Physics from Symmetry

294 Pages·2017·2.917 MB·English

by  Jakob Schwichtenberg

Undergraduate Lecture Notes in Physics
Jakob Schwichtenberg
Physics from
Symmetry
Second Edition
Undergraduate Lecture Notes in Physics
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Jakob Schwichtenberg
Physics from Symmetry
Second Edition
123
JakobSchwichtenberg
Karlsruhe
Germany
ISSN 2192-4791 ISSN 2192-4805 (electronic)
Undergraduate Lecture Notesin Physics
ISBN978-3-319-66630-3 ISBN978-3-319-66631-0 (eBook)
https://doi.org/10.1007/978-3-319-66631-0
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1stedition:©SpringerInternationalPublishingSwitzerland2015
2ndedition:©SpringerInternationalPublishingAG2018
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NATURE ALWAYS CREATES THE BEST OF ALL OPTIONS
ARISTOTLE
AS FAR AS I SEE, ALL A PRIORI STATEMENTS IN PHYSICS HAVE THEIR
ORIGIN IN SYMMETRY.
HERMANN WEYL
THE IMPORTANT THING IN SCIENCE IS NOT SO MUCH TO OBTAIN NEW FACTS
AS TO DISCOVER NEW WAYS OF THINKING ABOUT THEM.
WILLIAM LAWRENCE BRAGG
Dedicated to my parents
Preface to the Second Edition
InthetwoyearssincethefirsteditionofthisbookwaspublishedI’ve
receivednumerousmessagesfromreadersallaroundtheworld. I
wassurprisedbythislargenumberofresponsesandhowpositive
mostofthemwere. Ofcourse,Iwascautiouslyconfidentthatread-
erswouldlikethebook. OtherwiseIwouldn’thavespentsomany
monthswritingit. However,thereiscertainlynoshortageofbooks
ongrouptheoryorontheroleofsymmetriesinphysics. Toquote
1
PredragCvitanovic 1PredragCvitanovic´. GroupTheory:
Birdtracks,Lie’s,andExceptionalGroups.
Almostanybodywhoseresearchrequiressustaineduseofgroup PrincetonUniversityPress,72008.
theory(anditishardtothinkofaphysicalormathematicalproblem ISBN9780691118369
thatiswhollydevoidofsymmetry)writesabookaboutit.
Moreover,I’mnotaworldrenownedexpert. Therefore,Iknewno
onewouldbuythebookbecausemynameiswrittenonthecover. So
thechanceswerehighthat"PhysicsfromSymmetry"wouldsimply
drowninthefloodofnewtextbooksthatarepublishedeveryyear.
Therefore,it’sreasonabletowonder: Whyandhowdid"Physics
fromSymmetry"avoidthisfate?
IthinkthemainreasonforthesuccessofthefirsteditioniswhatI
framedassomethingnegativeabove: itwasn’twrittenbyaworld
renownedexpert. IwrotethebookwhileIwasstillastudentand,
asIremarkedintheprefacetothefirstedition,"IwrotethebookI
wishedhadexistedwhenIstartedmyjourneyinphysics". Somy
motivationforwritingthebookwasn’ttocreateanauthoritativeref-
erenceoraconcisetextthatexpertswouldlove. Instead,myonlyfo-
cuswastowriteabookthathelpsstudentsunderstand. Asastudent
myselfIalwayshadstillfreshinmemorywhatIfoundconfusing
andwhatfinallyhelpedmeunderstand.
Thispointofviewisnicelysummarizedinthefollowingquoteby
2
C.S.Lewis 2C.S.Lewis. ReflectionsonthePsalms.
HarperOne,reprintedition,22017.
Itoftenhappensthattwoschoolboyscansolvedifficultiesintheirwork ISBN9780062565488
foroneanotherbetterthanthemastercan. Whenyoutooktheproblem
X
toamaster,asweallremember,hewasverylikelytoexplainwhat
youunderstoodalready,toaddagreatdealofinformationwhichyou
didn’twant,andsaynothingatallaboutthethingthatwaspuzzling
you. [...] Thefellow-pupilcanhelpmorethanthemasterbecause
heknowsless. Thedifficultywewanthimtoexplainisonehehas
recentlymet. Theexpertmetitsolongagohehasforgotten. Hesees
thewholesubject,bynow,inadifferentlightthathecannotconceive
whatisreallytroublingthepupil;heseesadozenotherdifficulties
whichoughttobetroublinghimbutaren’t.
Whilemostreaderslikedthestudent-friendlyspiritofthefirstedi-
tion,itwas,ofcourse,notperfect. Severalreaderspointedouttypos
andparagraphswithconfusingnotationorexplanations. Thisfeed-
backguidedmeduringthepreparationofthissecondedition. I
focusedoncorrectingtypos,improvingthenotationandIrewrote
entiresectionsthatwerecausingconfusion.
Ihopethesechangesmake"PhysicsfromSymmetry"evenmore
3
3NobookiseverperfectandI’mal- student-friendlyanduseful .
wayshappytoreceivefeedback.Soif
youfindanerror,haveanideaforim-
Karlsruhe,September2017 JakobSchwichtenberg
provementorsimplywanttocomment
onsomething,alwaysfeelfreetowrite
[email protected]
Preface to the First Edition
Themostincomprehensiblethingabouttheworldisthatitisatall
comprehensible.
4
-AlbertEinstein 4AsquotedinJonFripp,Deborah
Fripp,andMichaelFripp. Speakingof
Science. Newnes,1stedition,42000.
InthecourseofstudyingphysicsIbecame,likeanystudentof ISBN9781878707512
physics,familiarwithmanyfundamentalequationsandtheirsolu-
tions,butIwasn’treallyabletoseetheirconnection.
IwasthrilledwhenIunderstoodthatmostofthemhaveacom-
monorigin: symmetry. Tome,themostbeautifulthinginphysicsis
whensomethingincomprehensible,suddenlybecomescomprehen-
sible,becauseofadeepexplanation. That’swhyIfellinlovewith
symmetries.
Forexample,forquitesometimeIcouldn’treallyunderstand
spin,whichissomekindofcuriousinternalangularmomentumthat
almostallfundamentalparticlescarry. ThenIlearnedthatspinis
adirectconsequenceofasymmetry,calledLorentzsymmetry,and
everythingstartedtomakesense.
Experienceslikethiswerethemotivationforthisbookandin
somesense,IwrotethebookIwishedhadexistedwhenIstartedmy
journeyinphysics. Symmetriesarebeautifulexplanationsformany
otherwiseincomprehensiblephysicalphenomenaandthisbookis
basedontheideathatwecanderivethefundamentaltheoriesof
physicsfromsymmetry.
Onecouldsaythatthisbook’sapproachtophysicsstartsatthe
end: Beforeweeventalkaboutclassicalmechanicsornon-relativistic
quantummechanics,wewillusethe(asfarasweknow)exactsym-
metriesofnaturetoderivethefundamentalequationsofquantum
fieldtheory. Despiteitsunconventionalapproach,thisbookisabout
standardphysics. Wewillnottalkaboutspeculative,experimentally
unverifiedtheories. Wearegoingtousestandardassumptionsand
developstandardtheories.