Christoph Schiller MOTION MOUNTAIN the adventure of physics – vol.iv the quantum of change www.motionmountain.net ChristophSchiller Motion Mountain The Adventure of Physics Volume IV The Quantum of Change Edition25.01,available asfreepdfat www.motionmountain.net Editiovicesimaquinta. Proprietasscriptoris©ChrestophoriSchiller primoannoOlympiadistrigesimae. Omniaproprietatisiurareservanturetvindicantur. Imitatioprohibitasineauctorispermissione. Nonlicetpecuniamexpetereproaliqua,quae partemhorumverborumcontinet;liber proomnibussempergratuituseratetmanet. Twenty-fifthedition. Copyright©2012byChristophSchiller, thefirstyearofthe30thOlympiad. ThispdffileislicensedundertheCreativeCommons Attribution-Noncommercial-NoDerivativeWorks3.0Germany Licence,whosefulltextcanbefoundonthewebsite creativecommons.org/licenses/by-nc-nd/3.0/de, withtheadditionalrestrictionthatreproduction,distributionanduse, inwholeorinpart,inanyproductorservice,beit commercialornot,isnotallowedwithoutthewrittenconsentof thecopyrightowner.Thepdffilewasandremainsfreeforeverybody toread,storeandprintforpersonaluse,andtodistribute electronically,butonlyinunmodifiedformandatnocharge. ToBritta,EstherandJustusAaron τῷἐμοὶδαὶμονι DieMenschenstärken,dieSachenklären. PREFACE “Primummovere,deindedocere.* ” Antiquity M This book is written for anybody who is curious about nature and motion. Have you otio n everasked: Whydopeople,animals, things,imagesand spacemove?Theanswerleads M o u tomanyadventures;thisvolumepresentsthoseduethediscoverythatthereisasmallest n tain change in nature. This smallest change leads to what is called quantum theory. In the – Th structure of modern physics, shown in Figure 1, quantum physics covers three points; e A d this volume covers the introduction to the point in the lower right: the foundations of ve n tu quantumtheory. re o f ThepresentintroductiontoquantumphysicsarosefromathreefoldaimIhavepur- Ph sued since 1990: to presentthe basics of motion in a way thatis simple,up todate and ysics captivating. pd f fi Inordertobesimple,thetextfocusesonconcepts,whilekeepingmathematicstothe le necessary minimum. Understanding the concepts of physics is given precedence over availab usingformulaeincalculations.Thewholetextiswithinthereachofanundergraduate. lefree Inordertobeuptodate,thetextisenrichedbythemanygems–boththeoreticaland o f ch empirical–thatarescatteredthroughoutthescientificliterature. arg e Inordertobecaptivating,thetexttriestostartlethereaderasmuchaspossible.Read- at w ing a book on general physics should be like going to a magic show. We watch, we are ww .m astonished, we do not believe our eyes, we think, and finally we understand the trick. o tio n Whenwelookatnature,weoftenhavethesameexperience.Indeed,everypagepresents m o u atleastonesurpriseorprovocationforthereadertothinkabout.Numerousinteresting ntain challengesareproposed. .n et Themottoofthetext,dieMenschenstärken,dieSachenklären,afamousstatementby C o p HartmutvonHentigonpedagogy,translatesas:‘Tofortifypeople,toclarifythings.’Clar- yrig h ifyingthingsrequirescourage,aschanginghabitsofthoughtproducesfear,oftenhidden t© C byanger.Butbyovercomingourfearswegrowinstrength.Andweexperienceintense hristo and beautifulemotions.Allgreatadventuresin life allow this, and exploringmotion is ph S oneofthem.Enjoyit! ch iller N o Munich,9October2011. vem b e r 1 9 9 7 – O cto b *‘Firstmove,thenteach.’Inmodernlanguages,thementionedtypeofmoving(theheart)iscalledmotivat- er 2 ing;bothtermsgobacktothesameLatinroot. 01 1 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 M universe, space How do small ou and time. things move? ntain What are things? – Th e How do Ad Classical gravity everyday, Special relativity Quantum theory ven tu Adventures: fast and large Adventures: light, Adventures: death, re o climbing, skiing, things move? magnetism, length sexuality, biology, fP h space travel, contraction, time enjoying art and ysics the wonders of dilation and colours, all high-tech p astronomy and E = mc2. business, medicine, df 0 fi geology. G c h, e, k chemistry, evolution. leavailab le free o Galilean physics, heat and electricity fch Adventures: sport, music, sailing, cooking, arg e describing beauty and understanding its origin, at w using electricity and computers, ww understanding the brain and people. .mo tio n m FIGURE 1 Acompletemapofphysics:theconnectionsaredefinedbythespeedoflightc,the o u n gravitationalconstantG,thePlanckconstanth,theBoltzmannconstantkandtheelementarychargee. tain .n et C o p Advice for learners yrig h t © C h Inmyexperienceasateacher,therewasonelearningmethodthatneverfailedtotrans- risto p h form unsuccessful pupilsintosuccessful ones: if you readabook for study, summarize S ch everysectionyouread,inyourownwords,aloud.Ifyouareunabletodoso,readthesec- iller N tionagain.Repeatthisuntilyoucanclearlysummarizewhatyoureadinyourownwords, ovem aloud.Youcandothisaloneinaroom,orwithfriends,orwhilewalking.Ifyoudothis b e r witheverythingyouread,youwillreduceyourlearningandreadingtimesignificantly. 19 9 7 – Themostinefficientlearningmethodistouseamarkerortounderlinetext:itwastes O cto time,providesfalsecomfortandmakesthetextunreadable.Nobodymarkingtextisan be r 2 efficientlearner.Instead,byrepeatingeverysectioninyourownwords,aloud,youwill 01 1 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). M o tio Feedback and support nM o u n Thistextisandwillremainfreetodownloadfromtheinternet.Iwouldbedelightedto tain – [email protected],especiallyonthefollowingissues: The A d ve Challenge1s — Whatwasunclearandshouldbeimproved? ntu — Whatstory,topic,riddle,pictureormoviedidyoumiss? reo f P — Whatshouldbecorrected? hysics Inordertosimplifyannotations,thepdffileallowsaddingyellowstickernotesinAdobe p d f Reader. file Alternatively,youcanprovidefeedbackonwww.motionmountain.net/wiki.Helpon availab thespecificpointslistedonthewww.motionmountain.net/help.htmlwebpagewouldbe le particularly welcome.Allfeedback willbeused toimprovethenext edition.On behalf freeo f ofallreaders,thankyouinadvanceforyourinput.Foraparticularlyusefulcontribution charg you will be mentioned – if you want – in the acknowledgements, receive a reward, or eat w both. w w .m Your donation to the charitable, tax-exempt non-profit organisation that produces, o tio translatesandpublishesthisbookseriesiswelcome!Fordetails,seethewebpagewww. nm o motionmountain.net/donation.html. If you want, your name will be included in the un sponsorlist.Thankyouinadvanceforyourhelp,onbehalfofallreadersacrosstheworld. tain.n et Apapereditionofthisbook,printedondemandanddeliveredbymailtoanyaddress, C o canbeorderedatstores.lulu.com/motionmountain.Butaboveall,enjoythereading! pyrig h t © C h risto p h S ch iller N o vem b e r 1 9 9 7 – O cto b e r 2 0 1 1 Contents 13 1 Minimum action – quantum theory for poets Theeffectsofthequantumofactiononrest 16 •Theconsequences ofthequan- tumofactionforobjects 17 •Why‘quantum’? 20 •Theeffectofthequantumof action on motion 21 •Quantum limits and surprises 22 •Transformation, life andDemocritus 24 •Randomness–aconsequenceofthequantumofaction 27 • Waves–aconsequenceofthequantumofaction 28 •Particles–aconsequenceof thequantumofaction 29 •Quantuminformation 30 •Curiositiesandfunchal- lengesaboutthequantumofaction 30 •Thedangersofbuyingacanofbeans 32 •Asummary:quantumphysics,thelawandindoctrination 33 35 2 Light – the strange consequences of the quantum of action M Whatisthefaintestlamp? 35 •Photons 39 •Whatislight? 41 •Thesizeof otio n photons 42 •Are photons countable? –Squeezed light 42 •Thepositions M o of photons 44 •Are photons necessary? 47 •How can a wave be made up of un particles? 49 •Canlightmovefasterthanlight? –Virtualphotons 54 •Inde- tain– terminacyofelectricfields 55 •Curiositiesandfunchallengesaboutphotons 56 The A •Asummaryonlight:particleandwaves 58 dve n tu 60 3 Motion of matter – beyond classical physics re o f Wineglasses,pencilsandatoms–norest 60 •Noinfiniteprecision 61 •Cool Ph gas 61 •Flows and the quantization of matter 62 •Fluid flows and quan- ysics tons 62 •Knockingtablesandquantizedconductivity 62 •Matterquantonsand pd f theirmotion–matterwaves 64 •Massandaccelerationofquantons 66 •Why file areatomsnotflat? Whydoshapesexist? 67 •Rotation, quantizationofangular availab momentum,andthelackofnorthpoles 68 •Rotationofquantons 70 •Silver, le SternandGerlach–polarizationofquantons 71 •Curiositiesandfunchallenges free o f aboutquantummatter 72 •Firstsummaryonthemotionofquantumparticles 73 ch arg 74 4 The quantum description of matter and its motion eat w Visualizing the wave function: rotating arrows and probability clouds 75 •The w w stateevolution–theSchrödingerequation 77 •Self-interferenceofquantons 79 • .mo Thespeedofquantons 79 •Dispersionofquantons 79 •Tunnellingandlimitson tion m memory–dampingofquantons 80 •Thequantumphase 83 •Theleastaction ou n principleinquantumphysics 86 •Themotionofquantonswithspin 87 •Rela- tain .n tivisticwaveequations 89 •Compositevs.elementaryquantons 90 •Curiosities et C andfunchallengesaboutquantummotionofmatter 92 •Asummaryonmotion op ofquantons 93 yrig h t © 94 5 Permutation of particles – are particles like gloves? C h Whydoesindistinguishabilityappearinnature? 96 •Canparticlesbecounted? 97 risto p h •Whatispermutationsymmetry? 98 •Indistinguishabilityandsymmetry 98 • S ch Thebehaviourofphotons 99 •Bunchingandantibunching 100 •Theenergyde- iller N pendence of permutationsymmetry 100 •Indistinguishability in quantum field o theory 102 •How accurately is permutation symmetry verified? 102 •Copies, vemb e r clonesandgloves 103 1 9 9 7 – 105 6 Rotations and statistics – visualizing spin O cto Quantumparticlesandsymmetry 105 •Typesofquantumparticles 107 •Thebelt be r 2 trickanditsextension 110 •Angels,Pauli’sexclusionprincipleandthehardness 01 1