Stephen Hawking

by John Gribbin

  The couple decided to buy the house in Little St. Mary’s Lane. Hawking swallowed his pride and returned to the Bursary at Caius to ask the college for a mortgage. The Bursary conducted a survey of the property, decided that it would not be a sound investment, and turned him down. Once again, his status as a fellow was opening up very few “real life” privileges. Undeterred, they went to a building society for the loan and were granted a mortgage. Stephen’s parents gave them the money to do up the house, and the usual gang of friends once more helped out, this time with wallpapering and painting.

  Although the house was small, they remained there for a number of years until, in the mid-seventies, it became too cramped for the growing family. But in the meantime it served their purposes as well as it had ever done. Newly decorated, it was even cozier than it had been as a rented property, and—what was more important—it was now their own home, providing a secure environment in which they could begin to raise a family.

  The sixties were a great time to be alive and young. They were a time of tremendous, although in some ways misplaced, hope, an era of reawakening two decades after the end of the Second World War and all the privations that followed, a time of fresh beginnings and optimism in all spheres of life. The second half of the decade heralded the first real counter-cultural revolution in the West, bringing with it new music, new art, and new literature. A few years earlier, the trial surrounding the censorship of D. H. Lawrence’s Lady Chatterley’s Lover had seen the dam of elitism and Victorian morality burst wide open with the immortal question, “Is it a book you would wish your wife or your servant to read?” The Beatles, the Rolling Stones, and, so it seemed, half the youth of Britain and America were experimenting with psychedelic drugs; dresses were getting shorter and hair longer.

  The Hawkings and their friends in Cambridge showed little interest in fashion and pop music, although Jane was keen on mini-dresses and the latest hairstyles. But in the world of science, things were also on the move. George Ellis clearly remembers watching the maiden flight of the Concorde in April 1969 and being filled with excitement at the new technology taking the world by storm. Then, only a few months later, they sat glued to their TV screens to watch the “one small step” of Neil Armstrong when the lunar module Eagle landed in the Sea of Tranquility, 240,000 miles away on the surface of the Moon. “The Eagle has landed,” he said. “The surface is like a fine powder. It has a soft beauty all its own, like some desert in the United States.” At that moment, anything seemed possible.

  The Hawkings and the Ellises went on holiday together in 1969. Foreign holidays were suddenly in vogue because of drastically reduced prices, and it had become very fashionable to take a package trip to such destinations as Spain or its outlying islands, especially Majorca. The two families flew to Palma airport, Majorca, and spent a short break walking through the unspoiled almond groves, sampling the local wine, and sunning themselves on the clean, unmolested beaches, almost untouched by visiting Anglo-Saxons and certainly lager-lout-free.

  Hawking was working harder than he had ever worked before, and it was paying dividends. In 1966 he won the Adams Prize for an essay entitled “Singularities and the Geometry of Spacetime.” Much of his research during this period was a continuation of the work that had yielded the astonishing last chapter of his Ph.D. thesis. He spent most of this time in collaboration with Roger Penrose, who was by then professor of applied mathematics at Birkbeck College in London.

  One of the major difficulties the two of them faced was that they had to devise new mathematical techniques in order to carry out the calculations necessary to verify their theories—to make them empirically sound and not just ideas. Einstein had experienced a similar problem fifty years earlier with the mathematics of general relativity. He, like Hawking, was not a particularly brilliant mathematician. Fortunately for Hawking, however, Penrose was. In fact, he was fundamentally a mathematician rather than a physicist, but at the deep level at which the two subjects become almost indistinguishable.

  It really boils down to a difference in approach. Hawking’s way of working is largely intuitive—he just knows if an idea is correct or not. He has an amazing feel for the subject, a bit like a musician playing by ear. Penrose thinks and works in a different way, more like a concert pianist following a musical score. The two approaches meshed perfectly and soon began to produce some very interesting results on the nature of the early Universe. As Dennis Sciama once put it, “[The theories] required very highbrow methods, at least by the standards of theoretical physicists.”9 Penrose liked to work in a highly visual way, using diagrams and pictures, which suited Hawking fine. He always felt more at home with visual representations than with mathematical formulas. It was also so much easier for him to manipulate these pictures rather than trying to work with equations that he could not write out and had to retain in his head.

  Since his undergraduate days, Hawking has been a keen follower of the philosopher Karl Popper. The main thrust of Popper’s philosophy of science is that the traditional approach to the subject, “the scientific method” as originally espoused by the likes of Newton and Galileo, is in fact inadequate.

  The traditional approach to science can be broken down into six stages. First comes an observation or an experiment. Scientists then try to devise a general theory to explain by induction what they have observed, and then they go on to propose a hypothesis based on this general theory. Next come attempts to verify this hypothesis by further experimentation. The original theory is thus proved or disproved, and the scientist then assumes the truth or otherwise of the matter until proven wrong.

  Popper stands this process on its head and suggests the following approach. Take a problem. Propose a solution or a theory to explain what is happening. Work out what testable propositions you can deduce from your theory. Carry out tests or experiments on these deductions in order not to prove them but to refute them. The refutations, combined with the original theory, will yield a better one.

  The primary difference between the two approaches is that, according to the traditional scientific method, after making an observation the scientist attempts to verify a theory by further experiment; in Popper’s system, the scientist tries to disprove the theory in an attempt to find a better one. It is this aspect of Popper’s thought that is so appealing to Hawking and many other scientists, and he has often applied it in his own scientific work. The science writer Dennis Overbye once asked him how his mind worked. In reply, Hawking said:

  Sometimes I make a conjecture and then try to prove it. Many times, in trying to prove it, I find a counter-example, then I have to change my conjecture. Sometimes it is something that other people have made attempts on. I find that many papers are obscure and I simply don’t understand them. So, I have to try to translate them into my own way of thinking. Many times I have an idea and start working on a paper and then I will realize halfway through that there’s a lot more to it.

  I work very much on intuition, thinking that, well, a certain idea ought to be right. Then I try to prove it. Sometimes I find I’m wrong. Sometimes I find that the original idea was wrong, but that leads to new ideas. I find it a great help to discuss my ideas with other people. Even if they don’t contribute anything, just having to explain it to someone else helps me sort it out for myself.10

  Little did he know, at the end of the 1960s, just how important his ideas would soon prove to be.

  * Pronounced “keys”; its full name is Gonville and Caius College.

  7

  SINGULAR SOLUTIONS

  During the 1960s, four new developments, two concerning black holes and two cosmological, led to a revival of interest in the singular solutions to Einstein’s equations. As a result of the work stimulated by these developments, especially the collaboration between Hawking and Roger Penrose, physicists realized at the beginning of the 1970s that they might have to come to terms with the unthinkable: the prediction from the general theory of relativity that points of infinite density�
��singularities—could exist in the Universe did not, after all, indicate a flaw in those equations, and singularities might really exist. Even worse, for those still trying to cling to an older picture of reality, because the Universe itself seems to be a black hole viewed from within the Schwarzschild horizon, there might indeed be a singularity at the beginning of time that could not be obscured from our view—a “naked” singularity.

  It all began with the discovery of quasars in 1963. The quasar story actually began on the last day of 1960. During the 1950s, astronomers using telescopes sensitive to radio waves rather than visible light had identified many objects in the Universe that produce a lot of radio noise. Some of these objects were also visible as bright galaxies and were known as radio galaxies, but others had not yet been identified with any known visible object. Then, at the end of 1960, the American astronomer Allan Sandage reported that one of the radio sources (known as 3C 48) discovered during a survey carried out by radio astronomers in Cambridge, England could be identified not with a distant galaxy but with what seemed to be a bright star. More of these radio “stars” were identified over the next few years, but nobody could explain how they produced the radio noise. Then, in 1963, Maarten Schmidt, working at the Mount Palomar Observatory in California, explained why another of these objects, known as 3C 273, had a very unusual spectrum.

  All stars (and other hot objects) reveal their composition by the nature of the light they emit. Each kind of atom, such as hydrogen, helium, or oxygen, absorbs or emits energy only at very precise wavelengths, because of the quantum effects mentioned in Chapter 2. So when light from a star or galaxy is spread out, using a prism, into a spectrum, we see that the spectrum is crossed by a series of dark and bright lines at different wavelengths, corresponding to the presence of atoms of different elements in the atmosphere of the star (or in the stars that make up the galaxy). These spectral lines are as characteristic as fingerprints, and for a particular type of atom they are always produced at the same distinctive wavelengths.

  Astronomers already knew, though, that these spectral lines are shifted a little bit toward the red end of the spectrum in the light from galaxies outside the Milky Way. This famous “redshift” is caused by the expansion of the Universe, which stretches space, and therefore stretches the wavelength of light en route to us from a distant galaxy. Indeed, it was the discovery of the redshift that told astronomers the Universe must be expanding, just as Einstein’s equations had predicted, but Einstein himself had at first refused to believe it.

  The fact that light from 3C 273 was redshifted—the discovery Maarten Schmidt made—was not a surprise; but the size of the shift, nearly 16 percent toward the red end of the spectrum, astonished astronomers in 1963. Typical redshifts for galaxies are much less than this, about 1 percent, or 0.01. With the realization that such large redshifts were possible, other radio “stars” were re-examined, and it turned out that they all showed similar—or even larger—shifts. 3C 48, for example, has a redshift of 0.368 (nearly 37 percent), more than twice that of 3C 273, and the record redshift now stands above 4 (in other words, the light from the most distant quasars known is stretched to more than four times its original wavelength).

  In the expanding Universe, redshift is a measure of distance (the farther light has to travel on its way to us, the more it will be stretched by Universal expansion). So these objects were not stars at all, but something previously unknown—objects that looked like stars but were far away, in most cases farther away than the known galaxies. They soon became known as quasi-stellar objects, or “quasars.”

  In order to be visible at all at the huge distances implied by their redshifts, quasars must produce prodigious amounts of energy. A typical quasar shines with the brightness of three hundred billion stars like the Sun, three times as bright as our whole Milky Way Galaxy. Having sought in vain to find any alternative means to explain the power of quasars, astronomers were reluctantly forced to consider the possibility that they might be black holes. We now know that each quasar is a black hole containing at least a hundred million times as much mass as our Sun, contained within a volume of space with about the same diameter as our Solar System. (This is just the kind of large, low-density black hole described in Chapter 5.) Each one actually lies at the heart of an ordinary galaxy and feeds off the stellar material of the galaxy itself. Ever-improving telescope technology has enabled us, in many cases, to photograph the surrounding galaxy itself, faint alongside the quasar.

  Although a hundred million solar masses is large by everyday standards, this still represents only one-tenth of 1 percent of the mass of the parent galaxy in which a quasar lurks. When such an object swallows matter, as much as half the mass of the matter can be converted into energy, in line with Einstein’s famous equation E = mc2. As we saw in Chapter 5, the factor c2 is so huge that this corresponds to a vast amount of energy. This process of energy production is so efficient that, even if only about 10 percent of the infalling mass is actually converted into energy, a quasar can shine as brightly as three hundred billion Suns, bright enough to be seen across the vast reaches of intergalactic space, if it is swallowing just one or two solar masses of material every year. The material forms a great, hot, swirling disc around the black hole itself. This disc is where the energy that produces the radio noise, and the visible light, comes from, even though the hole itself, as the name implies, is black. And with a hundred billion stars to eat, even if a quasar only dines off 1 percent of the mass of the parent galaxy, it can shine that brightly for a billion years.

  The existence of quasars shows that large, low-density black holes really do exist. In 1967, just four years after the redshift of 3C 273 was measured, the Cambridge radio astronomers achieved another breakthrough with the discovery of the rapidly varying radio sources that became known as “pulsars.” And although pulsars are not themselves black holes, they opened the eyes of most astronomers to the possibility that super-dense, compact black holes might also really exist, just as the general theory of relativity predicted.

  The first pulsars were discovered by a research student, Jocelyn Bell, while testing a new radio telescope. The astonishing thing about these radio sources is that they flick on and off several times a second (some of them several hundred times a second) with exquisite precision. This is so much like an artificial signal, a kind of cosmic metronome, that, only half-jokingly, the first pulsars discovered were labeled “LGM 1” and “LGM 2”—the initials “LGM” stood for “Little Green Man.” As more of them were discovered, though, it became clear that there were far too many to be explained as interstellar traffic beacons set up by some super-civilization, and the accepted name became pulsar, from a contraction of “pulsating radio source” and because the name chimed with quasar.

  But what natural phenomenon could produce such regular, rapid pulses of radio noise? There were only two possibilities. The pulses had to signal either the rotation or the vibration of a very compact star. Anything bigger than a white dwarf would certainly rotate or vibrate too slowly to explain the speed of the known pulsars, and rotating white dwarfs were soon ruled out—a simple calculation showed that a white dwarf rotating that fast would break apart.

  For a short time early in 1968, it seemed that vibrations of a white dwarf, literally pulsing in and out, might explain the variations in the radio noise from pulsars. But it was fairly straightforward to calculate the maximum rate at which a white dwarf could pulsate without breaking apart. Indeed, one of us (J.G.) did exactly that as part of the work for his Ph.D. The answer was disappointing (for him) but conclusive: white dwarfs simply cannot pulsate at the required speed, which meant that the stars involved in the pulsar phenomenon must be even more compact, and denser, than white dwarfs.

  They must, in short, be neutron stars, predicted by theory but never previously discovered. Within months of the announcement of the discovery of pulsars, it was established that these objects are actually rotating neutron stars, definitely within our Galaxy
, producing beams of radio noise that sweep past us like the flashing beams of a lighthouse. They are created by supernovas, explosions of giant stars. And, as theorists were well aware from the outset, the same theory that predicted the existence of neutron stars, a prediction which had been largely ignored for thirty-odd years, also predicted that if you added just a little more mass to a neutron star (or by having a little more debris left over from a supernova explosion), you would create a collapsar.

  It is no coincidence that John Wheeler coined the term “black hole” in this connection the year following the discovery of pulsars, for the realization that pulsars must be neutron stars triggered an explosion of interest in the even more exotic predictions of the general theory of relativity. That explosion had already been primed, however, by yet another discovery made using radio telescopes, which had confirmed the reality of the Big Bang itself.

  When the Universe was more compressed, it was hotter, just as the air in a bicycle pump gets hot when it is compressed. The Big Bang was a fireball of radiation in which matter initially played an insignificant role. But as the Universe expanded and cooled, the radiation faded away, and matter, in the form of stars and galaxies, came to dominate the scene.

  All this was known to astronomers in the 1940s and 1950s. George Gamow and his colleagues even carried out a rough calculation of what temperature this leftover radiation would have cooled to by now. In 1948 they came up with a figure of about 5 K (minus 268°C). By 1952 Gamow was inclined to think that it might be rather higher, and in his book, The Creation of the Universe, he said that the temperature ought to be somewhere below 50 K. But 5 K or 50 K, it was still a very low temperature, and in the 1950s nobody seriously contemplated the possibility of trying to detect this echo of creation, a cold background sea of radiation filling the entire Universe and left over from the Big Bang.