Explaining gravity as an exchange of messenger particles presents problems. When you think of the force holding you to the Earth as the exchange of gravitons (messenger particles of gravity) between the matter particles in your body and the matter particles that make up the Earth, you are describing the gravitational force in a quantum-mechanical way. But because all these gravitons are also exchanging gravitons among themselves, mathematically this is a messy business. We get infinities, mathematical nonsense.
Physical theories cannot really handle infinities. When they have appeared in other theories, theorists have resorted to something known as ‘renormalization’. Richard Feynman used renormalization when he developed a theory to explain the electromagnetic force, but he was far from pleased about it. ‘No matter how clever the word,’ he wrote, ‘it is what I would call a dippy process!’7 It involves putting in other infinities and letting the infinities cancel each other out. It does sound dubious, but in many cases it seems to work in practice. The resulting theories agree with observation remarkably well.
Renormalization works in the case of electromagnetism, but it fails in the case of gravity. The infinities in the gravitational force are of a much nastier breed than those in the electromagnetic force. They refuse to go away. Supergravity, the theory Hawking spoke about in his Lucasian lecture, and superstring theory, in which the basic objects in the universe are not pointlike particles but tiny strings or loops of string, began to make promising inroads in the twentieth century; and later in this book we shall be looking at even more promising recent developments. But the problem is not completely solved.
On the other hand, what if we allow quantum mechanics to invade the study of the very large, the realm where gravity seems to reign supreme? What happens when we rethink what general relativity tells us about gravity in the light of what we know about the uncertainty principle, the principle that you can’t measure accurately the position and the momentum of a particle at the same time? Hawking’s work along these lines has had bizarre results: black holes aren’t black, and the boundary conditions may be that there are no boundaries.
While we are listing paradoxes, here’s another: empty space isn’t empty. Later in this book we’ll discuss how we arrive at that conclusion. For now be content to know that the uncertainty principle means that so-called empty space teems with particles and antiparticles. (The matter–antimatter used in science fiction is a familiar example.)
General relativity tells us that the presence of matter or energy makes spacetime curve, or warp. We’ve already mentioned one result of that curvature: the bending of light beams from distant stars as they pass a massive body like the sun.
Keep those two points in mind: (1) ‘Empty’ space is filled with particles and antiparticles, adding up to an enormous amount of energy. (2) The presence of this energy causes curvature of spacetime.
If both are true the entire universe ought to be curled up into a small ball. This hasn’t happened. When general relativity and quantum mechanics work together, what they predict seems to be dead wrong. Both general relativity and quantum mechanics are exceptionally good theories, two of the outstanding intellectual achievements of the twentieth century. They serve us magnificently not only for theoretical purposes but in many practical ways. Nevertheless, put together they yield infinities and nonsense. The Theory of Everything must somehow resolve that nonsense.
Predicting the Details
Once again imagine that you are an alien who has never seen our universe. With the Theory of Everything you ought nevertheless to be able to predict everything about it … right? It’s possible you can predict suns and planets and galaxies and black holes and quasars – but can you predict next year’s Derby winner? How specific can you be? Not very.
The calculations necessary to study all the data in the universe are ludicrously far beyond the capacity of any imaginable computer. Hawking points out that although we can solve the equations for the movement of two bodies in Newton’s theory of gravity, we can’t solve them exactly for three bodies, not because Newton’s theory doesn’t work for three bodies but because the maths is too complicated. The real universe, needless to say, has more than three bodies in it.
Nor can we predict our health, although we understand the principles that underlie medicine, the principles of chemistry and biology, extremely well. The problem again is that there are too many billions upon billions of details in a real-life system, even when that system is just one human body.
With the Theory of Everything in our hands we’d still be a staggeringly long way from predicting everything. Even if the underlying principles are simple and well understood, the way they work out is enormously complicated. ‘A minute to learn, the lifetime of the universe to master’, to paraphrase an advertising slogan. ‘Lifetime of the universe to master’ is a gross understatement.fn1
Where does that leave us? What horse will win the Grand National next year is predictable with the Theory of Everything, but no computer can hold all the data or do the maths to make the prediction. Is that correct?
There’s a further problem. We must look again at the uncertainty principle of quantum mechanics.
The Fuzziness of the Very Small
At the level of the very small, the quantum level of the universe, the uncertainty principle also limits our ability to predict.
Think of all those odd, busy inhabitants of the quantum world, both fermions and bosons. They’re an impressive zoo of particles. Among the fermions there are electrons, protons and neutrons. Each proton or neutron is, in turn, made up of three quarks, which are also fermions. Then we have the bosons: photons (messengers of the electromagnetic force), gravitons (the gravitational force), gluons (the strong force), and Ws and Zs (the weak force). It would be helpful to know where all these and many others are, where they are going, and how quickly they are getting there. Is it possible to find out?
The diagram of an atom in Figure 2.1 is the model proposed by Ernest Rutherford at the Cavendish Labs in Cambridge early in the twentieth century. It shows electrons orbiting the nucleus of the atom as planets orbit the sun. We now know that things never really look like this on the quantum level. The orbits of electrons cannot be plotted as though electrons were planets. We do better to picture them swarming in a cloud around the nucleus. Why the blur?
The uncertainty principle makes life at the quantum level a fuzzy, imprecise affair, not only for electrons but for all the particles. Regardless of how we go about trying to observe what happens, it is impossible to find out precisely both the momentum and the position of a particle at the same time. The more accurately we measure how the particle is moving, the less accurately we know its position, and vice versa. It works like a seesaw: when the accuracy of one measurement goes up, the accuracy of the other must go down. We pin down one measurement only by allowing the other to become more uncertain.
Figure 2.1. In the Rutherford model of a helium atom, the electrons orbit the nucleus the way planets orbit the sun. We now know that, because of the uncertainty principle of quantum mechanics, electron orbits are not really well-defined paths as shown in this model.
The best way to describe the activity of a particle is to study all the possible ways it might be moving and then calculate how likely one way is as opposed to another. It becomes a matter of probabilities. A particle has this probability to be moving – that way – or it has that probability to be – here. Those probabilities are nevertheless very useful information.
It’s a little like predicting the outcome of elections. Election poll experts work with probabilities. When they deal with large enough numbers of voters, they come up with statistics that allow them to predict who will win the election and by what margin, without having to know how each individual will vote. When quantum physicists study a large number of possible paths that particles might follow, the probabilities of their moving thus and so or of being in one place rather than another become concrete information.
Po
llsters admit that interviewing an individual can influence a vote by causing the voter to become more aware of issues. Physicists have a similar dilemma. Probing the quantum level influences the answers they find.
Thus far the comparison between predicting elections and studying the quantum level seems a good one. Now it breaks down: on election day, each voter does cast a definite vote one way or another, secret perhaps but not uncertain. If pollsters placed hidden cameras in voting booths – and were not arrested – they could find out how each individual voted. It is not like that in quantum physics. Physicists have devised ingenious ways of sneaking up on particles, all to no avail. The world of elementary particles does not just seem uncertain because we haven’t been clever enough to find a successful way to observe it. It really is uncertain. No wonder Hawking, in his Lucasian lecture, called quantum mechanics ‘a theory of what we do not know and cannot predict’.8
Taking this limitation into account, physicists have redefined the goal of science: the Theory of Everything will be a set of laws that make it possible to predict events up to the limit set by the uncertainty principle, and that means in many cases satisfying ourselves with statistical probabilities, not specifics.
Hawking sums up our problem. In answer to the question of whether everything is predetermined either by the Theory of Everything or by God, he says yes, he thinks it is. ‘But it might as well not be, because we can never know what is determined. If the theory has determined that we shall die by hanging, then we shall not drown. But you would have to be awfully sure that you were destined for the gallows to put to sea in a small boat during a storm.’9 He regards the idea of free will as ‘a very good approximate theory of human behaviour’.10
Is There Really a Theory of Everything?
Not all physicists believe there is a Theory of Everything, or, if there is, that it is possible for anyone to find it. Science may go on refining what we know by making discovery after discovery, opening boxes within boxes but never arriving at the ultimate box. Others argue that events are not entirely predictable but happen in a random fashion. Some believe God and human beings have far more freedom of give-and-take within this creation than a deterministic Theory of Everything would allow. They believe that as in the performance of a great piece of orchestral music, though the notes are written down, there may yet be enormous creativity in the playing of the notes that is not at all predetermined.
Whether a complete theory to explain the universe is within our reach or ever will be, there are those among us who want to make a try. Humans are intrepid beings with insatiable curiosity. Some, like Stephen Hawking, are particularly hard to discourage. One spokesman for those who are engaged in this science, Murray Gell-Mann, described the quest:
It is the most persistent and greatest adventure in human history, this search to understand the universe, how it works and where it came from. It is difficult to imagine that a handful of residents of a small planet circling an insignificant star in a small galaxy have as their aim a complete understanding of the entire universe, a small speck of creation truly believing it is capable of comprehending the whole.11
fn1 The advertising slogan for the game Othello is ‘A minute to learn, a lifetime to master’.
3
‘Equal to anything!’
WHEN STEPHEN HAWKING was twelve years old, two of his schoolmates made a bet about his future. John McClenahan bet that Stephen ‘would never come to anything’; Basil King, that he would ‘turn out to be unusually capable’.1 The stake was a bag of sweets.
Young S. W. Hawking was no prodigy. Some reports claim he was brilliant in a haphazard way, but Hawking remembers that he was just another ordinary English schoolboy, slow learning to read, his handwriting the despair of his teachers. He ranked no more than halfway up in his school class, though he now says, in his defence, ‘It was a very bright class.’2 Maybe someone might have predicted a career in science or engineering from the fact that Stephen was intensely interested in learning the secrets of how things such as clocks and radios work. He took them apart to find out, but he could seldom put them back together. Stephen was never well-coordinated physically, and he was not keen on sports or other physical activities. He was almost always the last to be chosen for any sports team. John McClenahan had good reason to think he would win the wager.
Basil King probably was just being a loyal friend or liked betting on long shots. Maybe he did see things about Stephen that teachers, parents and Stephen himself couldn’t see. He hasn’t claimed his bag of sweets, but it’s time he did. Because Stephen Hawking, after such an unexceptional beginning, is now one of the intellectual giants of our modern world – and among its most heroic figures. How such transformations happen is a mystery that biographical details alone cannot explain. Hawking would have it that he is still ‘just a child who has never grown up. I still keep asking these how and why questions. Occasionally I find an answer.’3
1942–1959
Stephen William Hawking was born during the Second World War, on 8 January 1942, in Oxford. It was a winter of discouragement and fear, not a happy time to be born. Hawking likes to recall that his birth was exactly three hundred years after the death of Galileo, who is called the father of modern science. But few people in January 1942 were thinking about Galileo.
Stephen’s parents, Frank and Isobel Hawking, were not wealthy. Frank’s very prosperous Yorkshire grandfather had over-extended himself buying farm land and then gone bankrupt in the great agricultural depression of the early twentieth century. His resilient wife, Frank’s grandmother and Stephen’s great-grandmother, saved the family from complete ruin by opening a school in their home. Her ability and willingness to take this unusual step are evidence that reading and education must already have been a high priority in the family.
Isobel, Stephen’s mother, was the second oldest of seven children. Her father was a family doctor in Glasgow. When Isobel was twelve, they moved to Devon.
It wasn’t easy for either family to scrape together money to send a child to Oxford, but in both cases they did. Taking on a financial burden of this magnitude was especially unusual in the case of Isobel’s parents, for few women went to university in the 1930s. Though Oxford had been admitting female students since 1878, it was only in 1920 that the university had begun granting degrees to women. Isobel’s studies ranged over an unusually wide curriculum in a university where students tended to be much more specialized than in an American liberal arts college or university. She studied philosophy, politics and economics.4
Stephen’s father Frank was a meticulous, determined young man who kept a journal every day from the age of fourteen and would continue it until the end of his life.5 He was at Oxford earlier than Isobel, studying medical science with a speciality in tropical medicine. When the Second World War broke out he was in East Africa doing field research, and he intrepidly found his way overland to take ship for England and volunteer for military service. He was assigned instead to medical research.
Isobel held several jobs after graduation from Oxford, all of them beneath her ability and credentials as a university graduate. One was as an inspector of taxes. She so loathed that that she gave it up in disgust to become a secretary at a medical institute in Hampstead. There she met Frank Hawking. They were married in the early years of the war.
In January 1942 the Hawkings were living in Highgate, north London. In the London area hardly a night passed without air raids, and Frank and Isobel Hawking decided Isobel should go to Oxford to give birth to their baby in safety. Germany was not bombing Oxford or Cambridge, the two great English university towns, reputedly in return for a British promise not to bomb Heidelberg and Göttingen. In Oxford, the city familiar from her recent university days, Isobel spent the final week of her pregnancy first in a hotel and then, as the birth grew imminent and the hotel grew nervous, in hospital, but she was still able to go out for walks to fill her time. On one of those leisurely winter days, she happened into a bookshop and, with
a book token, bought an astronomical atlas. She would later regard this as a rather prophetic purchase.6
Not long after Stephen’s birth on 8 January his parents took him back to Highgate. Their home survived the war, although a V-2 rocket hit a few doors away when the Hawkings were absent, blowing out the back windows of their house and leaving glass shards sticking out of the opposite wall like little daggers.7 It had been a good moment to be somewhere else.
After the war the family lived in Highgate until 1950. Stephen’s sister Mary was born there in 1943 (when Stephen was less than two years old), and a second daughter, Philippa, arrived in 1946. The family would adopt another son, Edward, in 1955, when Stephen was a teenager. In Highgate Stephen attended the Byron House School, whose ‘progressive methods’ he would later blame for his not learning to read until after he left there.
When Dr Frank Hawking, beginning to be recognized as a brilliant leader in his field, became head of the Division of Parasitology at the National Institute for Medical Research, the family moved to St Albans.
Eccentric in St Albans
The Hawkings were a close family. Their home was full of good books and good music, often reverberating with the operas of Richard Wagner played at high volume on the record player. Frank and Isobel Hawking believed strongly in the value of education, a good bit of it occurring at home. Frank gave his children a grounding in, among other things, astronomy and surveying, and Isobel took them often to the museums in South Kensington, where each child had a favourite museum and none had the slightest interest in the others’ favourites. She would leave Stephen in the Science Museum and Mary in the Natural History Museum, and then stay with Philippa – too young to be left alone – at the Victoria and Albert. After a while she would collect them all again.8
Stephen Hawking, His Life and Work Page 3
