strong that even a real particle can have negativeenergy there.It is therefore possible, if a black hole is present, for the virtual particle withnegative energy to fall into the black hole and become a real particle. In thiscase it no longer has to annihilate its partner; its forsaken partner may fall intothe black hole as well. But because it has positive energy, it is also possible forit to escape to infinity as a real particle. To an observer at a distance, it willappear to have been emitted from the black hole. The smaller the black hole,the less far the particle with negative energy will have to go before it becomesa real particle. Thus, the rate of emission will be greater, and the apparent tem-perature of the black hole will be higher.The positive energy of the outgoing radiation would be balanced by a flow ofnegative energy particles into the black hole. By Einstein’s famous equationE = mc2, energy is equivalent to mass. A flow of negative energy into the blackhole therefore reduces its mass. As the black hole loses mass, the area of itsevent horizon gets smaller, but this decrease in the entropy of the black holeis more than compensated for by the entropy of the emitted radiation, so thesecond law is never violated.BLACK HOLE EXPLOSIONSThe lower the mass of the black hole, the higher its temperature is. So as theblack hole loses mass, its temperature and rate of emission increase. It there-fore loses mass more quickly. What happens when the mass of the black holeeventually becomes extremely small is not quite clear. The most reasonableguess is that it would disappear completely in a tremendous final burst of emis-sion, equivalent to the explosion of millions of H-bombs.A black hole with a mass a few times that of the sun would have a tempera-ture of only one ten-millionth of a degree above absolute zero. This is muchless than the temperature of the microwave radiation that fills the universe,about 2.7 degrees above absolute zero-so such black holes would give off lessthan they absorb, though even that would be very little. If the universe is des-tined to go on expanding forever, the temperature of the microwave radiationwill eventually decrease to less than that of such a black hole. The hole willthen absorb less than it emits and will begin to lose mass. But, even then, itstemperature is so low that it would take about 1066years to evaporatecompletely. This is much longer than the age of the universe, which is onlyabout 1010 years.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 HOLESBut 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 MECHANICSRadiation 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.