Stephen Hawking (37 page)

Mathematicians, in fact, have little difficulty in disposing of “extra” dimensions of space. They use a trick they call “compactification,” which can be understood by looking at the
appearance of objects viewed from different distances in the everyday world. The standard image that they ask us to conjure up is that of a garden hose. Viewed from close up, it is clear that a hose consists of a two-dimensional sheet of material wrapped around a third dimension. But if we move back from the hose and study it from far away, it looks like a one-dimensional line. If we look at this one-dimensional line end on, it even looks like a point, with zero dimensions.

Taking a slightly different example, we all know from everyday experience that the surface of the Earth is far from smooth—it has wrinkles and bumps that we call valleys and mountains, so extreme that in some places it is impossible to walk across the surface. Yet to an astronaut far out in space, the surface seems to be very smooth and regular.

This may be why we do not perceive the other twenty-two dimensions of space. They may be curled up, or “compactified” into the multidimensional equivalent of cylinders and spheres. Each point of space that we perceive must really be a 22-dimensional knot of space, curled up very tightly so that we cannot see the bumps. How tightly? Roughly speaking, the complex structure of space would only be apparent on a scale of less than 10
^−30
of a centimeter. (For comparison, a typical atomic nucleus is about 10
^−13
centimeters across. So a nucleus is about a hundred million billion times bigger than the knots in the structure of space. In relation to a nucleus, the knots are one hundred thousand times
smaller
than a nucleus is compared with your thumb.)

Although mathematicians have no trouble describing such phenomenal compactification, it does raise the interesting
question of why twenty-two dimensions should have rolled up in this way, while the other three dimensions of space have been expanding ever since the Big Bang. Intriguingly, both the familiar law of gravity and the equations of electromagnetism discovered by Maxwell only “work” in a universe where there are three dimensions of space plus one of time. If, for example, there were more spatial dimensions, there would be no stable orbits for planets to follow around a central star. The slightest disturbance and the planet would either fall into the star and be burned up or drift away into space and freeze. In fact, as Hawking points out, there wouldn't even be any stable stars—any collection of gas and dust would either break apart or collapse immediately into a black hole.

So the laws of physics may be telling us that, whatever number of dimensions you start out with, all but three spatial dimensions and one time dimension must be unstable and will compactify. There is even a hint, from some new research, that the collapse of the other twenty-two dimensions might have provided the driving force that started the other three dimensions expanding. And all of this, of course, relates to the idea of anthropic cosmology, which we described in
Chapter 13
. Perhaps there are other universes, other bubbles in spacetime, where the compactification worked out slightly differently, leaving, maybe, six or seven spatial dimensions (or only one). But since those universes will contain no suitable home for life, there will be nobody in them trying to puzzle out the nature of physics. If life-forms like us can exist only in a universe with three spatial dimensions, it is no surprise to find that the Universe we live in does indeed have only three spatial dimensions!

So how close is the study of physics to answering the ultimate questions of life and the Universe? Is there no work left for theoretical physicists to do in the twenty-first century?

In 1980, in his Lucasian lecture, Hawking suggested that we might see the end of physics “by the end of the century.” By this, he meant that physicists would have a complete, consistent, and unified theory of the physical interactions that describe all observable phenomena. Something along the lines of superstring theory, perhaps.

As Hawking acknowledged, there have been previous occasions on which physicists have thought they were on the brink of finding all the answers. Most famously, at the end of the nineteenth century there was a general feeling that, with Maxwell's and Newton's equations firmly established, everything else would be merely a matter of detail, a question of dotting the i's and crossing the t's of science. Hardly was this feeling firmly established when physics was turned on its head by the twin revolutions of quantum theory and relativity theory. And yet by the late 1920s—just a generation later—the pioneering quantum physicist Max Born was telling people that there would be nothing significant left for theoretical physicists to do within six months.

At that time, the only fundamental particles known were the electron and the proton, and it seemed to Born that they were well understood. In the early 1930s, however, the neutron was discovered, and we now know that both the neutron and proton are made of yet more basic particles, the quarks.

Even taking Hawking's optimism of 1980 at face value, though, this would not mean that all physicists would be unemployed after the year 2000. As Hawking emphasized in that lecture, the laws of physics that Born was so proud of more than eighty years ago really are all that we need, in principle, to describe the behavior of chemical reactions. Biological processes, in turn, depend on the chemistry of complex molecules. Chemistry depends almost entirely on the properties of electrons, and in the 1920s Paul Dirac found a quantum equation that exactly describes how electrons behave. The snag is that this equation is so fiendishly complex that nobody has been able to solve it, except for the simplest possible atom (hydrogen), which has a single electron orbiting a single proton. In Hawking's words, from that Lucasian lecture:

[A]lthough in principle we know the equations that govern the whole of biology, we have not been able to reduce the study of human behavior to a branch of applied mathematics.

Even if we had a genuine unified theory that contained all the forces of nature, it would be far more difficult to use this to work out the behavior of the entire Universe than it is to work out your behavior using Dirac's equation. So there is plenty of work left for theoretical physicists to do.

By the time
A Brief History of Time
appeared in 1988, Hawking was being more cautious about the end being in sight for theoretical physics. He talked of “if” we discover a complete theory, not “when.” Indeed, although the millennial
resonance of the possibility of discovering a complete theory by the year 2000 obviously appealed in 1980, this is one of those prospects that keeps receding into the future. As we have said, physicists have been talking about such an end to physics being “just around the corner” for at least forty years, and usually, if pressed, they would say that the corner they expect to turn lies about twenty years ahead—whenever you ask them that question! As we entered the new century, even the most optimistic physicist set the date for finding a complete theory no earlier than about 2020, and most refuse to be drawn into such speculations.

Perhaps, though, they should regard the question of finding the ultimate theory with some urgency. For at the end of his Lucasian lecture, Hawking made another forecast, one that has stood the test of time (so far). Commenting on the rapid developments being made with computers during the 1970s, he said that “it would seem quite possible that they will take over altogether in theoretical physics” in the near future. That hasn't quite happened yet. Although progress with computers was even more dramatic in the 1980s than in the 1970s (for example, we wrote these words in the early 1990s using computers more powerful than those available to a whole room full of mathematicians in the 1970s), computers still have to be directed in their efforts by human scientists. But complex problems such as calculations involving 26-dimensional strings would be inconceivable without the aid of computers. It is, perhaps, more likely that computers will no longer need human direction in tackling these problems by the end of the present century than that human physicists will have found their
long-sought ultimate theory. The most prescient comment of all in Hawking's inaugural lecture may in fact have been his very last sentence, one that makes a suitable ending for our own discussion of his contribution to science:

Maybe the end is in sight for theoretical physicists, if not for theoretical physics.

16

FAME AND FORTUNE

F
rom conception to best-seller list,
A Brief History of Time
took over five years. During the same period, Hawking had continued his research and administration of the DAMTP. In 1984, long before the first draft of
Brief History
had been completed, Hawking went on a lecture tour of China. The itinerary for the trip would have been strenuous for an able-bodied man, but he insisted on cramming in as much as possible during the visit. He motored along the Great Wall in his wheelchair, saw the sights of Peking, and gave talks to packed auditoriums in several cities. Dennis Sciama said
that he believed the trip took a lot out of Hawking and has even suggested that it helped precipitate his subsequent illness in Switzerland less than a year later.

However, there were other exertions along the way. In the early summer of 1985, Hawking undertook a lecture tour of the world. One of the most important stopovers was at Fermilab, in Chicago. At the core of the cosmology group at Fermilab were three larger-than-life characters, Mike Turner, David Schramm, and Edward Kolb, who have perhaps contributed as much to legend and anecdote surrounding the global cosmology fraternity as they have hard science.

Mike Turner is a tall handsome Californian with a voice indistinguishable from Harrison Ford's. His office at Fermilab, where he spends most of his working life, is filled with toys and gadgets. Hanging from the ceiling are inflatable airliners and UFOs. The walls are plastered with postcards from friends around the world, humorous messages, and wacky pictures, the floor littered with books and boxes of scientific papers. One wall is taken up by a blackboard covered in the hieroglyphs of physics; another opens onto a view of the lakes and woods surrounding the massive concrete columns of the central building which splay at the bottom and converge at the top to form an inverted V.

Edward Kolb, known as “Rocky” because of his penchant for fighting, is a cosmologist from Los Alamos who joined the cosmology group at the same time as Turner in the early eighties. He and Turner became great friends and gained a reputation as a comic duo at Fermilab, forever playing practical jokes and initiating mischief. Their lectures were invariably
witty, entertaining occasions, Turner's often featuring brightly colored cartoons of Darth Vader to illustrate his ideas.

The cosmology group was set up by David Schramm, who was chairman of the astronomy department of the University of Chicago, a close friend of Hawking, and a formidable personality on the international cosmology scene.

Hawking arrived at Fermilab to give a technical lecture to a large group of physicists from around the globe and promptly discovered that there was neither elevator nor ramp to enable him to reach the lecture theater in the basement. Turner recalls how he and Kolb were escorting Hawking into the building when the horrifying thought suddenly struck them: how were they to get Stephen to the stage? They looked at each other and, without saying a word, Turner lifted Hawking's featherweight body into his arms and Kolb grabbed the wheelchair. Halfway down the aisle of the lecture theater, Turner became aware that the entire audience was watching agog as they struggled to the stage, and suddenly remembered how Hawking hated to have attention drawn to his disabilities. In the event, Stephen said nothing about the incident, realizing, he mentioned later, that there was absolutely no alternative.

Next day he gave a public lecture in Chicago, receiving a rock star's reception. The standing-room-only audience packed the auditorium, and a number of people had to be turned away. He was recognized everywhere he went, and people stopped him on the street to express their interest in what he was doing. The title of his lecture was “The Direction of Time.” To a startled audience he declared that, at some point in the far distant future, the Universe would begin to contract back to a singularity and that during this collapse
time would reverse—everything that had ever happened during the expansion phase would be reenacted but backward.