Symmetry, structure, and spacetime

242 Pages·2008·1.258 MB·English

by  Rickles, Dean

Symmetry, Structure, and Spacetime
Philosophy and Foundations of Physics
Series Editors: Dennis Dieks and Miklos Redei
Inthisseries:
Vol.1: TheOntologyofSpacetime
EditedbyDennisDieks
Vol.2: TheStructureandInterpretationoftheStandardModel
By GordonMcCabe
Vol.3: Symmetry, Structure,andSpacetime
ByDeanRickles
Symmetry, Structure,
and Spacetime
By
Dean Rickles
UnitforHistory andPhilosophyofScience
UniversityofSydney
Amsterdam–Boston–Heidelberg–London–NewYork–Oxford–Paris
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PREFACE
Symmetry is increasingly becoming a central, and indeed ‘hot’ topic for philoso-
phers of physics: it is linked to various metaphysical issues having to do with
space,time,motion,change,identity,modality,ontologyandmuchmorebesides.
This book examines the current interpretive landscape of symmetry in physics
withtheemphasisonthoseissuesjustlisted.Iconsideranumberofphysicalthe-
ories for which symmetry poses a particular and universal interpretive difficulty:
the same difficulty can be found across many theories dealing with apparently
different subject matter. The problem, roughly, is this: certain symmetries imply
‘redundancies,’ and this leads to an ‘inability’ of the theory to ‘choose’ between
statesorconfigurationsrelatedbythesymmetry.1 Incertaincasesthisleadstoin-
determinism, but in general we have an underdetermination of the state by the
theory.Itisthisunderdetermination,or,rather,howonedealswithit,thatisatthe
rootofmanydebates,newandold,inthephilosophyofphysics.
Theconnectionsofsuchmatterstoontologicalissuesareoldnews:thedebate
between Newton (or, rather, Rev. Samuel Clarke) and Leibniz over the nature of
space and time was just such an underdetermination problem (as presented in
the ‘shift argument’). Historical niceties aside, two sides were carved out of this
debate:absolutism(or‘absolutistsubstantivalism’),whichacceptedtheexistence
of multiple physical states that the theory could not distinguish between (these
states differing solely haecceitistically), and relationism, whichdenied such a pro-
fusion. As is well known, mutatis mutandis, the hole argument, as revived by Σ
i
Johni(i = Stachel,Earman,andNorton)hangsonthesamechoice,thoughhere
theunderdeterminationofstatesbytheoryistantamounttoindeterminism—the
latterbeingunderstoodasanunpalatableconsequenceofsubstantivalism,amere
metaphysicalposition.
Morerecenttimeshaveseentheemergenceofso-called“sophisticated”forms
ofsubstantivalismwhichclaimtocheckcertainessentialboxesofthecoresubstan-
tivalistpositionwithoutimplyingtheprofusionofindistinguishablestatesgener-
ated by the more naïve substantivalism at work in the shift and hole arguments.
However,alongsidethesemodificationscomethecries,ledchieflybyRobertRy-
nasiewicz[1996],thatthewholedebatedegeneratedintoameaninglessfarceever
sincethenotionoffieldsappearedinphysics,comingtoaheadingeneralrelativ-
1 Strictlyspeakingweshouldavoidusing“symmetry”todescribethesecasesbecausesymmetriesconnectphysically
distinctstates,butthisisstillthecommonparlanceandIshallsticktoitinwhatfollows.Abetterterm,whichisgaining
currencyamongphysicists,wouldbe‘gaugeredundancy’(cf.[Guilini,2003]).Gaugeherereferstoacertainclassoftrans-
formationsthatleave‘physicalaspects’unchanged—wherethephysicalaspectsarecashedoutintermsoftheobservables
ofthetheory.Theideaisthatstatesorconfigurationsrelatedbysuchatransformationrepresentoneandthesamephysical
stateorconfiguration.
v
vi Preface
itywherethegeometricstructureofspacetimeisrepresentedbyalocaldynamical
variable(themetricfield)notreadilydistinguishable,ontologicallyspeaking,from
‘ordinary material fields’. This sentiment seems to be shared by Carlo Rovelli,
a leading quantum gravity researcher, who argues that the distinction between
viewingthemetricfieldasmatterorspacetimeislargelyverbal—see,forexample,
[Rovelli,2004],§2.4.2.But,despitethis,Rovelli,andmanyotherquantumgravity
researchers,nonethelessarguethatthegrandolddebatebetweensubstantivalism
andrelationalismisplayingacrucialanddivisiveroleintheirfield.GordonBelot
andJohnEarman,andahandfulofphilosophy-mindedphysicists,thinkthatthere
isacloseconnectionbetweenthevarioustheoriesofquantumgravityandtradi-
tional ontological positions concerning spacetime: they think whatever research
programme eventually is crowned victor in the race for quantum gravity could
settlethedebatebetweenrelationalistsandsubstantivalists!Iarguethatthisisnot
so;theirviewsstemeitherfromamisunderstandingofthetermsofthedebateor
else from a desire to breathe some life into the dying corpse of the debate. I fear
itistoolate.Suchviewsinvolveanalignmentbetweenthesepositionsandapair
of other positions that certainly do play such a crucial and divisive role, namely
backgrounddependenceandbackgroundindependence.Theprimaryaimofthis
book is to argue against this view, a view that is fast on its way to becoming the
receivedwisdom.Thealignmentdoesnotholduptoscrutiny.Iargueinsteadthat
thestateofplayinmodernphysics,especiallyquantumgravity,pointstowardsa
novelinterpretivestance:astructuralistontologythatdoesnotinvolveobjects(in
thesenseofsubjects)atall—hence,bothrelationalismandsubstantivalismareout.
Itisn’tjustspacetimetheoriesthatfacethesekindsofproblems:thequantum
theory of indistinguishable particles and gauge theories in general face similar
problemsandcanbemetbythesamekindsofinterpretiveresponses.Thisbook
seekstoshowhowthesevariouscasesareessentiallythesamebyprovidingauni-
fiedaccountoftheproblemsandtheirinterpretiveoptions.2However,throughout
this book my eye is always directed firmly towards quantum gravity, the as yet
non-existenttheorythatwillbringtogethertheprinciplesofquantumfieldtheory
and general relativity. The position I develop is ultimately intended to provide
a satisfactory, and indeed safe and sane, interpretation of quantum gravity. Ulti-
mately, then, this is a defense of structuralism about modern spacetime physics.
Structuralism has been ‘creeping up’ in physics for some time, and with the ad-
ventofgaugetheoriesIthinkitistheobviousinterpretivestancetoadopt;when
wegettobackgroundindependenttheorieslikegeneralrelativity,whereeventhe
dynamicsispuregauge,thenstructuralismisalmostforceduponus.
The book begins with a fairly informal survey of some background material
involvingelementsfromphilosophyofscience(interpretationandontology)and
somebasicconceptsfromthetheoriesweshallbedealingwith.IroundChapter1
off with a discussion of symmetry where I outline the type of symmetries that
I am interested in—this chapter could easily be skipped by those philosophers
of science who already understand the basics of symmetry. In Chapter 2 I ap-
plythesematerialstothedebatebetweensubstantivalistsandrelationalistswhere
2 Indeed,examiningtheseothercasesprovidesuswithabetterhandleontheinterpretationofspacetimephysics,and
viceversa.
Preface vii
I focus on the ‘Leibniz-shift’ argument. The main task in this chapter is to high-
lightthephilosophicalsignificanceofthegeometricspacesoutlinedintheopening
chapterandtodetachthesespacesfromthetraditionaldebateconcerningspace-
time ontology—a running theme. Chapter 3 situates the Leibniz-shift argument
intheframeworkofgaugetheoriesandanalyzestheinterpretiveoptionsofsuch
theories. Themainresultisthat thereis a lot ofelbow room concerning therela-
tionshipbetweeninterpretiveoptionsandformalmethodsfordealingwithgauge
freedom—this is the gauge-theoretical analogue of the detachment of spacetime
ontology from geometric spaces.3 The results from this chapter are then applied
to the hole argument in Chapters 4 and 5—I show that the methods for dealing
withgaugefreedomhavecounterpartsinthevariousresolutionsoftheholeargu-
ment.Chapter6focusesontheconceptofobservableingeneralrelativistictheories
andprovideswhatItaketobethemostnaturalresolutiontotheholeargument,
and the true ‘lesson’ of that argument: the observable content of general relativ-
ity (and background independent theories in general) is exhausted by structural
(manifold-independent) quantities having the form of correlations between field
values. Hence, the view I advocate involves thinking of the observables of gen-
eralrelativityascorrelationalquantitiesthatmakenomentionofspacetime—this,
Isay,isbestunderstoodasastructuralistposition.Thisviewisthenputtowork
againsttheproblemsoftimeandchangeinclassicalandquantumgravityinChap-
ter7—theideaisthatinunderstandingcorrelationsstructurally(sothattheyare
notdecomposableintoindependentcorrelates)weareabletosidestepanumberof
standardproblemsandobjectionsthatotherinterpretationsface.Chapter8tiesthe
otherchapterstogetherbyfocusingsquarelyontherelationshipbetweenthetreat-
ment of symmetry and various interpretive positions, and draws some general
metaphysical and ontological morals. Finally, in Chapter 9 I defend a ‘minimal’
structuralistpositionmoreexplicitly.Thekeyresultsinthisandthepreviouschap-
terare:(1)ademonstrationoftheirrelevanceofpossibilitycounting(connectedto
geometric space descriptions and the treatment of symmetries) to spacetime on-
tology,and(2)theexposingofanextremeunderdeterminationofmetaphysicsby
physics that engulfs both subject-based ontologies (such as substantivalism and
relationalism) and those structural realist ontologies that eliminate objects by re-
conceptualizing them in terms of structures. The more deflationary structuralism
Iespouseisintendedtodojusticetobothofthesefactors.
Although the book is written fairly linearly, each chapter making use of the
previous,theycannonethelessbereadindependentlyofoneanother.Inorderto
makethispossibleitwasnecessarytogooversomeofthematerialseveraltimes.
However, in order to avoid ugly repetition, the treatments generally come at the
samematerialfromadifferentangle.
Thisbookgrewoutofmydoctoralthesis,Spacetime,Change,andIdentity:Classical
andQuantumGravityinPhilosophicalFocus,writtenattheUniversityofLeedsun-
der the supervision of Prof. Steven French (completed in June 2004). My thanks
3 InessenceIwanttotakeNickHuggett’sconclusionaboutthephilosophicalimplicationsofstatisticalphysics—that
permutationsymmetryhasno“heavymetaphysicalimplications”([1999],p.24)—andapplyittoavarietyofareasinwhich
similarsymmetriesoperate.
viii Preface
toStevenforshowingmetheropesvis-à-visphilosophyofphysics;forentrusting
mewithsuchanambitiousproject;andforbeingagoodfriend.Mythanksalsoto
themembersofmythesisexaminationcommittee:DrJosephMeliaandProf.Carl
Hoefer. I have resisted the very strong temptation to modify the content of the
originalthesis,leavingtheoriginalpresentationlargelyintact(anyalterationsbe-
ingmostlystylistic).Ihave,however,alteredmystancewithrespecttonumerous
of the arguments presented here, but the main one I still hold fast to: structural-
ism is the only gamein town in backgroundindependent (gauge)theories. I did
feel the need to change the title though: the present title much better reflects the
contentandaimsofthebook.4
The finishing touches to this monograph were completed while I was a post-
doctoral fellow at the University of Calgary: I would like to thank both the de-
partmentofphilosophyandtheMarkinInstitute(Prof.PennyHaweinparticular
from the latter) for their support, financial and otherwise. I thank Dennis Dieks
and Miklos Redei for taking this project on as part of their excellent new series.
Workingwiththemhasbeenaverysmoothexperience.Iwouldalsoliketothank
GordonBelot,StevenWeinstein,andOliverPooleyforsupplyingmewithcopies
their doctoral theses: my own thesis (this book) owes a great deal to them. Any
errors—and I’m sure there are plenty—are, of course, entirely my own. My en-
tréeintophilosophyofphysicswasoverseenbyNickUnwinattheUniversityof
Bolton, who let me attend his excellent MA philosophy of physics course while
stillalowlyundergraduate.Thatcourseleftagreatimpressiononme,andIthank
himforthat.Finally,IthankKirsty,Sophie,andGaiafortheirconstantlove,sup-
port,andlaughs.Idedicatethisbooktomyparents,MurielandPeterRickles,for
givingmedriveanddetermination.
D.P.R.
4 IwouldcertainlydoneanumberofthingsdifferentlyasregardsthepresentationofmaterialhadIstartedthisproject
fromscratch:thechapterongaugetheoryIwouldhavereframedinthelanguageoffiberbundles;thechaptersonthe
holeargumentandobservablesIwouldhaveconsideredfromtheperspectiveoftheKretschmannobjectionandtheon-
goingdebateconcerninggeneralcovariance,diffeomorphisminvariance,absoluteobjects,andbackgroundindependence.
However,thoughtheseareindeednotableabsences,Ithinkthebookmanagestoholdupdespitethem.
ACKNOWLEDGEMENTS
Parts of Chapter 1 appeared as “Interpreting Quantum Gravity” (Studies in the
History and Philosophy of Modern Physics 36 (2005) 691–715). Parts of Chapter 6
appearedas“ANewSpinontheHoleArgument”(StudiesintheHistoryandPhi-
losophy of Modern Physics 36 (2005) 415–434). I thank Elsevier for allowing me to
reproducethismaterialhere.
Chapter 7 is largely identical to “Time and Structure in Canonical Gravity”,
whichappearedinD.Rickles,S.French,andJ.Saatsi(eds.).TheStructuralistFoun-
dationsofQuantumGravity,OxfordUniversityPress,2006(pp.152–195).Mythanks
toOUPforallowingmetoreproducethis.
ix