Christoph Schiller

MOTION MOUNTAINthe adventure of physics vol.ifall, flow and heat

www.motionmountain.net

Christoph Schiller

Motion Mountain

The Adventure of PhysicsVolume I

Fall, Flow and Heat

Edition 26, available as free pdfwith films at www.motionmountain.net

Editio vicesima sexta.

Proprietas scriptoris Chrestophori Schillertertio anno Olympiadis trigesimae.

Omnia proprietatis iura reservantur et vindicantur.Imitatio prohibita sine auctoris permissione.Non licet pecuniam expetere pro aliqua, quaepartem horum verborum continet; liberpro omnibus semper gratuitus erat et manet.

Twenty-sixth edition.

Copyright 19902014 by Christoph Schiller,the third year of the 30th Olympiad.

This pdf file is licensed under the Creative CommonsAttribution-Noncommercial-No Derivative Works 3.0 GermanyLicence, whose full text can be found on the websitecreativecommons.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 itcommercial or not, is not allowed without the written consent ofthe copyright owner. The pdf file was and remains free for everybodyto read, store and print for personal use, and to distributeelectronically, but only in unmodified form and at no charge.

To Britta, Esther and Justus Aaron

Die Menschen strken, die Sachen klren.

PREFACE

Primum movere, deinde docere.* AntiquityThis book is written for anybody who is curious about nature and motion. Curiosityabout how people, animals, things, images and empty space move leads to many adven-tures. This volume presents the best of them in the domain of everyday motion.

Carefully observing everyday motion allows us to deduce six essential statements:everyday motion is continuous, conserved, relative, reversible, mirror-invariant andlazy. Yes, nature is indeed lazy: in every motion, it minimizes change. This text exploreshow these six results are deduced and how they fit with all those observations that seemto contradict them.

In the structure of modern physics, shown in Figure 1, the results on everyday motionform the major part of the starting point at the bottom.The present volume is the first ofa six-volume overview of physics. It resulted from a threefold aim I have pursued since1990: to present motion in a way that is simple, up to date and captivating.

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. The whole text is within the reach of an undergraduate.

In order to be up to date, the text is enriched by the many gems both theoretical andempirical that are scattered throughout the scientific literature.

In order to be captivating, the text tries to startle the reader as much as possible. Read-ing a book on general physics should be like going to a magic show. We watch, we areastonished, we do not believe our eyes, we think, and finally we understand the trick.When we look at nature, we often have the same experience. Indeed, every page presentsat least one surprise or provocation for the reader to think about. Numerous interestingchallenges are proposed.

The motto of the text, die Menschen strken, die Sachen klren, a famous statement byHartmut von Hentig on pedagogy, translates as: To fortify people, to clarify things. Clar-ifying things and adhering only to the truth requires courage, as changing the habitsof thought produces fear, often hidden by anger. But by overcoming our fears we growin strength. And we experience intense and beautiful emotions. All great adventures inlife allow this, and exploring motion is one of them. Enjoy it.

Munich, 15 February 2014.

* First move, then teach. In modern languages, the mentioned type ofmoving (the heart) is calledmotivat-ing; both terms go back to the same Latin root.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

8 preface

Galilean physics, heat and electricityAdventures: sport, music, sailing, cooking, describing beauty and understanding its origin(vol. I), using electricity, light and computers,understanding the brain and people (vol. III).

Special relativityAdventures: light, magnetism, length contraction, timedilation and E0 = mc2 (vol. II).

Quantum theoryAdventures: death,reproduction, biology, chemistry, evolution,enjoying colours andart, all high-techbusiness, medicine(vol. IV and V).

Quantum theory with gravity Adventures: bouncing neutrons, under- standing tree growth (vol. V).

Final, unified description of motion Adventures: understanding motion, intense joy with thinking, calculating couplings and masses, catching a glimpse of bliss (vol. VI).

G c h, e, k

PHYSICS:Describing motion with the least action principle.

Quantum field theoryAdventures: building accelerators, under-standing quarks, stars, bombs and the basis oflife, matter, radiation(vol. V).

How do everyday, fast and largethings move?

How do small things move?What are things?

Why does motion occur? What are space, time and quantum particles?

General relativityAdventures: the night sky, measu-ring curved space, exploring black holes and the universe, spaceand time (vol. II).

Classical gravityAdventures: climbing, skiing, space travel, the wonders of astronomy andgeology (vol. I).

F I G U R E 1 A complete map of physics: the connections are dened by the speed of light c, thegravitational constant G, the Planck constant h, the Boltzmann constant k and the elementary charge e.

Advice for learners

Learningwidens knowledge, improves intelligence and allows us to discover what kind ofperson we can be. Learning from a book, especially one about nature, should be efficientand enjoyable. The most inefficient and the most tedious learning method is to use amarker to underline text: it is a waste of time, provides false comfort and makes the textunreadable. Nobody marking text is learning efficiently or is enjoying it.

In my experience as a student and teacher, one learning method never failed to trans-form unsuccessful pupils into successful ones: if you read a text for study, summarizeevery section you read, in your own words and images, aloud. If you are unable to doso, read the section again. Repeat this until you can clearly summarize what you read

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

preface 9

in your own words and images, aloud. You can do this alone or with friends, in a roomor while walking. If you do this with everything you read, you will reduce your learningand reading time significantly, enjoy learning from good texts much more and hate badtexts much less. Masters of the method can use it even while listening to a lecture, in alow voice, thus avoiding to ever take notes.

Advice for teachers

A teacher likes pupils and likes to lead them into exploring the field he chose. His or herenthusiasm for the job is the key to job satisfaction. If you are a teacher, before the start ofa lesson, picture, feel and tell yourself how you enjoy the topic of the lesson; then picture,feel and tell yourself how you will lead each of your pupils into enjoying that topic asmuch as you do. Do this exercise consciously, every time. You will minimize trouble inyour class and maximize your teaching success.

This book is not written with exams in mind; it is written to make teachers and stu-dents understand and enjoy physics, the science of motion.

Using this book

Marginal notes refer to bibliographic references, to other pages or to challenge solutions.In the colour edition, such notes and also the pointers to footnotes and to other websitesare typeset in green. In the free pdf edition, all green links are clickable. The pdf editionalso contains all films; they can be watched in Adobe Reader.

Solutions and hints for challenges are given in the appendix. Challenges are classifiedas research level (r), difficult (d), standard student level (s) and easy (e). Challenges forwhich no solution has yet been included in the book are marked (ny).

Links on the internet tend to disappear with time. Most links can be recovered viawww.archive.org, which keeps a copy of old internet pages.

Feedback and support

This text is and will remain free to download from the internet. I would be delighted toreceive an email from you at fb@motionmountain.net, especially on the following issues:

What was unclear and should be improved?Challenge 1 s What story, topic, riddle, picture or film did you miss?

In order to simplify annotations, the pdf file allows adding yellow sticker notes in AdobeReader. Help on the specific points listed on the www.motionmountain.net/help.htmlweb page are particularly welcome. All feedback will be used to improve the next edition.On behalf of all readers, thank you in advance for your input. For a particularly usefulcontribution you will be mentioned if you want in the acknowledgements, receive areward, or both.

Your donation to the charitable, tax-exempt non-profit organisation that produces,translates and publishes this book series is welcome! For details, see the web page www.motionmountain.net/donation.html. The German tax office checks the proper use of

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

10 preface

your donation. If you want, your name will be included in the sponsor list. Thank you inadvance for your help, on behalf of all readers across the world.

The pdf version of this book, with embedded films, is available for free at www.motionmountain.net. The paper edition of this book is available, printed on demand, ei-ther in colour or in black and white. It is delivered by mail to any address of your choiceand can be ordered at www.amazon.com or www.createspace.com. And now, enjoy thereading.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

Contents

15 1 Why should we care about motion?Does motion exist? 16 How should we talk about motion? 18 What arethe types of motion? 20 Perception, permanence and change 24 Doesthe world need states? 26 Galilean physics in six interesting statements 28 Curiosities and fun challenges about motion 29 Summary on motion 32

33 2 From motion measurement to continuityWhat is velocity? 34 What is time? 39 Clocks 43 Why do clocks goclockwise? 47 Does time flow? 47 What is space? 48 Are spaceand time absolute or relative? 52 Size why area exists, but volume does not 53 What is straight? 57 A hollow Earth? 57 Curiosities and fun challenges abouteveryday space and time 58 Summary about everyday space and time 71

72 3 How to describe motion kinematicsThrowing, jumping and shooting 75 Enjoying vectors 77 What is rest? Whatis velocity? 78 Acceleration 80 Objects and point particles 82 Legs andwheels 86 Curiosities and fun challenges about kinematics 88 Summary ofkinematics 90

91 4 From objects and images to conservationMotion and contact 92 What is mass? 93 Momentum and mass 95 Ismotion eternal? Conservation of momentum 99 More conservation en-ergy 102 The cross product, or vector product 105 Rotation and angular mo-mentum 108 Rolling wheels 113 How do we walk? 114 Curiosities and funchallenges about conservation and rotation 115 Summary on conservation 124

125 5 From the rotation of the earth to the relativity of motionHow does the Earth rotate? 133 Does the Earth move? 137 Is velocity absolute?The theory of everyday relativity 143 Is rotation relative? 144 Curiosities andfun challenges about relativity 144 Legs or wheels? Again 150 Summary onGalilean relativity 153

154 6 Motion due to gravitationProperties of gravitation 158 The gravitational potential 163 The shape of theEarth 164 Dynamics how do things move in various dimensions? 166 Gravi-tation in the sky 167 TheMoon 170 Orbits and conic sections 172 Tides 175 Can light fall? 179 What is mass? Again 180 Curiosities and fun chal-lenges about gravitation 181 Summary on gravitation 198

199 7 Classical mechanics and the predictability of motionShould one use force? Power? 199 Forces, surfaces and conservation 202 Friction and motion 202 Friction, sport, machines and predictability 204 Complete states initial conditions 207 Do surprises exist? Is the future deter-mined? 208 Free will 210 Summary on predictability 212 Predictabilityand global descriptions of motion 212

217 8 Measuring change with actionThe principle of least action 221 Lagrangians and motion 224 Why is motionso often bounded? 226 Curiosities and fun challenges about Lagrangians 229 Summary on action 232

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

12 contents

233 9 Motion and symmetryWhy canwe think and talk about the world? 234 Viewpoints 237 Symme-tries and groups 239 Representations 239 Symmetries, motion and Galileanphysics 242 Reproducibility, conservation and Noethers theorem 245 Cu-riosities and fun challenges about symmetry 249 Parity and time invariance 250 Summary on symmetry 251

252 10 Simple motions of extended bodies oscillations and wavesOscillations 252 Resonance 255 Waves: general and harmonic 257 Waterwaves 257 Waves and their motion 262 Why can we talk to each other? Huygens principle 265 Wave equations 267 Why are music and singing voicesso beautiful? 269 Is ultrasound imaging safe for babies? 272 Signals 273 Solitary waves and solitons 275 Curiosities and fun challenges about waves andextended bodies 278 Summary on waves and oscillations 289

290 11 Do extended bodies exist? Limits of continuityMountains and fractals 290 Can a chocolate bar last forever? 290 The caseof Galileo Galilei 292 How high can animals jump? 294 Felling trees 294 Little hard balls 295 The sound of silence 296 How to count what cannotbe seen 296 Experiencing atoms 298 Seeing atoms 299 Curiosities and funchallenges about solids 301 Summary on atoms 307

309 12 Fluids and their motionThe state of a fluid 309 Laminar and turbulent flow 309 Curiosities and funchallenges about fluids 314 What can move in nature? Flows 325 Summaryon fluids 327

328 13 From heat to time-invarianceTemperature 328 Thermal energy 330 Why do balloons take up space? Theend of continuity 333 Brownianmotion 335 Why stones can be neither smoothnor fractal, nor made of little hard balls 338 Entropy 338 Entropy from par-ticles 340 The minimum entropy of nature the quantum of information 342 Is everything made of particles? 343 The second principle of thermody-namics 345 Why cant we remember the future? 346 Flow of entropy 347 Do isolated systems exist? 348 Curiosities and fun challenges about heat andreversibility 348 Summary on heat and time-invariance 356

357 14 Self-organization and chaos the simplicity of complexityAppearance of order 360 Self-organization in sand 361 Self-organizationof spheres 364 Appearance of order 364 The mathematics of order appear-ance 365 Chaos 366 Emergence 367 Curiosities and fun challengesabout self-organization 368 Summary on self-organization and chaos 373

375 15 From the limitations of physics to the limits of motionResearch topics in classical dynamics 375 What is contact? 376 Precision andaccuracy 377 Can all of nature be described in a book? 377 Something iswrong about our description ofmotion 378 Why ismeasurement possible? 379 Is motion unlimited? 379

381 a Notation and conventionsThe Latin alphabet 381 The Greek alphabet 383 The Hebrew alphabet andother scripts 385 Numbers and the Indian digits 385 The symbols used in thetext 386 Calendars 388 People Names 390 Abbreviations and eponyms or

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

contents 13

concepts? 390392 b Units, measurements and constants

SI units 392 The meaning of measurement 395 Curiosities and fun challengesabout units 395 Precision and accuracy of measurements 397 Limits to preci-sion 399 Physical constants 399 Useful numbers 407

408 c Sources of information on motion

414 Challenge hints and solutions

459 Bibliography

491 CreditsAcknowledgements 491 Film credits 492 Image credits 492

497 Name index

509 Subject index

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

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.We learn to use them tomeasure changeand find that nature minimizes it.We discover how to float in free space,why we have legs instead of wheels,why disorder can never be eliminated,and why one of the most difficult open issuesin science is the flow of water through a tube.

Cha p t e r 1

WHY SHOULD WE CARE ABOUTMOTION?

All motion is an illusion. Zeno of Elea*Wham! The 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 fire start and fade again. The gentle wind moving the leaves aroundus helps to restore the calmness of the place. Nearby, the water in a small river followsits complicated way down the valley, reflecting on its surface the ever-changing shapesof the clouds.

Motion is everywhere: friendly and threatening, terrible and beautiful. It is fundamen-tal to our human existence. We need motion for growing, for learning, for thinking andfor enjoying life. We use motion for walking through a forest, for listening to its noisesand for talking about all this. Like all animals, we rely on motion to get food and tosurvive dangers. Like all living beings, we need motion to reproduce, to breathe and todigest. 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. There 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. The fascination of motion has alwaysmade it a favourite object of curiosity. By the fifth century bce in ancient Greece, itsstudy had been given a name:Ref. 1 physics.

Motion is also important to the human condition. What can we know? Where doesthe world come from? Who are we? Where do we come from? What will we do? Whatshould we do?What will the future bring?What is death?Where does life lead? All thesequestions are about motion. The study of motion provides answers that are both deepand surprising.

Motion is mysterious. Though found everywhere in the stars, in the tides,Ref. 2 in oureyelids 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 recentlyan answer has finally been found. This is the story of the way to find it.

Motion is a part of human experience. If we imagine human experience as an island,then destiny, symbolized by the waves of the sea, carried us to its shore. Near the centre of

* Zeno of Elea (c. 450 bce), one of the main exponents of the Eleatic school of philosophy.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

16 1 why should we care about motion?

Physics

MotionMountain

Social Sea

Emotion Bay

Medicine

MathematicsThe humanities

Astronomy

Materials science

Geosciences

Biology

Chemistry

Engineering

Theoryof motion

Quantum field theory

Quantum theory

Mechanics

Electromagnetism

Relativity

Thermodynamics

F I G U R E 2 Experience Island, with Motion Mountain and the trail to be followed.

the island an especially high mountain stands out. From its top we can see over the wholelandscape and get an impression of the relationships between all human experiences, andin particular between the various examples of motion.This is a guide to the top of what Ihave called Motion Mountain (see Figure 2; a less artistic but more exact version is givenin Figure 1). The hike is one of the most beautiful adventures of the human mind. Thefirst 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, 6.5To sharpen themind for the issue ofmotions existence, have a look at Figure 3 or Figure 4and follow the instructions.Ref. 3 In all cases the figures seem to rotate. You can experiencesimilar effects if you walk over cobblestone pavement that is arranged in arched patternsor if you look at the numerous motion illusions collected by Kitaoka Akiyoshi at www.ritsumei.ac.jp/~akitaoka.Ref. 4 How can we make sure that real motion is different from theseor other similarChallenge 2 s illusions?

Many scholars simply argued that motion does not exist at all.Their arguments deeplyinfluenced the investigation of motion over many centuries.Ref. 5 For example, the Greek

* The riddle does not exist. If a question can be put at all, it can also be answered.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

1 why should we care about motion? 17

F I G U R E 3 Illusions of motion: look at the gure on the left and slightly move the page, or look at thewhite dot at the centre of the gure on the right and move your head back and forward.

philosopher Parmenides (born c. 515 bce in Elea, a small town near Naples) arguedthat since nothing comes from nothing, change cannot exist. He underscored the per-manence of nature and thus consistently maintained that all change and thus all motionis an illusion.Ref. 6

Heraclitus (c. 540 to c. 480 bce) held the opposite view. He expressed it in his famousstatement panta rhei or everything flows.* He saw change as the essence ofnature, in contrast to Parmenides. These 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 3 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 first 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 infinity and its opposite, finitude, in the description of motion.In modern quantum theory, a related issue is a subject of research 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. He argued that at a single instant of time, there isno difference between a moving and a resting body. He then deduced that if there is nodifference at a single time, there cannot be a difference 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 differences between motion and rest. Eventually, we will dare to ask whethersingle instants of time do exist at all. Answering this question is essential for reachingthe top of Motion Mountain.

When we explore quantum theory, we will discover that motion is indeed to a cer-tain extent an illusion, as Parmenides claimed. More precisely, we will show that mo-tion is observed only due to the limitations of the human condition. We will find that weexperience motion only because

* Appendix A explains how to read Greek text.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

18 1 why should we care about motion?

F I G U R E 4 Zoom this image to largesize or approach it closely in orderto enjoy its apparent motion( Michael Bach after the discoveryof Kitaoka Akiyoshi).

we have a finite size, we are made of a large but finite number of atoms, we have a finite but moderate temperature, we move much more slowly than the speed of light, we live in three dimensions, we are large compared with a black hole of our same mass, we are large compared with our quantum mechanical wavelength, we are small compared with the universe, we have a limited memory, we are forced by our brain to approximate space and time as continuous entities, and we are forced by our brain to approximate nature as made of different parts.If any one of these conditions were not fulfilled, we would not observe motion; motion,then, would not exist! If that were not enough, note that none of the conditions requireshuman beings; they are equally valid for many animals and machines. Each of these con-ditions can be uncovered most efficiently 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 it

* Charles Baudelaire (b. 1821 Paris, d. 1867 Paris)Beauty: I hatemovement, which changes shapes, and neverdo I weep and never do I laugh.Ref. 8

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

1 why should we care about motion? 19

Thales

Plato

Sosigenes

StraboCtesibius

Archimedes

Konon

Chrysippos

Philoof Byz.

Dositheus

Biton

Asclepiades

Varro

Athenaius

Diodorus Siculus

Virgilius

Horace

Cicero

FrontinusMaria

the JewJosephus

Epictetus

Marinus

Menelaos

Nicomachos Apuleius

Cleomedes

Artemidor

Sextus EmpiricusAthenaios

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

KidinnuNaburimannu

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 5 A time line of scientic and political personalities in antiquity (the last letter of the name isaligned with the year of death).

worthwhile. Be it an eclipse, a beautiful piece of music, or a feat at the Olympic games:the world is full of fascinating examples of motion.*

If you ever find yourself talking about motion, whether to understand it more pre-cisely ormore deeply, you are taking steps upMotionMountain.The examples of Figure 6make the point. An empty bucket hangs vertically. When you fill the bucket with a cer-tain amount of water, it does not hang vertically anymore. (Why?) If you continue addingwater, it starts to hang vertically again. How much water is necessary for this last tran-sition?Challenge 4 s The second illustration in Figure 6 is for the following puzzle. When you pull athread from a reel in the way shown, the reel will move either forwards or backwards,depending on the angle at which you pull. What is the limiting angle between the twopossibilities?

High precision means going into fine details, and being attuned to details actuallyincreases the pleasure of the adventure.** Figure 7 shows an example. The higher we geton Motion Mountain, the further we can see and the more our curiosity is rewarded.The views offered are breathtaking, especially from the very top. The path we will follow one of the many possible routes starts from the side of biology and directly enters theforest that lies at the foot of the mountain.Ref. 10

* For a collection of interesting examples of motion in everyday life, see the excellent book byRef. 9 Walker.** Distrust anybody who wants to talk you out of investigating details. He is trying to deceive you.Challenge 6 s Detailsare important. Be vigilant also during this journey.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

20 1 why should we care about motion?

F I G U R E 6 How much water is required to make a bucket hang vertically? At what angle does thepulled reel (drawn incorrectly) change directionChallenge 5 s of motion? ( Luca Gastaldi).

F I G U R E 7 An example of how precision of observation can lead to the discovery of new effects: thedeformation of a tennis ball during the c. 6 ms of a fast bounce ( International Tennis Federation).

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.

What are the types of motion?

Every movement is born of a desire for change.AntiquityA good place to obtain a general overview on the types of motion is a large library (seeTable 1). The domains in which motion, movements and moves play a role are indeedvaried. Already the earliest researchers in ancient Greece listed in Figure 5 had thesuspicion that all types of motion, as well as many other types of change, are related.Three categories of change are commonly recognized:

1. Transport. The only type of change we call motion in everyday life is material trans-port, such as a person walking, a leaf falling from a tree, or a musical instrumentplaying. Transport is the change of position or orientation of objects, fluids included.To a large extent, the behaviour of people also falls into this category.

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. Thesechanges of colour, brightness, hardness, temperature and other material properties

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

1 why should we care about motion? 21

TA B L E 1 Content of books about motion found in a public library.

Mo t i o n t o p i c s M o t i o n t o p i c s

motion pictures and digital effects motion as therapy for cancer, diabetes, acne anddepression

motion perception Ref. 11 motion sicknessmotion for fitness and wellness motion for meditationmotion control and training in sport andsinging

motion ability as health check

perpetual motion motion in dance, music and other performing artsmotion as proof of various gods Ref. 12 motion of planets, stars and angels Ref. 13economic efficiency of motion the connection between motional and emotional

habitsmotion as help to overcome trauma motion in psychotherapy Ref. 14locomotion of insects, horses, animals androbots

motion of cells and plants

collisions of atoms, cars, stars and galaxies growth of multicellular beings, mountains,sunspots and galaxies

motion of springs, joints, mechanisms, liq-uids and gases

motion of continents, bird flocks, shadows andempty space

commotion and violence motion in martial artsmotions in parliament movements in art, sciences and politicsmovements in watches movements in the stock marketmovement teaching and learning movement development in children Ref. 15musical movements troop movements Ref. 16religious movements bowel movementsmoves in chess cheating moves in casinos Ref. 17connection between gross national product and citizen mobility

are all transformations. Transformations are changes not visibly connectedwith trans-port. To this category, a few ancient thinkers added the emission and absorption oflight. In the twentieth century, these two effects were proven to be special cases oftransformations, as were the newly discovered appearance and disappearance of mat-ter, as observed in the Sun and in radioactivity.Mind change, such as change of mood,of health, of education and of character, is also (mostly) a type of transformation.Ref. 18

3. Growth. This last and especially important category of change,Ref. 19 is observed for an-imals, 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.The difference is one of complexity and of time scale.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

22 1 why should we care about motion?

F I G U R E 8 Anexample oftransport, atMount Etna( Marco Fulle).

At the beginnings of modern science during the Renaissance, only the study of transportwas seen as the topic of physics. Motion was equated to transport.The other two domainswere neglected by physicists. Despite this restriction, the field of enquiry remains large,covering a large part of Experience Island.Page 16 Early scholars differentiated types of trans-port by their origin. Movements such as those of the legs when walking were classifiedas volitional, because they are controlled by ones will, whereas movements of externalobjects, such as the fall of a snowflake, which cannot be influenced by will-power, wereclassified as passive. Young humans, especially young male humans, spend considerabletime in learning elaborate volitional movements. An example is shown in Figure 10.

The complete distinction between passive and volitional motion is made by childrenby the age of six, and this marks a central step in the development of every human to-wards a precise description of the environment.* From this distinction stems the histor-ical but now outdated definition of physics as the science of the motion of non-livingthings.

The 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? The accumulation of observations inthe last 100 years made it clear that volitional movement** indeed has the same physi-

* Failure to pass this stage completely can result in a person having various strange beliefs, such as believingin the ability to influence 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,The 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.** The 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.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

1 why should we care about motion? 23

F I G U R E 9 Transport, growthand transformation ( PhilipPlisson).

F I G U R E 10 One of the most difcultvolitional movements known, performedby Alexander Tsukanov, the rst man ableto do this: jumping from one ultimatewheel to another ( Moscow State Circus).

cal properties as passive motion in non-living systems. (Of course, from the emotionalviewpoint, the differences are important; for example, grace can only be ascribed to voli-tional movements.Ref. 20 ) A distinction between the two types of motion is thus unnecessary.But 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. Thisis most evident when touching the topics of determinism, causality, probability, infin-ity, time, love and death, to name but a few of the themes we will encounter during ouradventure.

In the nineteenth and twentieth centuries other classically held beliefs about mo-tion fell by the wayside. Extensive observations showed that all transformations andall growth phenomena, including behaviour change and evolution, are also examples oftransport. In other words, over 2 000 years of studies have shown that the ancient classi-

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

24 1 why should we care about motion?

fication of observations was useless: all change is transport.In the middle of the twentieth century the study of motion culminated in the exper-

imental confirmation of an even more specific idea, previously articulated in ancientGreece:

Every type of change is due to the motion of particles.It takes time and work to reach this conclusion, which appears only when we relentlesslypursue higher and higher precision in the description of nature. The first five parts ofthis adventure retrace the path to this result. (Do you agree with it?)Challenge 7 s

The last decade of the twentieth century again completely changed the descriptionof motion: the particle idea turns out to be wrong. This new result, reached through acombination of careful observation and deduction, will be explored in the last part ofour adventure. But we still have some way to go before we reach that part, just below thesummit of our journey.

In summary, history has shown that classifying the various types of motion is notproductive. Only by trying to achieve maximum precision can we hope to arrive at thefundamental properties of motion. Precision, not classification, is the path to follow. AsErnest Rutherford said jokingly: All science is either physics or stamp collecting.

In order to achieve precision in our description of motion, we need to select specificexamples of motion and study them fully in detail. It is intuitively obvious that the mostprecise description is achievable for the simplest possible examples. In everyday life, thisis the case for the motion of any non-living, solid and rigid body in our environment,such as a stone thrown through the air. Indeed, like all humans, we learned to throw ob-jects long before we learned to walk.Ref. 21 Throwing is one of the first physical experimentswe performed by ourselves. The importance of throwing is also seen from the terms de-rived from it: in Latin, words like subject or thrown below, object or thrown in front,and interjection or thrown in between; in Greek, the act of throwing led to terms likesymbol or thrown together, problem or thrown forward, emblem or thrown into, and last but not least devil or thrown through. And indeed, during our early childhood,by throwing stones, toys and other objects until our parents feared for every piece of thehousehold, we explored the perception and the properties of motion. We do the samehere.

Die Welt ist unabhngig von meinemWillen.* Ludwig Wittgenstein, Tractatus, 6.373Perception, permanence and change

Only wimps study only the general case; realscientists pursue examples. Beresford ParlettHuman beings enjoy perceiving. Perception starts before birth, and we continue enjoyingit for as long as we can.That 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 avoid

* The world is independent of my will.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

1 why should we care about motion? 25

F I G U R E 11 How do we distinguish a deerfrom its environment? ( Tony Rodgers).

perceiving. Perception is first of all the ability to distinguish. We use the basic mental actof distinguishing in almost every instant of life; for example, during childhood we firstlearned to distinguish familiar from unfamiliar observations. This 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. They 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 after many beers (not a challenge). The 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. Thenerve cells that detect motion are part of the most ancient part of our brain, shared withbirds and reptiles: the brain stem.Ref. 22 Then the cortex, or modern brain, takes over to ana-lyse the type of motion and to identify its origin. Watching the motion across our fieldof vision, we observe two invariant entities: the fixed landscape and the moving animal.After we recognize the animal as a deer, we relax again.

How did we distinguish, in case of Figure 11, between landscape and deer? Perceptioninvolves several processes in the eye and in the brain. An essential part for these pro-cesses is motion, as is best deduced from the flip film shown in the lower left cornersof these pages.Ref. 23 Each image shows only a rectangle filled with a mathematically randompattern. But when the pages are scanned in rapid succession, you discern a shape asquare moving against a fixed background. At any given instant, the square cannotbe distinguished from the background; there is no visible object at any given instant of

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

26 1 why should we care about motion?

time. Nevertheless it is easy to perceive its motion.* Perception experiments such as thisone have been performed in many variations. For example, it was found that detectinga moving square against a random background is nothing special to humans; flies havethe same ability, as do, in fact, all animals that have eyes.

The flip film in the lower left 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 define both the object and the environment, and to distinguishthem from each other. In fact, the concept of space is among others an abstractionof the idea of background. The background is extended; the moving entity is localized.Does this seem boring? It is not; just wait a second.

We call the set of localized aspects that remain invariant or permanent during mo-tion, such as size, shape, colour etc., taken together, a (physical) object or a (physical)body. We will tighten the definition shortly, since otherwise images would be objects aswell. In other words, right from the start we experience motion as a relative process; it isperceived in relation and in opposition to the environment. The concept of an object istherefore also a relative concept. But the basic conceptual distinction between localized,isolable objects and the extended environment is not trivial or unimportant. First, it has

Challenge 8 s the appearance of a circular definition. (Do you agree?)This issue will keep us busy lateron.Page 378 Second, we are so used to our ability of isolating local systems from the environmentthat we take it for granted. However, as we will see in the last part of our walk, this dis-tinction turns out to be logically and experimentallyVol. VI, page 79 impossible!*** Our walk will leadus to discover the reason for this impossibility and its important consequences. Finally,apart from moving entities and the permanent background, we need a third concept, asshown in Table 2.

Wisdom is one thing: to understand the thoughtwhich steers all things through all things. Heraclitus of EphesusRef. 24Does the world need states?

Das Feste, das Bestehende und der Gegenstandsind Eins. Der Gegenstand ist das Feste,Bestehende; die Konfiguration ist dasWechselnde, Unbestndige.**** Ludwig Wittgenstein, Tractatus, 2.027 2.0271* The 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 fixed image. Details ofthis and similar topics for the other senses are the domain of perception research.Ref. 11**The 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 associatedwww.cogsci.uci.edu/~ddhoff website.*** Contrary to what is often read in popular literature, the distinction is possible in quantum theory. Itbecomes impossible only when quantum theory is unified with general relativity.**** The fixed, the existent and the object are one. The object is the fixed, the existent; the configuration isthe changing, the variable.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

1 why should we care about motion? 27

TA B L E 2 Family tree of the basic physical concepts.

motionthe basic type of change

parts relations backgroundpermanent variable measurablebounded produce boundaries unbounded

have shapes produce shapes extended

objects images states interactions phase space space-timeimpenetrable penetrable global local composed simple

The corresponding aspects:

mass intensity instant source dimension curvaturesize colour position domain distance topologycharge appearance momentum strength volume distancespin disappearance energy direction subspaces areaetc. etc. etc. etc. etc. etc.

world nature universe cosmosthe collection of all parts, relations and backgrounds

What distinguishes the various patterns in the lower left corners of this text? In everydaylife we would say: the situation or configuration of the involved entities. The situationsomehow describes all those aspects that can differ 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.

The situations in the lower left corners differ first 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 differ in their position, or their velocity, or their orientation.The state pinpointsthe individuality of a physical system,* and allows us to distinguish it from exact copies ofitself. Therefore, 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 on

* A physical system is a localized entity of investigation. In the classification 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 physicalChallenge 9 s systems?

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

28 1 why should we care about motion?

the observer.These 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. The observation of motion requires the distinction ofpermanent, intrinsic properties describing the objects that move and changing states describing the way the objects move. Without this distinction, there is no motion.

The various aspects of objects and of their states are called observables. All these rough,preliminary definitions will be refined step by step in the following. Using the terms justintroduced, we can say thatmotion is the change of state 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. The first approach, called Galilean physics,consists in specifying our everyday environment as precisely as possible.

Galilean physics in six interesting statements

The study of everyday motion, Galilean physics, is already worthwhile in itself: we willuncover many results that are in contrast with our usual experience. For example, if werecall our own past, we all have experienced how important, delightful or unwelcomesurprises can be. Nevertheless, the study of everyday motion shows that there are no sur-prises in nature. Motion, and thus the world, is predictable or deterministic.

Themain surprise is thus that there are no surprises in nature. In fact, we will uncoversix aspects of the predictability of everyday motion:

1. We know that eyes, cameras and measurement apparatus have a finite resolution. Allhave a smallest distance they can observe. We know that clocks have a smallest timethey can measure. Despite these limitations, in everyday life all movements, theirstates, as well as space and time themselves, are continuous.

2. We all observe that people, music and many other things in motion stop moving aftera while. The study of motion yields the opposite result: motion never stops. In fact,three aspects of motion do not change, but are conserved: momentum, angular mo-mentum and energy (together with mass) are conserved, separately, in all examplesof motion. No exception to these three types of conservation has ever been observed.In addition, we will discover that conservation implies that motion and its propertiesare the same at all places and all times: motion is universal.

3. We all know that motion differs from rest. Despite this experience, careful studyshows that there is no intrinsic difference between the two. Motion and rest dependon the observer. Motion is relative. This is the first step towards understanding thetheory of relativity.

4. We all observe thatmany processes happen only in one direction. For example, spilledmilk never returns into the container by itself. Despite such observations, the study

* The 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 shift the distinctionbetween the object and its state; the distinction itself does not disappear at least not for quite a while.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

1 why should we care about motion? 29

F I G U R E 12 A block and tackle and a differential pulley (left) and a farmer (right).

of motion will show us that all everyday motion is reversible. Physicists call this theinvariance of everyday motion under motion reversal (or, sloppily, under time rever-sal).

5. Most of us find scissors difficult to handle with the left hand, have difficulties to writewith the other hand, and have grown with a heart on the left side. Despite such obser-vations, our exploration will show that everyday motion ismirror-invariant or parity-invariant. Mirror processes are always possible in everyday life.

6. We all are astonished by the many observations that the world offers: colours, shapes,sounds, growth, disasters, happiness, friendship, love.The variation, beauty and com-plexity of nature is amazing. We will confirm that all observations are due to motion.And despite the appearance of complexity, all motion is simple. Our study will showthat all observations can be summarized in a simple way: Nature is lazy. All motionhappens in a way that minimizes change. Change can be measured, using a quantitycalled action, and nature keeps it to a minimum. Situations or states, as physicistslike to say evolve by minimizing change. Nature is lazy.

These six aspects are essential in understanding motion in sport, in music, in animals, inmachines and among the stars. This first volume of our adventure will be an explorationof such movements. In particular, we will confirm the mentioned six key properties ofeverydaymotion: continuity, conservation, reversibility,mirror-invariance, relativity andminimization.

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;

* Sections entitled curiosities are collections of topics and problems that allow one to check and to expandthe usage of concepts already introduced.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

30 1 why should we care about motion?

poisons include caffeine, nicotine, and curare. Poisons such as these are at the basis ofmost medicines. Therefore, most medicines exist essentially because plants have no legs.A man climbs a mountain from 9 a.m. to 1 p.m. He sleeps on the top and comes downthe next day, taking again from 9 a.m. to 1 p.m. for the descent. Is there a place on thepath that he passes at the same time on the two days?Challenge 11 s 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?Challenge 14 s How would you show it?Does a body moving forever in a straight line show that nature or space is infinite?Challenge 15 s What is the length of rope one has to pull in order to lift a mass by a height h with a blockand tackle with four wheels, as shown on the left of Figure 12?Challenge 16 s Does the farmer on theright of the figure do something sensible? Can the universe move?Challenge 17 s To talk about precision with precision, we need to measure precision itself. How wouldyou do that?Challenge 18 s Would we observe motion if we had no memory?Challenge 19 s What is the lowest speed you have observed?Challenge 20 s Is there a lowest speed in nature?According to legend, Sissa ben Dahir, the Indian inventor of the game of chaturanga orchess, demanded from King Shirham the following reward for his invention: he wantedone grain of wheat for the first square, two for the second, four for the third, eight forthe fourth, and so on. How much time would all the wheat fields of the world take toproduce the necessary grains?Challenge 21 s

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

1 why should we care about motion? 31

ball

perfectly flat table

F I G U R E 13 What happens?

vblock

F I G U R E 14 What is the speed of the rollers? Areother roller shapes possible?

When a burning candle is moved, the flame lags behind the candle. How does the flamebehave if the candle is inside a glass, still burning, and the glass is accelerated?Challenge 22 s A good way to make money is to build motion detectors. A motion detector is a smallbox with a few wires. The box produces an electrical signal whenever the box moves.What types of motion detectors can you imagine? How cheap can you make such a box?How precise?Challenge 23 d A perfectly frictionless and spherical ball lies near the edge of a perfectly flat and hori-zontal table, as shown in Figure 13. What happens? In what time scale?Challenge 24 d You step into a closed box without windows. The box is moved by outside forces un-known to you. Can you determine how you are moving from inside the box?Challenge 25 s When a block is rolled over the floor over a set of cylinders, as shown in Figure 14, 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 methodRef. 18 to changethe situation. It is worth trying it, as it will make you enjoy this book much more.Challenge 27 s Life isshort; as much of it as possible, like reading this text, should be a pleasure.1. Close your eyes and recall an experience that was absolutely marvellous, a situation

when you felt excited, curious and positive.2. Open your eyes for a second or two and look at page 245 or any other page that

contains many formulae.3. Then 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.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

32 1 why should we care about motion?

Then leave the memory, look around yourself to get back into the here and now, and testyourself. Look again at page 245. How do you feel about formulae now?In the sixteenth century, Niccol Tartaglia* proposed the following problem. Threeyoung couples want to cross a river. Only a small boat that can carry two people is avail-able. The men are extremely jealous, and would never leave their brides with anotherman. How many journeys across the river are necessary?Challenge 28 s Cylinders can be used to roll a flat object over the floor, as shown in Figure 14. The cylin-ders keep the object plane always at the same distance from the floor.What cross-sectionsother than circular, so-called curves of constant width, can a cylinder have to realize thesame feat? How many examples can you find?Challenge 29 s Are objects different than cylinders possi-ble? Hanging pictures on the walls is not easy. First puzzle: what is the best way to hang a pic-ture on one nail? The method must allow you to move the picture in horizontal positionafter the nail is in the wall, in the case that the weight is not equally distributed.Challenge 30 s Secondpuzzle: Can you hang a picture on a wall this time with a long rope over two nails insuch a way that pulling either nail makes the picture fall? And with three nails? And nnails?Challenge 31 s

Summary on motion

Motion is the most fundamental observation in nature. Everyday motion is predictableand deterministic. Predictability is reflected in six aspects of motion: continuity, con-servation, reversibility, mirror-invariance, relativity and minimization. Some of these as-pects are valid for all motion, and some are valid only for everyday motion. Which ones,and why?Challenge 32 d We explore this now.

* Niccol Fontana Tartaglia (14991557), important Renaissance mathematician.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

Cha p t e r 2

FROM MOTION MEASUREMENT TOCONTINUITY

Physic ist wahrlich das eigentliche Studium desMenschen.* Georg Christoph LichtenbergThe simplest description of motion is the one we all, like cats or monkeys, usehroughout our everyday life: only one thing can be at a given spot at a given time.his general description can be separated into three assumptions: matter is impen-etrable and moves, time is made of instants, and space is made of points. Without thesethree assumptions (do you agree with them?)Challenge 33 s it is not possible to define velocity in every-day life. This description of nature is called Galilean physics, or sometimes Newtonianphysics.

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 theexperimental physics of Renaissance Italy.**

The English alchemist, occultist, theologian, physicist and politician Isaac Newton(16431727) was one of the first to pursue with vigour the idea that different types of mo-tion have the same properties, and hemade important steps in constructing the conceptsnecessary to demonstrate this idea.***

The explorations by Galileo and his predecessors provided the first clear statementson the properties of speed, space and time.

* Physics truly is the proper study of man. Georg Christoph Lichtenberg (b. 1742 Ober-Ramstadt,d. 1799 Gttingen) was an important physicist and essayist.** The best and most informative book on the life of Galileo and his times is by Pietro Redondi (see thesection on page 292). Galileo was 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 after Galileo died. Newtons other hobby, asmaster of theMint, 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 Clifford Truesdell.Ref. 26

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

34 2 from motion measurement to continuity

F I G U R E 15 Galileo Galilei (15641642).

F I G U R E 16 Some speed measurement devices: an anemometer, a tachymeter for inline skates, a sportradar gun and a PitotPrandtl tube in an aeroplane ( Fachhochschule Koblenz, Silva, Tracer, Wikimedia).

What is velocity?

There is nothing else like it. Jochen Rindt*Velocity fascinates. To physicists, not only car races are interesting, but anymoving entityis. Therefore they first measure as many examples as possible. A selection of measuredspeed values is given in Table 3. The units and prefixes used are explained in detail inAppendix B.Page 392 Some speed measurement devices are shown in Figure 16.

Everyday life teaches us a lot about motion: objects can overtake each other, and theycanmove in different directions.We also observe that velocities can be added or changedsmoothly.The precise list of these properties, as given in Table 4, is summarized bymath-ematicians in a special term; they say that velocities form a Euclidean vector space.**Moredetails about this strange term will be given shortly.Page 77 For now we just note that in describ-ing nature, mathematical concepts offer the most accurate vehicle.

When velocity is assumed to be an Euclidean vector, it is called Galilean velocity. Ve-locity is a profound concept. For example, velocity does not need space and time mea-surements to be defined. Are you able to find a means of measuring velocities without

* Jochen Rindt (19421970), famous Austrian Formula One racing car driver, speaking about speed.** It is named after 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. The text presents the whole knowledge on geometry of that time. For thefirst 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. The book, still in print today, hasbeen the reference geometry text for over 2000 years. On the web, it can be found at aleph0.clarku.edu/~djoyce/java/elements/elements.html.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

2 from motion measurement to continuity 35

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 find something slower? Challenge 34 sStalagmite growth 0.3 pm/sLichen growth down to 7 pm/scm Typical motion of continents 10mm/a = 0.3 nm/sHuman growth during childhood, hair growth 4 nm/sTree growth up to 30 nm/sElectron drift in metal wire 1 m/sSperm motion 60 to 160 m/sSpeed of light at Suns centreRef. 27 1mm/sKetchup motion 1mm/sSlowest speed of light measured in matter on Earth Ref. 28 0.3m/sSpeed of snowflakes 0.5m/s to 1.5m/sSignal speed in human nerve cells Ref. 29 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 fish, sailfish (Istiophorus platypterus) 22m/s2006 Speed sailing record over 500m (by windsurfer Finian Maynard) 25.1m/s2008 Speed sailing record over 500m (by kitesurfer Alex Caizergues) 26.0m/s2009 Speed sailing record over 500m (by trimaran Hydroptre) 26.4m/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 smash 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/sSpeed of a rifle bullet 1 km/sSpeed of crack propagation in breaking silicon 5 km/sHighest macroscopic speed achieved by man the Voyager satellite 14 km/sSpeed of Earth through universe 370 km/sAverage speed (and peak speed) of lightning tip 600 km/s (50Mm/s)Highest macroscopic speed measured in our galaxy Ref. 30 0.97 108m/sSpeed of electrons inside a colour TV 1 108m/sSpeed of radio messages in space 299 792 458m/sHighest ever measured group velocity of light 10 108m/sSpeed of light spot from a light tower when passing over the Moon 2 109m/sHighest proper velocity ever achieved for electrons by man 7 1013m/sHighest possible velocity for a light spot or shadow no limit

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

36 2 from motion measurement to continuity

TA B L E 4 Properties of everyday or Galilean velocity.

Ve l o c i t i e sc a n

P h y s i c a lp r o p e r t y

M at h e m at i c a ln a m e

D e f i n i t i o n

Be distinguished distinguishability element of set Vol. III, page 242Change gradually continuum real vector space Page 77, Vol. V,

page 349

Point somewhere direction vector space, dimensionality Page 77Be compared measurability metricity Vol. V, page 340Be added additivity vector space Page 77Have defined angles direction Euclidean vector space Page 77Exceed any limit infinity unboundedness Vol. III, page 243

measuring space and time?Challenge 35 d If so, you probably want to skip to the next volume, jump-ing 2000 years of enquiries. If you cannot do so, consider this: whenever we measure aquantity we assume that everybody is able to do so, and that everybody will get the sameresult. In other words, we definemeasurement as a comparison with a standard. We thusimplicitly assume that such a standard exists, i.e., that an example of a perfect velocitycan be found. Historically, the study of motion did not investigate this question first, be-cause for many centuries nobody could find such a standard velocity. You are thus ingood company.

Some researchers have specialized in the study of the lowest velocities found in nature:they are called geologists.Ref. 31 Do not miss the opportunity to walk across a landscape whilelistening to one of them.

How is velocitymeasured in everyday life? Animals and people estimate their velocityin two ways: by estimating the frequency of their own movements, such as their steps, orby using their eyes, ears, sense of touch or sense of vibration to deduce how their ownposition changes with respect to the environment. But several animals have additionalcapabilities: certain snakes can determine speeds with their infrared-sensing organs, oth-ers with their magnetic field sensing organs. Still other animals emit sounds that createechoes in order to measure speeds to high precision.The same range of solutions is usedby technical devices. Table 5 gives an overview.

Velocity is not always an easy subject. Physicists like to say, provokingly, that what can-not be measured does not exist. Can youmeasure your own velocity in empty interstellarspace?Challenge 36 s

Velocity is of interest to both engineers and evolution. In general, self-propelled sys-tems are faster the larger they are. As an example, Figure 17 shows how this applies tothe cruise speed of flying things. In general, cruise speed scales with the sixth root ofthe weight, as shown by the trend line drawn in the graph. (Can you find out why?)Challenge 37 d Bythe way, similar allometric scaling relations hold for many other properties of movingsystems, as we will see later on.

Velocity is a profound subject for an additional reason: we will discover that all sevenproperties of Table 4 are only approximate; none is actually correct. Improved experi-ments will uncover exceptions for every property of Galilean velocity. The failure of thelast three properties of Table 4 will lead us to special and general relativity, the failure of

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

2 from motion measurement to continuity 37

Boeing 747DC10Concorde

Boeing 727

wing load W/A [N/m2]w

eigh

t W [N

]

Boeing 737

Pteranodon

cruise speed at sea level v [m/s] 1 2 3 5 7 10 20 30 50 70 100 200

F-14

F-16MIG 23

Learjet 31

Beechcraft Baron

Skysurferhuman-powered plane

whooper swan (Cygnus cygnus)

hummingbird (Trochilidae)

common wasp (Vespa vulgaris)honey bee (Apis mellifera)

fruit fly (Drosophila melanogaster)

canary (Serinus canaria)

Piper Warrior

Fokker F-28Fokker F-27

Beechcraft King Air

Beechcraft Bonanza

1041031021011

106

105

104

103

102

10-1

10-210-2

10-3

10-4

10-5

10

1

UltralightQuicksilver B

Schleicher ASW33BSchleicher ASK23

wandering albatross (Diomedea exulans)

pheasant (Phasianus colchicus)wild duck (Anas platyrhynchos)

damsel fly(Coenagrionidae)

mosquito (Culicidae)gnat (Culicidae)

midge (Chironomidae)house fly (Musca domestica)

graylag goose (Anser anser)

starling (Sturnus vulgaris)blackbird (Turdus merula)

crane fly (Tipulidae)

ant lion (Myrmeleo formicarius)

small white (P. rapae)

large white (P. brassicae)

blowfly (Calliphora vicina)

green dragonfly (Anax junius)

yellow-striped dragonfly(S. flaveolum)

eyed hawk-moth (S. ocellata)swallowtail (P. machaon)

garden bumble bee (Bombus hortorum)

scorpionfly (Panorpidae)

june bug (Amphimallon solstitialis)small stag beetle (Dorcus parallelopipedus)

cockchafer (Melolontha melolontha)sawyer beetle (Prionus coriarius)

stag betle (Lucanus cervus)blue underwing (Catocala fraxini)

privet hawkmoth (Sphinx ligustri) goldcrest (Regulus Regulus)

winter wren (Troglodytes troglodytes)great tit (Parus major)house martin (Delichon urbica)

European Robin (Erithacus rubecula)barn swallow (Hirundo rustica)

sky lark (Alauda arvensis) common swift (Apus Apus)

house sparrow (Passer domesticus)ortolan bunting (Emberiza hortulana)

moorhen (Gallinula chloropus)

coot (Fulica atra)peregrine falcon (Falco peregrinus)

cormorant (Phalacrocorax carbo)

common tern (Sterna hirundo)black headed gull (Larus ridibundus)

barn owl (Tyto alba) carrion craw (Corvus corone)

herring gull (Larus argentatus)

griffon vulture (Gyps fulvus) white-tailed eagle (Haliaeetus albicilla)

white stork (Ciconia ciconia)black-backed gull (Larus marinus)

Airbus 380

F I G U R E 17 How wing load and sea-level cruise speed scales with weight in ying objects, comparedwith the general trend line (after a graph Henk Tennekes).

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

38 2 from motion measurement to continuity

TA B L E 5 Speed measurement devices in biological and engineered systems.

Me a s u r e m e n t D e v i c e R a n g e

Own running speed in insects,mammals and humans

leg beat frequency measuredwith internal clock

0 to 33m/sOwn car speed tachymeter attached to

wheels0 to 150m/s

Predators and hunters measuring preyspeed

vision system 0 to 30m/sPolice measuring car speed radar or laser gun 0 to 90m/sBat measuring own and prey speed atnight

doppler sonar 0 to 20m/sSliding door measuring speed ofapproaching people

doppler radar 0 to 3m/sOwn swimming speed in fish andhumans

friction and deformation ofskin

0 to 30m/sOwn swimming speed in dolphins andships

sonar to sea floor 0 to 20m/sDiving speed in fish, animals, diversand submarines

pressure change 0 to 5m/sWater predators and fishing boatsmeasuring prey speed

sonar 0 to 20m/sOwn speed relative to Earth in insects often none (grasshoppers) n.a.Own speed relative to Earth in birds visual system 0 to 60m/sOwn speed relative to Earth inaeroplanes or rockets

radio goniometry, radar 0 to 8000m/sOwn speed relative to air in insectsand birds

filiform hair deflection,feather deflection

0 to 60m/sOwn speed relative to air in aeroplanes PitotPrandtl tube 0 to 340m/sWind speed measurement inmeteorological stations

thermal, rotating orultrasound anemometers

0 to 80m/sSwallows measuring prey speed visual system 0 to 20m/sBats measuring prey speed sonar 0 to 20m/sMacroscopic motion on Earth Global Positioning System,

Galileo, Glonass0 to 100m/s

Pilots measuring target speed radar 0 to 1000m/sMotion of stars optical Doppler effect 0 to 1000 km/sMotion of star jets optical Doppler effect 0 to 200Mm/s

the middle two to quantum theory and the failure of the first two properties to the uni-fied description of nature. But for now, well stick with Galilean velocity, and continuewith another Galilean concept derived from it: time.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

2 from motion measurement to continuity 39

F I G U R E 18 A typical path followed by a stone thrown through the air a parabola with photographs(blurred and stroboscopic) of a table tennis ball rebounding on a table (centre) and a stroboscopicphotograph of a water droplet rebounding on a strongly hydrophobic surface (right, AndrewDavidhazy, Max Groenendijk).

Without the concepts place, void and time,change cannot be. [...] It is therefore clear [...]that their investigation has to be carried out, bystudying each of them separately. Aristotle* Physics, Book III, part 1.What is time?

Time is an accident of motion. Theophrastus**Time does not exist in itself, but only throughthe perceived objects, from which the conceptsof past, of present and of future ensue. Lucretius,*** De rerum natura, lib. 1, v. 460 ss.In their first years of life, children spend a lot of time throwing objects around.The term

object is a Latin word meaning that which has been thrown in front. Developmentalpsychology has shown experimentally that from this very experienceRef. 21 children extractthe concepts of time and space. Adult physicists do the same when studying motion atuniversity.

When we throw a stone through the air, we can define a sequence of observations.Figure 18 illustrates how. Our memory and our senses give us this ability. The sense of

* Aristotle (b. 384/3 Stageira, d. 322 bce Euboea), important Greek philosopher and scientist, founder ofthe Peripatetic school located at the Lyceum, a gymnasium dedicated to Apollo Lyceus.**Theophrastus of Eresos (c. 371 c. 287) was a revered Lesbian philosopher, successor of Aristoteles at theLyceum.*** Titus Lucretius Carus (c. 95 to c. 55 bce), Roman scholar and poet.

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

40 2 from motion measurement to continuity

TA B L E 6 Selected time measurements.

O b s e rvat i o n T i m e

Shortest measurable time 1044 sShortest time ever measured 10 ysTime for light to cross a typical atom 0.1 to 10 asShortest laser light pulse produced so far 200 asPeriod of caesium ground state hyperfine transition 108.782 775 707 78 psBeat of wings of fruit fly 1msPeriod of pulsar (rotating neutron star) PSR 1913+16 0.059 029 995 271(2) sHuman instant 20msShortest lifetime of living being 0.3 dAverage length of day 400 million years ago 79 200 sAverage length of day today 86 400.002(1) sFrom birth to your 1000 million seconds anniversary 31.7 aAge of oldest living tree 4600 aUse of human language 0.2MaAge of Himalayas 35 to 55MaAge of oldest rocks, found in Isua Belt, Greenlandand in Porpoise Cove, Hudson Bay

3.8Ga

Age of Earth 4.6GaAge of oldest stars 13.7GaAge of most protons in your body 13.7GaLifetime of tantalum nucleus 180mTa 1015 aLifetime of bismuth 209Bi nucleus 1.9(2) 1019 ahearing registers the various sounds during the rise, the fall and the landing of the stone.Our eyes track the location of the stone from one point to the next. All observations havetheir place in a sequence, with some observations preceding them, some observationssimultaneous to them, and still others succeeding them. We say that observations areperceived to happen at various instants and we call the sequence of all instants time.

An observation that is considered the smallest part of a sequence, i.e., not itself asequence, is called an event. Events are central to the definition of time; in particular,starting or stopping a stopwatch are events. (But doChallenge 38 s events really exist? Keep this questionin the back of your head as we move on.)

Sequential phenomena have an additional property known as stretch, extension orduration. Some measured values are given in Table 6.* Duration expresses the idea thatsequences take time. We say that a sequence takes time to express that other sequencescan take place in parallel with it.

How exactly is the concept of time, including sequence and duration, deduced fromobservations? Many people have looked into this question: astronomers, physicists,watchmakers, psychologists and philosophers. All find:

* A year is abbreviated a (Latin annus).

Motion

Mountain

The

Adventure

ofPhysicscopyright

Christoph

SchillerJune

1990February2014

freepdfle

availableat

ww

w.m

otionmountain.net

2 from motion measurement to continuity 41

Time is deduced by comparing motions.This is even the case for children and animals. Beginning at a very young age, theydevelop the concept of time from the comparison of motions in their surroundings.Ref. 21Grown-ups take as a standard the motion of the Sun and call the resulting type of timelocal time. From the Moon they deduce a lunar calendar. If they take a particular villageclock on a European island they call it the universal time coordinate (UTC), once knownas Greenwich mean time.*Astronomers use the movements of the stars and call the re-sult ephemeris time (or one of its successors). An observer who uses his personal watchcalls the reading his proper time; it is often used in the theory of relativity.

Not every movement is a good standard for time. In the year 2000, an Earth rotationdidPage 395 not take 86 400 seconds any more, as it did in the year 1900, but 86 400.002 seconds.Can you deduce in which year your birthday will have shifted by a whole day from thetime predicted with 86 400 seconds?Challenge 40 s

All methods for the definition of time are thus based on comparisons of motions.In order to make the concept as precise and as useful as possible, a standard referencemotion is chosen, and with it a standard sequence and a standard duration is defined.The device that performs this task is called a clock. We can thus answer the question ofthe section title:

Time is what we read from a clock.Note that all definitions of time used in the various branches of physics are equivalentto this one; no deeper or more fundamental definition is possible.** Note that the wordmoment is indeed derived from the word movement. Language follows physics in thiscase. Astonishingly, the definition of time just given is final; it will never be changed,not even at the top of Motion Mountain. This is surprising at first sight, because manybooks have beenwritten on the nature of time. Instead, they should investigate the natureof motion! But this is the aim of our walk anyhow. We are thus set to discover all thesecrets of time as a side result of