Motion Mountain - The Adventure of Physics, Vol 2 of 6 - Relativity

344 Pages·2011·32.69 MB·English

by  Christoph Schiller

Christoph Schiller
MOTION MOUNTAIN
the adventure of physics – vol.ii
relativity
www.motionmountain.net

ChristophSchiller
Motion Mountain
The Adventure of Physics
Volume II
Relativity
Edition25.03,available asfreepdfat
www.motionmountain.net
Editiovicesimaquinta.
Proprietasscriptoris©ChrestophoriSchiller
primoannoOlympiadistrigesimae.
Omniaproprietatisiurareservanturetvindicantur.
Imitatioprohibitasineauctorispermissione.
Nonlicetpecuniamexpetereproaliqua,quae
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Twenty-fifthedition.
Copyright©2012byChristophSchiller,
thefirstyearofthe30thOlympiad.
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ToBritta,EstherandJustusAaron
τῷἐμοὶδαὶμονι
DieMenschenstärken,dieSachenklären.
PREFACE
“Primummovere,deindedocere.* ”
Antiquity
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This book is written for anybody who is curious about nature and motion. Curiosity otio
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abouthowpeople,animals,things,imagesandemptyspacemoveleadstomanyadven- M
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u
tures.Thisvolumepresentsthebestoftheminthedomainsofrelativityandcosmology. n
tain
In the study of motion – physics – special and general relativity form two important –
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buildingblocks,asshowninFigure1. e
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Specialrelativityistheexplorationoftheenergyspeedlimitc.Generalrelativityisthe ve
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explorationoftheforcelimit c4/4G.Thetextshowsthatinbothdomains,allequations ture
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follow from these two limit values. This simple, intuitive and unusual way of learning Ph
relativityshouldrewardthecuriosityofeveryreader–whetherstudentorprofessional. ysics
Thepresentvolumeisthesecondofasix-volumeoverviewofphysicsthatarosefrom pd
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athreefoldaimthatIhavepursuedsince1990:topresentmotioninawaythatissimple, le
uptodateandcaptivating. availab
Inordertobesimple,thetextfocusesonconcepts,whilekeepingmathematicstothe lefree
necessary minimum. Understanding the concepts of physics is given precedence over o
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usingformulaeincalculations.Thewholetextiswithinthereachofanundergraduate. arg
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Inordertobeuptodate,thetextisenrichedbythemanygems–boththeoreticaland at
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empirical–thatarescatteredthroughoutthescientificliterature. ww
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Inordertobecaptivating,thetexttriestostartlethereaderasmuchaspossible.Read- o
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ing a book on general physics should be like going to a magic show. We watch, we are m
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astonished, we do not believe our eyes, we think, and finally we understand the trick. ntain
Whenwelookatnature,weoftenhavethesameexperience.Indeed,everypagepresents .n
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atleastonesurpriseorprovocationforthereadertothinkabout.Numerousinteresting C
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challengesareproposed. yrig
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Themottoofthetext,dieMenschenstärken,dieSachenklären,afamousstatementby t©
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HartmutvonHentigonpedagogy,translatesas:‘Tofortifypeople,toclarifythings.’Clar- hristo
ifyingthingsrequirescourage,aschanginghabitsofthoughtproducesfear,oftenhidden ph
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byanger.Butbyovercomingourfearswegrowinstrength.Andweexperienceintense ch
and beautifulemotions.Allgreatadventuresin life allow this, and exploringmotion is illerN
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oneofthem.Enjoyit! vem
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Munich,12October2011. 7–
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*‘Firstmove,thenteach.’Inmodernlanguages,thementionedtypeofmoving(theheart)iscalledmotivat- er
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ing;bothtermsgobacktothesameLatinroot. 01
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8 preface
PHYSICS: Unified description of motion Why does motion
Describing motion with action. Adventures: understanding occur? What are
motion, intense joy with space, time and
thinking, catching a quantum particles?
glimpse of bliss,
calculating
masses and
couplings.
Quantum
General relativity theory with gravity Quantum field theory
Adventures: the Adventures: bouncing Adventures: building
night sky, measu- neutrons, under- accelerators, under-
ring curved space, standing tree standing quarks, stars,
exploring black growth. bombs and the basis of M
o
holes and the life, matter, radiation. tion
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universe, space How do small ou
and time. things move? ntain
What are things? –
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How do Ad
Classical gravity everyday, Special relativity Quantum theory ven
tu
Adventures: fast and large Adventures: light, Adventures: death, re
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climbing, skiing, things move? magnetism, length sexuality, biology, fP
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space travel, contraction, time enjoying art and ysics
the wonders of dilation and colours, all high-tech
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astronomy and E = mc2. business, medicine, df
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geology. G c h, e, k chemistry, evolution. leavailab
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free
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Galilean physics, heat and electricity fch
Adventures: sport, music, sailing, cooking, arg
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describing beauty and understanding its origin, at
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using electricity and computers, ww
understanding the brain and people. .mo
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FIGURE 1 Acompletemapofphysics:theconnectionsaredefinedbythespeedoflightc,the o
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gravitationalconstantG,thePlanckconstanth,theBoltzmannconstantkandtheelementarychargee. tain
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Advice for learners yrig
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Inmyexperienceasateacher,therewasonelearningmethodthatneverfailedtotrans- risto
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form unsuccessful pupilsintosuccessful ones: if you readabook for study, summarize S
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everysectionyouread,inyourownwords,aloud.Ifyouareunabletodoso,readthesec- iller
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tionagain.Repeatthisuntilyoucanclearlysummarizewhatyoureadinyourownwords, ovem
aloud.Youcandothisaloneinaroom,orwithfriends,orwhilewalking.Ifyoudothis b
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witheverythingyouread,youwillreduceyourlearningandreadingtimesignificantly. 19
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Themostinefficientlearningmethodistouseamarkerortounderlinetext:itwastes O
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time,providesfalsecomfortandmakesthetextunreadable.Nobodymarkingtextisan be
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efficientlearner.Instead,byrepeatingeverysectioninyourownwords,aloud,youwill 01
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preface 9
save time and money, enjoy learning from good texts much more and hate bad texts
much less. Masters of the method can use it even while listening to a lecture, in a low
voice,thusavoidingtoevertakenotes.
Using this book
Textingreen,asfoundinmanymarginalnotes,marksalinkthatcanbeclickedinapdf
reader. Such green links are either bibliographic references, footnotes, cross references
tootherpages,challengesolutions,orpointerstowebsites.
Solutionsandhintsforchallengesaregivenintheappendix.Challengesareclassified
as research level (r), difficult (d), standard student level (s) and easy (e). Challenges of
typer,dorsforwhichnosolutionhasyetbeenincludedinthebookaremarked(ny).
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Feedback and support nM
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Thistextisandwillremainfreetodownloadfromtheinternet.Iwouldbedelightedto tain
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[email protected],especiallyonthefollowingissues: The
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Challenge1s — Whatwasunclearandshouldbeimproved? ntu
— Whatstory,topic,riddle,pictureormoviedidyoumiss? reo
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— Whatshouldbecorrected? hysics
Inordertosimplifyannotations,thepdffileallowsaddingyellowstickernotesinAdobe p
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Alternatively,youcanprovidefeedbackonwww.motionmountain.net/wiki.Helpon availab
thespecificpointslistedonthewww.motionmountain.net/help.htmlwebpagewouldbe le
particularly welcome.Allfeedback willbeused toimprovethenext edition.On behalf freeo
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ofallreaders,thankyouinadvanceforyourinput.Foraparticularlyusefulcontribution charg
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Apapereditionofthisbook,printedondemandanddeliveredbymailtoanyaddress,
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canbeorderedatstores.lulu.com/motionmountain.Butaboveall,enjoythereading! pyrig
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Contents
14 1 Maximum speed, observers at rest, and motion of light
Canoneplaytennisusingalaserpulseastheballandmirrorsasrackets? 20 •
AlbertEinstein 22 •Aninvariantlimitspeedanditsconsequences 22 •Special
relativity with a few lines 25 •Acceleration of light and the Doppler effect 27
•The difference between light and sound 32 •Can one shoot faster than one’s
shadow? 32 •Thecompositionofvelocities 34 •Observersandtheprincipleof
specialrelativity 35 •Whatisspace-time? 40 •Canwetraveltothepast? –
Timeandcausality 42 •Curiositiesaboutspecialrelativity 43 •Fasterthanlight:
howfarcanwetravel? 43 •Synchronizationandtimetravel–canamotherstay
youngerthanherowndaughter? 44 •Lengthcontraction 47 •Relativisticfilms
–aberrationandDopplereffect 49 •Whichisthebestseatinabus? 50 •How M
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fastcanonewalk? 53 •Isthespeedofshadowgreaterthanthespeedoflight? 53 tio
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•Paralleltoparallelisnotparallel–Thomasrotation 56 •Anever-endingstory– o
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temperatureandrelativity 57 tain
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59 2 Relativistic mechanics Th
e
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Massinrelativity 59 •Why relativistic snookeris moredifficult 61 •Massand d
ve
energy are equivalent 63 •Weighing light 64 •Collisions, virtual objects and ntu
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tachyons 66 •Systemsofparticles–nocentreofmass 67 •Whyismostmotionso o
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energy–momentum or momenergy 74 •4-force 75 •Rotation in relativity 76 df
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•Wave motion 78 •The action of a free particle – how do things move? 79 • le
Conformaltransformations 81 •Acceleratingobservers 82 •Acceleratingframes availab
ooffrheoferrizeonncse 8849••CAocncsetlaenrattaioccnelcehraantigoens8c6olo•uErvsen9t0ho•rCizaonnslig8h8t•mThoveeimfasptoerrttahnacne lefreeo
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c? 91 •Thecomposition of accelerations 91 •A curiosity: what is the one-way charg
speedoflight? 92 •Limitsonthelengthofsolidbodies 93 e
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95 3 Special relativity in four sentences w
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Couldthespeedoflightvary? 95 •Wheredoesspecialrelativitybreakdown? 96 o
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97 4 Simple general relativity: gravitation, maximum speed and max- mo
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imum force ntain
Maximumforce–generalrelativityinonestatement 98 •Theforceandpower .net
limits 99 •The experimentalevidence 101 •Deducing general relativity 103 • C
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Space-timeiscurved 107 •Conditionsofvalidityoftheforceandpowerlimits 108 yrig
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•Gedankenexperimentsandparadoxesabouttheforcelimit 109 •Gedanken t
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experimentswiththepowerlimitandthemassflowlimit 114 •Whymaximum Ch
forcehasremainedundiscoveredforsolong 117 •Anintuitiveunderstandingof ristop
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generalrelativity 118 •Anintuitiveunderstandingofcosmology 120 •Exper- Sch
imentalchallengesfor thethirdmillennium 121 •Asummaryofgeneralrelativ- iller
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ity 122 ovem
124 5 How maximum speed changes space, time and gravity be
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Restandfreefall 124 •Whatclockstellusaboutgravity 125 •Whattidestellus 99
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aboutgravity 129 •Bentspaceandmattresses 130 •Curvedspace-time 132 • Octo
Thespeedoflightandthegravitationalconstant 134 •Whydoesastonethrown be
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intotheairfallbacktoEarth?–Geodesics 136 •Canlightfall? 138 •Curiosities 01
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