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 pro-
duce 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 discovered during a survey carried out by radio astronomers in Cambridge, England (and known as 3C 48) 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 reexamined, 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 by adding 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.
In the early 1960s, though, the possibility of actually measuring the strength of this background radiation, and thereby testing the
Big Bang model, occurred to a few astronomers. One way of understanding how and why the radiation has cooled is in terms of redshift. Radiation that filled the Universe in the Big Bang still fills the Universe, but because space has stretched since then the waves making up that radiation have had to stretch accordingly in order to fill the space available. This means that energy that started out in the form of X-rays and gamma rays would now be in the form of microwaves, with wavelengths of around 1 millimeter or so. These are just the kind of radio waves used in some communications links and in radar. With the technology developed for radar and radio communications, and the associated rapid development of radio astronomy, researchers in both the Soviet Union and the United States saw that the background radiation predicted by the Big Bang model might be detectable and set about designing and building radio telescopes to do the job.
But they started just too late. The American team, based at Princeton University, was headed by Robert Dicke, who had worked in radar during the Second World War. In the early 1960s he gave a team of young researchers the task of building a microwave background detector using an updated version of equipment he had helped to design during the war. By 1965 things were progressing nicely, when Dicke received a phone call from a young researcher at Bell Laboratories, just 30 miles away from Princeton. The caller, Arno Penzias, wanted Dicke’s advice about some puzzling radio interference that Penzias and his colleague Robert Wilson had been getting on their radio telescope at Bell Labs since the middle of 1964.
Penzias and Wilson had, in fact, been using an antenna designed for use with the early communications satellites, modified to operate as a radio telescope. They found that, wherever they pointed the telescope in the sky, they seemed to be getting a signal corresponding to microwave radiation with a temperature of just under 3 K. After trying everything they could to sort out what was wrong with
the telescope (including cleaning pigeon droppings off the antenna, in case that was what was causing the interference), they gave up and called Dicke, an expert on microwaves, to ask if he had any idea what was going on.
Dicke soon realized that Penzias and Wilson had, in fact, detected the background radiation left over from the Big Bang. The Princeton detector, completed hurriedly a little later, confirmed the discovery, and soon radio astronomers around the world were getting in on the act. We now know that the Universe is indeed filled with a weak hiss of microwave background radiation, with wavelengths of around 1 millimeter, corresponding to a temperature of 2.73 K.
It was this discovery that opened the eyes of cosmologists to the reality of the Big Bang model: not just a model, after all, but also an accurate description of the real Universe we live in. First, the existence of the background radiation showed that there really had been a Big Bang; then, by using the precise measurement of the temperature of that radiation today, it was possible to work backward to the Big Bang to calculate the exact temperature of the fireball itself. We got slightly ahead of our story in Chapter 5, when we described the first few minutes of the life of the Universe—the accuracy of that description, dating from the mid-1970s, depends in part on our present-day knowledge of the precise temperature of the background radiation. But there is something else significant about that description of the early stages of the Universe. The First Three Minutes was not written by a specialist in cosmology, or even an astronomer, but by a mainstream physicist, Nobel Prize winner Steven Weinberg.
Before 1965, cosmology was a quiet backwater of science, almost a little ghetto where a few mathematicians could play with their models without annoying anybody else. Today, a quarter of a century later, the study of the Big Bang is at the center of mainstream physics, and Big Bang cosmology is seen as offering the key to
understanding the fundamental laws and forces by which the physical world operates. It is because of the measurements of the background radiation that we can be so confident about how nuclei were synthesized in the Big Bang. And it was the first calculations of this kind made after the discovery of the background radiation that convinced many physicists (not just cosmologists) that hot Big Bang cosmology had to be taken seriously as a description of the Universe.
These calculations were not something hurriedly cooked up in the light of the discovery of the background radiation but represented the culmination of more than ten years’ work. In the 1950s, inspired by Fred Hoyle’s lead, a team of British and American researchers had worked out how all the elements more complex than helium are synthesized inside stars. This was an astonishing tour de force. In essence, the process consists of sticking helium-4 nuclei together to build up more complex nuclei. Some of the complex nuclei then either spit out or absorb the odd proton, making nuclei of other elements.
As we mentioned in Chapter 5, though, there is a bottleneck for this process at its earliest stage. There is no stable nucleus that can be made by sticking two helium-4 nuclei together, and that is why nucleosynthesis stopped with helium in the Big Bang. Hoyle found a way round this bottleneck, via extremely rare collisions of three helium-4 nuclei almost simultaneously. This makes it possible to create a nucleus of carbon-12, but only if the energies (speeds) of the helium-4 nuclei are just right. The energies are just right inside stars, thanks to an unusual quantum effect known as a resonance. Nobody realized this until Hoyle explained how the crucial step in the chain must take place. He predicted the existence of the crucial resonance, which was then found during experiments here on Earth. Together with his colleagues, Hoyle went on to explain how every-
thing is built up from hydrogen and helium inside stars—including the atoms in your body and in this book.
In one of the strangest decisions ever made by a Nobel committee, one of Hoyle’s colleagues, Willy Fowler, later received a share of the 1983 Nobel Prize for Physics for this work. Fowler is a fine physicist in his own right and was a key member of the team. But he is the first to acknowledge that Hoyle made the key breakthrough on carbon-12 production and was the inspiration for the team’s efforts. Unfortunately, later in his career Hoyle espoused some decidedly unconventional ideas about the possibility that outbreaks of disease on Earth might be caused by viruses from comets. It seems that the Nobel committee, in its wisdom (?), decided not to give him a share of the physics prize with Fowler for fear of seeming to lend credence to what they regarded as his more cranky work. At least the British establishment, for once belying its stuffy image, acknowledged Hoyle’s true worth with a knighthood. All that, however, lay far in the future in 1967, when Fowler, Hoyle, and their colleague Robert Wagoner put the icing on the nucleosynthesis cake.
The one problem with the story of stellar nucleosynthesis as developed in the 1950s was that it could not explain where helium came from. Starting out with stars in which 75 percent of the material was hydrogen and 25 percent helium, the theory could explain beautifully the presence of every other element and could even explain why some elements are more common than others and how much more common. But it all starts with the triple-helium/carbon-12 resonance, and without that initial 25 percent of helium stars would not be able to cook up the rest of the elements. It was Wagoner, Fowler, and Hoyle who together showed that the kind of Big Bang that would leave a background radiation with a temperature of 2.73 K today would also produce a mixture of 25 percent helium and 75 percent hydrogen at the end of the first four minutes.
Their findings were unveiled at a meeting in Cambridge in 1967. One of us (J.G.) was present, as a very junior research student, somewhat in awe of the occasion. He clearly recalls the deep questions being asked at the meeting by another member of the audience, a slightly older but still junior researcher, who seemed to have a slight speech impediment but whose words were listened to closely by the more eminent researchers on the platform. Stephen Hawking was already known to be someone worth listening to, even at this early stage of his career. And the reason for his keen interest in Big Bang cosmology soon became clear, when the results of the investigation he was carrying out with Roger Penrose were published.
Hawking had begun puzzling over the singularity at the beginning of time in the early 1960s but had soon been deflected, as we have seen, by the diagnosis of his illness, temporarily giving up his work. But by 1965 things were looking up. He had decided that he wasn’t going to die quite so quickly as the doctors had predicted, after all; he had met and married Jane; and he was back at work with a vengeance. He was one of the few people, at that time, to take seriously the more extreme predictions of the general theory of relativity. Two years after the identification of the first quasar (but before its energy source was explained), and two years before the discovery of pulsars, only a handful of people believed in the possibility that black holes might exist or that the Universe really had been born out of a singularity.
One of the few other people who did take the notion of black holes seriously was a young mathematician, Roger Penrose, working at Birkbeck College in London. It was Penrose who showed that every black hole must contain a singularity and that there is no way for material particles to slide past each other in the middle of the hole. Not just matter, but space-time itself simply disappears at the
singularity. At such a point the laws of physics break down, and it is impossible to predict what will happen next.
But as we have seen, this need not be too worrying, provided such bizarre objects are always safely hidden behind the horizon of a black hole. In this spirit, Penrose proposed a “cosmic censorship” hypothesis, suggesting that all singularities must be hidden in this way and that “nature abhors a naked singularity.” In other words, observers outside the horizon of the black hole are always protected from any consequences of the breakdown of the laws of physics at the singularity.
Hawking was intrigued by Penrose’s work on singularities but saw that there was no way nature’s abhorrence of a singularity could shield us from the singularity at the beginning of time—if it existed. In 1965 the two of them joined forces to investigate this puzzle.
Previously, researchers had expected that if you tried to wind back the equations describing the expanding Universe, things would get more and more complicated as you approached the Big Bang. Particles would collide and bounce off one another, producing a chaotic and confusing fireball. To many people this looked like the ideal way to make a model universe bounce at high densities, without encountering a singularity. But over the next few years Hawking and Penrose developed a new mathematical technique for analyzing the way that points in space-time are related to one another. This did away with the confusion of the messy interactions between material particles and highlighted the underlying significance of the expansion (or collapse) of space itself.
The end result of this study was their proof that there must have been a singularity at the beginning of time, if the general theory of relativity is the correct description of the Universe. There is no way for particles in a contracting universe to slide past one another and avoid meeting in a singularity in the fireball, any more than it is pos-
sible to avoid the singularity inside a black hole. After all, when space shrinks to zero volume, there is literally no room left for particles to slip past one another. In other words, the expansion of the Universe away from the singularity in the beginning really is the exact opposite of the collapse of matter (and space-time) into a singularity inside a black hole. The cosmic censor has slipped up, and there is at least one naked singularity in the Universe that we are exposed to, even if it is separated from us by 15 billion years of time.
While Hawking and Penrose were working all this out, the discovery of the background radiation was announced; pulsars were discovered; and Wagoner, Fowler, and Hoyle were explaining how helium had been made in the Big Bang. By the time the Hawking-Penrose theorems were published, John Wheeler had given astronomers the term “black hole,” and newspaper stories were being written about the phenomenon. What had started out as an esoteric (but erudite) piece of mathematical research had evolved by the end of the 1960s into a major contribution to one of the hottest topics in science at the time.
And yet this was Hawking’s first real piece of research, stemming from his Ph.D. work—the journeyman piece for his scientific apprenticeship. What on earth would he come up with next? And what did it mean to say that there had been a definite beginning to time in the Big Bang? There seemed very little prospect, however, that the young researcher would come up with anything of comparable importance. The deterioration in his physical condition seemed to rule out a long career.