HOW to BECOME a GOOD THEORETICAL PHYSICIST.docx
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HOW to BECOME a GOOD THEORETICAL PHYSICIST.docx
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HOWtoBECOMEaGOODTHEORETICALPHYSICIST
HOWtoBECOMEaGOODTHEORETICALPHYSICIST
byGerard'tHooft
Thisisawebsite(stillunderconstruction)foryoungstudents-andanyoneelse-whoare(likeme)thrilledbythechallengesposedbyrealscience,andwhoare-likeme-determinedtousetheirbrainstodiscovernewthingsaboutthephysicalworldthatwearelivingin.Inshort,itisforallthosewhodecidedtostudytheoreticalphysics,intheirowntime.
ItsooftenhappensthatIreceivemail-well-intendedbuttotallyuseless-byamateurphysicistswhobelievetohavesolvedtheworld.Theybelievethis,onlybecausetheyunderstandtotallynothingabouttherealwayproblemsaresolvedinModernPhysics.Ifyoureallywanttocontributetoourtheoreticalunderstandingofphysicallaws-anditisanexcitingexperienceifyousucceed!
-therearemanythingsyouneedtoknow.Firstofall,beseriousaboutit.AllnecessarysciencecoursesaretaughtatUniversities,so,naturally,thefirstthingyoushoulddoishaveyourselfadmittedataUniversityandabsorbeverythingyoucan.Butwhatifyouarestillyoung,atSchool,andbeforebeingadmittedataUniversity,youhavetoendurethechildishanecdotesthattheycallsciencethere?
Whatifyouareolder,andyouarenotatalllookingforwardtojointhosenoisycrowdsofyoungstudents?
Itshouldbepossible,thesedays,tocollectallknowledgeyouneedfromtheinternet.Problemthenis,thereissomuchjunkontheinternet.Isitpossibletoweedoutthoseveryrarepagesthatmayreallybeofuse?
Iknowexactlywhatshouldbetaughttothebeginningstudent.Thenamesandtopicsoftheabsolutelynecessarylecturecoursesareeasytolist,andthisiswhatIhavedonebelow.Itismyintentiontosearchonthewebwherethereallyusefulpapersandbooksare,preferablydownloadableaswell.Thisway,thecostsofbecomingatheoreticalphysicistshouldnotexceedmuchthepriceofacomputerwithinternetconnection,aprinter,andlotsofpaperandpens.Unfortunately,Istillhavetorecommendtobuytextbooksaswell,butitishardertoadviseyouhere;perhapsinafuturesite.Let'sfirstlimitourselvestotheabsoluteminimum.Thesubjectslistedbelowmustbestudied.Anyomissionwillbepunished:
failure.Dogetmeright:
youdon'thavetobelieveanythingyoureadonfaith-checkit.Tryalternativeapproaches,asmanyasyoucan.Youwilldiscover,timeandagain,thatreallywhatthoseguysdidindeedwasthesmartestthingpossible.Amazing.thebestofthetextscomewithexercises.Dothem.findoutthatyoucanunderstandeverything.Trytoreachthestagethatyoudiscoverthenumerousmisprints,tinymistakesaswellasmoreimportanterrors,andimaginehowyouwouldwritethosetextsinasmarterway.
Icantellyouofmyownexperiences.Ihadtheextremeluckofhavingexcellentteachersaroundme.Thathelpsonefromrunningastray.IthelpedmeallthewaytoearnaNobelPrize.ButIdidn'thaveinternet.Iamgoingtotrytobeyourteacher.Itisaformidabletask.Iamaskingstudents,colleagues,teacherstohelpmeimprovethissite.Itispresentlysetuponlyforthosewhowishtobecometheoreticalphysicists,notjustordinaryones,buttheverybest,thosewhoarefullydeterminedtoearntheirownNobelPrize.Ifyouaremoremodestthanthat,well,finishthoselousyschoolsfirstandfollowtheregularroutesprovidedbyeducatorsandspecialized-gogueswhoaresodamncarefullychewingallthosetinyportionsbeforefeedingthemtoyou.Thisisasiteforambitiouspeople.Iamsurethatanyonecandothis,ifoneisgiftedwithacertainamountofintelligence,interestanddetermination.
TheoreticalPhysicsislikeaskyscraper.Ithassolidfoundationsinelementarymathematicsandnotionsofclassical(pre-20thcentury)physics.Don'tthinkthatpre-20thcenturyphysicsis"irrelevant"sincenowwehavesomuchmore.Inthosedays,thesolidfoundationswerelaidoftheknowledgethatweenjoynow.Don'ttrytoconstructyourskyscraperwithoutfirstreconstructingthesefoundationsyourself.ThefirstfewfloorsofourskyscraperconsistofadvancedmathematicalformalismsthatturntheClassicalPhysicstheoriesintobeautiesoftheirown.Theyareneededifyouwanttogohigherthanthat.So,nextcomemanyoftheothersubjectslistedbelow.Finally,ifyouaremadenoughthatyouwanttosolvethosetremendouslyperplexingproblemsofreconcilinggravitationalphysicswiththequantumworld,youendupstudyinggeneralrelativity,superstringtheory,M-theory,Calabi-Yaucompactificationandsoon.That'spresentlythetopoftheskyscraper.ThereareotherpeakssuchasBose-Einsteincondensation,fractionalHalleffect,andmore.AlsogoodforNobelPrizes,asthepastyearshaveshown.Awarningiscalledfor:
evenifyouareextremelysmart,youarestilllikelytogetstucksomewhere.Surfthenetyourself.Findmore.Tellmeaboutwhatyoufound.IfthissitehasbeenofanyhelptosomeonewhilepreparingforaUniversitystudy,ifthishasmotivatedsomeone,helpedsomeonealongtheway,andsmoothenedhisorherpathtowardsscience,thenIcallthissitesuccessful.Pleaseletmeknow.Hereisthelist.
NotethatthissiteNOTmeanttobeverypedagogical.Iavoidtextswithlotsofcolorfulbutdistractingpicturesfromauthorswhotryhardtobefunny.Also,thesubjectsincludedaresomewhatfocusedtowardsmyowninterests.
LISTOFSUBJECTS,INLOGICALORDER(noteverythinghastobedoneinthisorder,butthisapproximatelyindicatesthelogicalcoherenceofthevarioussubjects.Somenotesareatahigherlevelthanothers).
▪Languages
▪PrimaryMathematics
▪ClassicalMechanics
▪Optics
▪StatisticalMechanicsandThermodynamics
▪Electronics
▪Electromagnetism
▪QuantumMechanics
▪AtomsandMolecules
▪SolidStatePhysics
▪NuclearPhysics
▪PlasmaPhysics
▪AdvancedMathematics
▪SpecialRelativity
▪AdvancedQuantumMechanics
▪Phenomenology
▪GeneralRelativity
▪QuantumFieldTheory
▪SuperstringTheory
Moreresources
The.psfilesarePostScriptfiles§.
(Inthisinitialphasethispageisstillincomplete!
)
Languages:
Englishisaprerequisite.Ifyouhaven'tmasteredityet,learnit.Youmustbeabletoread,write,speakandunderstandEnglish,butyoudon'thavetobeperfecthere.ThelousyEnglishusedinthistextismine.That'senough.AllpublicationsareinEnglish.NotetheimportanceofbeingabletowriteinEnglish.Soonerorlateryouwillwishtopublishyourresults.Peoplemustbeabletoreadandunderstandyourstuff.
FreeEnglishcoursesandresources.
BBCworldservicelearningEnglish.
French,German,SpanishandItalianmaybeusefultoo,buttheyarenotatallnecessary.Theyarenowherenearthefoundationsofoursky-scraper,sodon'tworry.YoudoneedtheGreekalphabet.Greeklettersareusedalot.Learntheirnames,otherwiseyoumakeafoolofyourselfwhengivinganoralpresentation.Now,herebeginstheseriousstuff.Don'tcomplainthatitlookslikebeingalot.Youwon'tgetyourNobelPrizeforfree,andremember,allofthistogethertakesourstudentsatleast5yearsofintensestudy(atleastonereaderwassurprisedatthisstatement,sayingthat(s)hewouldnevermasterthisin5years;indeed,Iamaddressingpeoplewhoplantospendmostoftheirtimetothisstudy).Morethanrudimentaryintelligenceisassumedtobepresent,becauseordinarystudentscanmasterthismaterialonlywhenassistedbypatientteachers.Itisnecessarytodoexercises.Someofthetextscomewithexercises.Dothem,orbetter,inventyourownexercises.Trytooutsmarttheauthors,butpleaserefrainfrommailingtomeyouralternativetheoriesuntilyouhavestudiedtheentirelot;ifyoudothiswellyouwilldiscoverthatmanyoftheseauthorswerenotsostupidafterall.
ReturntoList
Now,firstthingsfirst:
PrimaryMathematics:
Areyoucomfortablewithnumbers,adding,subtracting,squareroots,etc.?
*BeginningAlgebra*(WestTexasA&M)
*IntermediateAlgebra*(WestTexasA&M)
▪Naturalnumbers:
1,2,3,...
▪Integers:
...,-3,-2,-1,0,1,2,...
▪Rationalnumbers(fractions):
¼,½,¾,23791/773,...
▪Realnumbers:
Sqrt
(2)=1.4142135...,pi=3.14159265...,e=2.7182818...,...
▪Complexnumbers:
2+3i,eia=cos(a)+isin(a),...theyareveryimportant!
DaveE.Joyce'strigonometrycourse
Thisisamust:
Prof.JamesBinney'scourseoncomplexnumbers(PDF)
(nearly)completeoverviewofprimarymathematics(K.Kubota,Kentucky)
SeealsoChrisPope'slecturenotes:
Methods1-ch1
Methods1-ch2
Thecomplexplane.Cauchytheoremsandcontourintegration(G.Cain,Atlanta)
Settheory:
opensets,compactspaces.Topology.Youmaybesurprisedtolearnthattheydoplayaroleindeedinphysics!
Algebraicequations.Approximationtechniques.Seriesexpansions:
theTaylorseries.Solvingequationswithcomplexnumbers.Trigonometry:
sin(2x)=2sinxcosx,etc.
Infinitesimals.Differentiation.Differentiatebasicfunctions(sin,cos,exp).Integration.Integratebasicfunctions,whenpossible.Differentialequations.Linearequations.
TheFouriertransformation.Theuseofcomplexnumbers.Convergenceofseries.
Thecomplexplane.Cauchytheoremsandcontourintegration(nowthisisfun).
TheGammafunction(enjoystudyingitsproperties).
Gaussianintegrals.Probabilitytheory.
Partialdifferentialequations.DirichletandNeumannboundaryconditions.
Thisisforstarters.Someofthesetopicsactuallycomeasentirelecturecourses.MuchofthoseareessentialingredientsoftheoriesinPhysics.Youdon'thavetofinishitallbeforebeginningwithwhatfollowsnext,but
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