Illustrated Theory of Everything: The Origin and Fate of the Universe (5 page)

On the other hand, as we learned in the last lecture, there might be primor-dial black holes with a very much smaller mass that were made by the collapseof irregularities in the very early stages of the universe. Such black holes wouldhave a much higher temperature and would be emitting radiation at a muchgreater rate. A primordial black hole with an initial mass of a thousand mil-lion tons would have a lifetime roughly equal to the age of the universe.Primordial black holes with initial masses less than this figure would alreadyhave completely evaporated. However, those with slightly greater masseswould still be emitting radiation in the form of X rays and gamma rays. Theseare like waves of light, but with a much shorter wavelength. Such holeshardly deserve the epithet black. They really are white hot, and are emittingenergy at the rate of about ten thousand megawatts.

One such black hole could run ten large power stations, if only we could har-ness its output. This would be rather difficult, however. The black hole wouldhave the mass of a mountain compressed into the size of the nucleus of anatom. If you had one of these black holes on the surface of the Earth, therewould be no way to stop it falling through the floor to the center of the Earth.It would oscillate through the Earth and back, until eventually it settled downat the center. So the only place to put such a black hole, in which one mightuse the energy that it emitted, would be in orbit around the Earth. And theonly way that one could get it to orbit the Earth would be to attract it thereby towing a large mass in front of it, rather like a carrot in front of a donkey.This does not sound like a very practical proposition, at least not in theimmediate future.

THE SEARCH FOR PRIMORDIALBLACK HOLES

But even if we cannot harness the emission from these primordial black holes,what are our chances of observing them? We could look for the gamma raysthat the primordial black holes emit during most of their lifetime. Althoughthe radiation from most would be very weak because they are far away, thetotal from all of them might be detectable. We do, indeed, observe such abackground of gamma rays. However, this background was probably generatedby processes other than primordial black holes. One can say that the observa-tions of the gamma ray background do not provide any positive evidence forprimordial black holes. But they tell us that, on average, there cannot be morethan three hundred little black holes in every cubic light-year in the universe.This limit means that primordial black holes could make up at most one mil-lionth of the average mass density in the universe.

With primordial black holes being so scarce, it might seem unlikely that therewould be one that was near enough for us to observe on its own. But sincegravity would draw primordial black holes toward any matter, they should bemuch more common in galaxies. If they were, say, a million times more com-mon in galaxies, then the nearest black hole to us would probably be at adistance of about a thousand million kilometers, or about as far as Pluto, thefarthest known planet. At this distance it would still be very difficult to detectthe steady emission of a black hole even if it was ten thousand megawatts.In order to observe a primordial black hole, one would have to detect severalgamma ray quanta coming from the same direction within a reasonable spaceof time, such as a week.

Otherwise, they might simply be part of the background. But Planck’s quan-tum principle tells us that each gamma ray quantum has a very high energy,because gamma rays have a very high frequency. So to radiate even ten thou-sand megawatts would not take many quanta. And to observe these few quan-ta coming from the distance of Pluto would require a larger gamma ray detec-tor than any that have been constructed so far. Moreover, the detector wouldhave to be in space, because gamma rays cannot penetrate the atmosphere.

Of course, if a black hole as close as Pluto were to reach the end of its life andblow up, it would be easy to detect the final burst of emission. But if the blackhole has been emitting for the last ten or twenty thousand million years, thechances of it reaching the end of its life within the next few years are reallyrather small. It might equally well be a few million years in the past or future.So in order to have a reasonable chance of seeing an explosion before yourresearch grant ran out, you would have to find a way to detect any explosionswithin a distance of about one light-year. You would still have the problem ofneeding a large gamma ray detector to observe several gamma ray quanta fromthe explosion. However, in this case, it would not be necessary to determinethat all the quanta came from the same direction. It would be enough toobserve that they all arrived within a very short time interval to be reasonablyconfident that they were coming from the same burst.

One gamma ray detector that might be capable of spotting primordial blackholes is the entire Earth’s atmosphere. (We are, in any case, unlikely to be ableto build a larger detector.) When a high-energy gamma ray quantum hits theatoms in our atmosphere, it creates pairs of electrons and positrons. Whenthese hit other atoms, they in turn create more pairs of electrons and positrons.So one gets what is called an electron shower. The result is a form of lightcalled Cerenkov radiation. One can therefore detect gamma ray bursts bylooking for flashes of light in the night sky.

Of course, there are a number of other phenomena, such as lightning, whichcan also give flashes in the sky. However, one could distinguish gamma raybursts from such effects by observing flashes simultaneously at two or morethoroughly widely separated locations. A search like this has been carried outby two scientists from Dublin, Neil Porter and Trevor Weekes, using telescopesin Arizona. They found a number of flashes but none that could be definitelyascribed to gamma ray bursts from primordial black holes.

Even if the search for primordial black holes proves negative, as it seems itmay, it will still give us important information about the very early stages ofthe universe. If the early universe had been chaotic or irregular, or if the pres-sure of matter had been low, one would have expected it to produce manymore primordial black holes than the limit set by our observations of thegamma ray background. It is only if the early universe was very smooth anduniform, and with a high pressure, that one can explain the absence ofobservable numbers of primordial black holes.

GENERAL RELATIVITY ANDQUANTUM MECHANICS

Radiation from black holes was the first example of a prediction that depend-ed on both of the great theories of this century, general relativity and quantummechanics. It aroused a lot of opposition initially because it upset the existingviewpoint: “How can a black hole emit anything?” When I first announced theresults of my calculations at a conference at the Rutherford Laboratory nearOxford, I was greeted with general incredulity. At the end of my talk the chair-man of the session, John G. Taylor from Kings College, London, claimed it wasall nonsense. He even wrote a paper to that effect.

However, in the end most people, including John Taylor, have come to theconclusion that black holes must radiate like hot bodies if our other ideasabout general relativity and quantum mechanics are correct. Thus eventhough we have not yet managed to find a primordial black hole, there isfairly general agreement that if we did, it would have to be emitting a lot ofgamma and X rays. If we do find one, I will get the Nobel Prize.The existence of radiation from black holes seems to imply that gravitationalcollapse is not as final and irreversible as we once thought. If an astronaut fallsthat extra mass will be returned to the universe in the form of radiation. Thus,in a sense, the astronaut will be recycled. It would be a poor sort of immortal-ity, however, because any personal concept of time for the astronaut wouldalmost certainly come to an end as he was crushed out of existence inside theblack hole. Even the types of particle that were eventually emitted by theblack hole would in general be different from those that made up the astro-naut. The only feature of the astronaut that would survive would be his massor energy.

The approximations I used to derive the emission from black holes shouldwork well when the black hole has a mass greater than a fraction of a gram.However, they will break down at the end of the black hole’s life, when itsmass gets very small. The most likely outcome seems to be that the black holewould just disappear, at least from our region of the universe. It would takewith it the astronaut and any singularity there might be inside the black hole.This was the first indication that quantum mechanics might remove the sin-gularities that were predicted by classical general relativity. However, themethods that I and other people were using in 1974 to study the quantumeffects of gravity were not able to answer questions such as whether singulari-ties would occur in quantum gravity.

From 1975 onward, I therefore started to develop a more powerful approach toquantum gravity based on Feynman’s idea of a sum over histories. The answersthat this approach suggests for the origin and fate of the universe will bedescribed in the next two lectures. We shall see that quantum mechanicsallows the universe to have a beginning that is not a singularity. This meansthat the laws of physics need not break down at the origin of the universe. Thestate of the universe and its contents, like ourselves, are completely deter-mined by the laws of physics, up to the limit set by the uncertainty principle.So much for free will.

The Theory of Everything: The Origin and Fate of the Universe

Chapter 5 - FIFTH LECTURE - THE ORIGIN AND FATE OF THE...

T H E O R I G I N A N D F A T E O F T H E U N I V E R S EThroughout the 1970s I had been working mainly on black holes. However,n 1981 my interest in questions about the origin of the universe wasreawakened when I attended a conference on cosmology in the Vatican. TheCatholic church had made a bad mistake with Galileo when it tried to laydown the law on a question of science, declaring that the sun went around theEarth. Now, centuries later, it had decided it would be better to invite a num-ber of experts to advise it on cosmology.

At the end of the conference the participants were granted an audience withthe pope. He told us that it was okay to study the evolution of the universeafter the big bang, but we should not inquire into the big bang itself becausethat was the moment of creation and therefore the work of God.I was glad then that he did not know the subject of the talk I had just given atthe conference. I had no desire to share the fate of Galileo; I have a lot of sym-pathy with Galileo, partly because I was born exactly three hundred years afterhis death.

THE HOT BIG BANG MODEL

In order to explain what my paper was about, I shall first describe the generallyaccepted history of the universe, according to what is known as the “hot bigbang model.” This assumes that the universe is described by a Friedmannmodel, right back to the big bang. In such models one finds that as the uni-verse expands, the temperature of the matter and radiation in it will go down.Since temperature is simply a measure of the average energy of the particles,this cooling of the universe will have a major effect on the matter in it. At veryhigh temperatures, particles will be moving around so fast that they can escapeany attraction toward each other caused by the nuclear or electromagneticforces. But as they cooled off, one would expect particles that attract eachother to start to clump together.

At the big bang itself, the universe had zero size and so must have been infi-nitely hot. But as the universe expanded, the temperature of the radiationwould have decreased. One second after the big bang it would have fallen toabout ten thousand million degrees. This is about a thousand times the tem-perature at the center of the sun, but temperatures as high as this are reachedin H-bomb explosions. At this time the universe would have contained mostlyphotons, electrons, and neutrinos and their antiparticles, together with someprotons and neutrons.

As the universe continued to expand and the temperature to drop, the rate atwhich electrons and the electron pairs were being produced in collisions wouldhave fallen below the rate at which they were being destroyed by annihilation.So most of the electrons and antielectrons would have annihilated each otherto produce more photons, leaving behind only a few electrons.

About one hundred seconds after the big bang, the temperature would havefallen to one thousand million degrees, the temperature inside the hotteststars. At this temperature, protons and neutrons would no longer have suffi-cient energy to escape the attraction of the strong nuclear force. They wouldstart to combine together to produce the nuclei of atoms of deuterium, orheavy hydrogen, which contain one proton and one neutron. The deuteriumnuclei would then have combined with more protons and neutrons to makehelium nuclei, which contained two protons and two neutrons. There wouldalso be small amounts of a couple of heavier elements, lithium and beryllium.One can calculate that in the hot big bang model about a quarter of the pro-tons and neutrons would have been converted into helium nuclei, along witha small amount of heavy hydrogen and other elements. The remaining neu-trons would have decayed into protons, which are the nuclei of ordinaryhydrogen atoms. These predictions agree very well with what is observed.The hot big bang model also predicts that we should be able to observe theradiation left over from the hot early stages. However, the temperature wouldhave been reduced to a few degrees above absolute zero by the expansion of theuniverse. This is the explanation of the microwave background of radiationthat was discovered by Penzias and Wilson in 1965. We are thereforethoroughly confident that we have the right picture, at least back to about onesecond after the big bang. Within only a few hours of the big bang, theproduction of helium and other elements would have stopped. And after that,for the next million years or so, the universe would have just continuedexpanding, without anything much happening. Eventually, once the tempera-ture had dropped to a few thousand degrees, the electrons and nuclei would nolonger have had enough energy to overcome the electromagnetic attractionbetween them. They would then have started combining to form atoms.

The universe as a whole would have continued expanding and cooling.However, in regions that were slightly denser than average, the expansionwould have been slowed down by extra gravitational attraction. This wouldeventually stop expansion in some regions and cause them to start to recol-lapse. As they were collapsing, the gravitational pull of matter outside theseregions might start them rotating slightly. As the collapsing region gotsmaller, it would spin faster-just as skaters spinning on ice spin faster as thedraw in their arms. Eventually, when the region got small enough, it would bespinning fast enough to balance the attraction of gravity. In this way, disklikerotating galaxies were born.

As time went on, the gas in the galaxies would break up into smaller cloudsthat would collapse under their own gravity. As these contracted, the temper-ature of the gas would increase until it became hot enough to start nuclearreactions. These would convert the hydrogen into more helium, and the heatgiven off would raise the pressure, and so stop the clouds from contracting anyfurther. They would remain in this state for a long time as stars like our sun,burning hydrogen into helium and radiating the energy as heat and light.More massive stars would need to be hotter to balance their stronger gravita-tional attraction. This would make the nuclear fusion reactions proceed somuch more rapidly that they would use up their hydrogen in as little as a hun-dred million years. They would then contract slightly and, as they heated upfurther, would start to convert helium into heavier elements like carbon oroxygen. This, however, would not release much more energy, so a crisis wouldoccur, as I described in my lecture on black holes.

What happens next is not completely clear, but it seems likely that the centralregions of the star would collapse to a very dense state, such as a neutron staror black hole. The outer regions of the star may get blown off in a tremendousexplosion called a supernova, which would outshine all the other stars in thegalaxy. Some of the heavier elements produced near the end of the star’s lifewould be flung back into the gas in the galaxy. They would provide some ofthe raw material for the next generation of stars.

Our own sun contains about 2 percent of these heavier elements because it isa second- or third-generation star. It was formed some five thousand millionyears ago out of a cloud of rotating gas containing the debris of earlier super-novas. Most of the gas in that cloud went to form the sun or got blown away.However, a small amount of the heavier elements collected together to formthe bodies that now orbit the sun as planets like the Earth.

OPEN QUESTIONS

This picture of a universe that started off very hot and cooled as it expanded isin agreement with all the observational evidence that we have today.Nevertheless, it leaves a number of important questions unanswered. First, whywas the early universe so hot? Second, why is the universe so uniform on a largescale-why does it look the same at all points of space and in all directions?Third, why did the universe start out with so nearly the critical rate of expan-sion to just avoid recollapse? If the rate of expansion one second after the bigbang had been smaller by even one part in a hundred thousand millionmillion, the universe would have recollapsed before it ever reached its presentsize. On the other hand, if the expansion rate at one second had been largerby the same amount, the universe would have expanded so much that it wouldbe effectively empty now.

Fourth, despite the fact that the universe is so uniform and homogenous on alarge scale, it contains local lumps such as stars and galaxies. These are thoughtto have developed from small differences in the density of the early universefrom one region to another. What was the origin of these density fluctuations?The general theory of relativity, on its own, cannot explain these features oranswer these questions. This is because it predicts that the universe started offwith infinite density at the big bang singularity. At the singularity, general rel-ativity and all other physical laws would break down. One cannot predict whatwould come out of the singularity. As I explained before, this means that onemight as well cut any events before the big bang out of the theory, because theycan have no effect on what we observe. Space-time would have a boundary-a beginning at the big bang. Why should the universe have started off at thebig bang in just such a way as to lead to the state we observe today? Why is theuniverse so uniform, and expanding at just the critical rate to avoid recollapse?One would feel happier about this if one could show that quite a number ofdifferent initial configurations for the universe would have evolved to producea universe like the one we observe.

If this is the case, a universe that developed from some sort of random initialconditions should contain a number of regions that are like what we observe.There might also be regions that were very different. However, these regionswould probably not be suitable for the formation of galaxies and stars. Theseare essential prerequisites for the development of intelligent life, at least as weknow it. Thus, these regions would not contain any beings to observe that theywere different.

When one considers cosmology, one has to take into account the selectionprinciple that we live in a region of the universe that is suitable for intelligentlife. This fairly obvious and elementary consideration is sometimes called theanthropic principle. Suppose, on the other hand, that the initial state of theuniverse had to be chosen extremely carefully to lead to something like whatwe see around us. Then the universe would be unlikely to contain any regionin which life would appear.

In the hot big bang model that I described earlier, there was not enough timein the early universe for heat to have flowed from one region to another. Thismeans that different regions of the universe would have had to have startedout with exactly the same temperature in order to account for the fact that themicrowave background has the same temperature in every direction we look.Also, the initial rate of expansion would have had to be chosen very preciselyfor the universe not to have recollapsed before now. This means that the ini-tial state of the universe must have been very carefully chosen indeed if thehot big bang model was correct right back to the beginning of time. It wouldbe very difficult to explain why the universe should have begun in just thisway, except as the act of a God who intended to create beings like us.

THE INFLATIONARY MODEL

In order to avoid this difficulty with the very early stages of the hot big bangmodel, Alan Guth at the Massachusetts Institute of Technology put forward anew model. In this, many different initial configurations could have evolved tosomething like the present universe. He suggested that the early universe mighthave had a period of very rapid, or exponential, expansion. This expansion issaid to be inflationary-an analogy with the inflation in prices that occurs to agreater or lesser degree in every country. The world record for price inflationwas probably in Germany after the first war, when the price of a loaf of breadwent from under a mark to millions of marks in a few months. But the inflationwe think may have occurred in the size of the universe was much greater eventhan that-a million million million million million times in only a tiny frac-tion of a second. Of course, that was before the present government.

Guth suggested that the universe started out from the big bang very hot. Onewould expect that at such high temperatures, the strong and weak nuclearforces and the electromagnetic force would all be unified into a single force.As the universe expanded, it would cool, and particle energies would go down.Eventually there would be what is called a phase transition, and the symmetrybetween the forces would be broken. The strong force would become differentfrom the weak and electromagnetic forces. One common example of a phasetransition is the freezing of water when you cool it down. Liquid water is sym-metrical, the same at every point and in every direction. However, when icecrystals form, they will have definite positions and will be lined up in somedirection. This breaks the symmetry of the water.

In the case of water, if one is careful, one can “supercool” it. That is, one canreduce the temperature below the freezing point-0 degrees centigrade-with-out ice forming. Guth suggested that the universe might behave in a similarway: The temperature might drop below the critical value without the symme-try between the forces being broken. If this happened, the universe would bein an unstable state, with more energy than if the symmetry had been broken.This special extra energy can be shown to have an antigravitational effect. Itwould act just like a cosmological constant.

Einstein introduced the cosmological constant into general relativity when hewas trying to construct a static model of the universe. However,in this case,the universe would already be expanding. The repulsive effect of this cosmo-logical constant would therefore have made the universe expand at an ever-increasing rate. Even in regions where there were more matter particles thanaverage, the gravitational attraction of the matter would have been out-weighed by the repulsion of the effective cosmological constant. Thus, theseregions would also expand in an accelerating inflationary manner.