by John Gribbin
“I’ve always found I could communicate,”31 he snapped back, and went for Overbye’s toes.
Black-hole astronaut or not, the amount Hawking traveled during the seventies was increasing each year. In the winter of 1976 he undertook an American tour, taking in talks at important conferences in Chicago and Boston. Even to other scientists who knew him from symposia and conferences around the globe, his speech was all but unintelligible, and when members of the general public and journalists were in attendance they found it almost as difficult to grapple with Hawking’s speaking voice as with his subject matter.
Despite the fact that conference organizers were invariably forewarned of Hawking’s disabilities, more often than not there would be no easy access to the stage in the lecture theater. He would have to make it there without ramps or lifts. On such occasions, Hawking’s friends and colleagues would come to his rescue, up to six of them manhandling his heavy wheelchair. Although Hawking himself weighed little more than ninety pounds, the chair ran on car batteries, which added to the weight, and, according to those who have taken part in these exercises, there was always the fear that they would drop him or that he would hurt his neck. One friend has described how he could see Hawking’s head bobbing around as six of the biggest scientists in his group lifted the wheelchair five feet up onto the stage, and how he was terrified that one day something would go disastrously wrong, simply because the organizers hadn’t thought things through.
Hawking made a great impression during his 1976 trip to the States. The stick-like figure hunched in his wheelchair was, to the vast majority of the audience, mumbling incomprehensibly, appearing to make his pronouncements to a point on the stage six feet in front of him. But despite this, those who came to hear him speak always took him very seriously. Close colleagues who could understand what he was saying translated for their neighbors as best they could, with one ear concentrating on the mathematics Hawking was describing. Slides and the relief of numerous corny jokes helped, but it was always hard work.
By this time, he had completely reversed his ideas about black holes and thermodynamics, the very ideas that had created such arguments a few years earlier. At a talk in Boston entitled “Black Holes Are White Hot,” he caused a stir with a conclusion refuting Einstein’s famous statement “God doesn’t play dice.” “God not only plays dice,” Hawking proclaimed, “he sometimes throws them where they can’t be seen.”
Interviewers were queuing up to speak to Hawking. In January 1977, the BBC broadcast a program called The Key to the Universe, with an accompanying book by Nigel Calder. The program was in large part devoted to Stephen Hawking’s latest work and profiled the man and his efforts to unify general relativity and quantum mechanics—“the key to the Universe” of the title. For the first time, the general public was exposed to the thirty-five-year-old Dr. Stephen Hawking and the facts of his disability as well as his work. It had the British public watching in their millions.
From 1977, publicity surrounding Hawking and his achievements began to escalate on a local, national, and global scale. Between reports of punks signing record contracts in front of Buckingham Palace and growing excitement over the Queen’s Jubilee that coming summer, there were mutterings in the Cambridge press about the odd fact that this famous scientist, a member of the Royal Society and black-hole celebrity, appearing on television and with his face in the papers on an increasingly regular basis, did not hold a professorial position at Cambridge University.
There were muted suggestions that perhaps the university was disinclined to give the severely disabled scientist a professorship because he might not live too long. By March 1977, however, the university had decided to offer him a specially created chair of gravitational physics, which would be his for as long as he remained in Cambridge; the same year, he was awarded the status of professorial fellow at Caius, a separate professorship bestowed by the college authorities.
The awards and honors continued to flood in. Robert Berman, Hawking’s undergraduate supervisor at Oxford, had recommended him as an honorary fellow of University College. In his letter to the General Purposes Committee, he said:
The current issue of Who’s Who shows some of his achievements, but cannot keep pace with the rate of award of honors.
I can’t imagine that the College has ever produced a more distinguished scientist, and it would bring us honor if our association with his career were made manifest (the outside world assumes he is entirely a Cambridge product).
It might seem surprising to ask to consider someone not yet 35 as an Honorary Fellow, but there are two reasons for this. First, his distinction is quite exceptional and we don’t have to wait for it to be generally recognized that he has made his mark. Hawking is mentioned in practically every article or lecture on black holes. His book (The Large Scale Structure of Spacetime) was what every cosmologist was waiting for.
Secondly, Hawking is gravely ill and is confined to a wheelchair with a type of creeping paralysis that normally cuts the lives of its victims very short. He is in an appalling physical state but his mind functions normally.
I hope that it won’t be felt that we must wait to see whether he actually gets a Nobel Prize!
Berman thought that he might have to argue his case further. He was subsequently staggered when the recommendation was accepted without a single objection at the committee’s first meeting.
The graffiti-daubing sluggard who, at Oxford University only sixteen years earlier, had spent more time drinking than working had come a very long way.
11
BACK TO THE BEGINNING
By the end of 1974, Hawking’s work on black holes had shown that, using the general theory of relativity alone, the equations said that the surface area of a black hole could not shrink—but adding the quantum rules to the equations revealed that they could not only shrink but would eventually disappear in a puff of gamma radiation. His earlier work with Penrose had shown that, using the general theory of relativity alone, the equations said that the Universe must have been born out of a singularity, a point of infinite density and zero volume, at a time some 14 billion years ago. It was natural that the next scientific question Hawking asked himself was what would happen to this prediction if the quantum rules were added to that set of equations.
This was no easy question to answer. Physicists had been trying to combine quantum theory and relativity theory into one complete, unified theory ever since the quantum revolution in the 1920s; Einstein himself spent the last twenty years of his working life on the problem and failed to come up with a solution. Indeed, a full theory of quantum gravity still eludes mathematicians. But by restricting himself to the specific puzzle of how relativity and quantum mechanics interacted at the beginning of time, Hawking was able to make progress, to such an extent that by the early 1980s he was posing the question of whether there ever had been a beginning to time at all. To understand how he arrived at this startling hypothesis, we have to look again at quantum theory, in a variation developed by the great American physicist Richard Feynman. It is known as the “sum-over-histories” or “path integral” approach.
The essential features of quantum mechanics are demonstrated most clearly in what is known as “the experiment with two holes.” In such an experiment, a beam of light, or a stream of electrons, is directed through two small holes in a wall and onto a screen on the other side. The version using light is known as Young’s experiment and may be familiar from school physics. What happens is that the pattern of light on the screen forms a characteristic arrangement of dark and light stripes, caused when the electromagnetic waves passing through each of the holes interfere with each other. Where the two sets of waves add together, there is a bright stripe; where they cancel each other out, the screen is dark.
This interference is easy to understand in terms of waves. You can get exactly the same effect by making waves in a tank of water and letting them pass through two slits in a barrier. But it is much harder to understand how
electrons, which we are used to thinking of as hard particles like tiny billiard balls, can behave in the same way. Yet they do.
What is even stranger is that the same pattern of dark and light stripes slowly builds up on the screen (which can be almost exactly the same as a TV screen) when electrons are fired through the holes one at a time. Why should this be strange? Think about what happens when electrons are fired through just one hole. Instead of a striped pattern on the screen, there is just a bright patch behind the hole. This is indeed what we see if we block off either of the two holes and fire the electrons through. “Obviously,” each electron can go through only one hole. But when both holes are open, even with electrons fired one at a time through the experiment, we do not see just two patches of brightness behind the holes, but the characteristic stripy pattern of Young’s experiment.
This is the clearest example of the wave-particle duality (see Chapter 2) that lies at the heart of the quantum world. When each electron arrives at the screen, it makes a pinpoint of light, just as you would expect from the arrival of a tiny “billiard ball” particle. But when thousands of those points of light are added together, they produce the striped pattern corresponding to a wave passing through both holes at once. It is as if each individual electron is a wave that passes through both holes simultaneously, interferes with itself, decides which bit of the striped pattern it belongs in, and heads off there to arrive as a particle that makes a pinpoint of light.
Don’t worry if you find this incomprehensible. Niels Bohr, one of the physicists who pioneered the quantum revolution, used to say that “anyone who is not shocked by quantum theory has not understood it,” while Feynman, probably the greatest theoretical physicist since the Second World War, went even further and was fond of saying that nobody understands quantum mechanics. The important thing is not to understand how such a strange behavior as wave-particle duality can occur, but to find a set of equations that describe what is going on and make it possible for physicists to predict how electrons, light waves, and the rest will behave. The sum-over-histories approach was Feynman’s contribution to this more pragmatic form of “understanding” at the quantum level, and in the late 1970s Hawking applied it to the study of the Big Bang.
Feynman said that, instead of thinking of an object such as an electron as a simple particle that follows a single route from A to B (for example, through one of the two holes in Young’s experiment), we have to regard it as following every possible path from A to B through spacetime. It would be easier for a “classical” particle to follow some paths (some “histories”) than others, and this is allowed for in Feynman’s equations by assigning each path a probability, which can be calculated from the quantum rules.
These probabilities can interfere with the probabilities from neighboring “world lines,” as they are called, rather like the way ripples on the surface of a pond interfere with one another. The actual path followed by the particle is then calculated by adding together all the probabilities for individual paths (which is why this is also known as the path integral approach).
In the vast majority of cases, the various probabilities cancel each other out almost entirely, leaving just a few paths, or trajectories, that are reinforced. This is what happens for the trajectories corresponding to an electron moving near the nucleus of an atom. The electron is not allowed to go just anywhere because of the way the probabilities cancel; it is only allowed to move in one of the few orbits around the nucleus where the probabilities reinforce one another.
The experiment with two holes is unusual because it offers the electrons a choice of two equally probable sets of trajectories, one through each hole, and this is why the basic strangeness of the quantum world shows up so clearly in this example. Only Hawking, though, had the chutzpah to apply the path integral approach to calculating the history, not of an individual electron but of the entire Universe; but even he started out in a smaller way, with black-hole singularities.
When a black hole evaporates, what happens to the singularity inside it? One simple guess might be that in the final stages of the evaporation, the horizon around the hole vanishes, leaving behind the naked singularity that nature is supposed to abhor. In fact, though, the equations developed by Hawking in the early 1970s to describe exploding black holes could not be pushed to such extremes. Strictly speaking, they could only be applied if the mass of the black hole were still a reasonable fraction of a gram—almost big enough to be weighed on your kitchen scales. The best guess that Hawking, or anyone else, could make in 1974 was that when a black hole has evaporated to this point, it would completely disappear, taking the singularity with it. But this was only a guess, based on some general quantum principles.
These principles are aspects of the basic uncertainty principle. Just as there is a fundamental uncertainty about the energy content of the vacuum, so there is a fundamental uncertainty about basic measures such as length and time. The size of these uncertainties is determined by Planck’s constant, which gives us basic “quanta” known as the Planck length and the Planck time.
Both are very small. The Planck length, for example, is 10−35 of a meter, far smaller than the nucleus of an atom. According to the quantum rules, not only is it impossible in principle ever to measure any length more accurately than this (we should be so lucky!), but also there is no meaning to the concept of a length shorter than the Planck length. So if an evaporating black hole were to shrink to the point where it was just one Planck length in diameter, it could not shrink any more and still exist. If it lost more energy, it could only disappear entirely. The quantum of time is, similarly, the smallest interval of time that has any meaning. This Planck time is a mere 10−43 of a second, and there is no such thing as a shorter interval of time. (Don’t worry about the exact size of these numbers; what matters is that, although they are exceedingly small, they are not zero.) Quantum theory tells us that we can neither shrink away a black hole to a mathematical point nor look back in time literally to the moment when time “began.” Even if we pushed the Big Bang model to its most extreme limit, we would have to envisage the Universe being created with an “age” equal to the Planck time.
In both cases, quantum mechanics seems to remove the troublesome singularities. If there is no meaning to the concept of a volume with a diameter less than the Planck length, then there is no meaning to the concept of a point of zero volume and infinite density. Quantum theory is telling us that, although the densities reached inside black holes, and at the birth of the Universe, may be staggeringly high by any human measure, they are not infinite. And if the infinities and singularities can be removed, there is at least a hope of finding a set of equations to describe the origin (and, it turns out, the fate) of the Universe. Having started out in 1975 from the puzzle of what happens in the last stages of the evaporation of a black hole, by 1981 Hawking was ready to unveil his new ideas, incorporating Feynman’s sum-over-histories version of quantum mechanics, to explain how the Universe had come into being. The place he chose for the unveiling was—the Vatican.
In fact, the choice of venue was not entirely Hawking’s whim. It happened that the Catholic Church had invited several eminent cosmologists to attend a conference in Rome in 1981, to discuss the evolution of the Universe from the Big Bang onward. By the 1980s, the Church was much more receptive to scientific teaching than it had been in the days of Galileo, and the official view was that it was quite okay for science to investigate events that happened since the Big Bang, leaving the mystery of the moment of creation in the hands of God.
Fortunately, perhaps, Hawking’s investigation of the moment of creation was still couched in rather abstruse mathematical language when he presented it to that conference. Since then, however, he has developed the ideas in a more accessible way (most notably with the help of James Hartle of the University of California). It doesn’t take much intuition to guess that the Pope would probably not approve of the fully developed version of Hawking’s ideas, which seems to do aw
ay entirely with a role for God.
What Hawking has tried to do is to develop a sum over histories describing the entire evolution of the Universe. Now this is, of course, impossible. Just one history of this kind would involve working out the trajectory of every single particle through spacetime from the beginning of the Universe to the end, and there would be a huge number of such histories involved in the “integration.” But Hawking found that there is a way to simplify the calculations, provided the Universe has a particularly simple form.
Quantum theory comes into the calculations in the form of the sum over histories. General relativity enters in the form of curved spacetime. In Hawking’s models, a complete curved spacetime that describes the entire history of a model universe is equivalent to a trajectory of a single particle in Feynman’s sum over histories. General relativity allows for the possibility of many different kinds of curvature, and some sorts of curvature turn out to be more probable than others.
If the Universe is like the interior of a black hole, with spacetime closed around it, we can imagine, in the standard picture of the Big Bang, that everything (including space) expands outward from the initial singularity, reaches a certain size, and then collapses back into a mirror image of the Big Bang, the so-called “Big Crunch.” In this picture, there is a beginning of time in the initial singularity and an end of time in the final singularity. Hawking calls the beginning and end of time “edges” to this model of the Universe—such a model has no edge in space because space is folded around into a smooth surface like the surface of a balloon, or the surface of the Earth; but there is an edge in time in the beginning, when the Universe appears as a point of zero size.
