by John Gribbin
By the time he was fourteen, Stephen knew that he wanted to make a career out of studying mathematics, and it was around this time that his scientific aptitude began to show. He would spend very little time on mathematics homework and still obtain full marks. As a contemporary recalled, “He had incredible, instinctive insight. While I would be worrying away at a complicated mathematical solution to a problem, he just knew the answer—he didn’t have to think about it.”4 The “average” bright kid was beginning to reveal a prodigious talent.
One particular example of Stephen’s highly developed insight left a lasting impression on John McClenahan. During a sixth-form physics lesson, the teacher posed the question, “If you have a cup of tea, and you want it with milk and it’s far too hot, does it get to a drinkable temperature quicker if you put the milk in as you pour the tea, or should you allow the tea to cool down before adding the milk?” While his contemporaries were struggling with a muddle of concepts to argue the point, Stephen went straight to the heart of the matter and almost instantly announced the correct answer: “Ah! Milk in first, of course,” and then went on to give a thorough explanation of his reasoning: because a hot liquid cools more quickly than a cool one, it pays to put the milk in first, so that the liquid cools more slowly.
He sailed through his Ordinary Level exams, obtaining nine in July 1957 and his tenth, in Latin, a year later, midway through his Advanced Levels. When he sat down to decide on his A Level subjects, parental pressure began to play a part in his plans. He wanted to do mathematics, physics, and further mathematics in preparation for a university course in physics or mathematics. However, Frank Hawking had other plans. He wanted his son to follow him into a career in medicine, for which Stephen would have to study A Level chemistry. After much discussion and argument, Stephen agreed to take mathematics, physics, and chemistry A Levels, leaving open the question of his university course until the need for a final decision arose a year later.
The sixth form was probably Hawking’s happiest time at St. Albans. The boys were allowed greater freedom in their final two years, and they basked a little in the respect they had gained by their success at O Level. In the sixth form, the close group of school-friends began to fragment as their A Level subjects diverged. Those taking arts subjects began, quite naturally, to lose touch with the “scientists,” and different cliques established themselves. Basil King, John McClenahan, and Hawking took only science subjects; the others followed the arts. The scientists gathered others of like mind around them and new groups formed.
In the spring of 1958, Hawking and his friends, including new recruits to the group, Barry Blott and Christopher Fletcher, built a computer called LUCE—Logical Uniselector Computing Engine. In the 1950s in Britain, only a few university departments and the Ministry of Defense had computers. However, with the help and enthusiasm of a young mathematics master named Dick Tartar, who had been recruited specifically to generate new ideas and inject some life into the mathematics department, they designed and built a very primitive logic machine.
It took a month to get anything at all out of the machine. The biggest problem, it seems, was not the design or the theoretical side of the project, but simply bad soldering. The guts of the device were recycled parts from an old office telephone exchange, but a vast number of electrical connections were needed to make the device work, and the group was forever finding faults in their soldering. Nevertheless, when they did eventually get it to work, it caused considerable excitement in the sixth form. The Mathematical Society write-up in the Albanian, the school magazine, sounds as though plucked straight from a time warp:
It is not unknown for the mathematician to leave his ivory tower and fulfill his original role as a calculator. Thus in 1641 Pascal invented an arithmetical machine—forerunner of the modern computer that specifically replaces tally-stick, abacus or slide-rule [as] an aid to calculation. Until the happy day when every fourth-former has his pocket Ernie,* we have to be content with logarithm tables. Meanwhile, as a modest start we have LUCE, the St. Albans School Logical Uniselector Computing Engine.
This machine answers some useless, though quite complex[,] logical problems. Last term’s meetings of the society were devoted to it and proved lively and well attended. With gained experience [the designers] forge ahead with the construction of a digital computer, as yet unchristened, that will actually “do sums.” (Fourth-formers, take heart!)5
Hawking and his friends received their first exposure to the press when the local newspaper, the Herts Advertiser, covered the story of the “schoolboy boffins” building their newfangled machine. And, as promised in the school magazine article, they did go on to make a more sophisticated version of the machine later in the sixth form.
When the present head of computing at St. Albans School, Nigel Wood-Smith, took over the post many years later, he found a box under one of the tables in the mathematics room. To him the box appeared to contain nothing more than a pile of old junk, transistors, and relays, with “LUCE” on a nameplate lying discarded atop the tangle of wire and metal. He deposited the entire jumble in the rubbish bin. It was only many years later that he realized how, unaware of the potential historical significance of things, he had thrown out the computer that Stephen Hawking had built.
* The computer used to select winners of the premium bonds.
2
CLASSICAL COSMOLOGY
Cosmology is the study of the Universe at large, its beginning, its evolution, and its ultimate fate. In terms of ideas, it is the biggest of big science. Yet in terms of hardware, it is less impressive. True, cosmologists do make use of information about the Universe gleaned from giant telescopes and space probes, and they do sometimes use large computers to carry out their calculations. But the essence of cosmology is still mathematics, which means that cosmological ideas can be expressed in terms of equations written down using pencil and paper. More than any other branch of science, cosmology can be studied by using the mind alone. This is just as true today as it was seventy-five years ago when Albert Einstein developed the general theory of relativity and thereby invented the science of theoretical cosmology.
When scientists refer to the “classical” ideas of physics, they are not referring back to the thoughts of the ancient Greeks. Strictly speaking, classical physics is the physics of Isaac Newton, who laid the foundations of the scientific method for investigating the world back in the seventeenth century. Newtonian physics reigned supreme until the beginning of the twentieth century, when it was overtaken by two revolutions, the first sparked by Einstein’s general theory of relativity and the second by quantum theory. The first is the best theory we have of how gravity works; the second explains how everything else in the material world works. Together, these two topics, relativity theory and quantum mechanics, formed the twin pillars of modern twentieth-century science. The Holy Grail of modern physics, sought by many, is a theory that will combine the two into one mathematical package.
But to the modern generation of Grail seekers in the twenty-first century, even these twin pillars of physics, in their original form, are old hat. There is another, more colloquial, way in which scientists use the term “classical physics”—essentially to refer to anything developed by previous generations of researchers and therefore more than about twenty-five years old. In fact, going back twenty-five years from the time the first edition of this book was written does bring us to a landmark event in science: the discovery of pulsars in 1967, the year Stephen Hawking celebrated his own twenty-fifth birthday. These objects are now known to be neutron stars, the collapsed cores of massive stars that have ended their lives in vast outbursts known as supernova explosions. It was the discovery of pulsars, collapsed objects on the verge of becoming black holes, that revived interest in the extreme implications of Einstein’s theory of gravity, and it was the study of black holes that led Hawking to achieve the first successful marriage between quantum theory and relativity.
Typically, though (as we shall
see), Hawking had already been working on the theory of black holes at least two years before the discovery of pulsars, when only a few mathematicians bothered with such exotic implications of Einstein’s equations, and the term “black hole” itself had not even been used in this connection. Like all his contemporaries, Hawking was brought up, as a scientist, on the classical ideas of Newton and on relativity theory and quantum physics in their original forms. The only way we can appreciate how far the new physics has developed since then, partly with Hawking’s aid, is to take a look at those classical ideas ourselves, a gentle workout in the foothills before we head for the dizzy heights. “Classical cosmology,” in the colloquial sense, refers to what was known prior to the revolution triggered by the discovery of pulsars—exactly the stuff that students of Hawking’s generation were taught.
Isaac Newton made the Universe an ordered and logical place. He explained the behavior of the material world in terms of fundamental laws that were seen to be built into the fabric of the Universe. The most famous example is his law of gravity. The orbits of the planets around the Sun had been a deep mystery before Newton’s day, but he explained them by a law of gravity which says that a planet at a certain distance from the Sun feels a certain force, tugging on it, proportional to one over the square of the distance to the Sun—what is known as an inverse-square law. In other words, if the planet is magically moved out to twice as far from the Sun, it will feel one-quarter of the force; if it is put three times as far away, it will feel one-ninth of the force; and so on. As a planet in a stable orbit moves through space at its own speed, this inward force exactly balances the tendency of the planet to fly off into space. Moreover, Newton realized, the same inverse-square law explains the fall of an apple from a tree and the orbit of the Moon about the Earth, and even the ebb and flow of the tides. It is a universal law.
Newton also explained the way in which objects respond to forces other than gravity. Here on Earth, when we push something it moves, but only as long as we keep pushing it. Any moving object on Earth experiences a force, called friction, which opposes its motion. Stop pushing, and friction will bring the object to a halt. Without friction, though (like the planets in space or the atoms that everyday things are composed of), according to Newton, an object will keep moving in a straight line at a steady speed until a force is applied to it. Then, as long as the force continues to operate, the object will accelerate, changing its direction, its speed, or both. The lighter the object, or the stronger the force, the greater the acceleration that results. Take away the force, however, and once again the object moves at a steady speed in a straight line but at the new velocity that has built up during the time it was accelerating.
When you push something, it pushes back, and the action and reaction are equal and opposite. This is how a rocket works—it throws material out from its exhaust in one direction, and the reaction pushes the rocket along in the opposite direction. This last law is familiar these days from the billiard table, where balls collide and rebound off each other in a very “Newtonian” manner. And that is very much the image of the world that comes out of Newtonian mechanics—an image of balls (or atoms) colliding and rebounding, or of stars and planets moving under the influence of gravity, in an exactly regular and predictable manner.
All these ideas were encapsulated in Newton’s masterwork, the Principia, published in 1687 (usually referred to simply by the short version of its Latin title; the full English title of Newton’s great work is Mathematical Principles of Natural Philosophy). The view Newton gave us of the world is sometimes referred to as the “clockwork universe.” If the Universe is made up of material objects interacting with each other through forces that obey truly universal laws, and if rules like that of action and reaction apply precisely throughout the Universe, then the Universe can be regarded as a gigantic machine, a kind of cosmic clockwork, which will follow an utterly predictable path forever once it has been set in motion.
This raises all kinds of puzzles, deeply worrying to philosophers and theologians alike. The heart of the problem is the question of free will. In such a clockwork universe, is everything predetermined, including all aspects of human behavior? Was it preordained, built into the laws of physics, that a collection of atoms known as Isaac Newton would write a book known as the Principia that would be published in 1687? And if the Universe can be likened to a cosmic clockwork machine, who wound up the clockwork and set it going?
Even within the established framework of religious belief in seventeenth-century Europe, these were disturbing questions, since although it might seem reasonable to say that the clockwork could have been wound up and set in motion by God, the traditional Christian view sees human beings as having free will, so that they can choose to follow the teachings of Christ or not, as they wish. The notion that sinners might actually have no freedom of choice concerning their actions, but were sinning in obedience to inflexible laws, following a path to eternal damnation actually laid out by God in the beginning, simply could not be fit into the established Christian world view.
Strangely, though, in Newton’s day, and down into the twentieth century, science did not really contemplate the notion of a beginning to the Universe at all. The Universe at large was perceived as eternal and unchanging, with “fixed” stars hanging in space. The biblical story of the Creation, still widely accepted in the seventeenth century by scientists as well as ordinary people, was thought of as applying only to our planet, Earth, or perhaps to the Sun’s family, the Solar System, but not to the whole Universe.
Newton believed (incorrectly, as it turns out) that the fixed stars could stay as they were in space forever if the Universe were infinitely big, because the force of gravity tugging on each individual star would then be the same in all directions. In fact, we now know that such a situation would be highly unstable. The slightest deviation from a perfectly uniform distribution of stars would produce an overall pull in one direction or another, making the stars start to move. As soon as a star moves toward any source of gravitational force, the distance to the source decreases, so the force gets stronger, in line with Newton’s inverse-square law. So once the stars have started to move, the force causing the nonuniformity gets bigger, and they keep on moving at an accelerating rate. A static universe would soon start to collapse under the pull of gravity. But that became clear only after Einstein had developed a new theory of gravity—a theory, moreover, that contained within itself a prediction that the Universe would certainly not be static and might actually be not collapsing, but expanding.
Like Newton, Albert Einstein made many contributions to science. Also like Newton, his masterwork was his theory of gravity, the general theory of relativity. It is some measure of just how important this theory is to the modern understanding of the Universe that even Einstein’s special theory of relativity, the one that leads to the famous equation E = mc2, is by comparison a relatively minor piece of work. Nevertheless, the special theory, which was published in 1905, contributed a key ingredient to the new understanding of the Universe. Before we move on to this, though, we should at least give a brief outline of the main features of the special theory.
Einstein developed the special theory of relativity in response to a puzzle that had emerged from nineteenth-century science. The great Scottish physicist, James Clerk Maxwell, had found the equations that describe the behavior of electromagnetic waves. Maxwell’s equations were soon developed to explain the behavior of radio waves, which were discovered in 1888. But Maxwell had found that the equations automatically gave him a particular speed,* which is identified as the speed at which electromagnetic waves travel. The unique speed that came out of Maxwell’s equations turned out to be exactly the speed of light, which physicists had already measured by that time. This revealed that light must be a form of electromagnetic wave, like radio waves but with shorter wavelength (that is, higher frequency). And it also meant, according to those equations, that light (as well as other forms of electromagnetic r
adiation, including radio waves) always travels at the same speed.
This is not what we expect from our everyday experience of how things move. If I stand still and toss a ball to you gently, it is easy for you to catch the ball. If I am driven toward you at 60 miles an hour in a car and toss the ball equally gently out the window, it hurtles toward you at 60 miles an hour plus the speed of the toss. You would, rightly, be dumbfounded if the ball tossed gently out the car window reached you traveling only at the gentle speed of the toss, without the speed of the car being added in, yet that is exactly what happens with light pulses. Equally, if one vehicle traveling at 50 miles an hour along a straight road is overtaken by another traveling at 60 miles an hour, the second vehicle is moving at 10 miles an hour relative to the first one. Speed, in other words, is relative. And yet, if you are overtaken by a light pulse, and measure its speed as it goes past, you will find it has the same speed you would measure for a light pulse going past you when you are standing still.
Nobody knew this until the end of the nineteenth century. Scientists had assumed that light behaved in the same way, as far as adding and subtracting velocities is concerned, as objects like balls being thrown from one person to another. And they explained the “constancy” of the speed of light in Maxwell’s equations by saying that the equations applied to some “absolute space,” a fundamental reference frame for the entire Universe.
