Stephen Hawking

by John Gribbin

  But QED did not become established until the 1940s, by which time two “new” forces were on the agenda. Both these forces have only very short range and operate only within the nucleus of an atom (which is why they were unknown in the nineteenth century before the nucleus was discovered). One is called the strong force and acts as the glue that holds the particles in the nucleus together; the other is known as the weak force (because, logically enough, it is weaker than the strong force), and it is responsible for radioactive decay.

  In many ways, however, the weak force resembles the electromagnetic force. Building from the success of QED, in the 1950s and 1960s physicists developed a mathematical theory that could describe both the weak force and electromagnetism with one set of equations. It was called the “electroweak” theory, and it made one key prediction: with the weak force there should be associated three types of particles which, between them, play much the same role that the photon (the particle of light) does in QED. Unlike the photon, however, these particles (known as W+, W−, and Z0) should, according to the new theory, have mass. Not just any old mass, either, but very well-determined masses—about nine times the mass of a proton for the two W particles and eight times the mass of the proton for the Z0. In 1983, the particle accelerator team at CERN in Geneva found traces of particles with exactly the right properties. The electroweak theory was a proven success, and physicists were back to just three theories needed to explain the workings of the Universe.

  With this success under their belts, theorists have developed a theory similar to QED to describe the strong force. We now know that nuclear particles (protons and neutrons) are actually made of fundamental entities known as quarks. Quarks come in different varieties, and physicists whimsically give these the names of colors—red, green, and blue. This doesn’t mean that quarks really are red, green, or blue any more than the fact that a drink is called a rusty nail means that it really does contain oxidized iron. They are just names. But, extending the whimsy, physicists call the quantum theory that describes how quarks interact, and which is responsible for the strong force, “quantum chromodynamics” (from the Greek word for color) or QCD. There are several promising ways now being investigated that might lead to a single theory that encompasses both QCD and the electroweak theory. Such sets of equations are known, rather pretentiously, as Grand Unified Theories, or GUTs. But QCD is not yet as well established as the electroweak theory, and the GUTs themselves are only indicative of the form a future definitive theory might take.

  Even worse, the pretentiousness of calling these Grand Unified Theories is highlighted by the fact that none of this progress toward unification takes any account of gravity at all! The first force of nature to be investigated, and at least partially understood, it has proved the most intractable when it comes to trying to fit it into the quantum mold. Without gravity included in their mesh, it seems fair to say that—paraphrasing Hawking’s famous comment about black holes—Grand Unified Theories ain’t so grand after all. In spite of Hawking’s success in using a partial unification of quantum theory and general relativity in his investigations of black holes and the beginning of time, gravity is still best described by the general theory of relativity—a classical continuum theory.

  The prospect of incorporating gravity into what, we suppose, would have to be called a “super-unified theory” has been “just around the corner” for decades. Logically, we might guess that first we need to develop a quantum theory of gravity and then build from this to a unification with the other three forces. One feature of any such quantum theory of gravity is that it, too, must incorporate particles that are associated with the gravitational force, again reminiscent of the way photons are associated with electromagnetism. (In case you are wondering, yes, there are similar particles involved in QCD, the theory of the strong force; they are called “gluons,” but nobody has yet detected one.) Physicists even have a name for these hypothetical particles of gravity—“gravitons.” But just as calling a quark “red” does not mean that it is actually colored red, so giving the quantum gravity particle a name does not mean that anybody has yet found one or even that anybody has come up with a satisfactory quantum theory of gravity.

  At the time of Hawking’s inaugural lecture in 1980, researchers were getting excited about a family of possible quantum gravity theories that together go by the name of supergravity. One version of supergravity is called “N = 8” because as well as predicting the existence of one type of graviton, it also requires an additional eight varieties of particles known as gravitinos (together with a further 154 varieties of other as yet undiscovered particles). The plethora of particles associated with this favored version of supergravity may seem unwieldy—and it is, but it does represent a considerable advance on previous attempts to find a quantum theory of gravity, which seemed to require an infinite number of “new” particles. Indeed, out of all the variations on the supergravity theme, N = 8 is the only one that operates naturally in four dimensions (three of space plus one of time) and contains a finite number of particles. It certainly got Hawking’s vote as the theory most likely to succeed in 1980.

  In the next few years, everything changed. By the mid-1980s, enthusiasm for supergravity had been swept away in a rising tide of support for a completely different kind of idea, known as string theory. The central idea of string theory is that entities that we are used to thinking of as points (such as electrons and quarks) are actually linear—tiny “strings.” Such strings would be very small indeed: it would take 1020 of them, laid end to end, to stretch across the diameter of a proton. Such strings might be open, with their ends waving free, or closed into little loops. Either way, some theorists believe, the way they vibrate and interact with one another could explain many features of the physical world.

  String theory actually dates back to the late 1960s, when it was invoked to describe the strong force. The success of QCD left this early version of string theory by the wayside, although a few mathematicians dabbled with it out of interest in the equations, rather than in any expectation of making a major breakthrough in unifying our understanding of the forces of nature. In the mid-1970s, two of those researchers, Joël Scherk in Paris and John Schwarz at Caltech, actually found a way to describe gravity using string theory. But the response of their colleagues was, essentially, “Who needs it?” At that time, most gravity researchers were more interested in supergravity. String theory wasn’t needed to explain the strong force, supergravity looked promising, so why bother with strings at all?

  Their attitude changed when it turned out to be horrendously difficult to do any calculations at all using the N = 8 supergravity theory. Even if there were no infinities to worry about, 154 types of particles, in addition to the graviton and eight gravitinos, were almost too much of a handful to keep mathematical tabs on. Hawking says that it was generally reckoned in the early 1980s that, even using a computer, it would take four years to complete a calculation, checking that all the particles in the theory were accounted for, with no infinities still hidden away somewhere, and that it would be almost impossible to carry out the calculation without making a mistake. So nobody was prepared to give up his career to do the calculation.

  The main reason for the revival of interest in string theory in the mid-1980s, however, was the realization that in their most satisfactory form, these theories automatically include the graviton. In other attempts to build a quantum theory of gravity, researchers had started out knowing the properties a graviton ought to have and tried to build a theory around it, even if that meant taking 162 other particles on board as well. With string theory, they were working with the quantum equations in a general way, playing mathematical games, and found that the closed loops of string described by some of the equations have just the properties required to provide a description of gravity—they are, indeed, gravitons. Inevitably, the new variation on the string theme was dubbed “superstring theory.” By 1988, with the publication of A Brief History of Time, it was this ro
ad toward superunification that Hawking was enthusiastically endorsing.

  But there are still snags. One is that people are still unsure what all the equations mean. As the example of the graviton illustrates, the equations have come first, with physical insight into their significance lagging, and there are still plenty of equations for which, as yet, there is no physical insight. This is quite different from the way the great developments in physics were made earlier in the twentieth century and, indeed, in the centuries back to Newton’s time. For example, Einstein used to tell how he was sitting in his office in Berne one day when he was suddenly struck by the thought that a man falling from a roof would not feel the force of gravity while he was falling. That insight into the nature of gravity led directly to the general theory of relativity—physical insight first and then the equations. Exactly the same process was at work when Newton watched the apple fall from a tree and went on to develop his theory of gravity.

  But it seems that science, or at least physics, no longer works like that. One of the pioneers of superstring theory is Michael Green, of Queen Mary College in London. In an article in Scientific American in 1986, he pointed out that with string theory

  details have come first; we are still groping for a unifying insight into the logic of the theory. For example, the occurrence of the massless graviton . . . appears accidental and somewhat mysterious; one would like them to emerge naturally in a theory after the unifying principles are well established.2

  Another oddity of superstring theory does not seem to trouble the mathematicians but demonstrates all too clearly to lesser mortals how far these ideas have strayed from everyday reality. What appeared to be the best versions of superstring theories, the ones in which gravitons seem to emerge naturally (if mysteriously) from the equations, only work in a little matter of twenty-six dimensions. So if superstrings really do describe the workings of the Universe, where are all the extra dimensions hidden?

  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.

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sp; 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: