Stephen Hawking

by John Gribbin

  Einstein’s equations—the general theory of relativity—said that the Universe could not be static, but must be either expanding or contracting. Observations showed that the Universe is, indeed, expanding. So what did Einstein’s equations say about conditions long ago, when galaxies were packed tightly together, and before? Taken at face value, the equations said that the Universe must have emerged from a point of infinite density, a singularity, about 13.8 billion years ago. “Obviously” (to astronomers of the 1940s and 1950s, that is), that was ridiculous. The fact that the equations predicted a singularity must mean that they were flawed in some way; no doubt in due course somebody would come up with a better theory, one that didn’t make such extreme predictions. But meanwhile it seemed fairly reasonable to take the equations at face value as far as they applied to conditions that bore some resemblance to those we observe today.

  The densest form of matter familiar to us today is nuclear matter: protons and neutrons packed together in the hearts of atoms. So a few brave souls were prepared to contemplate the possibility that the general theory might provide a good guide to how the Universe had evolved from a state in which the overall density was as great as that of the nucleus of an atom, a “primeval atom,” if you like, containing all the mass of the Universe in a kind of neutron superstar.

  What came “before” that? How did this primeval super-density—sometimes referred to as the “cosmic egg”—come into being? Nobody knew; they could only make guesses. Perhaps the cosmic egg had existed for all eternity, until something triggered it into expansion. Or perhaps there had been a previous phase of the Universe in which spacetime was collapsing, in line with Einstein’s equations. Such a contracting universe might compress itself to nuclear densities and then “bounce” outward again, into a phase of expansion, without encountering the troublesome singularity.

  The notion of the primeval atom, or cosmic egg, emerged in the early 1930s and was refined over the next couple of decades. Even at the beginning of the 1960s, however, this was all still just a mathematical game played by a few experts, as much as anything for their own amusement. The notion of a super-dense cosmic egg, only about thirty times bigger than our Sun but containing everything that had burst asunder to create the expanding Universe, fitted Einstein’s equations and the observations. But nobody seems to have felt, deep down in their hearts, that their equations described the Universe. Nobody would have been too worried if it had turned out that the whole idea of the cosmic egg was wrong.

  You can get a feel for the way people regarded the idea in the 1950s from their own shorthand terms for describing their work. The equations of the general theory of relativity actually allow for more than one possible description of the overall behavior of spacetime. As we have mentioned, either expansion or contraction (but not stasis) is allowed by the equations. Obviously, the Universe we live in cannot be expanding and contracting at the same time; the two solutions to the equations cannot both apply to the Universe today. So the solutions are called models. A cosmological model is a set of equations that describes how a universe (with a small “u”) might behave. The equations have to obey the known laws of physics, but they do not necessarily purport to describe the actual behavior of the real Universe (with a capital “U”). Both the expanding and the contracting solutions to Einstein’s equations describe model universes, intriguing mathematical toys; the expanding solution might describe the real Universe. At the beginning of the 1960s, however, most cosmologists would have preferred to call even the expanding solution simply a model universe.

  But during the 1960s the whole notion of the Big Bang, as the theory was known, firmed up. Cosmologists began to believe, as more evidence came in confirming the accuracy of the predictions implicit in the general theory of relativity, that their equations really did describe what was going on out there in the real Universe. This encouraged more theoretical calculations, leading to new predictions, and more observations, in a self-stimulating upward spiral that led to a dramatic revolution in our understanding of the birth of the Universe. By 1976 the Big Bang theory was so well established that American physicist Steven Weinberg was able to write a best-selling popular book, The First Three Minutes, describing the early stages of the Big Bang, how the Universe had emerged from the super-dense state of the cosmic egg. Although written in the 1970s, the book encapsulated what was essentially the 1960s understanding of the Big Bang; we will not be getting too far ahead of our story if we give a brief résumé of that understanding now.

  One of the strangest things to grasp about all these descriptions of the Universe—the relativistic cosmological models—is that the Big Bang does not consist of a huge primeval atom sitting in empty space and then exploding outward. Many people still have this image, in which the galaxies are like fragments of an exploding bomb, hurtling outward through space. But it is wrong.

  What Einstein’s equations tell us is that it is space itself that expands, taking galaxies along for the ride. Galaxies were closer together long ago, when the Universe was younger, because the distances between them were more compressed than they are today. You can see this by imagining two spots of paint on a strip of elastic or on a rubber band. When you pull on the ends of the strip, it stretches, and the two paint spots move apart, but they do not move through the material the strip is made of.

  So in the very early Universe, at the time of the explosion of the primeval atom, there was no “outside” for the fragments of the explosion to move into. Space was tightly wrapped around itself, so that the cosmic egg was a completely self-contained ball of matter, energy, space, and time. It was, indeed, a super-dense black hole. It still is a black hole—the only difference is that, by expanding, it has become a very low-density black hole in which light now follows very gently curving orbits at the horizon.

  We live inside a black hole, but one so huge that the bending of spacetime within it is too small to be measured by any astronomical instruments on Earth. The “explosion” of the Big Bang stretched space, literally creating more room in which the material components of the cosmic egg could move. Starting out very hot and dense, the fireball thinned and cooled as the space available expanded. The process is exactly the same as the way the fluid in the pipes of your refrigerator keeps the fridge cool. In the fridge, fluid expands into a large chamber and cools; at the back of the fridge, it is squeezed into a smaller space and gets hot, but the heat escapes from the piping on the outside before the fluid goes back into the fridge to repeat the cycle. Like that fluid being squeezed, or like air being compressed in a bicycle pump when we use it to inflate a tire, the Universe must have been much hotter when it was more compressed.

  How much hotter? If you run your cosmological model all the way back to the singularity predicted by Einstein’s equations, you would be dealing with infinite temperatures, as well as infinite density. But nobody in the 1960s went to that extreme. The infinities were still taken as indicating a breakdown in the general theory of relativity, but even so the moment at which the infinities occurred in the models could be used as a marker for the beginning of time (at least until someone came up with a better theory).

  Although the physics of the 1960s could not say what went on during the split second following that beginning of time, it could describe in great detail everything that had happened to the Universe in the 14 billion years (the most precise current measurement of the age of the Universe is 13.798±0.037 billion years, which we’ll round up to 14 billion) beginning just a tenth of a second later. To an increasing number of cosmologists, the general theory did not really seem such a bad description of the Universe, if it could explain everything that has happened in the past 14 billion years except for the very first tenth of a second. This is what it told them.

  One tenth of a second after the “beginning” (or after the “bounce,” as many cosmologists of the 1960s would have argued), the density of the Universe was 30 million times greater than the density of water. The temperature was 30 billion degr
ees,* and the Universe consisted of a mixture of very high-energy radiation (photons) and material particles, including neutrons, protons, and electrons but also more exotic, unstable particles created ephemerally out of pure radiation. This is the ultimate example of the equivalence between mass and energy, expressed in Einstein’s famous equation E = mc2. On the Earth, in an atomic bomb, and inside the Sun, where nuclear reactions take place, tiny amounts of matter (m) are converted into large amounts of energy (E), because c is the speed of light, which is 300,000 kilometers a second, and c2 is a very large number indeed. (The E and m are in terms of joules and kilograms, respectively, and c is in terms of meters per second; 300,000,0002 = 90 quadrillion.) But if you had enough energy to play with, you could actually make matter out of energy; and there was ample energy available to do the trick in the Big Bang—even if many of the particles created in this way were unstable, destined to disappear again in a puff of radiation in far less than the blink of an eye.

  One second later, 1.1 seconds after the beginning, the Universe had cooled dramatically—all the way down to 10 billion K. At that time, the density was just 380,000 times the density of water, and from then on the reactions between particles were very similar to the nuclear reactions that go on inside the Sun and other stars today.

  At a temperature of 3 billion K, just under 14 seconds from the beginning, the first nuclei of deuterium could form, albeit temporarily. Hydrogen is the simplest atom, with just a single proton in its nucleus and one electron orbiting outside the nucleus. (In a sense, lone protons can be regarded as nuclei of hydrogen atoms.) The next most complicated atom is deuterium, which has a nucleus composed of one proton and one neutron, still with a single electron orbiting around it. Atoms that have the same number of electrons as each other but different numbers of neutrons still have identical chemical properties and are known as isotopes; deuterium is an isotope of hydrogen and is often known as “heavy hydrogen.”

  Temperature is a measure of how fast, on average, the particles that make up matter are moving (which is why there can be no temperature colder than –273°C, at which atomic motion stops), and at temperatures above 3 billion K, protons and neutrons move too fast to do anything except bounce off each other. Some particles move faster than the average for a particular temperature and some slower, although most have speeds close to the average. So as the temperature fell below that value, some protons and neutrons were moving slowly enough to stick together when they collided. The thing that makes them stick is an attraction known as the strong force. As its name suggests, this is a powerful force of attraction that operates between all protons and neutrons. But it has a very short range, and fast-moving particles brush past or bounce off each other too quickly for the strong force to take hold of them during the brief time they are in range. At first, most of the deuterium nuclei produced in this way were knocked apart by collisions with faster-moving particles; but as the fireball cooled still further, the deuterium nuclei had a better and better chance of survival.

  Just 3 minutes and 2 seconds after the beginning, the temperature had cooled to below 1 billion K—the entire Universe was then only seventy times as hot as the heart of the Sun is today. At this point, almost all the deuterium nuclei were able to combine in pairs to form nuclei of helium. Helium nuclei each contain two protons and two neutrons, making four “nucleons” in all, so they are known as helium-4 nuclei (and helium atoms, of course, each have two electrons orbiting around the nucleus).

  It happens that helium-4 nuclei are particularly stable. But there are no stable nuclei containing five nucleons (such as you might expect to get if you added a proton or a neutron to a nucleus of helium-4) or eight nucleons (such as you might expect to get if you stuck two helium-4 nuclei together). So the process of “nucleosynthesis” in the Big Bang stopped with the production of helium-4. Less than 4 minutes after the beginning, matter had settled down into a mixture of about 75 percent hydrogen nuclei and 25 percent helium, intermingling with fast-moving electrons and bathed in a sea of hot radiation.

  Half an hour later, 34 minutes after the beginning, the temperature was down to 300 million K, and the density of the Universe was only 10 percent of the density of water. But it took a further 700,000 years for the Universe to cool enough to allow electrons to become attached to the nuclei and form stable atoms. Before then, as soon as a positively charged nucleus tried to latch on to a negatively charged electron, the electron would have been knocked away by an energetic photon. After 700,000 years, however, the temperature of the Universe had fallen to about 4,000 K (roughly the temperature at the surface of the Sun today), and nuclei and electrons were at last able to hold together to form stable atoms.

  For most of the past 14 billion years, protons, neutrons, and electrons have been bound up in stars and galaxies formed out of this primeval stuff, as gravity pulled clouds of gas together in space. The radiation left over from the Big Bang had nothing more to do with the matter, once it was no longer hot enough to separate electrons from their atomic nuclei and simply cooled steadily as the Universe expanded. But as we shall see, that background radiation, the echo of creation, had a key role to play in persuading cosmologists that one of their “model universes” might actually be telling them something deeply significant about the real Universe. And all this was happening while the person who was to become a key player in taking cosmology that step further in the 1970s, back to the beginning itself, was experiencing upheavals of his own, both personal and professional.

  * Physicists measure temperature in degrees kelvin, denoted by the letter K. This scale of measurement starts from the absolute zero of temperature, at –273°C, where all thermal motion of atoms stops. But a little matter of 273 degrees is neither here nor there when we are measuring temperatures in billions of degrees, so for all practical purposes the temperatures given for the fireball are the same as degrees Celsius.

  6

  MARRIAGE AND FELLOWSHIP

  The mid-sixties turned out to be one of the most important times in Stephen Hawking’s life. Having become engaged to Jane, he realized that he would need to find a job very quickly if they were to be married. After obtaining a doctorate, the next stage in the career of any academic is usually to secure a fellowship, accompanied by a grant, in order to continue research. Much like the transition from undergraduate studies to postgraduate research, applications for fellowships are usually made while working on a Ph.D. rather than leaving things until afterward. So while in the throes of writing his thesis, and with a wedding planned for the coming summer, Hawking had to look around for available posts. Fortunately he did not have to look far. He heard about a theoretical physics fellowship being offered by another college at the university, Caius,* to begin that autumn. Without hesitating, he began to organize his application. However, getting such a relatively simple thing off the ground did not turn out to be as easy as he had hoped.

  At this stage of his illness, he was unable to write and had planned to ask Jane to type his application during her next visit to Cambridge the coming weekend. But when his fiancée stepped off the train, she greeted him with her arm in plaster up to the elbow. She had had an accident the previous week, breaking her arm. Hawking admits that he was not as sympathetic toward her as perhaps he should have been when he saw the state she was in, but hurt feelings were quickly mended and together they tried to work out how they could get the application written. Jane’s left arm had been broken and she is right-handed, so Hawking dictated the information and she was able to write the application by hand. They then managed to get a friend in Cambridge to type it up for them.

  However, that was not the end of Hawking’s problems. As a requirement of the application he had to give two references. Obviously Dennis Sciama was his first referee; he was, naturally, very supportive, and suggested Hermann Bondi as the second. Hawking had met Bondi on several occasions at the King’s College seminars given by Roger Penrose earlier that year, and Bondi had communicated to him a paper he h
ad written to the Royal Society a few months earlier. Encouraged by this, Hawking decided, with near-catastrophic consequences, to ask Bondi to give him a reference. As Hawking puts it:

  I asked him after a lecture he gave in Cambridge. He looked at me in a vague way, and said, yes he would. Obviously, he didn’t remember me, for when the College wrote to him for a reference, he replied that he had not heard of me.1

  If such a serious blow had happened today, he would almost certainly not have had a hope of getting his fellowship. In the sixties, however, competition for academic posts was not quite as fierce as it is now, and the authorities at Caius showed great tolerance in writing to tell him of the embarrassing situation. Sciama came to the rescue again and contacted Bondi to refresh his memory about the promising young researcher. Bondi then gave Hawking a glowing reference, possibly far kinder than one he might originally have written.

  The college council at Caius meets annually during the Lent term to elect new fellows. There are usually six or seven positions on offer, covering the full spectrum of subjects, and if elected, the successful applicant joins the seventy-odd fellows already in residence at the college. The council consists of around a dozen senior fellows, headed by the college master. In 1965 the master was the famous historian of Chinese science, Joseph Needham. Hawking came with good recommendations, and a number of the science fellows on the council, including Needham, had heard of him via the early reputation he had already gained in Cambridge academic circles. As Shakespeare says, “Sweet are the uses of adversity,” and maybe this has never been truer than in Hawking’s case. Despite the confusion over references, the council favored him over his competitors, and he received his fellowship at Caius. As far as Hawking’s career was concerned, he and Jane could now look to the future with a degree of confidence.