by John Gribbin
During his first two years at Cambridge, the effects of the ALS rapidly worsened. He was beginning to experience enormous difficulty in walking and was compelled to use a stick in order to move just a few feet. His friends helped him as best they could, but most of the time he shunned any assistance. Using walls and objects as well as sticks, he would manage, painfully slowly, to traverse rooms and open areas. There were many occasions when these supports were not enough. Sciama remembered clearly, as do his colleagues, that on some days Hawking would turn up at the office with a bandage around his head, having fallen heavily and received a nasty bump.
His speech was also becoming seriously affected by the disease. Instead of being merely slurred, his speaking voice was now rapidly becoming unintelligible, and even close colleagues were experiencing some difficulty in understanding what he was saying. Nothing slowed him down, however; in fact, he was just hitting his stride. Work was progressing faster and more positively than it had ever done in his entire career, and this serves to illustrate his attitude to his illness. Crazy as it may seem, ALS is simply not that important to him. Of course he has had to suffer the humiliations and obstructions facing all those in our society who are not able-bodied, and naturally he has had to adapt to his condition and to live under exceptional circumstances. But the disease has not touched the essence of his being, his mind, and so has not affected his work.
More than anyone else, Hawking himself would wish to underplay his disability and to concentrate on his scientific achievements, for that is really what is important to him. Those working with him, and the many physicists around the world who hold him in the highest regard, do not view Hawking as anything other than one of them. The fact that he cannot now speak and is immobile without the technology at his fingertips is quite irrelevant. To them he is friend, colleague, and, above all, great scientist.
Having come to terms with ALS and found someone in Jane Wilde with whom he could share his life on a purely personal level, he began to blossom. The couple became engaged, and the frequency of weekend visits increased. It was obvious to everyone that they were sublimely happy and immensely important to each other. Jane recalls, “I wanted to find some purpose to my existence, and I suppose I found it in the idea of looking after him. But we were in love.”9 On another occasion, she said, “I decided what I was going to do, so I did. He was very, very determined, very ambitious. Much the same as now. He already had the beginnings of the condition when I first knew him, so I’ve never known a fit, able-bodied Stephen.”10
For Hawking, his engagement to Jane was probably the most important thing that had ever happened to him: it changed his life, gave him something to live for, and made him determined to live. Without the help that Jane gave him, he almost certainly would not have been able to carry on, nor would he have had the will to do so.
From this point on, his work went from strength to strength, and Sciama began to believe that Hawking might, after all, manage to bring together the disparate strands of his Ph.D. research. It was still touch and go, but another chance encounter was just around the corner.
Sciama’s research group became very interested in the work of a young applied mathematician, Roger Penrose, who was then based at Birkbeck College in London. The son of an eminent geneticist, Penrose had studied at University College in London and had gone on to Cambridge in the early fifties. After research in the United States, he had begun in the early sixties to develop ideas of singularity theory that interfaced perfectly with the ideas then emerging from the DAMTP.
The group from Cambridge began to attend talks at King’s College in London, where the great mathematician and co-creator of the steady state theory, Hermann Bondi, was professor of applied mathematics. King’s acted as a suitable meeting point for Penrose (who traveled across London), those from Cambridge, and a small group of physicists and mathematicians from the college itself. Sciama took Carter, Ellis, Rees, and Hawking to the meetings with the idea that the discussions might spark applications to their own work. However, there were times when Hawking almost failed to make it to London.
Brandon Carter remembers one particular occasion when the group arrived late at the railway station and the train was already drawing in. They all ran for it, forgetting about Stephen, who was struggling along with his sticks. It was only after they had installed themselves in the carriage that they were aware he was not with them. Carter recalls looking out of the window, seeing a pathetic figure struggling toward them along the platform, and realizing that Stephen might not make it before the train pulled away. Knowing how Hawking was fiercely against being treated differently from others, they did not like to help him too much. However, on this occasion Carter and one of the others jumped out to help him along the platform and onto the train.
It would have been an odd twist of fate indeed if Hawking had not made it to at least one of those London meetings, because it was through them that his whole career took another positive turn. Over the course of the talks at King’s, Roger Penrose had introduced his colleagues to the idea of a spacetime singularity at the center of a black hole, and naturally the group from Cambridge was tremendously excited by this.
One night, on the way back to Cambridge, they were all seated together in a second-class compartment and had begun to discuss what had been said at the meeting that evening. Feeling disinclined to talk for a moment, Hawking peered through the window, watching the darkened fields stream past and the juxtaposition of his friends reflected in the glass. His colleagues were arguing over one of the finer mathematical points in Penrose’s discussion. Suddenly, an idea struck him, and he looked away from the window. Turning to Sciama sitting across from him, he said, “I wonder what would happen if you applied Roger’s singularity theory to the entire Universe.” It was that single idea that saved Hawking’s Ph.D. and set him on the road to science superstardom.
Penrose published his ideas in January 1965, by which time Hawking was already setting to work on the flash of inspiration that had struck him on the way home from London to Cambridge that night after the talk. Applying singularity theory to the Universe was by no means an easy problem, and within months Sciama was beginning to realize that his young Ph.D. student was doing something truly exceptional. For Hawking, this was the first time he had really applied himself to anything. As he says:
I . . . started working hard for the first time in my life. To my surprise, I found I liked it. Maybe it is not really fair to call it work. Someone once said, “Scientists and prostitutes get paid for doing what they enjoy.”11
When he was satisfied with the mathematics behind the ideas, he began to write up his doctoral thesis. In many respects, it ended up as a pretty messy effort because he had been in something of a wilderness for much of the first half of his time at Cambridge. The problems he and Sciama had experienced in finding him suitable research projects had left a number of holes and unanswered questions in the thesis. However, it had one saving grace—his application of singularity theory during his third year.
The final chapter of Hawking’s thesis was a brilliant piece of work and made all the difference to the awarding of the Ph.D. The work was judged by an internal examiner, Dennis Sciama, and an expert external referee. As well as being passed or failed, a Ph.D. can be deferred, which means that the student has to resubmit the thesis at a later date, usually after another year. Thanks to his final chapter, Hawking was saved this humiliation and the examiners awarded him the degree. From then on, the twenty-three-year-old physicist could call himself Dr. Stephen Hawking.
5
FROM BLACK HOLES TO THE BIG BANG
In the early 1960s, astronomers already knew that any star which contains more than about three times as much matter as our Sun ought to end its life by collapsing inward to form what is now known as a black hole. More than twenty years previously, researchers had used Einstein’s equations of general relativity to calculate that such an object would bend spacetime completely around upon itself, cutting th
e central mass off from the rest of the Universe. Light rays passing near such an object would be deflected so much that even photons would orbit around the central “star” in closed loops and could never escape into the Universe outside. Obviously, since it could emit no light, such an object would be black, which is why the American relativist John Archibald Wheeler dubbed them “black holes” in 1969.
But although it was well known that the general theory made this prediction, at the time Hawking was completing his undergraduate studies and moving on to research, no one took the notion of black holes seriously. The reason is that there are very many known stars that have more than three times the mass of our Sun. They do not collapse because nuclear reactions going on inside the stars make them hot. The heat creates an outward pressure that holds the star up against the pull of gravity. Astronomers knew that when such stars run out of nuclear “fuel,” they explode, blasting away their outer layers into space. As recently as fifty years ago, astronomers assumed that such an explosion would always blow away so much matter that the core left behind would have less than three times the mass of our Sun—or, perhaps, that some as-yet undiscovered pressure would come into play as the remnant of star stuff began to shrink.
This prejudice was reinforced by the fact that astronomers had indeed discovered many old, dead stars. These stellar cinders all had a bit less than the mass of our Sun, but that mass was compressed into a volume only about as big as that of the Earth. Such planet-sized stars are known as white dwarfs. They are held up against the inward pull of gravity by the pressure of the electrons associated with the atoms of which they are made, acting like a kind of electron gas. A white dwarf is so dense that each cubic centimeter of the star contains a million grams of material. Before 1967, these were the densest known objects in the Universe.
But although astronomers did not seriously believe that anything denser than a white dwarf could exist, a few mathematicians enjoyed playing with Einstein’s equations to work out what would happen to matter if it were squeezed to still greater densities. The equations said that if three times as much matter as our Sun contains were squeezed until it occupied a spherical region with a radius of just under 9 kilometers, spacetime in its vicinity would be so distorted that not even light could escape. Because nothing can travel faster than light, this meant that nothing at all could ever escape from such an object, which the mathematicians sometimes referred to as a collapsar (from “collapsed star”). It would have become the ultimate bottomless pit into which anything could fall but from which nothing could ever emerge. And the density inside the collapsar would be greater than the density of the nucleus of an atom; this, theorists of the time thought, was clearly impossible.
In fact, they did consider (but not too seriously) the possibility of stars as dense as the nucleus of an atom. By the 1930s, physicists knew that the nucleus of an atom is made of closely packed particles called protons and neutrons. The protons each carry one unit of positive charge; the neutrons, as their name suggests, are electrically neutral, but each has about the same mass as a proton. In everyday atoms, like the ones this book is made of, each nucleus is surrounded by a cloud of electrons. Each electron carries one unit of negative charge, and there is the same number of electrons as protons, so the atom as a whole is electrically neutral.
But an atom is largely empty space. The nucleus is tiny but very dense, and the cloud of electrons is (by comparison) huge and insubstantial. In proportion to the size of a whole atom, the nucleus is like a grain of sand in the middle of a concert hall. In white dwarf stars, some of the electrons are knocked off their atoms by the high prevailing pressure, and the nuclei are embedded in a sea of electrons that belong to the whole star, not to any particular nucleus. But there is still a lot of space between the nuclei, even though that space contains electrons. Each nucleus has a positive charge, and like charges repel, so the nuclei keep their distance from each other.
But quantum theory said that there is a way to make a star denser than a white dwarf. If the star were squeezed even more by gravity, the electrons could be forced to combine with protons to make more neutrons. The result would be a star made entirely of neutrons, and these could be packed together as closely as the protons and neutrons in an atomic nucleus. This would be a neutron star.
Calculations suggested that this ought to happen for any dead star with a mass more than 20 percent larger than that of our Sun (that is, more than 1.2 solar masses). A neutron star would have that much mass packed within a radius of about 10 kilometers, no bigger than many mountains on Earth. The density of the matter in a neutron star, in grams per cubic centimeter, would be 1014—that is, 1 followed by 14 zeros, or one hundred thousand billion.
Even an object this dense would not be a black hole, though, for light could still escape from its surface into the Universe at large.
Making a black hole from a dead star would require, as the theorists of the early 1960s were well aware, crushing even neutrons out of existence. The quantum equations said, in fact, that there was no way that even neutrons could hold up the weight of a dead star of three solar masses or more and that, if any such object were left over from the explosive death throes of a massive star, it would collapse inward completely, shrinking to a mathematical point called a singularity. Long before the collapsing star could reach this state of zero volume and infinite density, it would have wrapped spacetime around itself, cutting off the collapsar from the outside Universe.
Indeed, the equations said that if you squeezed any collection of matter hard enough, it would collapse in this way. The special feature of objects of more than three solar masses is that they will collapse anyway, under their own weight. But if it were possible to squeeze our own Sun down into a sphere with a radius of about 3 kilometers, it would become a black hole. So would the Earth, if it were squeezed down to about a centimeter. In each case, once the object had been squeezed down to the critical size, gravity would take over, closing spacetime around the object while it continued to shrink away into the infinite density singularity inside the black hole. But notice that it is much easier to make a black hole if you have a lot of mass. The critical size is not simply proportional to the amount of mass you have; the density at which a black hole forms is larger if you have less mass to squeeze.
For any mass there is a critical radius, called the Schwarzschild radius, at which this will occur. As these examples indicate, the Schwarzschild radius is smaller for less massive objects—you have to squeeze the Earth harder than the Sun, and the Sun harder than a more massive star, in order to make a black hole. Once it had formed, there would be a surface around the hole (a bit like the surface of the sea) marking the boundary between the Universe at large and the region of highly distorted spacetime from which nothing could escape. It would be a one-way horizon (unlike the surface of the sea!) across which both radiation and material particles could happily travel inward, tugged by gravity to join the accumulating mass of the singularity, but across which nothing at all, not even light, could travel outward.
Some mathematicians worried, fifty years ago, about the prediction that black holes must contain singularities. The notion of a point of infinite density made them uneasy. But most astronomers were more pragmatic. First of all, they doubted whether black holes could really exist at all. Probably, they thought, some law of physics would prevent any dead star from having enough leftover mass to collapse in this way. And even if black holes did exist, by their very nature they would keep the singularities at their hearts locked away from sight or investigation. Did it really matter, after all, if theory said that points of infinite density could exist, if the same theory said that such singularities were safely locked away behind uncrossable horizons?
One thing, however, should have worried those astronomers, even in the early 1960s. Just as you need to squeeze a small mass hard to make a black hole, a larger mass needs less of a squeeze to do the same trick. Indeed, a mass of about 4.5 billion solar masses would form a bla
ck hole if it were all contained within a sphere only twice the diameter of our Solar System. That mass sounds ludicrous at first. But remember that there are a hundred billion stars in our Milky Way Galaxy. If just 5 percent of the total mass were involved, such a supermassive black hole could indeed form. And the density of such an object would be nothing like the density of the nucleus of an atom or a neutron star. It would be just 1 gram per cubic centimeter—the same density as water. You could actually make a black hole out of water, if you had enough of it!
One way to understand how this can happen is by analogy with running tracks. The important thing about a black hole is that it bends spacetime completely around itself, so that light rays at the horizon would circle endlessly around the central singularity. But the photon “orbits” can be either very tight or follow a gentle curve. Indoor running tracks are usually tightly curved, to make them fit into the space available. Outdoor running tracks are more gently curved and take up more space. But in both cases, if you run round the track, you get back to where you started from—you follow a closed loop. Similarly, a black hole can be very small, with spacetime tightly folded around itself, or very large, with light rays following gradual curves around the horizon (or, indeed, they can be any size in between).
Very slowly, during the 1960s, the implications of this began to dawn on cosmologists. The whole Universe, they realized, might behave in some ways like the biggest black hole of them all, with everything in the Universe held together by gravity, and all of spacetime forming a self-contained, closed entity that folded around on itself with the ultimate in gradual curvature. But there is one big difference—black holes pull matter inward, toward the singularity; the Universe expands, outward from the Big Bang. The Universe is like a black hole inside out.