Motion mountain PDF
Preview Motion mountain
ChristophSchiller Motion Mountain Hikingbeyondspaceandtime alongtheconceptsofmodernphysics availableat www.motionmountain.org Nunceditiosecundaemendata. ProprietasscriptorisChristophoriSchiller secundoannoOlympiadisvicesimaesextae tertioqueannoOlympiadisvicesimaeseptimae. Omniaproprietatisjurareservanturetvindicantur. Imitatioprohibitasineauctorispermissione. Secondrevisededition Copyright(cid:13)c 1997,1998,1999,2000,2001,2002byChristophSchiller, fromthesecondyearofthe26tholympiad tothethirdyearofthe27tholympiad. Allrightsreserved.Commercialreproductionor distribution,inwholeorinpart,isnotallowed withoutthewrittenconsentofthecopyrightowner. Picturecreditsarelistenonpage869. [email protected]. ToC. tw~| (cid:137)mo› da›moni DieMenschensta¨rken,dieSachenkla¨ren. CONTENT OVERVIEW 1. Anappetizer 20 FIRST PART: CLASSICAL PHYSICS HOWDO THINGS AND IMAGESMOVE? CHAPTER II CLASSICAL MOTION 25 2. Whycareaboutmotion? 25 3. Galileanphysics–motionineverydaylife 37 4. Globaldescriptionsofclassicalmotion–thesimplicityofcomplexity 113 5. LimitsofGalileanphysics–whatiswrongwithschoolphysics 164 6. Specialrelativity–restatanyspeed 168 CHAPTER III GRAVITATION ANDRELATIVITY 233 7. Thenewideasonspace,time,andgravity 233 8. Motioningeneralrelativity–bentlightandwobblingvacuum 250 9. Whycanweseethestars?–Motionintheuniverse 281 10. Doesspacedifferfromtime? 309 11. Blackholes–fallingforever 314 12. Generalrelativityintenpoints–asummaryforthelayman 325 CHAPTER IV CLASSICAL ELECTRODYNAMICS 339 13. Liquidelectricity,andinvisiblefields 339 14. Whatislight? 362 15. Lightning,levitation,andotherfunchallenges 379 CHAPTER V CLASSICAL PHYSICS IN ANUTSHELL 409 INTERMEZZO THE BRAIN,LANGUAGE, ANDTHE HUMANCONDITION 414 SECOND PART : QUANTUMTHEORY WHAT IS MATTER? WHAT ARE INTERACTIONS? CHAPTER VI QUANTAOF LIGHT ANDMATTER 480 16. Anappetizer–quantumtheoryforlawyers 480 17. Light–thestrangeconsequencesofthequantumofaction 491 18. Motionofmatter–theendofclassicalphysics 506 19. Interactionsoflightandmatter–simpleQED 510 CHAPTER VII PERMUTATION OF PARTICLES 519 20. Areparticleslikecondoms? 519 21. Rotationsandstatistics–visualizingspin 527 4 Amountainhikealongtheconceptsofmodernphysics 5 CHAPTER VIII DETAILS ONQUANTUMTHEORY ANDELECTROMAGNETISM 538 22. Superpositionsandprobabilities–quantumtheorywithoutideology 538 23. Applicationsofquantummechanics–livingbeings,pleasure,andmore 558 24. Quantumelectrodynamics–theoriginofvirtualreality 577 25. Quantummechanicswithgravitation–firstapproaches 590 CHAPTER IX INSIDE THE NUCLEUS 610 26. Thestructureofthenucleus–thedensestclouds 610 27. Thestrongnuclearinteraction 612 28. Theweaknuclearinteraction 618 29. Thestandardmodelofelementaryparticlephysics–asseenontv 626 30. Grandunification–adream 627 CHAPTER X ADVANCEDQUANTUMTHEORY 631 CHAPTER XI QUANTUMPHYSICS IN ANUTSHELL 645 INTERMEZZO BACTERIA, SPERM, FLIES, AND KNOTS 660 THIRD PART: MOTION WITHOUT MOTION WHAT ARE SPACE, TIME, ANDPARTICLES? CHAPTER XII GENERAL RELATIVITY VERSUS QUANTUMMECHANICS 669 31. Doesmatterdifferfromvacuum? 671 32. Natureatlargescales–istheuniversesomethingornothing? 700 33. Thephysicsofsex–asummaryofthefirsttwoandahalfparts 721 34. Theshapeofpoints 732 CHAPTER XIII M-THEORY 784 35. Awebofdualities 784 CHAPTER I THE TOP OF THE MOUNTAIN 787 APPENDICES APPENDIX A NOTATION AND CONVENTIONS 801 APPENDIX B UNITS, MEASUREMENTS, ANDCONSTANTS 811 APPENDIX C PARTICLE PROPERTIES 827 APPENDIX D NUMBERS AND SPACES 842 APPENDIX E INFORMATION SOURCES ON MOTION 858 APPENDIX F LIST OF FIGURES 863 APPENDIX G LIST OF TABLES 870 APPENDIX H CHALLENGE HINTS ANDSOLUTIONS 872 MotionMountain www.motionmountain.org Copyright(cid:13)c November1997–July2002 ChristophSchiller 6 Amountainhikealongtheconceptsofmodernphysics APPENDIX I SUBJECT ANDNAMEINDEX 874 MotionMountain www.motionmountain.org Copyright(cid:13)c November1997–July2002 ChristophSchiller CONTENTS Foreword 17 1. Anappetizer 20 FIRST PART: CLASSICAL PHYSICS HOWDO THINGS AND IMAGESMOVE? CHAPTER II CLASSICAL MOTION 25 2. Whycareaboutmotion? 25 Does motion exist? 26 How should one talk about motion? 28 What are the typesofmotion?29 Doyoudislikeformulas?32 Perception,permanence and change 32 Does the worldneed states? 34 Curiositiesand challenges on mo- tion36 3. Galileanphysics–motionineverydaylife 37 Whatisvelocity?37 Whatistime?38 Doestimeflow?43 Whatisspace?44 Arespaceandtimeabsoluteorrelative?47 Size:whyareaexists,butvolumedoes not47 What is straight?49 Curiositiesand funchallenges on everyday space andtime50 Howtodescribemotion:kinematics 51 Whatisrest?53 Objectsandpointparticles55 Legsandwheels57 Objects andimages59 Motionandcontact60 Whatismass?60 Ismotioneternal?64 Moreonconservation66 Rotation67 Rollingwheels70 Howdowewalk?71 Istheearthrotating?72 Doestheearthmove?76 Curiositiesandfunchallenges ofeverydaymotion79 Legsorwheels?–again82 Thedynamicsofgravitation 83 Propertiesofgravitation85 Gravitationinthesky89 Themoon89 Orbits91 Tides 93 Can lightfall? 95 What is mass? – again 95 Curiositiesand fun challengesaboutgravitation97 Whatisclassicalmechanics? 101 Shouldoneuseforce?102 Completestates:initialconditions107 Dosurprises exist?Isthefuturedetermined?108 Astrangesummaryaboutmotion111 4. Globaldescriptionsofclassicalmotion–thesimplicityofcomplexity 113 Theprincipleofleastaction 116 Why is motion so often bound? 122 Curiosities and challenges about La- grangians126 Motionandsymmetry 127 Whycan we thinkandtalk?128 Viewpoints128 Symmetriesand groups130 Representations 130 Symmetries, motion and Galilean physics 133 Repro- ducibility,conservation,andNoether’stheorem136 Simplemotionsofextendedbodies–Oscillationsandwaves 140 Funchallengesaboutwavesandextendedbodies140 Doextendedbodiesexist? 141 7 8 Amountainhikealongtheconceptsofmodernphysics Mountains, manifolds and fractals 141 Can a chocolate bar last forever? 142 How high can animals jump? 143 Felling trees 143 Listening to silence 144 Littlehardballs145 Challengesaboutfluidsandotherextendedbodies147 Whyareobjectswarm? 147 Brownianmotion149 Whydoballoonstakeupspace? 151 Entropy152 Do isolatedsystems exist?156 Whycan’tweremember thefuture?156 Isevery- thingmadeofparticles?157 Curiositiesandfunchallengesaboutheat157 Self-organizationandchaos 160 5. LimitsofGalileanphysics–whatiswrongwithschoolphysics 164 Research topicsinclassical dynamics165 Whatiscontact? 165 Precisionand accuracy166 Whyismeasurementpossible?166 6. Specialrelativity–restatanyspeed 168 Can one play tennis using a laser pulse as ball and mirrors as rackets? 171 Ac- celeration of light and the Doppler effect 172 Can one shoot faster than one’s shadow? 174 The principleof special relativity177 What is space-time? 180 Canwetraveltothepast?–Timeandcausality181 Curiositiesofspecialrelativity 182 Faster than light:how far can we travel? 182 Synchronizationand aging: can a motherstayyoungerthanherowndaughter?–Timetraveltothefuture183 Length contraction184 Whichisthebestseatinabus?185 Howfastcanonewalk?185 Is thespeed ofshadow greater thanthe speed of light?186 Parallel toparallelis notparallel–Thomasrotation188 Anever-endingstory:temperatureandrelativ- ity189 Relativisticmechanics 189 Massinrelativity190 Whyrelativisticpoolismoredifficult191 Massisconcen- tratedenergy191 Collisions,virtualobjectsandtachyons194 Systemsofparti- cles:nocentreofmass195 Whyismostmotionsoslow?196 Four-vectors196 Rotationinrelativity200 Theactionofafreeparticle202 Conformaltransfor- mations:Whyisthespeedoflightconstant?203 Acceleratingobservers 204 Acceleratingframesofreference206 Eventhorizons209 Accelerationchanges colours210 Canlightmove fasterthanc?210 Whatisthespeedoflight?211 Limitsonthelengthofsolidbodies211 Specialrelativityinfoursentences 213 References 215 CHAPTER III GRAVITATION AND RELATIVITY 233 7. Thenewideasonspace,time,andgravity 233 Rest and free fall233 What is gravity?234 What tides tellabout gravity236 Bentspace239 Thespeedoflightandtheconstantofgravitation242 Whydoes astonethrownintotheairfallback?–Geodesics243 Generalrelativityineverydaylife 246 Curiosities about gravitation 246 What is weight? 249 Why do apples fall?250 8. Motioningeneralrelativity–bentlightandwobblingvacuum 250 Weakfields 251 The Thirring effects 251 Gravitomagnetism 252 Gravitational waves 254 Lightandradiowavebending259 Timedelay260 Orbits260 Thegeodesic effect262 Howiscurvaturemeasured? 263 MotionMountain www.motionmountain.org Copyright(cid:13)c November1997–July2002 ChristophSchiller Amountainhikealongtheconceptsofmodernphysics 9 Curvature and space-time 266 Curvature and motion in general relativity 267 Universalgravity268 TheSchwarzschildmetric268 Curiositiesandfunchal- lenges269 Allobservers:heaviermathematics 269 The curvature of space-time 269 The description of momentum, mass and en- ergy 271 The symmetry of general relativity 272 Mass and ADM 272 Hilbert’saction273 Einstein’sfieldequations273 Howtocalculate theshape ofgeodesics276 Isgravityaninteraction?277 Riemanngymnastics279 9. Whycanweseethestars?–Motionintheuniverse 281 Which stars do we see at all? 281 What do we see at night?282 What is the universe? 285 The colour and the motion of the stars 285 Do stars shine ev- ery night? 287 A short history of the universe 287 The history of of space- time 290 Why is the sky dark at night? 294 Is the universe open, closed or marginal?295 Whyistheuniversetransparent?296 Thebigbanganditsconse- quences297 Wasthebigbangabigbang?298 Wasthebigbanganevent?298 Wasthebigbangabeginning?298 Doesthebigbangimplycreation?299 Why can we see the sun? 300 Why are the colours of the stars different? 300 Are theredarkstars?302 Areallstarsdifferent?–Gravitationallenses302 Whatis theshapeoftheuniverse?303 Whatisbehindthehorizon?304 Whyarethere starsallovertheplace?–Inflation305 Whyaretheresofewstars?Theenergyand entropycontentoftheuniverse305 Whyismatterlumped?306 Whyare stars sosmallcomparedwiththeuniverse?306 Arestarsandgalaxiesmovingapartor istheuniverseexpanding?306 Istheremore thanone universe?307 Whyare thestarsfixed?–Arms,stars,andMach’sprinciple307 Restingintheuniverse308 Doeslightattractlight?308 Doeslightdecay?309 10.Doesspacedifferfromtime? 309 Canspace andtimebemeasured? 311 Arespace andtimenecessary? 312 Do closed timelike curves exist? 312 Is general relativity local? – The hole argu- ment312 Istheearthhollow?313 Arespace,timeandmassindependent?314 11.Blackholes–fallingforever 314 Whystudythem? 314 Horizonsandorbits315 Hairandentropy318 Para- doxes,curiosities,andchallenges322 Formationofandsearchforblackholes323 Singularities324 Aquiz:istheuniverseablackhole?325 12.Generalrelativityintenpoints–asummaryforthelayman 325 The accuracy of the description 326 Research in general relativity and cosmol- ogy328 Thelimitsofgeneralrelativity328 References 329 CHAPTER IV CLASSICAL ELECTRODYNAMICS 339 13.Liquidelectricity,andinvisiblefields 339 Amber,lodestone,andmobilephones 340 Howcanonemake lightnings?341 Whatiselectriccharge? 343 Canone feel the inertia of electricity? 347 How fast do charges move? 348 How can one makeamotor?349 Howmotorsproverelativityright352 Thedescriptionofelectromagneticfieldevolution 353 The gauge field: the electromagnetic vector potential355 Collidingcharged par- ticles 357 The Lagrangian of electromagnetism 358 Symmetries: the energy- momentum tensor 359 What is a mirror? 360 What is the difference between electricandmagneticfields?361 14.Whatislight? 362 MotionMountain www.motionmountain.org Copyright(cid:13)c November1997–July2002 ChristophSchiller 10 Amountainhikealongtheconceptsofmodernphysics Doeslighttravelstraight?368 Canonetouchlight?370 War,light,andlies372 Whatiscolour?372 Whatisthespeedoflight?–Again374 Signalsandpredic- tions376 Whycanwetalktoeachother?–Huygens’principle377 Howdoes theworldlookwhenridingonalightbeam?377 Doestheaetherexist?378 15.Lightning,levitation,andotherfunchallenges 379 Islightinga discharge? –Electricityintheatmosphere 382 Electricalnerves 384 Howtoproveyou’reholy384 Doweseewhatexists?385 Howdoesonemake pictures of the inside of the eye? 386 Does gravity make charges radiate? 387 Howdoesonemakehologramsandother3-dimages?387 Researchquestions388 Levitation 389 Matter, levitation and electricity 391 Why can we see each other? 398 Couldelectrodynamics be different? 400 A summary of classical electrodynamicsandofitslimits400 References 401 CHAPTER V CLASSICAL PHYSICS INANUTSHELL 409 Thefutureofplanetearth 410 Theessenceofclassicalphysics 412 Whyisourmountainascentnotfinishedyet? 412 INTERMEZZO THEBRAIN, LANGUAGE, ANDTHE HUMAN CONDITION 414 Evolution415 Childrenandphysics 415 Why a brain? 419 What is information? 420 What is memory? 421 The capacityofthebrain422 Whatislanguage? 424 Aretheresemanticprimitivesinphysics?427 Whatisaconcept?427 Whatare sets?Whatarerelations?429 Infinity431 Functionsandstructures432 Num- bers 434 Whyuse maths? 438 Ismathematics a language? 439 Curiosities andfunchallenges440 Physicalconceptsandpatternsofnature 440 Arephysicalconceptsdiscoveredorcreated?441 Howdowefindphysicalpatterns andrules?443 Whatisalie?444 Isthisstatementtrue?448 Observations 449 Have enough observations been recorded? 449 Are all observables known? 450 Doobservationstaketime?452 Isinductionaprobleminphysics?452 Thequestforprecisionanditsimplications 455 Whatareinteractions?455 Whatisexistence?456 Dothingsexist?457 Does the voidexist? 459 Is nature infinite? 460 Is the universe a set? 460 Does theuniverseexist?462 Whatiscreation?462 Isnaturedesigned?464 What isadescription?465 Reason,purpose,andexplanation465 Unificationandde- marcation467 Pigs,apes,andtheanthropicprinciple468 Doesoneneedcause and effect in explanations? 469 Is consciousness required? 470 Curiosity470 Courage472 References 474 SECOND PART : QUANTUMTHEORY WHAT IS MATTER? WHAT ARE INTERACTIONS? MotionMountain www.motionmountain.org Copyright(cid:13)c November1997–July2002 ChristophSchiller
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