Whatwould happen if this drive, instead of being stied during school education, as it usuallyis, were allowed to thrive in an environment without bounds, reaching from the atomsto the stars? Probably most adolescents would then know more about nature than mostsenior physics teachers today. is text tries to provide this possibility to the reader. Itacts as a guide in an exploration, free of all limitations, of physics, the science of motion.e project is the result of a threefold aim I have pursued since 1990: to present the basicsof 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 thenecessary minimum. Understanding the concepts of physics is given precedence overusing formulae in calculations.e whole text is within the reach of an undergraduate. Itpresents simple summaries of the main domains of physics.
ere are three main stages in the physical description of motion. First, there is every-day physics, or classical continuum physics. It is based on the existence of the innitelysmall and the innitely large. In the second stage, each domain of physics is centredaround a basic inequality for the main observable. us, statistical thermodynamics lim-its entropy by S k/2; special relativity limits speeds by v c; general relativity limitsforce by F c4/4G; quantum theory limits action by L /2; and quantum electrody-namics limits change of charge by q e. ese results, though not so well known, areproved rigorously. It is shown that within each domain, the principal equations followfrom the relevant limit. Basing the domains of physics on limit principles allows them tobe introduced in a simple, rapid and intuitive way. e third and nal stage is the uni-cation of all these limits in a single description of motion. is unusual way of learningphysics should reward the curiosity of every reader whether student or professional.
In order to be up to date, the text includes introductions of quantum gravity, stringtheory andM theory.Meanwhile, the standard topics mechanics, electricity, light, quan-tum theory, particle physics and general relativity are enriched by themany gems boththeoretical and empirical that are scattered throughout the scientic literature.
In order to be vivid, a text must be challenging, questioning and daring.is text triesto startle the reader asmuch as possible. Reading a book on general physics should be likegoing to a magic show.We watch, we are astonished, we do not believe our eyes, we think,and nally maybe we understand the trick. When we look at nature, we oen havethe same experience. e text tries to intensify this by following a simple rule: on eachpage, 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 anappendix.
e strongest surprises are those that seem to contradict everyday experience.Most ofthe surprises in this text are taken from daily life: in particular, from the things one expe-riences when climbing a mountain. Observations about trees, stones, the Moon, the skyand people are used wherever possible; complex laboratory experiments are mentioned
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preface 11
only where necessary. ese surprises are organized so as to lead in a natural way to themost extreme conclusion of all, namely that continuous space and time do not exist. econcepts of space and time, useful as they may be in everyday life, are only approxima-tions. Indeed, they turn out to be mental crutches that hinder the complete explorationof the world.
Giving full rein to ones curiosity and thought leads to the development of a strong anddependable character. e motto of the text, die Menschen strken, die Sachen klren, afamous statement byHartmut vonHentig on pedagogy, translates as: To clarify things, tofortify people. Exploring any limit requires courage; and courage is also needed to aban-don space and time as tools for the description of the world. Changing habits of thoughtproduces fear, oen hidden by anger; but we grow by overcoming our fears. Achieving adescription of the world without the use of space and time may be the most beautiful ofall adventures of the mind.
Eindhoven and other places, 17 November 2007
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An appetizer
Die Lsung des Rtsels des Lebens in Raum undZeit liegt auerhalb von Raum und Zeit.*
Ludwig Wittgenstein, Tractatus, 6.4312
What is the most daring and amazing journey we can make in a lifetime?e can travel to remote places, like adventurers, explorers or cosmonauts;e can look at evenmore distant places, like astronomers; we can visit the past, like
historians, archaeologists, evolutionary biologists or geologists; or we can delve deeplyinto the human interior, like artists or psychologists. All these voyages lead either to otherplaces or to other times. However, we can do better.
e most daring trip of all is not the one leading to the most inaccessible place, butthe one leading to where there is no place at all. Such a journey implies leaving the prisonof space and time and venturing beyond it, into a domain where there is no position, nopresent, no future and no past, where we are free of the restrictions imposed by spaceand time, but also of the mental reassurance that these concepts provide. In this domain,many new discoveries and new adventures await us. Almost nobody has ever been there;humanitys journey there has so far taken at least 2500 years, and is still not complete.
To venture into this domain, we need to be curious about the essence of travel itself.e essence of travel ismotion. By exploringmotionwewill be led to themost fascinatingadventures in the universe.
e quest to understandmotion in all its details and limitations can be pursued behinda desk, with a book, some paper and a pen. But to make the adventure more vivid, thistext uses the metaphor of a mountain ascent. Every step towards the top corresponds toa step towards higher precision in the description of motion. In addition, with each stepthe scenery will become more delightful. At the top of the mountain we shall arrive in adomain where space and time are words that have lost all meaning and where the sightof the worlds beauty is overwhelming and unforgettable.
inking without time or space is dicult but fascinating. In order to get a taste ofthe issues involved, try to respond to the following questions without referring to eitherspace or time:Challenge 1 s
Can you prove that two points extremely close to each other always leave room for athird point in between?
Can you describe the shape of a knot over the telephone? Can you explain on the telephone what right and le mean, or what a mirror is? Can youmake a telephone appointment with a friend without using any terms of timeor position, such as clock, hour, place, where, when, at, near, before, aer, upon,under, above, below?
Can you describe the fall of a stone without using the language of space or time? Do you know of any observation at all that you can describe without concepts fromthe domains of space, time or object?
Can you explain what time is? And what clocks are? Can you imagine a nite history of the universe, but without a rst instant of time?
* e solution of the riddle of life in space and time lies outside space and time.
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an appetizer 13
Can you imagine a domain of nature wherematter and vacuum are indistinguishable? Have you ever tried to understand why motion exists?
is book explains how to achieve these and other feats, bringing to completion an an-cient dream of the human spirit, namely the quest to describe every possible aspect ofmotion.
Why do your shoelaces remain tied? ey do so because space has three dimensions.Why not another number?e question has taxed researchers for thousands of years.eanswer was only found by studying motion down to its smallest details, and by exploringits limits.
Why do the colours of objects dier?Why does the Sun shine?Why does theMoonnotfall out of the sky? Why is the sky dark at night? Why is water liquid but re not? Whyis the universe so big? Why is it that birds can y but men cant? Why is lightning notstraight?Why are atoms neither square, nor the size of cherries?ese questions seem tohave little in common but they are related.ey are all about motion about its detailsand its limitations. Indeed, they all appear, and are answered, in this text. Studying the lim-its of motion, we discover that when a mirror changes its speed it emits light. We also dis-cover that gravity can be measured with a thermometer.We nd that there are more cellsin the brain than stars in the galaxy, giving substance to the idea that people have a wholeuniverse in their head. Exploring any detail of motion is already an adventure in itself.
By exploring the properties of motion we will nd that, despite appearance, motionnever stops. We will nd out why the oor cannot fall. We will understand why comput-ers cannot be made arbitrarily fast. We will see that perfect memory cannot exist. Wewill understand that nothing can be perfectly black. We will learn that every clock has acertain probability of going backwards. We will discover that time does not exist. We willnd that all objects in the world are connected.We will learn that matter cannot be distin-guished precisely from empty space. We will learn that we are literally made of nothing.We will learn quite a few things about our destiny. And wewill understand why the worldis the way it is.
e quest to understand motion, together with all its details and all its limits, involvesasking and answering three specic questions.
How do things move?Motion is usually dened as an object changing position overtime. is seemingly mundane denition actually encompasses general relativity, one ofthemost amazing descriptions of nature ever imagined.We will nd that space is warped,that light does not usually travel in a straight line, and that time is not the same for every-body.We will discover that there is a maximum force of gravity, and that gravity is not aninteraction, but rather the change of time with position.We will see how the blackness ofthe sky at night proves that the universe has a nite age. We will also discover that thereis a smallest entropy in nature, which prevents us from knowing everything about a phys-ical system. In addition, we will discover the smallest electrical charge. ese and otherstrange properties and phenomena of motion are summarized in the rst three parts ofthis text, whose topics are classical physics: mechanics, relativity and electrodynamics.e question on how things move leads directly to the next question.
What are things?ings are composites of particles. Not only tangible things, but allinteractions and forces those of the muscles, those that make the Sun burn, those thatmake the Earth turn, those that determine the dierences between attraction, repulsion,
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14 an appetizer
friction, creation and annihilation aremade of particles as well.e growth of trees, thecolours of the sky, the burning of re, the warmth of a human body, the waves of the seaand themood changes of people are all composed of particles inmotion.is story is toldinmore detail in the fourth and h part of the text, which deal with the foundations andthe applications of quantummechanics. Here we will learn that there is a smallest changein nature.eminimumvalue of change forces everything in nature to keep changing. Inparticular, we will learn that it is impossible to completely ll a glass of wine, that eternallife is impossible, and that light can be transformed into matter. If you nd this boring,you can read about the substantial dangers involved in buying a can of beans.Page 1219
erst ve parts of this text can be summarizedwith the help of a few limit principles:
statistical thermodynamics limits entropy: S k/2special relativity limits speed: v cgeneral relativity limits force: F c4/4Gquantum theory limits action: L /2quantum electrodynamics limits change of charge: q equantum asthenodynamics limits change of weak isospin: T3 1/2quantum chromodynamics requires free particles of no color: C = 0 .
In other words, each of the constants of nature k/2, c, c4/4G, /2 and e that appear aboveis a limit value. We will discover in each case that the equations of the correspondingdomain of physics follow from this limit property. Aer these results, the path is preparedfor the nal part of our mountain ascent.
What are particles, position and time? e recent results of an age-long search aremaking it possible to start answering this question. One just needs to nd a descriptionthat explains all limit principles at the same time. is sixth and last part is not yet com-plete, because the necessary research results are not yet available. Nevertheless, some ofthe intermediate results are striking:
It is known already that space and time are not continuous; that to be precise nei-ther points nor particles exist; and that there is no way to distinguish space from time,nor vacuum from matter, nor matter from radiation.Page 1290
It is known already that nature is not simply made of particles and vacuum. It seems that position, time and particles are aspects of a complex, extended entity thatis incessantly varying in shape.
Among the mysteries that should be cleared up in the coming years are the origin ofthe three dimensions of space, the origin of time and the details of the big bang.
Current research indicates thatmotion is an intrinsic property of matter and radiationand that, as soon as we introduce these two concepts in our description of nature,motion appears automatically. Indeed, it is impossible not to introduce these concepts,because they necessarily appear when we divide nature into parts, an act we cannotavoid because of the mechanisms of our senses and therefore of our thinking.
Current research also indicates that the nal, completely precise, description of naturedoes not use any form of innity. We nd, step by step, that all innities appearing in
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an appetizer 15
the human description of nature both the innitely large and the innitely small result from approximations. Innity turns out to bemerely a conceptual conveniencethat has no place in nature. However, we nd that the precise description does not in-clude any nite quantities either!ese andmany other astonishing results of modernphysics appear in the sixth part of this text.
is sixth and nal part of the text thus describes the present state of the search for aunied theory encompassing general relativity and quantummechanics. To achieve sucha description, the secrets of space, time, matter and forces have to be unravelled. It is afascinating story, assembled piece by piece by thousands of researchers. At the end of theascent, at the top of the mountain, the idea of motion will have undergone a completetransformation. Without space and time, the world will look magical, incredibly simpleand fascinating: pure beauty.
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Advice for learners
In my experience as a teacher, there was one learning method that never failed to trans-form unsuccessful pupils into successful ones: if you read a book for study, summarizeevery section you read, in your own words, aloud. If you are unable to do so, read the sec-tion again. Repeat this until you can clearly summarize what you read in your ownwords,aloud. You can do this alone in a room, or with friends, or while walking. If you do thiswith everything you read, you will reduce your learning and reading time signicantly.In addition, you will enjoy learning from good texts muchmore and hate bad texts muchless. Masters of themethod can use it even while listening to a lecture, in a low voice, thusavoiding to ever take notes.
Using this book
Any green text, as found in many marginal notes, is a link that can be clicked in a pdfreader. Green links can be bibliographic references, footnotes, cross references to otherpages, challenge solutions or URLs of other websites.
Solutions and hints for challenges are given at the end of each part. Challenges are clas-sied as research level (r), dicult (d), standard student level (s) and easy (e). Challengesof type r, d or s for which no solution has yet been included in the book are marked (ny).
A request
e text is and remains free for everybody. In exchange for getting the le for free, pleasesend 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?Challenge 2 s
Feedback on the specic points listed on the www.motionmountain.net/help.html webpage is most welcome of all. You can also add feedback directly to www.motionmountain.net/wiki. On behalf of myself and all other readers, thank you in advance for your input.For a particularly useful contribution you will be mentioned if you want in the ac-knowledgements, receive a reward, or both. But above all, enjoy the reading.
Acknowledgements
Many people who have kept their gi of curiosity alive have helped to make this projectcome true. Most of all, Saverio Pascazio has been present or not a constant referencefor this project. Fernand Mayn, Anna Koolen, Ata Masafumi, Roberto Crespi, SergePahaut, Luca Bombelli, Herman Elswijk, Marcel Krijn, Marc de Jong, Martin van derMark, Kim Jalink, my parents Peter and Isabella Schiller, Mike van Wijk, Renate Georgi,Paul Tegelaar, Barbara and Edgar Augel, M. Jamil, Ron Murdock, Carol Pritchard and,most of all, my wife Britta have all provided valuable advice and encouragement.
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acknowledgements 17
Many people have helped with the project and the collection of material. Most usefulwas the help of Mikael Johansson, Bruno Barberi Gnecco, Lothar Beyer, the numerousimprovements by Bert Sierra, the detailed suggestions by Claudio Farinati, the many im-provements by Eric Sheldon, the detailed suggestions by Andrew Young, the continuoushelp and advice of Jonatan Kelu, the corrections of Elmar Bartel, and in particular theextensive, passionate and conscientious help of Adrian Kubala.
Important material was provided by Bert Peeters, Anna Wierzbicka, William Beaty,Jim Carr, John Merrit, John Baez, Frank DiFilippo, Jonathan Scott, Jon aler, LucaBombelli,Douglas Singleton,GeorgeMcQuarry, TilmanHausherr, BrianOberquell, PeerZalm, Martin van der Mark, Vladimir Surdin, Julia Simon, Antonio Fermani, Don Page,Stephen Haley, Peter Mayr, Allan Hayes, Norbert Dragon, Igor Ivanov, Doug Renselle,Wim de Muynck, Steve Carlip, Tom Bruce, Ryan Budney, Gary Ruben, Chris Hill-man, Olivier Glassey, Jochen Greiner, squark, Martin Hardcastle, Mark Biggar, PavelKuzin, Douglas Brebner, Luciano Lombardi, Franco Bagnoli, Lukas Fabian Moser, De-jan Corovic, Steve Carlip, Corrado Massa, Tom Helmond, Gary Gibbons, Heinrich Neu-maier, Peter Brown, Paul Vannoni, John Haber, Saverio Pascazio, Klaus Finkenzeller, LeoVolin, Je Aronson, Roggie Boone, Lawrence Tuppen, Quentin David Jones, ArnaldoUguzzoni, Frans van Nieuwpoort, Alan Mahoney, Britta Schiller, Petr Danecek, Ingoies, Vitaliy Solomatin, Carl Oner, Nuno Proena, Elena Colazingari, Paula Hender-son, Daniel Darre, Wolfgang Rankl, John Heumann, Joseph Kiss, Martha Weiss, An-tonio Gonzlez, Antonio Martos, John Heumann, Andr Slabber, Ferdinand Bautista,Zoltn Gcsi, Pat Furrie, Michael Reppisch, Enrico Pasi, omas Kppe, Martin Rivas,Herman Beeksma, Tom Helmond, John Brandes, Vlad Tarko, Nadia Murillo, CiprianDobra, Romano Perini, Harald van Lintel, Andrea Conti, Franois Belfort, Dirk Van deMoortel, HeinrichNeumaier, JarosawKrlikowski, JohnDahlman, Fathi Namouni, PaulTownsend, Sergei Emelin, Freeman Dyson, S.R. Madhu Rao, David Parks, Jrgen Janek,DanielHuber, Alfons Buchmann, William Purves, plus a number of people who wantedto remain unnamed.
e soware tools were rened with extensive help on fonts and typesetting byMichael Zedler and Achim Blumensath and with the repeated and valuable supportof Donald Arseneau; help came also from Ulrike Fischer, Piet van Oostrum, GerbenWierda, Klaus Bhncke, Craig Upright, Herbert Voss, Andrew Trevorrow, Danie Els,Heiko Oberdiek, Sebastian Rahtz, Don Story, Vincent Darley, Johan Linde, Joseph Hert-zlinger, Rick Zaccone, John Warkentin, Ulrich Diez, Uwe Siart, Will Robertson, JosephWright Enrico Gregorio and Alexander Grahn.
All illustrations and animations in the text were made available by the copyright hold-ers. A warm thank you to all of them. ey are mentioned in the image and lm creditsections. In particular, Luca Gastaldi, Antonio Martos and Ulrich Kolberg produced im-ages specically for this text; Lucas Barbosa and Jos Antonio Daz Navas produced spe-cial animations.e typesetting and book design is due to the professional consulting ofUlrichDirr.e design of the book and its website owe also much to the suggestions andsupport of my wife Britta.
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18 acknowledgements
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First Part
Fall , Flow and Heat
In our quest to learn how things move,the experience of hiking and other motionleads us to introduce the concepts ofvelocity, time, length, mass and temperature,and to use them to measure change.We discover how to oat in free space,why we have legs instead of wheels,why disorder can never be eliminated,and why one of the most dicult open issuesin science is the ow of water through a tube.
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Detailed Contents
10 Preface12 An appetizer16 Advice for learners16 Using this book16 A request16 Acknowledgements
First Part : Fall , Flow and Heat
22 Chapter I Galilean Motion
22 1. Why should we care about motion?Does motion exist? 23 How should we talk about motion? 25 What are thetypes of motion? 27 Perception, permanence and change 31 Does the worldneed states? 33 Curiosities and fun challenges about motion 34
37 2. Galilean physics motion in everyday life
What is velocity? 38 What is time? 43 Clocks 46 Why do clocks go clock-wise? 47 Does time ow? 50 What is space? 50 Are space and time absolute orrelative? 53 Size why area exists, but volume does not 53 What is straight? 59 A hollow Earth? 60 Curiosities and fun challenges about everyday space andtime 61
69 How to describe motion kinematicsrowing, jumping and shooting 71 What is rest? 73 Acceleration 77 Objectsand point particles 78 Legs and wheels 80 Curiosities and fun challenges aboutthrowing and more 82
84 Objects and imagesMotion and contact 85 What is mass? 86 Is motion eternal? 92 More onconservation energy 94 Is velocity absolute? e theory of everyday relativ-ity 97 Rotation 99 Rolling wheels 103 How do we walk? 104 Is the Earthrotating? 105 How does the Earth rotate? 112 Does the Earth move? 115 Isrotation relative? 120 Conservation 120 Curiosities and fun challenges abouteveryday motion 121 Legs or wheels? Again 130
133 Dynamics due to gravitationProperties of gravitation 137 Dynamics how do things move in various dimen-sions? 142 Gravitation in the sky 142 eMoon 144 Orbits 146 Tides 149 Can light fall? 152 What is mass? Again 153 Curiosities and fun challengesabout gravitation 154
167 What is classical mechanics?Should one use force? 168 Complete states initial conditions 174 Do surprisesexist? Is the future determined? 175 A strange summary about motion 179
180 3. Global descriptions of motion the simplicity of complexity
183 Measuring change with actione principle of least action 187 Why is motion so oen bounded? 191 Curiosi-ties and fun challenges about Lagrangians 194
196 Motion and symmetry
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21
Why can we think and talk about the world? 197 Viewpoints 198 Symme-tries and groups 199 Representations 200 Symmetries, motion and Galileanphysics 203 Reproducibility, conservation and Noethers theorem 206 Curiosi-ties and fun challenges about motion symmetry 211
211 Simple motions of extended bodies oscillations and wavesWaves and their motion 214 Why can we talk to each other? Huygens princi-ple 219 Why is music so beautiful? 220 Signals 223 Solitary waves and soli-tons 225 Curiosities and fun challenges about waves and extended bodies 227
232 Do extended bodies exist?Mountains and fractals 233 Can a chocolate bar last forever? 233 How highcan animals jump? 235 Felling trees 235 e sound of silence 237 Littlehard balls 237 e motion of uids 241 Curiosities and fun challenges aboutuids 244 Curiosities and fun challenges about solids 250
256 What can move in nature?256 How do objects get warm?259 Temperature
Entropy 261 Flow of entropy 263 Do isolated systems exist? 264 Why doballoons take up space? e end of continuity 265 Brownian motion 266 Entropy and particles 268 e minimum entropy of nature the quantum of in-formation 269 Why cant we remember the future? 271 Is everything made ofparticles? 271 Why stones can be neither smooth nor fractal, nor made of littlehard balls 273 Curiosities and fun challenges about heat 273
280 Self-organization and chaosCuriosities and fun challenges about self-organization 287
291 4. From the limitations of physics to the limits of motion
Research topics in classical dynamics 291 What is contact? 291 Precision andaccuracy 292 Can all of nature be described in a book? 293 Why ismeasurementpossible? 293 Is motion unlimited? 294
295 Bibliography
318 Excursion A Notation and Conventions
eLatin alphabet 318 eGreek alphabet 320 eHebrew alphabet and otherscripts 322 Digits and numbers 322 e symbols used in the text 323 Calen-dars 325 Abbreviations and eponyms or concepts? 327
328 Bibliography330 Challenge Hints and Solutions
Film credits 362 Image credits 363
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C hapter I
GALILEAN MOTION
Wham! e lightning striking the tree nearby violently disrupts our quiet forestalk and causes our hearts to suddenly beat faster. In the top of the treee see the re start and fade again. e gentle wind moving the leaves around
us helps to restore the calmness of the place. Nearby, the water in a small river followsits complicated way down the valley, reecting on its surface the ever-changing shapes ofthe clouds.
1. why should we care about motion?
All motion is an illusion.
Zeno of Elea*
Motion is everywhere: friendly and threatening, terrible and beautiful. It is fundamentalto our human existence. We need motion for growing, for learning, for thinking and forenjoying life. We use motion for walking through a forest, for listening to its noises andfor talking about all this. Like all animals, we rely on motion to get food and to survivedangers. 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 thateverything that happens in the world is some type of motion. ere are no exceptions.Motion is such a basic part of our observations that even the origin of the word is lost inthe darkness of Indo-European linguistic history. e fascination of motion has alwaysmade it a favourite object of curiosity. By the h century bce in ancient Greece, its studyhad been given a name: physics.Ref. 1
Motion is also important to the human condition. Who are we? Where do we comefrom?Whatwill we do?What shouldwe do?What will the future bring?Where do peoplecome from?Where do they go?What is death?Where does the world come from?Wheredoes life lead? All these questions are about motion. e study of motion provides an-swers that are both deep and surprising.
Motion is mysterious. ough found everywhere in the stars, in the tides, in ourRef. 2eyelids neither the ancient thinkers nor myriads of others in the 25 centuries since thenhave been able to shed light on the central mystery: what is motion? We shall discoverthat the standard reply, motion is the change of place in time, is inadequate. Just recently
* Zeno of Elea (c. 450 bce), one of the main exponents of the Eleatic school of philosophy.
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why should we care about motion? 23
Physics
Motion
Mountain
Social sea
Emotion bay
Medicine
MathematicsThe humanities
Astronomy
Material sciences
Geosciences
Biology
Chemistry
Engineering
theory
of motion
quantum
gravity
quantum
theory
mechanics
electromagnetism
relativity
thermodynamics
F I G U R E 1 Experience Island, with Motion Mountain and the trail to be followed
an answer has nally been found.is is the story of the way to nd 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 centreof the island an especially high mountain stands out. From its top we can see over thewhole landscape and get an impression of the relationships between all human experi-ences, in particular between the various examples of motion.is is a guide to the top ofwhat I have called Motion Mountain (see Figure 1).e hike is one of the most beautifuladventures of the human mind.e rst question to ask is:
Does motion exist?
Das Rtsel gibt es nicht. Wenn sich eine Frageberhaupt stellen lt, so kann sie beantwortetwerden.*
Ludwig Wittgenstein, Tractatus, 6.5
To sharpen the mind for the issue of motions existence, have a look at Figure 2 or atFigure 3 and follow the instructions. In all cases the gures seem to rotate. One can ex-Ref. 3perience similar eects if one walks over Italian cobblestone that is laid down in wavepatterns 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 dierent from these or otherRef. 4similar illusions?Challenge 3 s
*e riddle does not exist. If a question can be put at all, it can be answered.
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24 i galilean motion 1. why should we care about motion?
F I G U R E 2 Illusions of motion: look at the figure on the left and slightly move the page, or look at thewhite dot at the centre of the figure on the right and move your head back and forward
Many scholars simply argued that motion does not exist at all.eir arguments deeplyinuenced the investigation of motion. For example, the Greek philosopher ParmenidesRef. 5(born c. 515 bce in Elea, a small town near Naples) argued that since nothing comesfrom nothing, change cannot exist. He underscored the permanence of nature and thusconsistently maintained that all change and thus all motion is an illusion.Ref. 6
Heraclitus (c. 540 to c. 480 bce ) held the opposite view. He expressed it in his fam-ous statement panta rhei or everything ows.* He saw change as the essenceof nature, in contrast to Parmenides.ese two equally famous opinions induced manyscholars to investigate in more detail whether in nature there are conserved quantities orwhether creation is possible. We will uncover the answer later on; until then, you mightponder which option you prefer.Challenge 4 s
Parmenides collaborator Zeno of Elea (born c. 500 bce) argued so intensely againstmotion 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 rst has totravel halfway to the face, then travel through half the distance that remains, then againso, and so on; the hand therefore should never reach the face. Zenos argument focuseson the relation between innity and its opposite, nitude, in the description of motion.In modern quantum theory, a similar issue troubles many scientists up to this day.Ref. 7
Zeno also maintained that by looking at a moving object at a single instant of time,one cannot maintain that it moves. Zeno argued that at a single instant of time, there isno dierence between a moving and a resting body. He then deduced that if there is nodierence at a single time, there cannot be a dierence for longer times. Zeno thereforequestioned whether motion can clearly be distinguished from its opposite, rest. Indeed,in the history of physics, thinkers switched back and forward between a positive and anegative answer. It was this very question that led Albert Einstein to the development ofgeneral relativity, one of the high points of our journey. In our adventure, we will exploreall known dierences between motion and rest. Eventually, we will dare to ask whethersingle instants of time do exist at all. Answering this question is essential for reaching thetop of Motion Mountain.
Whenwe explore quantum theory, wewill discover thatmotion is indeed to a certainextent an illusion, as Parmenides claimed. More precisely, we will show that motion is
* refnotation explains how to read Greek text.
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why should we care about motion? 25
F I G U R E 3 Zoom this image tolarge size or approach it closely inorder to enjoy its apparent motion( Michael Bach after the discoveryof Kitaoka Akiyoshi)
observed only due to the limitations of the human condition. We will nd that we expe-rience motion only because we evolved on Earth, with a nite size, made of a large butnite number of atoms, with a nite but moderate temperature, electrically neutral, largecompared with a black hole of our same mass, large compared with our quantum me-chanical wavelength, small compared with the universe, with a limited memory, forcedby our brain to approximate space and time as continuous entities, and forced by ourbrain to describe nature as made of dierent parts. If any one of these conditions werenot fullled, we would not observe motion; motion, then, would not exist. Each of theseresults can be uncovered most eciently if we start with the following question:
How should we talk about motion?
Je hais le mouvement, qui dplace les lignes,Et jamais je ne pleure et jamais je ne ris.
Charles Baudelaire, La Beaut.*
Like any science, the approach of physics is twofold: we advance with precision and withcuriosity. Precision makes meaningful communication possible, and curiosity makes itworthwhile.** If you ever nd yourself talking about motion, whether to understand itmore precisely or more deeply, your are taking steps upMotionMountain.e examplesof Figure 6 make the point. When you ll a bucket with a small amount of water, it doesnot hang vertically. (Why?) If you continue adding water, it starts to hang vertically at acertain moment. How much water is necessary? When you pull a thread from a reel inChallenge 5 ny
* Charles Baudelaire (b. 1821 Paris, d. 1867 Paris)Beauty: I hatemovement, which changes shapes, and neverdo I weep and never do I laugh. Beauty.Ref. 8** For a collection of interesting examples of motion in everyday life, see the excellent book by Walker.Ref. 9
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26 i galilean motion 1. why should we care about motion?
Thales
Plato
Sosigenes
StraboCtesibius
Archimedes
Konon
Chrysippos
Philoof Byz.
Dositheus
Biton
Asclepiades
Varro
Athenaius
Diodorus Siculus
Virgilius
Horace
Cicero
Frontinus
Maria the Jew
Josephus
Epictetus
Marinus
Menelaos
Nicomachos Apuleius
Cleomedes
Artemidor
Sextus Empiricus
Athenaios of Nauc.
Philostratus
Alexander of Aphr.
Diogenes Laertius
PomponiusMela
Dioscorides
Plutarch
Ptolemy
Eudoxus
Aratos
Berossos
Aristotle
Heraclides
Theophrastus
Autolycus
Euclid
Epicure
Alexander
Ptolemaios I
Ptolemaios II Ptolemaios VIII
Straton
Pytheas
Dikaiarchus Poseidonius
Socrates
Anaximander
Anthistenes
Anaximenes
Pythagoras
Almaeon
Heraclitus
Xenophanes
Parmenides
Philolaos
600 BCE 400500 300 200 100 100 2001
Zeno
Archytas
Aristoxenus
Empedocles
Herophilus
Polybios
Diophantus
Aristarchus
SeleukosArchimedes
Erasistratus
Eudoxus of Kyz.
Eratosthenes
DionysiusThrax
Diocles
Apollonius Theodosius
Hipparchus Lucretius
Heron
Vitruvius
Livius
Geminos
Manilius
Valerius Maximus
Seneca
Plinius Senior
Nero Trajan
Galen
Aetius
Rufus
Dionysius Periegetes
Theon of Smyrna
Arrian
Demonax
Lucian
Anaxagoras
Leucippus
Protagoras
Oenopides
Hippocrates
Herodotus
Democritus
Hippasos Speusippos
Caesar
F I G U R E 4 A time line of scientific and political personalities in antiquity (the last letter of the name isaligned with the year of death)
F I G U R E 5 An example of how precision of observation can lead to the discovery of new effects: thedeformation of a tennis ball during the c. 6ms of a fast bounce ( International Tennis Federation)
the way shown, the reel will move either forwards or backwards, depending on the angleat which you pull. What is the limiting angle between the two possibilities?
High precision means going into ne details, and being attuned to details actually in-creases the pleasure of the adventure.*e higher we get onMotionMountain, the furtherwe can see and the more our curiosity is rewarded. e views oered are breathtaking,especially from the very top. e path we will follow one of the many possible routes starts from the side of biology and directly enters the forest that lies at the foot of themountain.Ref. 10
Intense curiosity drives us to go straight to the limits: understanding motion requiresexploration of the largest distances, the highest velocities, the smallest particles, thestrongest forces and the strangest concepts. Let us begin.
* Distrust anybody who wants to talk you out of investigating details. He is trying to deceive you. DetailsChallenge 6 sare important. Be vigilant also during this walk.
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why should we care about motion? 27
F I G U R E 6 How much water is required to make a bucket hang vertically? At what angle does thepulled reel change direction of motion? ( Luca Gastaldi)
TA B L E 1 Content of books about motion found in a public library
M o t i o n t o p i c s M o t i o n t o p i c s
motion pictures motion as therapy for cancer, diabetes, acne and de-pression
motion perception Ref. 11 motion sickness
motion for tness and wellness motion for meditation
motion control in sport motion ability as health check
perpetual motion motion in dance, music and other arts
motion as proof of various gods Ref. 12 motion of stars and angels Ref. 13
economic eciency of motion the connection between motional and emotionalhabits
motion as help to overcome trauma motion in psychotherapy Ref. 14
locomotion of insects, horses and robots commotion
motions in parliament movements in art, sciences and politics
movements in watches movements in the stock market
movement teaching and learning movement development in children Ref. 15
musical movements troop movements Ref. 16
religious movements bowel movements
moves in chess cheating moves in casinos Ref. 17
connection between gross national product and citizen mobility
What are the types of motion?
Every movement is born of a desire for change.
Antiquity
A good place to obtain a general overview on the types of motion is a large library (seeTable 1). e domains in which motion, movements and moves play a role are indeed
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28 i galilean motion 1. why should we care about motion?
F I G U R E 7 Anexample oftransport, at theEtna ( MarcoFulle)
varied. Already in ancient Greece people had the suspicion that all types of motion, aswell as many other types of change, are related.ree categories of change are commonlyrecognized:
1. Transport. e type of change we call motion in everyday life is material transport,such as a personwalking or a leaf falling froma tree. Transport is the change of positionor orientation of objects. To a large extent, the behaviour of people also falls into thiscategory.
2. Transformation. Another category of change groups observations such as the dissolu-tion of salt in water, the formation of ice by freezing, the rotting of wood, the cook-ing of food, the coagulation of blood, and the melting and alloying of metals. esechanges of colour, brightness, hardness, temperature and othermaterial properties areall transformations. Transformations are changes not visibly connected with transport.To this category, a few ancient thinkers added the emission and absorption of light. Inthe twentieth century, these two eects were proven to be special cases of transfor-mations, as were the newly discovered appearance and disappearance of matter, asobserved in the Sun and in radioactivity. Mind change, such as change of mood, ofhealth, of education and of character, is also (mostly) a type of transformation.Ref. 18
3. Growth.e last and especially important category of change, growth, is observed forRef. 19animals, plants, bacteria, crystals, mountains, planets, stars and even galaxies. In thenineteenth century, changes in the population of systems, biological evolution, andin the twentieth century, changes in the size of the universe, cosmic evolution, wereadded to this category. Traditionally, these phenomena were studied by separate sci-ences. Independently they all arrived at the conclusion that growth is a combinationof transport and transformation.e dierence is one of complexity and of time scale.
At the beginnings of modern science during the Renaissance, only the study of trans-port was seen as the topic of physics. Motion was equated to transport.e other two do-
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why should we care about motion? 29
F I G U R E 8 Transport, growthand transformation ( PhilipPlisson)
mains were neglected by physicists. Despite this restriction, the eld of enquiry remainslarge, covering a large part of Experience Island. Early scholars dierentiated types oftransport by their origin. Movements such as those of the legs when walking were classi-ed as volitional, because they are controlled by ones will, whereasmovements of externalobjects, such as the fall of a snowake, which cannot be inuenced by will-power, wereclassied as passive. Children are able tomake this distinction by about the age of six, andthis marks a central step in the development of every human towards a precise descrip-tion of the environment.* From this distinction stems the historical but now outdateddenition of physics as the science of the motion of non-living things.
e advent of machines forced scholars to rethink the distinction between volitionaland passive motion. Like living beings, machines are self-moving and thus mimic voli-tional motion. However, careful observation shows that every part in amachine is movedby another, so their motion is in fact passive. Are living beings also machines? Are hu-man actions examples of passive motion as well? e accumulation of observations inthe last 100 years made it clear that volitional movement** indeed has the same physi-cal properties as passive motion in non-living systems. (Of course, from the emotionalviewpoint, the dierences are important; for example, grace can only be ascribed to voli-tional movements.) A distinction between the two types of motion is thus unnecessary.Ref. 20But since passive and volitional motion have the same properties, through the study ofmotion of non-living objects we can learn something about the human condition. is
* Failure to pass this stage completely can result in a person having various strange beliefs, such as believingin the ability to inuence roulette balls, as found in compulsive players, or in the ability to move other bod-ies by thought, as found in numerous otherwise healthy-looking people. An entertaining and informativeaccount of all the deception and self-deception involved in creating and maintaining these beliefs is givenby James Randi,e Faith Healers, Prometheus Books, 1989. A professional magician, he presents manysimilar topics in several of his other books. See also his www.randi.org website for more details.** e word movement is rather modern; it was imported into English from the old French and becamepopular only at the end of the eighteenth century. It is never used by Shakespeare.
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30 i galilean motion 1. why should we care about motion?
F I G U R E 9 One of the most difficultvolitional movements known, performedby Alexander Tsukanov, the first manable to do this: jumping from oneultimate wheel to another ( MoscowState Circus)
is most evident when touching the topics of determinism, causality, probability, innity,time and sex, to name but a few of the themes we will encounter on the way.
In the nineteenth and twentieth centuries other classically held beliefs about motionfell by thewayside. Extensive observations showed that all transformations and all growthphenomena, including behaviour change and evolution, are also examples of transport.In other words, over 2 000 years of studies have shown that the ancient classication ofobservations was useless: all change is transport.
In the middle of the twentieth century the study of motion culminated in the exper-imental conrmation of an even more specic idea, previously articulated in ancientGreece: every type of change is due to themotion of particles. It takes time andwork to reachthis conclusion, which appears only when one relentlessly pursues higher and higher pre-cision in the description of nature.e rst ve parts of this adventure retrace the pathto this result. (Do you agree with it?)Challenge 7 s
e last decade of the twentieth century again completely changed the descriptionof motion: the particle idea turns out to be wrong. is new result, reached through acombination of careful observation and deduction, will be explored in the last part of ouradventure. But we still have some way to go before we reach that point, which is near thesummit of our journey.
At present, at the beginning of our walk, we simply note that history has shown thatclassifying the various types of motion is not productive. Only by trying to achieve maxi-mum precision can we hope to arrive at the fundamental properties of motion. Precision,not classication, is the path to follow. As Ernest Rutherford said: All science is eitherphysics or stamp collecting.
To achieve precision in our description of motion, we need to select specic examplesof motion and study them fully in detail. It is intuitively obvious that the most precisedescription is achievable for the simplest possible examples. In everyday life, this is thecase for the motion of any non-living, solid and rigid body in our environment, such asa stone thrown through the air. Indeed, like all humans, we learned to throw objects longbefore we learned to walk.rowing is one of the rst physical experiment we performedRef. 21
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why should we care about motion? 31
by ourselves.* During our early childhood, by throwing stones, toys and other objectsuntil our parents feared for every piece of the household, we explored the perception andthe properties of motion. We do the same.
Die Welt ist unabhngig von meinemWillen.**
Ludwig Wittgenstein, Tractatus, 6.373
Perception , permanence and change
Only wimps study only the general case; realscientists pursue examples.
Beresford Parlett
Human beings enjoy perceiving. Perception starts before birth, and we continue enjoyingit for as long as we can.at is why television, even when devoid of content, is so success-ful. During our walk through the forest at the foot of Motion Mountain we cannot avoidperceiving. Perception is rst of all the ability to distinguish. We use the basic mental actof distinguishing in almost every instant of life; for example, during childhood we rstlearned to distinguish familiar from unfamiliar observations. is is possible in combi-nation with another basic ability, namely the capacity tomemorize experiences. Memorygives us the ability to experience, to talk and thus to explore nature. Perceiving, classify-ing and memorizing together form learning. Without any one of these three abilities, wecould not study motion.
Children rapidly learn to distinguish permanence from variability. ey learn to rec-ognize human faces, even though a face never looks exactly the same each time it is seen.From recognition of faces, children extend recognition to all other observations. Recog-nition works pretty well in everyday life; it is nice to recognize friends, even at night, andeven aer many beers (not a challenge). e act of recognition thus always uses a formof generalization. When we observe, we always have some general idea in our mind. Letus specify the main ones.
Sitting on the grass in a clearing of the forest at the foot of Motion Mountain, sur-rounded by the trees and the silence typical of such places, a feeling of calmness and tran-quillity envelops us. We are thinking about the essence of perception. Suddenly, some-thing moves in the bushes; immediately our eyes turn and our attention focuses. enerve cells that detect motion are part of the most ancient part of our brain, shared withbirds and reptiles: the brain stem. en the cortex, or modern brain, takes over to ana-Ref. 22lyse the type of motion and to identify its origin. Watching the motion across our eldof vision, we observe two invariant entities: the xed landscape and the moving animal.Aer we recognize the animal as a deer, we relax again.
How did we distinguish between landscape and deer? Perception involves several pro-cesses in the eye and in the brain. An essential part for these processes is motion, as isbest deduced from the ip lm shown in the lower le corners of these pages. Each im-Ref. 23age shows only a rectangle lled with a mathematically random pattern. But when the
* e importance of throwing is also seen from the terms derived from it: in Latin, words like subject orthrown below, object or thrown in front, and interjection or thrown in between; in Greek, it led to termslike symbol or thrown together, problem or thrown forward, emblem or thrown into, and last but notleast devil or thrown through.**e world is independent of my will.
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32 i galilean motion 1. why should we care about motion?
F I G U R E 10 How do we distinguish a deerfrom its environment? ( Tony Rodgers)
pages are scanned in rapid succession, you discern a shape a square moving againsta xed background. At any given instant, the square cannot be distinguished from thebackground; there is no visible object at any given instant of time. Nevertheless it is easyto perceive its motion.* Perception experiments such as this one have been performedin many variations. For example, it was found that detecting a moving square against arandom background is nothing special to humans; ies have the same ability, as do, infact, all animals that have eyes.
e ip lm in the lower le corner, likemany similar experiments, illustrates two cen-tral attributes of motion. First, motion is perceived only if an object can be distinguishedfrom a background or environment. Many motion illusions focus on this point.** Second,motion is required to dene both the object and the environment, and to distinguish themfrom each other. In fact, the concept of space is among others an abstraction of theidea of background. e background is extended; the moving entity is localized. Doesthis seem boring? It is not; just wait a second.
We call the set of localized aspects that remain invariant or permanent duringmotion,such as size, shape, colour etc., taken together, a (physical) object or a (physical) body.We will tighten the denition shortly, since otherwise images would be objects as well. Inother words, right from the start we experiencemotion as a relative process; it is perceivedin relation and in opposition to the environment.e concept of an object is therefore alsoa relative concept. But the basic conceptual distinction between localized, isolable objectsand the extended environment is not trivial or unimportant. First, it has the appearanceof a circular denition. (Do you agree?)is issue will keep us busy later on. Second, weChallenge 8 sare so used to our ability of isolating local systems from the environment that we takeit for granted. However, as we will see in the last part of our walk, this distinction turns
*e human eye is rather good at detecting motion. For example, the eye can detect motion of a point oflight even if the change of angle is smaller than that which can be distinguished in a xed image. Details ofthis and similar topics for the other senses are the domain of perception research.Ref. 11**e topic of motion perception is full of interesting aspects. An excellent introduction is chapter 6 of thebeautiful text by Donald D. Hoffman,Visual Intelligence HowWe Create WhatWe See, W.W. Norton& Co., 1998. His collection of basic motion illusions can be experienced and explored on the associated aris.ss.uci.edu/cogsci/personnel/homan/homan.html website.
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why should we care about motion? 33
TA B L E 2 Family tree of the basic physical concepts
motion
the basic type of change
parts relations background
permanent variable permanent
bounded unbounded extended
shaped unshaped measurable
objects images states interactions phase space space-time
impenetrable penetrable global local composed simple
e corresponding aspects:
mass intensity instant source dimension curvature
size colour position domain distance topology
charge appearance momentum strength volume distance
spin disappearance energy direction subspaces area
etc. etc. etc. etc. etc. etc.
world nature universe cosmos
the collection of all parts, relations and backgrounds
out to be logically and experimentally impossible!* Our walk will lead us to discover thePage 1309reason for this impossibility and its important consequences. Finally, apart frommovingentities and the permanent background, we need a third concept, as shown in Table 2.
Wisdom is one thing: to understand the thoughtwhich steers all things through all things.
Heraclitus of Ephesus
Ref. 24
Does the world need states?
Das Feste, das Bestehende und der Gegenstandsind Eins. Der Gegenstand ist das Feste,Bestehende; die Konguration ist dasWechselnde, Unbestndige.**Ludwig Wittgenstein, Tractatus, 2.027 2.0271
What distinguishes the various patterns in the lower le corners of this text? In everydaylife we would say: the situation or conguration of the involved entities. e situation
* Contrary to what is oen read in popular literature, the distinction is possible in quantum theory. It be-comes impossible only when quantum theory is unied with general relativity.** Objects, the unalterable, and the subsistent are one and the same. Objects are what is unalterable andsubsistent; their conguration is what is changing and unstable.
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34 i galilean motion 1. why should we care about motion?
somehow describes all those aspects that can dier from case to case. It is customary tocall the list of all variable aspects of a set of objects their (physical) state of motion, orsimply their state.
e situations in the lower le corners dier rst of all in time. Time is what makesopposites possible: a child is in a house and the same child is outside the house. Timedescribes and resolves this type of contradiction. But the state not only distinguishes sit-uations in time: the state contains all those aspects of a system (i.e., of a group of objects)that set it apart from all similar systems. Two objects can have the same mass, shape,colour, composition and be indistinguishable in all other intrinsic properties; but at leastthey will dier in their position, or their velocity, or their orientation.e state pinpointsthe individuality of a physical system,* and allows us to distinguish it from exact copies ofitself.erefore, the state also describes the relation of an object or a system with respectto its environment. Or in short: the state describes all aspects of a system that depend onthe observer.ese properties are not boring just ponder this: does the universe have astate?Challenge 10 s
Describing nature as a collection of permanent entities and changing states is the start-ing point of the study of motion. e various aspects of objects and of their states arecalled observables. All these rough, preliminary denitions will be rened step by step inthe following. Using the terms just introduced, we can say that motion is the change ofstate of objects.**
States are required for the description of motion. In order to proceed and to achievea complete description of motion, we thus need a complete description of objects and acomplete description of their possible states.e rst approach, called Galilean physics,consists in specifying our everyday environment as precisely as possible.
Curiosities and fun challenges about motion***
In contrast to most animals, sedentary creatures, like plants or sea anemones, have nolegs and cannot move much; for their self-defence, they developed poisons. Examples ofsuch plants are the stinging nettle, the tobacco plant, digitalis, belladonna and poppy;poisons include caeine, nicotine, and curare. Poisons such as these are at the basis ofmost medicines.erefore, most medicines exist essentially because plants have no legs.
* *
Aman climbs a mountain from 9 a.m. to 1 p.m. He sleeps on the top and comes down thenext day, taking again from 9 am to 1 pm for the descent. Is there a place on the path thathe passes at the same time on the two days?Challenge 11 s
* A physical system is a localized entity of investigation. In the classication of Table 2, the term physicalsystem is (almost) the same as object or physical body. Images are usually not counted as physical systems(though radiation is one). Are holes physical systems?Challenge 9 s** e exact separation between those aspects belonging to the object and those belonging to the state de-pends on the precision of observation. For example, the length of a piece of wood is not permanent; woodshrinks and bends with time, due to processes at the molecular level. To be precise, the length of a piece ofwood is not an aspect of the object, but an aspect of its state. Precise observations thus shi the distinctionbetween the object and its state; the distinction itself does not disappear at least not for quite while.*** Sections entitled curiosities are collections of topics and problems that allow one to check and to expandthe usage of concepts already introduced.
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why should we care about motion? 35
F I G U R E 11 A block and tackle and a differential pulley
* *
Every time a soap bubble bursts, the motion of the surface during the burst is the same,even though it is too fast to be seen by the naked eye. Can you imagine the details?Challenge 12 s
* *
Is the motion of a ghost an example of motion?Challenge 13 s
* *
Can something stop moving? How would you show it?Challenge 14 s
* *
Does a body moving in straight line for ever show that nature is innite?Challenge 15 s
* *
Can the universe move?Challenge 16 s
* *
To talk about precision with precision, we need to measure precision itself. How wouldyou do that?Challenge 17 s
* *
Would we observe motion if we had no memory?Challenge 18 s
* *
What is the lowest speed you have observed? Is there a lowest speed in nature?Challenge 19 s
* *
According to legend, Sessa benZahir, the Indian inventor of the game of chess, demandedfrom King Shirham the following reward for his invention: he wanted one grain of ricefor the rst square, two for the second, four for the third, eight for the fourth, and so on.
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36 i galilean motion 1. why should we care about motion?
F I G U R E 12 What happens?
v
F I G U R E 13 What is the speed of the rolls?Are other roll shapes possible?
Howmuch time would all the rice elds of the world take to produce the necessary rice?Challenge 20 s
* *
When a burning candle is moved, the ame lags behind the candle. How does the amebehave if the candle is inside a glass, still burning, and the glass is accelerated?Challenge 21 s
* *
A goodway tomakemoney is to buildmotion detectors. Amotion detector is a small boxwith a few wires. e box produces an electrical signal whenever the box moves. Whattypes of motion detectors can you imagine? How cheap can you make such a box? Howprecise?Challenge 22 d
* *
A perfectly frictionless and spherical ball lies near the edge of a perfectly at and horizon-tal table, as shown in Figure 12. What happens? In what time scale?Challenge 23 d
* *
You step into a closed boxwithout windows.e box ismoved by outside forces unknownto you. Can you determine how you move from inside the box?Challenge 24 s
* *
What is the length of rope one has to pull in order to li a mass by a height h with a blockand tackle with four wheels, as shown in Figure 11?Challenge 25 s
* *
When a block is rolled over the oor over a set of cylinders, as shown in Figure 13, howare the speed of the block and that of the cylinders related?Challenge 26 s
* *
Do you dislike formulae? If you do, use the following three-minute method to changeRef. 18the situation. It is worth trying it, as it will make you enjoy this book much more. Life isChallenge 27 sshort; as much of it as possible, like reading this text, should be a pleasure.
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galilean physics motion in everyday life 37
1 - Close your eyes and recall an experience that was absolutely marvellous, a situationwhen you felt excited, curious and positive.
2 - Open your eyes for a second or two and look at page 419 or any other page thatcontains many formulae.
3 -en close your eyes again and return to your marvellous experience.4 - Repeat the observation of the formulae and the visualization of your memory
steps 2 and 3 three more times.en leave the memory, look around yourself to get back into the here and now, and testyourself. Look again at page 419. How do you feel about formulae now?
* *
In the sixteenth century,Niccol Tartaglia* proposed the following problem.ree youngcouples want to cross a river. Only a small boat that can carry two people is available.emen are extremely jealous, and would never leave their brides with another man. Howmany journeys across the river are necessary?Challenge 28 s
* *
Cylinders can be used to roll a at object over the oor, as shown in Figure 13.e cylin-ders keep the object plane always at the same distance from the oor.What cross-sectionsother than circular, so-called curves of constant width, can a cylinder have to realize thesame feat? How many examples can you nd? Are objects dierent than cylinders possi-Challenge 29 sble?
2. galilean physics motion in everyday life
Physic ist wahrlich das eigentliche Studium desMenschen.**
Georg Christoph Lichtenberg
e simplest description of motion is the one we all, like cats or monkeys, use uncon-sciously in everyday life: only one thing can be at a given spot at a given time.is generaldescription can be separated into three assumptions: matter is impenetrable and moves,time ismade of instants, and space ismade of points.Without these three assumptions (doyou agreewith them?) it is not possible to dene velocity in everyday life.is descriptionChallenge 30 sof nature is called Galilean or Newtonian physics.
Galileo Galilei (15641642), Tuscan professor of mathematics, was a founder of mod-ern physics and is famous for advocating the importance of observations as checks ofstatements about nature. By requiring and performing these checks throughout his life,he was led to continuously increase the accuracy in the description of motion. For ex-ample, Galileo studied motion by measuring change of position with a self-constructedstopwatch. His approach changed the speculative description of ancient Greece into the
* Niccol Fontana Tartaglia (14991557), important Venetian mathematician.** Physics truly is the proper study of man. Georg Christoph Lichtenberg (17421799) was an importantphysicist and essayist.
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38 i galilean motion 2. galilean physics motion in everyday life
F I G U R E 14 Galileo Galilei
experimental physics of Renaissance Italy.*e English alchemist, occultist, theologian, physicist and politician Isaac Newton
(16431727) was one of the rst to pursue with vigour the idea that dierent types ofmotion have the same properties, and he made important steps in constructing the con-cepts necessary to demonstrate this idea.**
What is velocity?
ere is nothing else like it.
Jochen Rindt***
Velocity fascinates. To physicists, not only car races are interesting, but anymoving entityis. erefore they rst measure as many examples as possible. A selection is given inTable 3.e units and prexes used are explained in detail in Appendix D.
Everyday life teaches us a lot about motion: objects can overtake each other, and theycanmove in dierent directions.We also observe that velocities can be added or changedsmoothly.e precise list of these properties, as given in Table 4, is summarized by math-ematicians in a special term; they say that velocities form a Euclidean vector space.****More details about this strange term will be given shortly. For now we just note that inPage 74describing nature, mathematical concepts oer the most accurate vehicle.
When velocity is assumed to be an Euclidean vector, it is called Galilean velocity. Ve-
* e best and most informative book on the life of Galileo and his times is by Pietro Redondi (see thefootnote onpage 234).Galileowas born in the year the pencil was invented. Before his time, it was impossibleto do paper and pencil calculations. For the curious, the www.mpiwg-berlin.mpg.de website allows you toread an original manuscript by Galileo.** Newton was born a year aer Galileo died. Newtons other hobby, as master of the Mint, was to supervisepersonally the hanging of counterfeiters. About Newtons infatuation with alchemy, see the books by Dobbs.Ref. 25Among others, Newton believed himself to be chosen by god; he took his Latin name, Isaacus Neuutonus,and formed the anagram Jeova sanctus unus. About Newton and his importance for classical mechanics, seethe text by Cliord Truesdell.Ref. 26*** Jochen Rindt (19421970), famous Austrian Formula One racing car driver, speaking about speed.**** It is named aer Euclid, or Eukleides, the great Greek mathematician who lived in Alexandria around300 bce. Euclid wrote a monumental treatise of geometry, the or Elements, which is one of themilestones of human thought. e text presents the whole knowledge on geometry of that time. For therst time, Euclid introduces two approaches that are now in common use: all statements are deduced froma small number of basic axioms and for every statement a proof is given. e book, still in print today,has been the reference geometry text for over 2000 years. On the web, it can be found at aleph0.clarku.edu/~djoyce/java/elements/elements.html.
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galilean physics motion in everyday life 39
TA B L E 3 Some measured velocity values
O b s e rvat i o n Ve l o c i t y
Growth of deep sea manganese crust 80 am/sCan you nd something slower? Challenge 31 s
Stalagmite growth 0.3 pm/sLichen growth down to 7 pm/sTypical motion of continents 10mm/a = 0.3 nm/sHuman growth during childhood, hair growth 4 nm/sTree growth up to 30 nm/sElectron dri in metal wire 1 m/sSpermmotion 60 to 160 m/sSpeed of light at Suns centre 0.1mm/sKetchup motion 1mm/sSlowest speed of light measured in matter on Earth Ref. 27 0.3m/sSpeed of snowakes 0.5m/s to 1.5m/sSignal speed in human nerve cells Ref. 28 0.5m/s to 120m/sWind speed at 1 Beaufort (light air) below 1.5m/sSpeed of rain drops, depending on radius 2m/s to 8m/sFastest swimming sh, sailsh (Istiophorus platypterus) 22m/sSpeed sailing record (by windsurfer Finian Maynard) 25.1m/sFastest running animal, cheetah (Acinonyx jubatus) 30m/sWind speed at 12 Beaufort (hurricane) above 33m/sSpeed of air in throat when sneezing 42m/sFastest throw: a cricket ball thrown with baseball technique while running 50m/sFreely falling human, depending on clothing 50 to 90m/sFastest bird, diving Falco peregrinus 60m/sFastest badminton serve 70m/sAverage speed of oxygen molecule in air at room temperature 280m/sSpeed of sound in dry air at sea level and standard temperature 330m/sCracking whips end 750m/sSpee
