The motion mountain physics book

778 Pages·2002·4.948 MB·English

by  Schiller C.

ChristophSchiller
Motion Mountain
Hikingbeyondspaceandtime
alongtheconceptsofmodernphysics
availableat
www.motionmountain.org
Nunceditiosecundaemendata.
ProprietasscriptorisChristophoriSchiller
secundoannoOlympiadisvicesimaesextae
tertioqueannoOlympiadisvicesimaeseptimae.
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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
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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
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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
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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
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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
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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