 On behalf of the astronomy and physics departments at Berkeley, it's my pleasure to welcome you to the second of three Hitchcock lectures to be delivered by Stephen Hawking, Lucasian Professor of Mathematics at Cambridge University. Professor Hawking is universally regarded as the world's foremost authority on gravitational physics, the inheritor of the legacy handed down by Isaac Newton and Albert Einstein. An illustrious career in which he has elucidated surprising and beautiful relationships between gravitation, thermodynamics, and quantum physics. Professor Hawking has won many scientific awards and honors, including the Adams Prize, the Eddington Medal, the Heinemann Prize, the Maxwell Medal, the Hughes Medal, the Einstein Medal, and most recently the Wolf Prize for Physics. In 1982, he was made a commander of the British Empire. His numerous scientific achievements are all the more remarkable for having been achieved in the face of great personal adversity. Few profiles of courage surpass in heroism and valor that of our speaker. To commemorate his inspirational visit to our campus, I call upon Dr. Forbes Norris, Vice President and Clinical Director of the San Francisco ALS Research Foundation and a member of the Scientific Advisory Board of the International ALS Foundation. Dr. Norris will make a presentation to Dr. Glenn Seaboard representing the Lawrence Hall of Science. The ALS Foundation for research on this disease in San Francisco is terribly pleased to share with you the great honor of the presence in the Bay Area of Stephen Hawking. And in commemoration of his visit, we would like to present to the university for the Lawrence Hall of Science a bust of Professor Hawking by the noted Irish sculptorist Marjorie Fitzgibbon. Thank you very much. I'm very proud to accept on behalf of the Lawrence Hall of Science this bust of Sir Stephen Hawking on this heartwarming occasion. I also want to express my gratitude to Dr. Norris and the ALS Research Foundation for their generosity in making this bust available. I think it's very appropriate that this go to the Lawrence Hall of Science. Sir Stephen Hawking symbolizes the best in our attempts to effect the public understanding of science to help us understand our place in the universe and the nature of things. And the Lawrence Hall of Science is dedicated to just these ideas, the public understanding of science and of its place in today's world. I invite you all, and not all at the same time, to come up to the Lawrence Hall of Science and see this bust of Professor Stephen Hawking on display. Thank you very much. Well, without further ado, I now call on Professor Stephen Hawking to give us his Hitchcock lecture. The title of his talk has been changed from the one that was originally announced. The new title is Baby Universes, Children of Black Holes. Ladies and gentlemen, please join me in welcoming once more Professor Stephen Hawking. Can you hear me? In this lecture, I want to talk about Black Holes and their offspring, Baby Universes. Calling into a black hole has become one of the horrors of science fiction. In fact, black holes can now be said to be really matters of science fact rather than science fiction. As I shall describe, there are good reasons for predicting that black holes should exist. On the observational evidence points strongly to the presence of a number of black holes in our own galaxy and more in other galaxies. Of course, where the science fiction writers really go to town is on what happens if you do fall in a black hole. The common suggestion is that if the black hole is rotating, you can fall through a little hole in space time and out into another region of the universe. This obviously raises great possibilities for space travel. Indeed, we need something like this. If travel to other stars, let alone other galaxies, there's to be a practical proposition in the future. Otherwise, the fact that nothing can travel faster than light means that the round trip to the nearest star would take at least eight years. So much for a weekend break on Alpha Centauri. On the other hand, if one could pass through a black hole, one might reemerge anywhere in the universe. Quite how you choose your destination is not clear. You might set out for a holiday in Virgo and end up in the crab nebula. I am sorry to disappoint prospective galactic tourists, but this scenario doesn't work. If you jump into a black hole, you will get torn apart and crushed out of existence. However, there is a sense in which the particles that make up your body do carry on into another universe. I don't know if it would be much consolation to someone being made into spaghetti in a black hole to know that his particles might survive. Pied the slightly flippant tone I have adopted, this talk will be based on hard science. Most of what I shall say is now agreed by other scientists working in this field, though this acceptance has come only fairly recently. The last part of the lecture, however, is based on very recent work on which there is, as yet, no general consensus. But this work is arousing great interest and excitement. Although the concept of what we now call a black hole goes back more than 200 years, the name black hole was introduced only in 1967 by the American physicist John Wheeler. It was a stroke of genius. The name ensured that black holes entered the mythology of science fiction. It also stimulated scientific research by providing a definite name for something that previously had not had a satisfactory title. The importance in science of a good name should not be underestimated. The first person, as far as I know, the distressed black holes was the Cambridge man called John Mitchell, who wrote a paper about them in 1783. His idea was this. Suppose you fire a cannon ball vertically upwards from the surface of the earth. As it goes up, it will be slowed down by the effect of gravity. Eventually, it will stop going up and will fall back to earth. However, if it had more than a certain critical speed, it would never stop and fall back but would continue to move away. This critical speed is called the escape velocity. It is about seven miles a second for the earth and about 100 miles a second for the sun. Both of these velocities are higher than the speed of a real cannon ball but they are much smaller than the velocity of light, which is 186,000 miles a second. This means that gravity doesn't have much effect on light. And light can escape without difficulty from the earth or the sun. However, Mitchell reasoned that it would be possible to have a star that was sufficiently massive and sufficiently small in size that its escape velocity would be greater than the velocity of light. We would not be able to see such a star because light from its surface would not reach us but would be dragged back by its gravitational field. However, we might be able to detect the presence of the star by the effect that its gravitational field would have on nearby matter. It is not really consistent to treat light like cannon balls because according to an experiment carried out in 1897, light always travels at the same constant velocity. So how then can gravity slow down light? A fully consistent theory of how gravity affects light came in 1915 when Einstein formulated the general theory of relativity. Even so, the implications of this theory for old stars, another massive bodies were not generally realized until the 1960s. According to general relativity, space and time together can be regarded as forming a four-dimensional space called spacetime. The space is not flat, but it is distorted or curved by the matter and energy in it. Objects try to move on straight lines through spacetime but because it is curved, they move on paths called geodesics which are the nearest thing to a straight line in the curved space. Thus, the earth tries to move on a straight line but because spacetime is bent by the mass of the sun it follows the spiral path going in a circle around the sun while advancing in time. Similarly, light tries to move on a straight line but because spacetime is curved, it appears to follow a path that is bent. We can actually observe this bending of light during an eclipse. The moon blocks out the sun and allows us to observe stars that are in almost the same direction as the sun. We find that the stars appear to be in slightly different positions because the light from them is bent by the curved spacetime near the sun. In the case of light passing near the sun, the bending is very small. However, if the sun were to shrink until it was only a few miles across, the bending would be so great that light leaving the sun would not get away but would be dragged back by the gravitational field. According to the theory of relativity, nothing can travel faster than light. So there would be a region from which it would be impossible for anything to escape. This region is called a black hole. Its boundary is called the event horizon. It is formed by the light that just fails to get away from the black hole but stays hovering on the edge. It might sound ridiculous to suggest that the sun could shrink. Sorry about that. It might sound ridiculous to suggest that the sun could shrink to being only a few miles across. Surely matter cannot be compressed so far. The answer is it can. The sun is the size it is because it is so hot. It is burning hydrogen into helium like a controlled H-bomb. The heat released in this process generates a pressure that enables the sun to resist the attraction of its own gravity which is trying to make it smaller. Eventually, however, the sun will run out of nuclear fuel. This will not happen for about another five billion years so there's no great rush to book your flight to another star. However, more massive stars will bring up their fuel much more rapidly. When they finish their fuel, they will start to lose heat under contract. If they are less than about twice the mass of the sun, they will eventually stop contracting and will settle down to a stable state. This state can be what is called a white dwarf. These have radii of a few thousand miles and densities of hundreds of tons per cubic inch. Earth can be a neutron star. These have a radius of about 10 miles and densities of millions of tons per cubic inch. We observe large numbers of white dwarfs in our immediate neighborhood in the galaxy. Neutron stars, however, were not observed until 1967 when Jocelyn Bell and Tony Ish at Cambridge discovered objects called pulsars which were emitting regular pulses of radio waves. At first, they wondered whether they had made contact with an alien civilization. Indeed, I remember that the seminar room in which they announced their discovery was decorated with figures of little green men. In the end, however, they and everyone else came to the less romantic conclusion that they were rotating neutron stars. This was bad news for riders of space westerns, but good news for the small number of us who believed in black holes at that time. If stars could shrink as small as 10 or 20 miles across to become neutron stars, one might expect that other stars could shrink even further to become black holes. Star with a mass more than about twice that of the sun cannot settle down as a white dwarf or neutron star. In some cases, the star may explode and grow of enough matter to bring its mass below the limit. But this won't happen in all the cases. Some stars will shrink so small that their gravitational fields will bend light so much that it comes back towards the star. No further light or anything else will be able to escape. The stars will have become black holes. We now have fairly good observational evidence for a number of black holes. One of the best cases is Cygnus X1. This is a system consisting of a normal star orbiting around an unseen companion. Matter seems to be being blown off the normal star and falling on the companion. As it falls towards the companion, it develops a spiral motion, like water running out of a bath. It will get very hot and will give off the x-rays that are observed. The unseen companion must be very small, a white dwarf, neutron star, or black hole. However, one can show that the mass of the companion must be at least six times that of the sun. This is too much for it to be a white dwarf or a neutron star, so it has to be a black hole. I once met Kip Thorne of the California Institute of Technology that Cygnus X1 does not contain a black hole. This was not because I didn't believe that there really was a black hole in Cygnus X1. Rather, it was an insurance policy. I had done a lot of work on black holes and it all would have been wasted if it had turned out that black holes didn't exist. But then, at least, I would have had the consolation of winning my bet. However, I now consider the evidence for black holes so compelling that I'm going to concede a bet. I will give Kip Thorne a subscription to Penthouse. Anything that falls into a black hole comes into a region of spacetime in which light is bent so much that it cannot get out. Since nothing can travel faster than light, this means that nothing else can get out either. So think carefully before you decide to jump into a black hole. You won't be able to change your mind if you don't like what you find inside. The laws of physics are time symmetric. If there are objects called black holes which things can fall into but not get out, there ought to be other objects that things can come out of but not fall into. One could call these white holes. One might speculate that one could jump into a black hole in one place and come out of a white hole in another. This would be the ideal method of long-distance spaced ravel mentioned earlier. All you would need would be to find a nearby black hole. At first, this form of spaced ravel seemed possible. There are solutions to Weinstein's general theory of relativity in which it is possible to fall into a black hole and come out of a white hole. However, later work showed that these solutions were all very unstable. The slightest disturbance such as the presence of a spaceship would destroy the wormhole or passage leading from the black hole to the white hole. The spaceship would be torn apart by infinitely strong forces. Anyone care to buy a ticket for the Titanic? After that, it seemed hopeless. Black holes might be useful for getting rid of garbage or even some of one's friends. But they were a country from which no traveler returns. However, everything I have been saying so far has been based on calculations using Weinstein's general theory of relativity. This theory is an excellent agreement with all the observations we have made. But we know it cannot be quite right because it doesn't incorporate the uncertainty principle of quantum mechanics. The uncertainty principle says that particles cannot have both a well-defined position and a well-defined velocity. The more precisely you measure the position of a particle, the less precisely you can measure its velocity and vice versa. In 1973, I started investigating what difference the uncertainty principle would make to black holes. To my great surprise and that of everyone else, I found that it meant that black holes are not completely black. They would be sending out radiation and particles at a steady rate. My results were received with general disbelief when I announced them at a conference near Oxford. The chairman of the session said they were nonsense and wrote a paper saying so. However, when other people repeated my calculations, they found the same effect. Please wait while I load the rest of my lecture. Yes, how can a black hole give off radiation? How can anything get out through the event horizon of a black hole? The answer is the uncertainty principle allows particles to travel faster than light for a small distance. This enables particles and radiation to get out through the event horizon and escape from the black hole. Thus, it is possible for things to get out of a black hole. However, what comes out of a black hole will be different from what fell in. Only the energy will be the same. As the black hole gives off particles and radiation, it will lose mass. This will cause the black hole to get smaller and to send out particles more rapidly. Eventually, it will get down to zero mass and will disappear completely. What will happen then to the objects, including possible spaceships, that fell into the black hole? According to some recent work of mine, the answer is that they go off into a little baby universe of their own. A small, self-contained universe branches off from our region of the universe. This baby universe may join on again to our region of spacetime. If it does, it would appear to us to be another black hole, which formed and then evaporated. Particles that fell into one black hole would appear as particles emitted by the other black hole and vice versa. This sounds just what is required to allow space travel through black holes. You just steer your spaceship into a suitable black hole. It better be a pretty big one, or the gravitational forces will tear you into spaghetti before you get inside. You would then hope to reappear out of some other hole, though you wouldn't be able to choose where. However, there's a snag in this intergalactic transportation scheme. The baby universes that take the particles that fell into the hole occur in what is called imaginary time. Imaginary time may sound like science fiction, but it is a well-defined mathematical concept that seems essential in order to formulate quantum mechanics and the uncertainty principle properly. However, it is not our subjective sense of time in which we feel ourselves as getting older with more gray hairs. Rather, it can be thought of as the direction of time that is at right angles to what we call real time. Thank you. In real time, an astronaut who fell into a black hole would come to a sticky end. He would be touring a park by the difference between the gravitational force on his head and his feet. Even the particles that made up his body would not survive. Their histories, in real time, would come to an end at a singularity. However, the histories of the particles in imaginary time would continue. They would pass into the baby universe and would reemerge as the particles emitted by another black hole. Thus, in a sense, the astronaut would be transported to another region of the universe. However, the particles that emerged would not look much like the astronaut. Might it be much consolation to him as he ran into the singularity in real time to know that his particles will survive in imaginary time? The motto for anyone who falls into a black hole must be think imaginary, what determines where the particles reemerge. The number of particles in the baby universe will be equal to the number of particles that fell into the black hole plus the number of particles that the black hole emits during its evaporation. This means that the particles that fall into one black hole will come out of another hole of about the same mass. Thus, one might try to select where the particles would come out by creating a black hole of the same mass as that which the particles went down. However, the black hole would be equally likely to give off any other set of particles with the same total energy. Even if the black hole did emit the right kinds of particles, one could not tell if they were actually the same particles that went down the other hole. Particles do not carry identity cards. All particles of a given kind look alike. What all this means is that going through a black hole is unlikely to prove a popular and reliable method of space travel. First of all, you would have to get there by traveling in imaginary time and not care that your history in real time came to a sticky end. Second, you couldn't really choose your destination. It would be a bit like traveling on some airlines I could name, but won't, because I would be sued. Although baby universes may not be much used for space travel, they have important implications for our attempt to find a complete unified theory that will describe everything in the universe. Our present theories contain a number of quantities like the size of the electric charge on a particle. The values of these quantities cannot be predicted by our theories. Instead, they have to be chosen to agree with observations. However, most scientists believe that there is some underlying unified theory that will predict the values of all these quantities. May well be such an underlying theory. Many people think it is the theory of super strings. This does not contain any numbers whose values can be adjusted. One would therefore expect that this unified theory should be able to predict all the values of quantities like the electric charge on a particle that are left undetermined by our present theories. Even though we have not yet been able to predict any of these quantities from super string theory, many people believe that we will be able to do so eventually. However, if this picture of baby universes is correct, our ability to predict these quantities will be reduced. This is because we cannot observe how many baby universes exist out there waiting to join on to our region of the universe. There can be baby universes that contain only a few particles. These baby universes are so small that one would not notice them joining on or branching off. However, by joining on, they will alter the apparent values of quantities like the electric charge on a particle. Thus, we will not be able to predict what the apparent values of these quantities will be because we don't know how many baby universes are waiting out there. There could be a population explosion of baby universes. However, unlike the human case, there seem to be no limiting factors such as food supply or standing room. Baby universes exist in the realm of their own. It is a bit like casking. How many angels can dance on the head of a pin? For most quantities, maybe universes seem to introduce a definite, although fairly small, amount of uncertainty in the predicted values. However, they may provide an explanation of the observed value of one very important quantity, the so-called cosmological constant. This is a quantity that would give the universe an inbuilt tendency to expand or contract. On general grounds, one might expect it to be very large. Yet we can observe how the expansion of the universe is varying with time and determine that the cosmological constant is very small. Up to now, there has been no good explanation for why the observed value should be so small. However, having baby universes branching off and joining on will affect the apparent value of the cosmological constant. Because we don't know how many baby universes there are, there will be different possible values for the apparent cosmological constant. However, a nearly zero value will be by far the most probable. This is fortunate because it is only if the value of the cosmological constant is very small that the universe would be suitable for beings like us. To sum up, it seems that particles can fall into black holes which then evaporate and disappear from our region of the universe. The particles go off into baby universes which branch off from our universe. These baby universes can then join back on somewhere else. They may not be much good for space travel, but their presence means that we will be able to predict less than we expected even if we do find a complete unified theory. On the other hand, we now may be able to provide explanations for the measured values of some quantities like the cosmological constant. In the last year, this has become a very active and exciting area of research. I'm wishing to get on with it. Thank you. Well, sir, Hawking will be willing to take some questions. We do have some time. If you have a question, please speak loudly so that we can hear you. The question is, how can radiation escape from a black hole if light cannot? To get out of a black hole, you have to travel faster than light. But the uncertainty principle allows particles to travel faster than light for a short distance. I won't repeat the question. No. Does it need a creator? Maybe it just exists. Does it need a creator? Maybe it just exists. That's true. That's just one question. I'm afraid we are running out of time. So perhaps those of you who have urgent questions can say them to the next talk before next place on Thursday. Ben Gellibach at the same time. Thank you.