The Arrows of Time: A Debate in Cosmology

222 Pages·2012·2.39 MB·English

by  Laura Mersini-Houghton

Fundamental Theories of Physics
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PHILIPPEBLANCHARD,Universita¨tBielefeld,Bielefeld,Germany
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BOBCOECKE,OxfordUniversityComputingLaboratory,Oxford,UnitedKingdom
DETLEFDUERR,MathematischesInstitut,Mu¨nchen,Germany
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DOMENICOGIULINI,UniversityofHannover,Hannover,Germany
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Laura Mersini-Houghton Rudy Vaas
(cid:2)
Editors
The Arrows of Time
A Debate in Cosmology
123
Editors
Prof.LauraMersini-Houghton Ru¨digerVaas
UniversityofNorthCarolina bildderwissenschaft
Dept.PhysicsandAstronomy Ernst-Mey-Str.8
ChapelHillNorthCarolina D-70771Leinfelden-Echt.
USA Germany
[email protected] [email protected]
ISBN978-3-642-23258-9 e-ISBN978-3-642-23259-6
DOI10.1007/978-3-642-23259-6
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2012939849
(cid:2)c Springer-VerlagBerlinHeidelberg2012
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Contents
Introduction ...................................................................... 1
TimeAfterTime—BigBangCosmologyandtheArrowsofTime........ 5
Ru¨digerVaas
FundamentalLossofQuantumCoherencefromQuantumGravity....... 43
RodolfoGambini,RafaelA.Porto,andJorgePullin
TheClockAmbiguity:ImplicationsandNewDevelopments ............... 53
AndreasAlbrechtandAlbertoIglesias
HolographicCosmologyandtheArrowofTime ............................. 69
TomBanks
The EmergentNatureofTimeandtheComplexNumbers
inQuantumCosmology ......................................................... 109
GaryW.Gibbons
ThePhantomBounce:ANewProposalforanOscillatingCosmology .... 149
KatherineFreese,MatthewG.Brown,andWilliamH.Kinney
NotesonTime’sEnigma......................................................... 157
LauraMersini-Houghton
AMomentousArrowofTime................................................... 169
MartinBojowald
CantheArrowofTimeBeUnderstoodfromQuantumCosmology?...... 191
ClausKiefer
OpenQuestionsRegardingtheArrowofTime............................... 205
H.DieterZeh
Index............................................................................... 219
v
Introduction
Time is of central importance to science and philosophy. And yet, the simplest
questions – “is time real, or is it an essential part of the structure of human
intellect?” – remain largely controversial. Theories of nature can be broadly
categorized into two sets of information:physicallaws which relate the sequence
ofstates ofa system, andinitialconditionsdeterminedata fixedmomentin time.
Clearly,adescriptionofthesuccessionofstatesorthechoiceofaninitialmoment
wheredataaboutthesystemisdefined,alsoinvolvetime.Understandingthisturns
outtobeasdifficultasprobingtheoriginsoftheuniversesincebothphysicallaws
andinitialconditionsassumeaconceptoftime,which,inmostcases,isinseparably
interwoveninto the theory and its predictedoutcomes. Thoughtime is ubiquitous
and intuitive, it still defies comprehension. Disentangling ourselves from time to
enableobjectiveandindependentinvestigationisthechallenge.
Understanding the nature and the direction of time has occupied the minds of
philosophers and scientists throughout history. It continues to do so. As far back
as the fifth century, St Augustine wrote in Confessions, Book 11: “what then is
time? If no one asks me I know. If I wish to explain it to one who asks, I know
not... Mysoulyearnstoknowthismostentangledenigma”.Theenigmapersists.
Theyearningfor understandinghasnow fallenon physicistsworkingonthe most
fundamentalquestionsaboutthecosmosandtheoriginsoftheuniverse.
Whatistheenigmaoftime?
1. Thenatureoftime:istimeaninherentandintrinsicingredientofnatureordidit
emergeonlyatthebigbang?
2. The arrow of time: why is there a clear direction from past to future, i.e. what
breaksthetimetranslationsymmetryandsetsanarrowoftime?Whyshouldthe
birthoftheuniversebedeterminedbythisdirection?
3. The time-symmetryof physicallaws: why is it that the laws of physics, which
describetheuniversewelivein,cannotdistinguishbetweenpastandfuture?How
canphysicallawsrespecttimetranslationsymmetrywhentheuniversebreaksit
atthebigbang?
L.Mersini-HoughtonandR.Vaas(eds.),TheArrowsofTime,FundamentalTheories 1
ofPhysics172,DOI10.1007/978-3-642-23259-6 1,
©Springer-VerlagBerlinHeidelberg2012
2 Introduction
This book describes contemporary views of physicists on the nature of time, the
originoftimetranslationsymmetrybreaking,andtheimplicationsthisenigmahas
ontheoriginandpredictionsofphysicallaws.
Aconsistenttreatmentofthethreetimeenigmasdescribedabove,ispresentedin
LauraMersini’schapterinthecontextofthemultiverse.Theproblemisaddressed
bytakingtheviewthatthe“local”timeinouruniverseshouldbedistinguishedfrom
the fundamentaltime of the multiverse.The multiverse is a closed system, thusit
preservesthetimesymmetry.Ouruniverseisanopensubsystemandtheeventofits
birthbreaksthetimesymmetrylocallycreatinganarrowoftimeinitsdomain.Since
the physicallaws in our universeare inheritedfromthe multiversethen it follows
thattheyaretimesymmetricdespitethefactthatthewholeuniversehasbrokenthe
timesymmetryfromthemomentofthebigbang.
An overview of the many arrows of time and their connections is given by
Ru¨diger Vaas. He discusses different explanations for their origin and focuses on
usefulconceptualdistinctions.Furthermorehesuggestsamultiverseframeworkin
whichthe(orour)big bangcreatedthearrowsoftime. Inthisframework,thebig
bangmighthaveoriginatedassomesortofpseudo-beginninginaquantumvacuum
thathasnodirectionoftime(macrotime)butneverthelesssomesortofsymmetric
microtime. It is even possible that time ends – although paradoxically, it may do
so only temporarily.Some recent cosmological models do in fact instantiate such
pseudo-beginningand-endingscenarios.
The close correlation between timekeeping devices and physical laws is
addressed both in the chapter by Rodolfo Gambini, Rafael A. Porto, and Jorge
PullinandinthatbyAndreasAlbrechtandAlbertoIglesias.AlbrechtandIglesias
focus on the general case of the ambiguity associated with the choice of clocks,
leadingtotheimmediateimplicationthatwecannothavea fixedsetoflawssince
different clocks would lead to different predictions of the theory. The view taken
there is that the problem of clock ambiguity may be bypassed if physical laws
emergestatisticallyfromarandomtime-independentHamiltonian.
Gambini, Porto, and Pullin present crucial aspects of the impact clocks have
on quantum theory, specifically the measurement problem. Devices that measure
time,likeallquantumsystems,aresubjecttoquantumfluctuations.Thereforethey
are constrained by a fundamental bound on the precision of their timekeeping
ability.Theintrinsicuncertaintyofclocks,givenbythisbound,makesitunrealistic
to expect an accurate, deterministic measurement of time in quantum systems,
includingphysicsnearthebigbangorablackhole.
Martin Bojowald tackles the issue of clock ambiguity and its quantum uncer-
tainty,basedona phenomenologicalmodelinspiredby quantumgravity,whereby
changingclocksisequivalenttoagaugetransformation.
Severalimplicationsof time’s arrow,alongwith proposalsthat circumventthis
problem, are presented in the chapters by Tom Banks, by Gary W. Gibbons, by
KatherineFreese,MatthewG.Brown,andWilliamH.Kinney,andbyH.DieterZeh.
Theoriginofthecosmicarrowoftimeiscloselyrelatedtotheoriginsoftheuniverse
bythesecondlawofthermodynamics.Accordingtothislaw,theuniversemusthave
Introduction 3
startedinanincrediblyordered(lowentropy)stateinordertobeconsistentwiththe
observedtime’sarrow.
The possibility that the origin of the arrow of time is rooted in quantum
cosmology is presented in the chapter by Claus Kiefer. This origin would be a
consequenceofimposinglowentropyboundaryconditionsonthewavefunctionof
theuniverse.Alowentropyboundaryconditionisanaturalchoicesincethedeco-
herenceprocessincreasestheentropyofthewavefunctioninanirreversiblemanner.
Tom Banks advocates applying the holographic principle to the Boltzmann–
Penrose question of why our universe started in such a low entropy state, while
Freese, Brown, and Kinney provide a concrete model of “phantom bounces and
oscillatingcosmology”inwhichtheuniverseisnaturallydriventhroughlowentropy
states at the start of each cycle. Gibbonsproposesa sharp form of Thorne’shoop
conjecturefortheformationofblackholes,whichrelatesBirkhoff’sinvarianttothe
ADMmassoftheoutmostapparenthorizon.
An interesting question related to time’s enigma is the puzzle of why different
arrowsoftime,suchasforexample,thecosmicarrowdeterminedbytheexpansion
of the universe, the biological arrow determined by (say) human ageing or the
thermodynamicarrowdeterminedbytheincreaseinentropy,agreewitheachother.
H.DieterZehmakesthecasethatthe“MasterArrowofTime”(thecombinationof
alltime’sarrows)doesnothavetobethesameasaformaltimeparameterneeded
to measure the succession of global states. Zeh also discusses the arrows in both
classical and quantum physics, the retardation of variouskinds of correlation,the
dynamicalroˆle of quantum indeterminism, and differentconcepts of timelessness
(quantumgravityincluded).
Reading through the chapters of this book takes us on a fascinating voyage
through the diversity of current schools of thought on the very basic question –
what is time? A question that remains stubbornly obscure despite centuries of
investigation.Time,theentityweareallintuitivelywiredtoacknowledgeandtake
forgrantedfrombirth.
As Lord Byron wrote: “Time! The corrector when our judgments err...”
Hopefully time will tell which of the judgmentspresented in this book will stand
thetestoftime.
Time After Time —
Big Bang Cosmology and the Arrows of Time
Ru¨digerVaas
Abstract Time, as familiar as it seems to us in everyday life, is one of the
greatestpuzzlesofscienceandphilosophy.Inphysicsandcosmologyitisespecially
mysterious why time appears to be “directed”, that is, why there seems to be an
essential difference between the past and the future. The most basic known laws
of nature do not contain this asymmetry. And yet, several arrows of time can be
distinguished – at least ten, in fact. However, it is unclear whether any of them
are fundamental or whether others can be reduced to these, and it is not known
how the direction of time could be explainedconvincingly.From the growingbut
still astonishingly low entropy of the observable universe, it seems plausible that
thesolutionofthemysteryisconnectedwithcosmologyandanexplanationofthe
big bang. This could require a new fundamental law of nature (which might be
related to a particular geometry)or specific boundaryconditions(which mightbe
comprehensible within the framework of a multiverse theory). Or it may be that
time’s direction is fundamental and irreducible, or an illusion and not explicable,
but can only be “explained away”. It is even more confusing that not all of these
alternativesaremutuallyexclusive.Furthermore,thereisa plethoraofapproaches
toexplainthebigbang.Somemodelspostulateanabsolutebeginningoftime,others
aneverlastinguniverseormultiverseinwhichthebigbangisaphasetransition,and
maybetherearemyriadsofbigbangs.Sothelowentropyoftheobservableuniverse
mightbea randomfluctuation–whereaselsewhereevenoppositethermodynamic
directionsoftimemayarise.Perhapsthe(orour)bigbangjustcreatedthearrowsof
time,ifitoriginatedassomesortofpseudo-beginninginaquantumvacuumthathas
nodirectionoftime.Thusitseemsusefultoconceptuallydistinguishanundirected
microtimeanda directedmacrotime.Itis evenpossible that time ends– although
paradoxically,itmaydosoonlytemporarily.
R.Vaas((cid:2))
bildderwissenschaft,Ernst-Mey-Str.8,D-70771Leinfelden-Echt.,Germany
e-mail:[email protected]
L.Mersini-HoughtonandR.Vaas(eds.),TheArrowsofTime,FundamentalTheories 5
ofPhysics172,DOI10.1007/978-3-642-23259-6 2,
©Springer-VerlagBerlinHeidelberg2012
6 R.Vaas
Man is ... related inextricably to all reality, known and unknowable ... plankton, a
shimmering phosphorescence on the sea and the spinning planets and an expanding
universe,allboundtogetherbytheelasticstringoftime.Itisadvisabletolookfromthe
tidepooltothestarsandthenbacktothetidepoolagain.
JohnSteinbeck:TheLogfromtheSeaofCortez(1951)
Talkin’boutthatyouthfulfountain
Talkin’boutyouandme
Talkin’bouteternity
Talkin’boutthebigtime
NeilYoung:BrokenArrow(1996)
1 TheDirection ofTime
“Time flowing in the middle of the night, / And all things creeping to a day of
doom,”wrotetheBritishpoetAlfredLordTennyson.Yetthisunceasingstreamof
time, existing apparently without dependence on its recognition, is perhaps only
an illusion – but also a problem. Because the known laws of physics are time-
symmetric.Sotheyneitherentailnorpreferadirectionfrompasttopresent.
However, our everydayexperience teaches us the opposite. For only processes
with a clear direction are observed in the complex systems of nature and culture:
blossomsbecomeapplesthatlaterdecompose;milkdropsintoblackcoffee,making
itbrown;aglassfallsfromthetableandburstsintoathousandpieces.Evencyclic
processesofnaturesuchastheseasonsorthephasesofthemoonarepartsofirre-
versibledynamics.Whoeverwatchesmoldturningintoaredapple,milkdropshop-
pingfromacoffeecup,orshardsbeingresurrectedintoaglassprobablywouldfeel
likeheisinthewrongmovie–orsimplywatchingonethatisrunningbackwards.
Irreversibility is why – or how – the formation and development of complex
structures is much less likely than their decay or something turning into dust and
ashes. By use of the concept of entropy this can be quantified physically: it is a
measure of a system’s degree of disorder. And disorder is much more probable
than order. There are, for example, significantly fewer possibilities of molecular
combinationforasmalldropofmilkincoffeethanforagoodmixing.Thisiswhy
entropy only increases on average, as the second law of thermodynamics states,
while the first law expresses the conservation of energy (see [28,29,32,91] for a
historicalintroductiontothermodynamics).
Thedevelopmentoflocalorderdoesnotcontradictthesecondlawofthermody-
namics.Contrariwise,itcreatesmoredisorderwithintheentiresystem.Ingeneral,
entropydoesnotdecreaseglobally,butcandosolocally.Therefore,theformation
ofcomplexstructures,inotherwordsorder,isnotimpossible,butitoccursonlyat
theexpenseofagreateramountofdisorderintheenvironment(see,e.g.,[65,66]).
Cleaning your desk, for instance, means eating more lettuce, the leaves of which
gaintheirenergyfromnuclearfusioninthesun–localorderincreases,yetsodoes
theamountofchaosinthesolarsystem.