Cyclical Serpent: Prospects for an Ever-Repeating Universe Paul Halpern
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Linde
Foreword
Library of Congress Cataloging-In-Publication Data
Halpern, Paul, 1961-
The cyclical serpent : prospects for an ever-repeating universe I Paul Halpern : foreword by Andrei Linde : all drawings courtesy of Felicia Hurewltz. p. cm.
Includes bibliographical references and Index.
1. Cosmology. I. Title.
CB981 . H25 1995
523. 1--dc20
95-1806 CIP
Some parts of the Foreword are based on the materials contained in "The Self-Reproducing Inflationary Universe," ScientificAmerican, Vol. 271, No. 5 (November 1994):48-55 and in ParticlePhysicsandInflationaryCosmology (Chur, Switzerland: Harwood Academic Publishers,1990), both of which were written by Andrei Linde.
ISBN 978-0-306-44923-9
ISBN 978-1-4899-6036-8 (eBook)
DOI 10.1007/978-1-4899-6036-8
©1995 Paul Halpern
Originally published by Plenum US in 1995.
Softcover reprint of the hardcover 1st edition 1995 10987654321
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form orby any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher
Thanks to Robert Marande, Nancy Cunningham, Elizabeth Bressi-Stoppe, Charles Gibley, Philip Gerbino, and Allen Misher for their strong support, to DuraiSabapathi forhisinsightfulcomments on Hinduism, andtoothermembersoffacultyandstaffofthePhiladelphia College of Pharmacy and Science. I also appreciate theencouragementofmy family and friends for thisproject, including my parents, Stanley and Bernice, and my brothers, Kenneth, Alan and Richard, as well as Elana Doering, Michael Erlich, Fred Schuepfer, Joseph and Arlene Finston, JanetGala,JenniferandFredSchwartz,SimoneZelitch,Scott Veggeberg,andCarolyn Brodbeck. Thanks toAndrei Linde fornumerous helpfulcomments. My agent,JohnWare, deservesaspecialwordofthanksforhisenthusiasticworkon thisproject, as does myeditor, Linda GreenspanRegan, for her many helpful suggestions. And most of all, heartfelt thanks to my new wife, Felicia Hurewitz, for her loving support.
Acknowledgments
The graphic art in this book, aside from the photographs,wasrenderedbyFeliciaHurewitz.
WheredidourUniversecomefrom?Whatisits fate?Whatistheoriginoflife?Whatwillhappentousinthefuture?
For thousands of years people have been trying to answer these questions. They came up with a variety of completelydifferent ideas. Westernscienceoriginally consideredtheUniverseasbeingstaticandperhapsevenfinite. Meanwhile, Indianculture gave rise to the idea ofaneternallychangingUniverse,comingthroughmanyperiods of formationanddestruction.
Tl}e20thcenturybroughttolifenewtheories describingourUniverse,andnewexperimentalevidencesupportingthem.Firstofall,itwasrealizedthatourUniverseisnot static.ItchangesintimeinaccordancewithEinstein'stheory ofgravity. Anewpicture oftheworld emerged,whichwas calledtheBigBangtheory.Thistheoryassertedthatatsome
initialmomentoftimethewholeUniversewascreatedfrom "nothing" as a huge rapidly growing ball of fire. As the Universe expanded, this fire subsided. Its remnants still surround us in the form of the cosmic microwave background radiation with a very small temperature (2.7 kelvins).
Creation of this new cosmological paradigm was extremely painful. Even Einstein originally did not want to accept the idea thattheUniverse changed intime;he tried to modify his own equations in order to come back to the oldpictureofa static Universe. However,the theory ofthe Big Bangwasinavery goodagreementwithobservational data, and gradually everybody agreed thatit mustbe correct. Itseemedthatwehavefinallydiscoveredtheultimate theorydescribingourcosmichome.
Unfortunately, this attitude was too optimistic. By the end of 1970's it was understood that it is very difficult to make cosmology consistent with the new theories of elementary particles. Then everybody suddenly realized that the standardBigBangtheoryisplaguedbymanydifferent problems. Whatwasbefore theBig Bang?Whyis theUniversesobig?Whyisitsgeometry sosimilartothegeometl) of a flat tablewhere parallel lines donotintersect? Why if the Universe sohomogeneous?Ifitmustbehomogeneous then how have galaxies been created? How could all th1 differentpartsoftheUniversesynchronizethebeginningo theirexpansion?
Alltheseproblems(andotherswhicharetootechnica to be discussed here) are extremely difficult. Fortunate!� fifteenyears ago it was realized thatmany of themcanb resolved in the context of a relatively simple theory, th theoryofinflationaryUniverse.Accordingtothistheory,th Universe at the very early stages of its evolution cam
through the stage of inflation, exponentially rapid expansion in a kind of unstable vacuum-like state (a state with large energy density, butwithout elementary particles). This stage could be very short, but the Universe within this time became exponentially large. At the end of inflation the vacuum-like state decayed, the Universe became hot, and its subsequent evolution could be described by the standard Big Bang theory.
This theory originally was considered as a particular version of the Big Bang scenario. However, at the present time inflationary theory seems to be much more general than the original Big Bang theory. During the last fifteen years, inflationary cosmology has encompassed the theory of the Big Bang, in the same sense as Einstein's general theory of relativity encompassed the theory of gravity developed by Newton. Without understanding of this theory it is difficult to appreciate many other ideas discussed in this book. Therefore we will say here a few words about inflation.
There were several different attempts to develop inflationary theory. Unfortunately, because of political barriers between Russia and the United States, the history of this theory is only partially known to American readers.
The first realistic version of inflationary cosmology was proposed in 1979 by Alexei Starobinsky of the L. D. Landau Institute of Theoretical Physics in Moscow. For two years his model remained the main topic of discussion at all conferences on cosmology in the USSR. However, his model was rather complicated, being based on the theory of anomalies in quantum gravity, and it did not really address the problem of initial conditions for inflation.
In 1981 Alan H. Guth of the Massachusetts Institute of Technology suggested a much simpler version of inflation-
arytheory,based onthetheoryofcosmologicalphasetransitionswithsupercooling.Thistheorywasproposedin1972 byDavidA. Kirzhnits andmeattheP.N. LebedevPhysics InstituteinMoscow. ThemodelsuggestedbyGuth (which now is called "old inflation") had a very clear physical motivation, and itimmediatelybecame very popular. Unfortunately,unliketheStarobinskymodel,theoldinflationarytheorydidnotwork.Afterinvestigatinghismodelfora year, Guth finally renounced-it in a paper he co-authored withErickJ. WeinbergofColumbiaUniversity.
In 1982 I introduced the new inflationary universe scenario, which later was also discovered by Andreas Albrecht and PaulJ. Steinhardt ofthe University ofPennsylvania.ThisscenariowasfreeofthemainproblemsofGuth's model,butitwasstillnotveryrealistic.
Mostoftheinflationarymodelswhichexistatpresent are based on the idea of chaotic inflation which I have proposedin1983.Chaoticinflationscenariodoesnotrequire complicated quantum gravity effects or phase transitions with supercooling. It does not require even the standard assumption thatthe Universe originally was hot. The simplest version ofthis scenario describes the Universefilled by a so-called massive scalar field. Such fields appear in mostofthetheoriesofelementaryparticlesdevelopedduringthe last25years. Itcanbe shownthatifthe scalar field originallywassufficientlylargeandhomogeneous,itcould changeitsvalueonlyveryslowly.Therefore,foralongtime itsenergydensity remainedalmostconstant. Accordingto Einstein's theory of gravity, the Universe filled by matter with a constant energy density should expand exponentially,whichcorresponds tothestageofinflation.
The main idea of the chaotic inflation scenario is so simple thatitishardto understandwhyitwasnotdiscov-
ered 50 years ago. Meanwhile its consequences are very dramatic.InthesimplestversionofthistheorytheUniverse during inflation could expand approximately 101012 times. Thisnumberismodel-dependent,butitishuge inallrealisticinflationarymodels.SuchanexpansionmakestheUniverse extremely large and stretches away all its inhomogeneities.Geometricpropertiesofourspacebecome similartothepropertiesofanalmostflatsurfaceofahuge inflatingballoon. ThisexplainswhyourUniverseissobig, why it is so homogeneous and isotropic, and why its geometricpropertiesaresoclosetothepropertiesofaflatspace. Not only the Universe, but even small quantum fluctuations of various fields rapidly grow during inflation. Suchfluctuationsalwaysexistinvacuum,buttypicallythey are microscopically small and short-lived. However, quantum fluctuations amplified during inflation may become extremelylarge.Thesefluctuationslatergaverisetogalaxies,andalsotosmallperturbationsinthe2.7kelvintemperatureofthemicrowavebackgroundradiation. In 1992these perturbations were found by the Cosmic Background Explorer(COBE)satellite,afindinglaterconfirmedbyseveral otherexperiments.
Thereisonepeculiarpropertyofthenewtheorywhich makes it especiallyrelevantto the discussion contained in this book. In certaincases quantum fluctuations amplified duringthe rapid expansion oftheUniverse may considerably increase the value of the scalar field which drives inflation. The probabilityof such events is very small, but those rare parts of the Universe where it happens begin expandingwithevengreaterspeed. This createsalotofnew spacewhereinflationmayoccur,andwherelargequantum fluctuations becomepossible. As a result, the Universe enters a stationary regime of self-reproduction: Inflationary
Universe permanently produces new inflationary domains, which in turn produce new inflationary domains. Such a Universe looks not like a single expanding fireball created in the Big Bang, but like a huge self-reproducing fractal, like a tree consisting of inflationary balls producing new and new balls, of all possible types.
According to many inflationary models, quantum fluctuations at the stage of inflation could be so large that they could change properties of the vacuum state in different parts of the Universe. As a result, the Universe becomes divided into many exponentially large parts where the laws of low-energy physics and even dimensionality of spacetime may be different.
If this theory is correct, we are witnessing the most dramatic change in our picture of the world. The Universe becomes immortal. Different parts of the Universe may appear and disappear again, but the Universe as a whole will exist forever. This does not mean that our own civilization can live for an indefinitely long time. Life in our part of the Universe may eventually disappear, but even if this happens, there will be infinitely many other parts of the Universe where life will appear again and again, in all its possible forms.
The new vision of the world may be considered as a synthesis of ideas elaborated by many different cultures. On a small scale the Universe looks like a single spherically symmetric expanding ball of matter created in the Big Bang. On a greater scale we see new parts of the Universe appearing and disappearing again. And if we try to investigate the global structure of the Universe-the distribution of these new balls, the properties of matter inside them-then we may see thattheseproperties allover thewholeUniverseon average donotdepend on time. Justlikea river whichbrings
new water but still looks the same, theUniversechanges all the time, but in a certain sense it remains stationary. If this is the case, then we may be forced to abandon the standard assumption that physics alone can give a complete explanation to the properties of the world around us. This assumption was based in part on the idea that the Universe is everywhere the same. This belief was called the "cosmological principle." If the Universe is everywhere the same, then there should be some physical reason why it appeared in this particular state. Thus one should find a theory which explains why our Universe must be the way it is, why the proton must be 2000 times heavier than the electron, why our space-time must be four-dimensional, etc.
The cosmological principle was based on the observational fact that our part of the Universe on a very large scale is almost exactly uniform. At present we know only one physical mechanism which explains why the Universe around us is so uniform. It is given by inflationary cosmology. However,simultaneously with explainingwhyour part of the Universe is homogeneous, this theory predicts that on a much greater scale the Universe must be absolutely inhomogeneous, that there are some places in the Universe where inflation still goes on, and that the Universe after inflation may become divided into many exponentially large parts with different properties.
Thus, inflationary theoryeffectivelyeliminates the cosmological principle. Instead of insisting that the Universe everywhere must be the same, we should examine all those exponentially large parts of the Universe which can emerge after inflation. Then we should take into account that we cannot live in those parts where the electrons are too heavy, where the gravity forces are much stronger, or where the number of dimensions of space-time is different from four.
Thus we can get a partial explanation of the properties of our world by eliminating from our consideration all those parts ofinflationaryUniversewherewecannotlive. This philosophy is based on the so-called anthropic principle. This principle was not particularly popular amongphysicists.Itwasbasedonahiddenassumptionthat the Universe was created many times, one after another, untilthefinalsuccess.Butwhowasdoingthisjob,whatwas the purpose, andwhy itwasnecessary forhim to work so hard?Therewasabsolutelynoneed to createtheUniverse whichwasalmostperfectlyhomogeneousfarawayfromus. Itwouldbequitesufficienttocreateasmallislandofhomogeneityinavicinityofasolarsystem.
The new cosmologicaltheorygives us apossibilityto answer these questions. Inflationary Universe recreates itselfin allits possible forms, andwhenit does so, itcreates islands ofhomogeneityofatypicalsize muchgreater than the size ofthe part oftheUniversewhichwecansee now. Thus, the anthropic principle becomes an important part of the scientific approach to an explanation of our world. There is nothing mysterious about it; we are just tryingtouseourknowledgeoftheinhabitantsofourcosmic home to explain the properties of the small part of the Universe where theycanlive. However, onemaytryto go in an opposite direction as well. We may try to use our investigationofthepropertiesoftheUniversetounderstand somethingaboutourselves.
For example, several years ago we thought that the wholeUniversewasbornabout15billionyearsago,andif theUniverseisclosedthenitshouldeventuallycollapseand disappear.However,nowinflationarytheoryteachesusthat the Universe as a whole never dies. Moreover, there is an interestingpossibilitypresentlyunderinvestigation.Itmay
Foreword
happen thatwhenthe density of a collapsing part of the Universe becomes sufficiently large, it begins to expand again, though not in our space, but in some other space whichisinacertainsensedualtoours.
Itishardtosaywhetherthisexamplecanteachusany lesson concerning ourownfate. Weknowthat each of us wasborn sometime ago. We alsoknowthat each ofus is goingtodie,andthewholeUniverseofourthoughts,feelings and memories is going to disappear. Butwhat if our knowledge of ourselves is as incomplete as our previous knowledgeabouttheUniverse?Theonlythingwecando atthispointistodrawuponanalogiesfromthehistoryof sciencewhichmayprovetobeinstructive.
PriortotheadventofEinstein'stheoryofgravity,space andmatterwereconsideredastwofundamentallydifferent entities. Space was thought to be a kind of three-dimensional coordinate grid which, when supplemented by clocks,couldbeusedtodescribethemotionofmatter.Space did not possess any intrinsic degrees of freedom, and it playedasecondary,subservientroleasatoolforthedescriptionofthetrulysubstantialmaterialworld.
Thegeneraltheoryofrelativitybroughtwithitadecisive change in thispoint of view. Space and matter were found tobe interdependent, and there was no longer any question of which was the more fundamental of the two. Space was also found tohave its owninherentdegrees of freedom, gravitational waves, which are associated with perturbations of the metric. Thus, space can exist and changewithtimeintheabsenceofelectrons,protons,photons,etc.;inotherwords,intheabsenceofanythingthathad previouslybeen subsumedby the termmatter. (Note that because oftheweaknesswithwhichtheyinteract,gravita-
tionalwavesare exceedinglydifficulttodetectexperimentally, anas-yetunsolvedproblem.)
A morerecenttrend,finally,hasbeentowardaunified geometrictheoryofallfundamentalinteractions,including gravitation. Prior to the end of the 1970's, such a program, a dream of Einstein's, seemed unrealizable; rigorous theorems were proven on the impossibility of unifying spatial symmetrieswiththeinternalsymmetriesofelementaryparticle theory. Fortunately, these theorems were sidestepped after the discovery of supersymmetric theories. With the help of supergravity and superstring theories, one may hopetoconstructatheoryinwhichallmatterfieldswillbe interpreted in terms of the geometric properties of some multidimensionalsuperspace.Spacewouldthenceasetobe simplyarequisitemathematicaladjunctforthedescription of the real world, and would instead take on increasingly greater independent significance, gradually encompassing allthematerialparticlesundertheguiseofitsownintrinsic degreesoffreedom.
Many people believe that consciousness, like space beforetheinventionofgeneralrelativity,playsasecondary, subservient role, being just a function of matter and a tool for the description of the truly existing material world. Indeed, itisveryeasytoforgetthatourperceptionsarethe only "objects"whichwereallyknowtoexist.Thenotionof matter appearsonlyatthesecondstageofourinvestigation of the world, when we find out that it is convenient to describetheevolutionofourperceptionsusingtheconcept ofmatter obeyinglawsofphysics. Theselawsappear tobe souniversal, thatatsomestageitbecomesveryconvenient to switch our position and to treat them rather than our perceptions aselementsofreality. Thereforeitisquitepossiblethatnothingsimilar tothemodificationoftheconcept
ofspacewilloccurwiththeconceptofconsciousnessinthe comingdecades. Butwhatif consciousness, likespace,has its own intrinsic degrees of freedom, and that neglecting these will lead to a description of theUniverse that is fundamentally incomplete? What if different perceptions shouldbe considered as really existing objects Whatif itwill tum out, with the further development of science, that the studyoftheUniverseandthestudyoflifeshouldbeinseparably linked, and that ultimate progress in the one will be impossiblewithoutprogressintheother?Isitpossibleatall thateventuallythetheoryofconsciousnesswillencompass thetheory ofthe "realworld"?
All ofthesequestionsmightseemsomewhat naive. A healthyconservatismofscienceshouldkeepusintherealm of the traditionalapproachtoour world and to the lawsof physics describing it, as longas this approach continues to be productive. However, it is impossible to avoid thinking aboutthesequestionsinthecontextofquantumcosmology. For example, those who study quantum cosmology know that the wave function of the Universe, which determines theprobabilitytofindtheUniverseinagivenstate, does not depend on time. However,weknowthattheworldaroundus changes. Theresolutionoftheparadox isthatwenever ask questions about the whole Universe. We are dividing the Universe into two systems: an observer and the rest of the Universe.Thenitcanbeshownthatthewavefunction ofthe rest ofthe Universe doesdependontimeasmeasuredbythe observer, even thoughthe wave function of the whole systemistime-independent.Inotherwords, weseetheUniverse evolvingintime,eventhoughthenotionofchangedoesnot apply to the Universe as a whole. Does this mean that the Universe without us is dead, and only observers make it alive?
We do not have final answers to all these questions. Fortunately,inmostsituationsofourdailylifewecansafely ignore them. However, working in the field of quantum cosmology without even trying to discuss these questions gradually becomes as difficult as working on the Big Bang theory withoutknowingwhytheUniverseissobigandso homogeneous, why nobody has ever seen parallel lines intersect, why space-time is four-dimensional, and so on. Now, with plausible answers to these questions given by inflationarycosmology,onecanonlybesurprisedthatprior tothe1980's,itwassometimestakentobebadformevento discuss them. The reason is really very simple: by asking such questions, one confesses one's own ignorance of the simplest facts of daily life, and moreover encroaches upon a realm which may seem not to belong to the world of positive knowledge. It is much easier to convince oneself thatsuchquestionsdonotexist,thattheyaresomehownot legitimate,or thatsomeoneansweredthemlongago. It would probably be best then not to repeat old mistakes,butinsteadtoforthrightlyacknowledgethattheproblemofconsciousnessandtherelatedproblemofhumanlife anddeatharenotonlyunsolved,butatafundamentallevel theyarevirtuallycompletelyunexamined.Itistemptingto seek connections and analogies of some kind, even if they are shallow and superficial ones at first, in studying one more greatproblem, thatofthebirth, life, and deathofthe Universe. It may conceivably become clear at some future time that these two problems are not so disparate as they mightseem.
Thisbookmakesseveral importantstepsinthisdirection. Itcontains manyinterestinginsightsandanalogies. It alsocontainsadiscussionofsomeideaswhichImighttake in a different direction. But that is what makes this subject
soexciting.Thenewcosmologicaltheoriesaresounusual that sometimes we do not even know how to formulate correct questions, so there is no surprise that we do not alwaysagreeabouttheanswers.Wearetryingtolearnmore abouttheUniverseandaboutourownplace in it.Thisisa challenging task, and we should try to fulfill it in a way whichwouldmatchtheeffortsofthosewhowerethinking aboutthefateoftheUniversethousandsofyearsbeforewe wereborn.
Whyworryaboutthefateoftheuniverse?Aren't there enough preoccupations in life-taxes, mortgage payments, school, work, kids, parents, etc.-to fill one's days and nights with sufficient anguish?Andhowaboutthosewhoarestrugglinghardjustto putfoodonthetable?Whyshouldtheytroublethemselves withtheultimatecosmicquestions?
As a cosmologist, studying the properties of the universe asawhole, I oftenfindithardtojustifyourspending billions of dollars for astrophysical projects such as space telescopes,whentherearesomanysocialproblemsyettobe solved. Yetthealternative-toretreatfromourcommitment tounderstandingthecosmos-wouldsurelybeatragedy.
Our species aspires to push ever onwardtoward new frontiers. In thisvein,theuniverseitselfrepresentstheultimatechallenge. Humankindwillscarcelybecontentuntilit has conquered the mysteries of space and time, and has learnedfromwhereithascomeandtowhereitisgoing.
This book ponders one possible answer to these riddles.Perhapsspaceperiodicallyrecreatesitselflikeasnake
sheddingitsskin(or,toemploythetitleimageofthisbook, like a serpent continuously devouring itself). This is an ancient descriptionofthe cosmosthathasbeenrevivedby contemporary theoretical physicists. Because there is no beginningnorend,itistrulyaself-containedpicture.Therefore,itavoidsalltheconundrumsassociatedwiththequestion:whatcamebeforethestartoftime?
There are othercompetingmodels that suggest alternative cosmological approaches. Insome,theuniversehas a startingpointbutno stoppingpoint; inothers, time has rigid boundaries. To resolve this debate, we need to peer fartherandfartherintospace,withinstrumentssuchasthe HubbleSpaceTelescope.
Space science comes witha cost, and requires a firm societalcommitment. I believethatthis generallyismoney andeffortwellspent. Studyingthecosmosinvolvesreplacing,foratime,one'spersonalconsiderationswithuniversal matters. Ibelievethatitiswellworththeexchange.
Solet'ssitback,relax,putasideourordinaryconcerns forthetimebeing,andcontemplatetheultimatedestinyof theuniverse.
REFERENCES 281
RELATEDREADING 283
INDEX 293
