Hawking Origin of the Universe

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Origin of the UniverseS.W. Hawking

(Copyright 1988 Stephen W. Hawking. All rights reserved.)

[Note: This is taken from the text used by Professor Hawking's speech synthesizer. hi!e most of the spe!!ing and punctuation pecu!iarities re"uired by the computer trans!ator ha#e been corrected$ some may sti!! exist %especia!!y names&. (nknown)

The proble o! the origin o! the "niverse# is a bit like the old $"estion%

Whi&h &ae !irst# the &hi&ken# or the egg. 'n other words# what agen&y

&reated the "niverse. And what &reated that agen&y. r perhaps# the"niverse# or the agen&y that &reated it# eisted !orever# and didn*t need to

be &reated. +p to re&ently# s&ientists have tended to shy away !ro s"&h

$"estions# !eeling that they belonged to etaphysi&s or religion# ratherthan to s&ien&e. However# in the last !ew years# it has eerged that the

,aws o! S&ien&e ay hold even at the beginning o! the "niverse. 'n that

&ase# the "niverse &o"ld be sel! &ontained# and deterined &opletely by

the ,aws o! S&ien&e.

The debate abo"t whether# and how# the "niverse began# has been going

on thro"gho"t re&orded history. -asi&ally# there were two s&hools o!

tho"ght. any early traditions# and the /ewish# Christian and 'slai&religions# held that the "niverse was &reated in the !airly re&ent past. 0or

instan&e# -ishop +sher &al&"lated a date o! !o"r tho"sand and !o"r -C#

!or the &reation o! the "niverse# by adding "p the ages o! people in the ld

Testaent. ne !a&t that was "sed to s"pport the idea o! a re&ent origin#was that the H"an ra&e is obvio"sly evolving in &"lt"re and te&hnology.

We reeber who !irst per!ored that deed# or developed this te&hni$"e.

Th"s# the arg"eent r"ns# we &an not have been aro"nd all that long.therwise# we wo"ld have already progressed ore than we have. 'n !a&t#

the bibli&al date !or the &reation# is not that !ar o!! the date o! the end o!

the last '&e Age# whi&h is when odern h"ans see !irst to haveappeared.

On the other hand, some people, such as the Greek philosopher,Aristotle, did not like the idea that the universe had a beginning.

They felt that would imply Divine intervention. They prefered tobelieve that the universe, had existed, and would exist, forever.omething that was eternal, was more perfect than something thathad to be created. They had an answer to the argument abouthuman progress, that ! described. !t was, that there had beenperiodic floods, or other natural disasters, which repeatedly set thehuman race right back to the beginning.


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"oth schools of thought held that the universe was essentiallyunchanging in time. #ither it had been created in its present form,or it had existed forever, like it is today. This was a natural belief inthose times, because human life, and, indeed the whole of

recorded history, are so short that the universe has not changedsignificantly during them. !n a static, unchanging universe, the$uestion of whether the universe has existed forever, or whether itwas created at a finite time in the past, is really a matter formetaphysics or religion% either theory could account for such auniverse. !ndeed, in &'(&, the philosopher, !mmanuel )ant, wrote amonumental, and very obscure work, The *riti$ue of +ure eason.!n it, he concluded that there were e$ually valid arguements, bothfor believing that the universe had a beginning, and for believingthat it did not. As his title suggests, his conclusions were basedsimply on reason. !n other words, they did not take any account of

observations about the universe. After all, in an unchanginguniverse, what was there to observe-

!n the &th century, however, evidence began to accumulate thatthe earth, and the rest of the universe, were in fact changing withtime. On the one hand, geologists reali/ed that the formation of therocks, and the fossils in them, would have taken hundreds orthousands of millions of years. This was far longer than the age ofthe #arth, according to the *reationists. On the other hand, theGerman physicist, "olt/mann, discovered the so0called econd1aw of Thermodynamics. !t states that the total amount of disorder

in the universe 2which is measured by a $uantity called entropy3,always increases with time. This, like the argument about humanprogress, suggests that the universe can have been going only fora finite time. Otherwise, the universe would by now havedegenerated into a state of complete disorder, in which everythingwould be at the same temperature.

Another difficulty with the idea of a static universe, was thataccording to 4ewton5s 1aw of Gravity, each star in the universeought to be attracted towards every other star. o how could theystay at a constant distance from each other. 6ouldn5t they all fall

together. 4ewton was aware of this problem about the starsattracting each other. !n a letter to ichard "entley, a leadingphilosopher of the time, he agreed that a finite collection of starscould not remain motionless% they would all fall together, to somecentral point. 7owever, he argued that an infinite collection of stars,would not fall together% for there would not be any central point forthem to fall to. This argument is an example of the pitfalls that onecan encounter when one talks about infinite systems. "y using


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different ways to add up the forces on each star, from the infinitenumber of other stars in the universe, one can get differentanswers to the $uestion% can they remain at constant distance fromeach other. 6e now know that the correct proceedure, is to

consider the case of a finite region of stars. One then adds morestars, distributed roughly uniformly outside the region. A finitecollection of stars will fall together. According to 4ewton5s 1aw ofGravity, adding more stars outside the region, will not stop thecollapse. Thus, an infinite collection of stars, can not remain in amotionless state. !f they are not moving relative to each other atone time, the attraction between them, will cause them to startfalling towards each other. Alternatively, they can be moving awayfrom each other, with gravity slowing down the velocity ofrecession.

Despite these difficulties with the idea of a static and unchanginguniverse, no one in the seventeenth, eighteenth, nineteenth orearly twentieth centuries, suggested that the universe might beevolving with time. 4ewton and #instein, both missed the chance ofpredicting, that the universe should be either contracting, orexpanding. One can not really hold it against 4ewton, because hewas two hundred and fifty years before the observational discoveryof the expansion of the universe. "ut #instein should have knownbetter. 8et when he formulated the General Theory of elativity toreconcile 4ewton5s theory with his own pecial Theory of elativity,he added a so0called, 99cosmological constant55. This had a

repulsive gravitational effect, which could balance the attractiveeffect of the matter in the universe. !n this way, it was possible tohave a static model of the universe.

#instein later said% The cosmological constant was the greatestmistake of my life. That was after observations of distant galaxies,by #dwin 7ubble in the &:;5s, had shown that they were movingaway from us, with velocities that were roughly proportional to theirdistance from us. !n other words, the universe is not static, as hadbeen previously thought% it is expanding. The distance betweengalaxies is increasing with time.

The discovery of the expansion of the universe, completelychanged the discussion about its origin. !f you take the presentmotion of the galaxies, and run it back in time, it seems that theyshould all have been on top of each other, at some moment,between ten and twenty thousand million years ago. At this time,which is called the "ig "ang, the density of the universe, and thecurvature of spacetime, would have been infinite.


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conditions, all the known laws of science would break down. This isa disaster for science. !t would mean that science alone, could notpredict how the universe began. All that science could say is that%The universe is as it is now, because it was as it was then. "ut

cience could not explain why it was, as it was, =ust after the "ig"ang.

4ot surprisingly, many scientists were unhappy with thisconclusion. There were thus several attempts to avoid the "ig"ang. One was the so0called teady tate theory. The idea wasthat, as the galaxies moved apart from each other, new galaxieswould form in the spaces inbetween, from matter that wascontinually being created. The universe would have existed, andwould continue to exist, forever, in more or less the same state as itis today.

The teady tate model re$uired a modification of generalrelativity, in order that the universe should continue to expand, andnew matter be created. The rate of creation needed was very low%about one particle per cubic kilometre per year. Thus, this wouldnot be in conflict with observation. The theory also predicted thatthe average density of galaxies, and similar ob=ects, should beconstant, both in space and time. 7owever, a survey of extra0galactic sources of radio waves, was carried out by >artin yle andhis group at *ambridge. This showed that there were many morefaint sources, than strong ones. On average, one would expect that

the faint sources were the more distant ones. There were thus twopossibilities% #ither, we were in a region of the universe, in whichstrong sources were less fre$uent than the average. Or, the densityof sources was higher in the past, when the light left the moredistant sources. 4either of these possibilities was compatible withthe prediction of the teady tate theory, that the density of radiosources should be constant in space and time. The final blow to theteady tate theory was the discovery, in &?@, of a background ofmicrowaves. These had the characteristic spectrum of radiationemited by a hot body, though, in this case, the term, hot, is hardlyappropriate, since the temperature was only :.' degrees above

Absolute ero. The universe is a cold, dark placeB There was noreasonable mechanism, in the teady tate theory, to generatemicrowaves with such a spectrum. The theory therefore had to beabandoned.

Another idea to avoid a singularity, was suggested by twoussians, 1ifshit/ and )halatnikov. They said, that maybe a stateof infinite density, would occur only if the galaxies were moving


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directly towards, or away from, each other. Only then, would thegalaxies all have met up at a single point in the past. 7owever, onemight expect that the galaxies would have had some smallsideways velocities, as well as their velocity towards or away from

each other. This might have made it possible for there to havebeen an earlier contracting phase, in which the galaxies somehowmanaged to avoid hitting each other. The universe might then havere0expanded, without going through a state of infinite density.

6hen 1ifshit/ and )halatnikov made their suggestion, ! was aresearch student, looking for a problem with which to complete my+hD thesis. Two years earlier, ! had been diagnosed as having

A1, or motor neuron disease. ! had been given to understand that! had only two or three years to live. !n this situation, it didn5t seemworth working on my +hD, because ! didn5t expect to finish it.

7owever, two years had gone by, and ! was not much worse.>oreover, ! had become engaged to be married. !n order to getmarried, ! had to get a =ob. And in order to get a =ob, ! needed tofinish my thesis.

! was interested in the $uestion of whether there had been a "ig"ang singularity, because that was crucial to an understanding ofthe origin of the universe. Together with oger +enrose, !developed a new set of mathematical techni$ues, for dealing withthis and similar problems. 6e showed that if General elativity wascorrect, any reasonable model of the universe must start with a

singularity. This would mean that science could predict that theuniverse must have had a beginning, but that it could not predicthow the universe should begin% for that one would have to appealto God.

!t has been interesting to watch the change in the climate of opinionon singularities. 6hen ! was a graduate student, almost no onetook singularities seriously. 4ow, as a result of the singularitytheorems, nearly everyone believes that the universe began with asingularity. !n the meantime, however, ! have changed my mind% !still believe that the universe had a beginning, but that it was not a

singularity.

The General Theory of elativity, is what is called a classicaltheory. That is, it does not take into account the fact that particlesdo not have precisely defined positions and velocities, but aresmeared out over a small region by the


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compared to the uncertainty in the position of a particle. 7owever,the singularity theorems indicate that spacetime will be highlydistorted, with a small radius of curvature, at the beginning of thepresent expansion phase of the universe. !n this situation, the

uncertainty principle will be very important. Thus, General elativitybrings about its own downfall, by predicting singularities. !n order todiscuss the beginning of the universe, we need a theory whichcombines General elativity with $uantum mechanics.

6e do not yet know the exact form of the correct theory of $uantumgravity. The best candidate we have at the moment, is the theory ofuperstrings, but there are still a number of unresolved difficulties.7owever, there are certain features that we expect to be present, inany viable theory. One is #instein5s idea, that the effects of gravitycan be represented by a spacetime, that is curved or distorted by

the matter and energy in it. Ob=ects try to follow the nearest thing toa straight line, in this curved space. 7owever, because it is curved,their paths appear to be bent, as if by a gravitational field.

Another element that we expect to be present in the ultimatetheory, is ichard Ceynman5s proposal that $uantum theory can beformulated, as a um Over 7istories. !n it simplest form, the idea isthat a particle has every possible path, or history, in space time.#ach path or history has a probability that depends on its shape.Cor this idea to work, one has to consider histories that take placein 99imaginary55 time, rather than the real time in which we perceive

ourselves as living. !maginary time may sound like something outof science fiction, but it is a well defined mathematical concept. !tcan be thought of as a direction of time that is at right angles to realtime, in some sense. One adds up the probabilities for all theparticle histories with certain properties, such as passing throughcertain points at certain times. One then has to extrapolate theresult, back to the real space time in which we live. This is not themost familiar approach to $uantum theory, but it gives the sameresults as other methods.

!n the case of $uantum gravity, Ceynman5s idea of a 99um over

7istories55 would involve summing over different possible historiesfor the universe. That is, different curved space times. One has tospecify what class of possible curved spaces should be included inthe um over 7istories. The choice of this class of spaces,determines what state the universe is in. !f the class of curvedspaces that defines the state of the universe, included spaces withsingularities, the probabilities of such spaces would not bedetermined by the theory. !nstead, they would have to be assigned


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in some arbitrary way. 6hat this means, is that science could notpredict the probabilities of such singular histories for spacetime.Thus, it could not predict how the universe should behave.7owever, it is possible that the universe is in a state defined by a

sum that includes only non singular curved spaces. !n this case,the laws of science would determine the universe completely% onewould not have to appeal to some agency external to the universe,to determine how it began. !n a way, the proposal that the state ofthe universe is determined by a sum over non singular historiesonly, is like the drunk looking for his key under the lamp post% itmay not be where he lost it, but it is the only place in which hemight find it. imilarly, the universe may not be in the state definedby a sum over non singular histories, but it is the only state in whichscience could predict how the universe should be.

!n &(, Eim 7artle and !, proposed that the state of the universeshould be given by a um over a certain class of 7istories. Thisclass consisted of curved spaces, without singularities, and whichwere of finite si/e, but which did not have boundaries or edges.They would be like the surface of the #arth, but with two moredimensions. The surface of the #arth has a finite area, but itdoesn5t have any singularities, boundaries or edges. ! have testedthis by experiment. ! went round the world, and ! didn5t fall off.

The proposal that 7artle and ! made, can be paraphrased as% Theboundary condition of the universe is, that it has no boundary. !t is

only if the universe is in this 99no boundary55 state, that the laws ofscience, on their own, determine the probabilities of each possiblehistory. Thus, it is only in this case that the known laws woulddetermine how the universe should behave. !f the universe is in anyother state, the class of curved spaces, in the 99um over7istories55, will include spaces with singularities. !n order todetermine the probabilities of such singular histories, one wouldhave to invoke some principle other than the known laws ofscience. This principle would be something external to ouruniverse. 6e could not deduce it from within the universe. On theother hand, if the universe is in the 99no boundary55 state, we could,

in principle, determine completely how the universe should behave,up to the limits set by the


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99no boundary55 state. Thus, the 99no boundary55 proposal is a goodscientific theory, in the sense defined by the philosopher, )arl+opper% it can be falsified by observation.

!f the observations do not agree with the predictions, we will knowthat there must be singularities in the class of possible histories.7owever, that is about all we would know. 6e would not be able tocalculate the probabilities of the singular histories. Thus, we wouldnot be able to predict how the universe should behave. One mightthink that this unpredictability wouldn5t matter too much, if itoccurred only at the "ig "ang. After all, that was ten or twentybillion years ago. "ut if predictability broke down in the very stronggravitational fields in the "ig "ang, it could also break downwhenever a star collapsed. This could happen several times aweek, in our galaxy alone. Thus, our power of prediction would be

poor, even by the standards of weather forecasts.

Of course, one could say that one didn5t care about a breakdown inpredictability, that occurred in a distant star. 7owever, in $uantumtheory, anything that is not actually forbidden, can and Fwillhappen. Thus, if the class of possible histories includes spaceswith singularities, these singularities could occur anywhere, not =ustat the "ig "ang and in collapsing stars. This would mean that wecouldn5t predict anything. *onversely, the fact that we are able topredict events, is experimental evidence against singularities, andfor the 99no boundary55 proposal.

o what does the no boundary proposal, predict for the universe.The first point to make, is that because all the possible histories forthe universe are finite in extent, any $uantity that one uses as ameasure of time, will have a greatest and a least value. o theuniverse will have a beginning, and an end. 7owever, thebeginning will not be a singularity. !nstead, it will be a bit like the4orth +ole of the #arth. !f one takes degrees of latitude on thesurface of the #arth to be the anallogue of time, one could say thatthe surface of the #arth began at the 4orth +ole. 8et the 4orth+ole is a perfectly ordinary point on the #arth. There5s nothing

special about it, and the same laws hold at the 4orth +ole, as atother places on the #arth. imilarly, the event that we mightchoose to label, as 99the beginning of the universe55, would be anordinary point of spacetime, much like any other, the laws ofscience would hold at the beginning, as elsewhere.

Crom the analogy with the surface of the #arth, one might expectthat the end of the universe would be similar to the beginning, =ust


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as the 4orth +ole is much like the outh +ole. 7owever, the 4orthand outh +oles correspond to the beginning and end of thehistory of the universe, in imaginary time, not the real time that weexperience. !f one extrapolates the results of the 99um over

7istories55 from imaginary time to real time, one finds that thebeginning of the universe in real time can be very different from itsend. !t is difficult to work out the details, of what the no boundaryproposal predicts for the beginning and end of the universe, for tworeasons. Cirst, we don5t yet know the exact laws that govern gravityaccording to the


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the inflationary period, the universe borrowed heavily from itsgravitational energy, to finance the creation of more matter. Theresult was a triumph for eagan economics% a vigorous andexpanding universe, filled with material ob=ects. The debt of

gravitational energy, will not have to be repaid until the end of theuniverse.

The early universe could not have been exactly homogeneous anduniform, because that would violate the


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God- #ven if there is only one, uni$ue set of possible laws, it isonly a set of e$uations. 6hat is it that breathes fire into thee$uations, and makes a universe for them to govern. !s the ultimateunified theory so compelling, that it brings about its own existence.

Although cience may solve the problem of Fhow the universebegan, it can not answer the $uestion% why does the universebother to exist- >aybe only God can answer that.

Siilar essays &an be !o"nd in ro!essor Hawking*s book# -la&k Holes

and -aby +niverses and ther 2ssays# -anta -ooks# 1993# 'S-4%

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