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which offers a broad range of a
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titles, both classic and more id
recent, representing some of O
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Edited by n
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Shahn Majid T
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With contributions by
Alain Connes, Michael Heller, Roger Penrose,
John Polkinghorne, Andrew Taylor
On Space and Time
This book gets to the heart of science by asking a fundamental
question about its essence: what is the true nature of space and
time? Both defy modern physics, and scientists find themselves
continually searching for answers. This unique volume brings
together world leaders in cosmology, particle physics, quantum
gravity, mathematics, philosophy and theology, to provide fresh
insights into the deep structure of space and time. In an attempt
to understand the question, subjects ranging from dark matter
to the philosophical and theological implications of spacetime
are covered, ensuring that the issue is thoroughly explored.
Interesting and thought-provoking answers provide a well-
rounded read.
‘ ... a unique collection of essays ... the philosophical Edited by
content is thought-provoking ... a worthwhile read’.
Federation of Astronomical Societies Newsletter
Majid
On Space
and Time
Cover image: © Floriana Barbu
Cover design: Andrew Ward
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On Space and Time
Whatisthetruenatureofspaceandtime?Theseconceptsareatthe
heartofscience,andareoftentakenforgrantedevenbypractising
scientists,but,asthisvolumeexplains,theyremaindeeplywrapped
inenigma.Theirstructureatboththesmallestpre-subatomicand
thelargestcosmologicallevelscontinuestodefymodernphysicsand
mayrequirerevolutionarynewideasforwhichscienceisstill
grasping.
Thisuniquevolumebringstogetherworldleadersincosmology,
particlephysics,quantumgravity,mathematics,philosophyand
theology,toprovidefreshinsightsintothedeepstructureofspace
andtimeanditswidercontext.AndrewTaylorexplainstheevidence
fordarkmatteranddarkenergy.ShahnMajidarguesthatspaceand
timeshouldbequantum.RogerPenroseexplainswhatinhisview
comesbeforethe‘BigBang’.AlainConnesarguesthatmatteris
geometryasafinestructuretospacetime.MichaelHellerexplores
thephilosophicalandtheologicalimplicationsofspacetime.John
Polkinghornearguesforatheoryofhowtimeunfolds.
Inthisbook,expertsoffer–ingenerallynontechnicallanguage–
somedistinctiveperspectivesonthefundamentalmysteriesand
gapsinourgraspofphysicalreality...enlighteningandfascinating
toanyonewithanenquiringmindwhohaseverwondered‘didtime
haveabeginning?’,‘isspaceinfinite’,‘whyaretherethree
dimensions?’or‘doesspacehaveanatomicstructure’?
MartinRees,ProfessorofCosmologyandAstrophysics,University
ofCambridge,andauthorofGravity’sFatalAttraction
On Space and Time
alain connes, michael heller,
shahn majid, roger penrose,
john polkinghorne and
andrew taylor
Edited by
shahn majid
cambridge university press
Cambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,Sa˜oPaulo,
Delhi, Mexico City
CambridgeUniversityPress
TheEdinburghBuilding,CambridgeCB28RU,UK
PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107641686
(cid:2)C CambridgeUniversityPress2008
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithout
thewrittenpermissionofCambridgeUniversityPress.
Firstpublished2008
Third printing 2011
Canto Classics edition 2012
Printedand bound by CPI Group (UK) Ltd, Croydon, CR0 4YY
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary
LibraryofCongressCataloguinginPublicationdata
Onspaceandtime/AlainConnes...[etal.];editedbyShahnMajid.
p. cm.
Includesindex.
ISBN978-0-521-88926-1(hardback)
1.Spaceandtime. I.Connes,Alain. II.Majid,Shahn. III.Title.
QC173.59.S65O49 2008
523.1–dc22 2008013428
ISBN 978-1-107-64168-6Paperback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracy
of URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication,
anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,
accurateorappropriate. Information regarding prices, travel timetables and other
factual information given in this work are correct at the time of first printing
butCambridge University Press does not guarantee the accuracy of such
information thereafter .
‘Absolute,true,andmathematicaltime,ofitself,andfromitsown
nature,flowsequablywithoutrelationtoanythingexternal’
IsaacNewton
‘Alreadythedistance-conceptislogicallyarbitrary;thereneedbe
nothingsthatcorrespondtoit,evenapproximately’
AlbertEinstein
‘Thefutureofourspaceandtime/Isnotgonnawitheranddie/
Thefutureofourspaceandtime/Isnotgonnasaygood-bye’
VanessaParadis/LennyKravitz
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Contents
Abouttheauthors pageviii
Preface xi
1 ThedarkUniverse 1
andrew taylor
2 Quantumspacetimeandphysicalreality 56
shahn majid
3 Causality,quantumtheoryandcosmology 141
roger penrose
4 Onthefinestructureofspacetime 196
alain connes
5 Wherephysicsmeetsmetaphysics 238
michael heller
6 Thenatureoftime 278
john polkinghorne
Index 284
About the authors
AlainConnesholdsthechairinAnalysisandGeometry
attheCollegedeFranceandisProfessorattheIHESin
ParisandatVanderbiltUniversityintheUSA.Awardeda
FieldsMedalin1982andtheCrafoordPrizein2002,he
haspioneeredthefieldofnoncommutativegeometryand
itsdiverseapplicationsinpuremathematicsandphysics.
Heisauthorofamajortextbookinthefieldand
numerousresearcharticles.
MichaelHellerisProfessorofPhilosophyatthe
PontificalAcademyofTheologyinCracow,Poland,and
anadjunctmemberoftheVaticanObservatorystaff.An
ordainedRomanCatholicpriest,heisauthorof
numerousbooksandresearcharticlesoncosmology,
philosophyandtheology.
ShahnMajidisProfessorofMathematicsatQueenMary,
UniversityofLondon.Trainedasatheoreticalphysicist
andmathematicianatCambridgeandHarvard,hehelped
pioneerthetheoryofquantumsymmetryinthe1980s
and1990s.Heisauthoroftwotextbooksinthefieldand
numerousresearcharticles.
SirRogerPenroseisEmeritusRouseBallProfessorof
MathematicsattheUniversityofOxford.Awardedthe
1988WolfPrizejointlywithStephenHawking,he
discoveredtwistortheoryinthe1970sandhasnumerous
otherresultsfromtilingstoastrophysicsandquantum
theory.PopularbookssuchasTheEmperor’sNewMind
havepresentedhisideasaboutthehumanmindandthe
relationshipsbetweenmathematicsandphysics.
Description:This book gets to the heart of science by asking a fundamental question about its essence: what is the true nature of space and time? Both defy modern physics, and scientists find themselves continually searching for answers. This unique volume brings together world leaders in cosmology, particle ph
