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Putting geometry into relativity
George Gamow
Stephen Hawking
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The people who put the geometry into relativity

With a little help from his friends
General relativity the hard way
The roots of relativity

Just how clever was Albert Einstein? The key feature of Einstein's general theory of relativity is the idea of bent spacetime. But Einstein was neither the originator of the idea of spacetime geometry, nor the first to conceive of space being bent. In a not-too-serious festive look at the roots of relativity, John Gribbin suggests that Einstein's unique genius is not all it was cracked up to be

John Gribbin

ALBERT EINSTEIN first presented his general theory of relativity to the Prussian Academy of Sciences in Berlin in November 1915, almost exactly 77 years ago. The anniversary has received less attention than might have been expected; but he was about ten years later than he should have been in coming up with the idea. What took him so long? Read on, and find out.

The easy way to understand Einstein's two theories of relativity is in terms of geometry. Space and time, we learn, are part of one four- dimensional entity, spacetime. The special theory of relativity, which deals with uniform motions at constant velocities, can be explained in terms of the geometry of a flat, four-dimensional surface. The equations of the special theory that, for example, describe such curious phenomena as time dilation and the way moving objects shrink are in essence the familiar equation of Pythagoras' theorem, extended to four dimensions, and with the minor subtlety that the time dimension is measured in a negative direction (see Inside Science, number 49). Once you have grasped this, it is easy to understand Einstein's general theory of relativity, which is a theory of gravity and accelerations. What we are used to thinking of as forces caused by the presence of lumps of matter in the Universe (like the Sun) are due to distortions in the fabric of spacetime. The Sun, for example, makes a dent in the geometry of spacetime, and the orbit of the Earth around the Sun is a result of trying to follow the shortest possible path (a geodesic) through curved spacetime (see Inside Science, number 31). Of course, you need a few equations if you want to work out details of the orbit. But that can be left to the mathematicians. The physics is disarmingly simple and straightforward, and this simplicity is often represented as an example of Einstein's "unique genius".

Only, none of this straightforward simplicity came from Einstein. Take the special theory first. When Einstein presented this to the world in 1905, it was a mathematical theory, based on equations. It didn't make a huge impact at the time, and it was several years before the science community at large really began to sit up and take notice. They did so, in fact, only after Hermann Minkowski gave a lecture in Cologne in 1908. It was this lecture, published in 1909 shortly after Minkowski died, that first presented the ideas of the special theory in terms of spacetime geometry. His opening words indicate the power of the new insight:

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade into mere shadows, and only a kind of union of the two will preserve an independent reality.

Minkowski's enormous simplification of the special theory had a huge impact. It is no coincidence that Einstein received his first honorary doctorate, from the University of Geneva, in July 1909, nor that he was first proposed for the Nobel Prize in physics a year later. There is a delicious irony in all this. Minkowski had, in fact, been one of Einstein's teachers at the Zrich polytechnic at the end of the nineteenth century. Just a few years before coming up with the special theory, Einstein had been described by Minkowski as a "lazy dog", who "never bothered about mathematics at all". The lazy dog himself was not, at first, impressed by the geometrization of relativity, and took some time to appreciate its significance. Never having bothered much with maths at the polytechnic, he was remarkably ignorant about one of the key mathematical developments of the nineteenth century, and he only began to move towards the notion of curved spacetime when prodded that way by his friend and colleague Marcel Grossman. This wasn't the first time Einstein had enlisted Grossman's help. Grossman had been an exact contemporary of Einstein at the polytechnic, but a much more assiduous student who not only attended the lectures (unlike Einstein) but kept detailed notes. It was those notes that Einstein used in a desperate bout of last-minute cramming which enabled him to scrape through his final examinations at the polytechnic in 1900.

What Grossman knew, but Einstein didn't until Grossman told him, in 1912, was that there is more to geometry (even multi-dimensional geometry) than good old Euclidean "flat" geometry.

Euclidean geometry is the kind we encounter at school, where the angles of a triangle add up to exactly 180o, parallel lines never meet, and so on. The first person to go beyond Euclid and to appreciate the significance of what he was doing was the German Karl Gauss, who was born in 1777 and had completed all of his great mathematical discoveries by 1799. But because he didn't bother to publish many of his ideas, non-Euclidean geometry was independently discovered by the Russian Nikolai Ivanovitch Lobachevsky, who was the first to publish a description of such geometry in 1829, and by a Hungarian, Janos Bolyai. They all hit on essentially the same kind of "new" geometry, which applies on what is known as a "hyperbolic" surface, which is shaped like a saddle, or a mountain pass. On such a curved surface, the angles of a triangle always add up to less than 180o, and it is possible to draw a straight line and mark a point, not on that line, through which you can draw many more lines, none of which crosses the first line and all of which are, therefore, parallel to it.

But it was Bernhard Riemann, a pupil of Gauss, who put the notion of non-Euclidean geometry on a comprehensive basis in the 1850s, and who realised the possibility of yet another variation on the theme, the geometry that applies on the closed surface of a sphere (including the surface of the Earth). In spherical geometry, the angles of a triangle always add up to more than 180o, and although all "lines of longitude" cross the equator at right angles, and must therefore all be parallel to one another, they all cross each other at the poles.

Riemann, who had been born in 1826, entered Gttingen University at the age of twenty, and learned his mathematics initially from Gauss, who had turned 70 by the time Riemann moved on to Berlin in 1847, where he studied for two years before returning to Gttingen. He was awarded his doctorate in 1851, and worked for a time as an assistant to the physicist Wilhelm Weber, an electrical pioneer whose studies helped to establish the link between light and electrical phenomena, partially setting the scene for James Clerk Maxwell's theory of electromagnetism.

The accepted way for a young academic like Riemann to make his way in a German university in those days was to seek an appointment as a kind of lecturer known as a "Privatdozent", whose income would come from the fees paid by students who voluntarily chose to take his course (an idea which it might be interesting to revive today). In order to demonstrate his suitability for such an appointment, the applicant had to present a lecture to the faculty of the university, and the rules required the applicant to offer three possible topics for the lecture, from which the professors would choose the one they would like to hear. It was also a tradition, though, that although three topics had to be offered, the professors always chose one of the first two on the list. The story is that when Riemann presented his list for approval, it was headed by two topics which he had already thoroughly prepared, while the third, almost an afterthought, concerned the concepts that underpin geometry.

Riemann was certainly interested in geometry, but apparently he had not prepared anything along these lines at all, never expecting the topic to be chosen. But Gauss, still a dominating force in the University of Gttingen even in his seventies, found the third item on Riemann's list irresistible, whatever convention might dictate, and the 27 year old would-be Privatdozent learned to his surprise that that was what he would have to lecture on to win his spurs.

Perhaps partly under the strain of having to give a talk he had not prepared and on which his career depended, Riemann fell ill, missed the date set for the talk, and did not recover until after Easter in 1854. He then prepared the lecture over a period of seven weeks, only for Gauss to call a postponement on the grounds of ill health. At last, the talk was delivered, on 10 June 1854. The title, which had so intrigued Gauss, was "On the hypotheses which lie at the foundations of geometry."

In that lecture -- which was not published until 1867, the year after Riemann died -- he covered an enormous variety of topics, including a workable definition of what is meant by the curvature of space and how it could be measured, the first description of spherical geometry (and even the speculation that the space in which we live might be gently curved, so that the entire Universe is closed up, like the surface of a sphere, but in three dimensions, not two), and, most important of all, the extension of geometry into many dimensions with the aid of algebra.

Although Riemann's extension of geometry into many dimensions was the most important feature of his lecture, the most astonishing, with hindsight, was his suggestion that space might be curved into a closed ball. More than half a century before Einstein came up with the general theory of relativity -- indeed, a quarter of a century before Einstein was even born -- Riemann was describing the possibility that the entire Universe might be contained within what we would now call a black hole. "Everybody knows" that Einstein was the first person to describe the curvature of space in this way -- and "everybody" is wrong.

Of course, Riemann got the job -- though not because of his prescient ideas concerning the possible "closure" of the Universe. Gauss died in 1855, just short of his 78th birthday, and less than a year after Riemann gave his classic exposition of the hypotheses on which geometry is based. In 1859, on the death of Gauss's successor, Riemann himself took over as professor, just four years after the nerve- wracking experience of giving the lecture upon which his job as a humble Privatdozent had depended (history does not record whether he ever succumbed to the temptation of asking later applicants for such posts to lecture on the third topic from their list).

Riemann died, of tuberculosis, at the age of 39. If he had lived as long as Gauss, however, he would have seen his intriguing mathematical ideas about multi-dimensional space begin to find practical applications in Einstein's new description of the way things move. But Einstein was not even the second person to think about the possibility of space in our Universe being curved, and he had to be set out along the path that was to lead to the general theory of relativity by mathematicians more familiar with the new geometry than he was. Chronologically, the gap between Riemann's work and the birth of Einstein is nicely filled by the life and work of the English mathematician William Clifford, who lived from 1845 to 1879, and who, like Riemann, died of tuberculosis. Clifford translated Riemann's work into English, and played a major part in introducing the idea of curved space and the details of non-Euclidean geometry to the English speaking world. He knew about the possibility that the three dimensional Universe we live in might be closed and finite, in the same way that the two-dimensional surface of a sphere is closed and finite, but in a geometry involving at least four dimensions. This would mean, for example, that just as a traveller on Earth who sets off in any direction and keeps going in a straight line will eventually get back to their starting point, so a traveller in a closed universe could set off in any direction through space, keep moving straight ahead, and eventually end up back at their starting point.

But Clifford realised that there might be more to space curvature than this gradual bending encompassing the whole Universe. In 1870, he presented a paper to the Cambridge Philosophical Society (at the time, he was a Fellow of Newton's old College, Trinity) in which he described the possibility of "variation in the curvature of space" from place to place, and suggested that "small portions of space are in fact of nature analogous to little hills on the surface [of the Earth] which is on the average flat; namely, that the ordinary laws of geometry are not valid in them." In other words, still seven years before Einstein was born, Clifford was contemplating local distortions in the structure of space -- although he had not got around to suggesting how such distortions might arise, nor what the observable consequences of their existence might be, and the general theory of relativity actually portrays the Sun and stars as making dents, rather than hills, in spacetime, not just in space.

Clifford was just one of many researchers who studied non- Euclidean geometry in the second half of the nineteenth century -- albeit one of the best, with some of the clearest insights into what this might mean for the real Universe. His insights were particularly profound, and it is tempting to speculate how far he might have gone in pre-empting Einstein, if he had not died eleven days before Einstein was born.

When Einstein developed the special theory, he did so in blithe ignorance of all this nineteenth century mathematical work on the geometry of multi-dimensional and curved spaces. The great achievement of the special theory was that it reconciled the behaviour of light, described by Maxwell's equations of electromagnetism (and in particular the fact that the speed of light is an absolute constant) with mechanics -- albeit at the cost of discarding Newtonian mechanics and replacing them with something better.

Because the conflict between Newtonian mechanics and Maxwell's equations was very apparent at the beginning of the twentieth century, it is often said that the special theory is very much a child of its time, and that if Einstein had not come up with it in 1905 then someone else would have, within a year or two.

On the other hand, Einstein's great leap from the special theory to the general theory -- a new, non-Newtonian theory of gravity -- is generally regarded as a stroke of unique genius, decades ahead of its time, that sprang from Einstein alone, with no precursor in the problems faced by physicists of the day.

That may be true; but what this conventional story fails to acknowledge is that Einstein's path from the special to the general theory (over more than ten tortuous years) was, in fact, more tortuous and complicated than it could, and should, have been. The general theory actually follows as naturally from the mathematics of the late nineteenth century as the special theory does from the physics of the late nineteenth century.

If Einstein had not been such a lazy dog, and had paid more attention to his maths lectures at the polytechnic, he could very well have come up with the general theory at about the same time that he developed the special theory, in 1905. And if Einstein had never been born, then it seems entirely likely that someone else, perhaps Grossman himself, would have been capable of jumping off from the work of Riemann and Clifford to come up with a geometrical theory of gravity during the second decade of the twentieth century.

If only Einstein had understood nineteenth century geometry, he would have got his two theories of relativity sorted out a lot quicker. It would have been obvious how they followed on from earlier work; and, perhaps, with less evidence of Einstein's "unique insight" and a clearer view of how his ideas fitted in to mainstream mathematics, he might even have got the Nobel Prize for his general theory.

Einstein's unique genius actually consisted of ignoring all the work that had gone before and stubbornly solving the problem his way, even if that meant ten years' more work. He was adept at rediscovering the wheel, not just with his relativity theories but also in much of his other work. The lesson to be drawn is that it is, indeed, OK to skip your maths lectures -- provided that you are clever enough, and patient enough, to work it all out from first principles yourself.

Gamow: Father of the Big Bang

John Gribbin

WHEN NASA's COBE satellite reported the discovery of "ripples" in the background radiation that filled the Universe, this was heralded as the final confirmation of the hot Big Bang theory, the idea that the Universe was born in a superdense, superhot fireball, some 15 billion (thousand million) years ago. But in all the press coverage of this great discovery, one name was conspicuously absent. It was that of George Gamow, a Russian emigre scientist who almost single-handedly invented the hot Big Bang theory, more than half a century ago. He also found time to predict the existence of the background radiation now probed by COBE, to explain how the Sun stays hot, to investigate the structure of the molecule of life (DNA), to play scientific practical jokes that still bring a wry smile to the lips of astronomers, and to write a series of best-selling books explaining new ideas in quantum physics, relativity and cosmology to the public. Born in the Ukraine, at Odessa, in 1904, Gamow lived through the turmoil of revolution and civil war in Russia, and studied at the University of Leningrad, where he learned about the new discoveries in quantum physics and Albert Einstein's new theory of the Universe, the general theory of relativity. Between 1928 and 1931, the newly- qualified young physicist travelled to the University of Gttingen, to the Institute of Physics in Copenhagen, and to the Cavendish Laboratory in Cambridge -- the three main centres at the heart of the quantum revolution. It was during his visit to Gttingen that he made his first major contribution to science.

At the end of the 1920s, physicists were puzzled at the way in which an alpha particle (now known to be the nucleus of a helium atom) could escape from radioactive nuclei. Within the nucleus, the particles are held tight by a force, now known as the "strong nuclear" force. This has a very short range, but overcomes the tendency of all the particles in the positively charged nucleus to repel each other electrically. A little way outside the nucleus, the strong force cannot be felt. An alpha particle just outside the nucleus, itself carrying two units of positive charge, would be repelled by the nucleus electrically, and fly away. It is as if the alpha particle in the nucleus sits in a dip at the top of a mountain -- like the crater of an extinct volcano. If it could climb out of the crater, it could roll away down the mountainside. But it turned out that the energy of alpha particles emerging from radioactive nuclei was too low for this to be possible. They did not carry enough energy to climb out of the crater -- so how did they escape?

Gamow's explanation was the first successful application of quantum physics to the nucleus. He took up the idea that each particle is also a wave. Because a wave is a spread-out entity, its location is not restricted to a point inside the "crater". Instead, the wave spreads right through the surrounding walls, and under the right circumstances the alpha "particle" can tunnel through those walls, without having to climb to the top of the mountain.

This quantum tunnelling also explains an astrophysical puzzle. Inside the Sun, nuclei of hydrogen (protons) collide and fuse together, in a step by step process, to make helium nuclei. The process releases energy, and that keeps the Sun hot. But protons are positively charged, and repel each other. According to calculations carried out in the 1920s, the protons inside the Sun do not move fast enough (they are not at a high enough temperature) to overcome their mutual electrical repulsion when they collide, and get close enough together for the strong force to take over. They do not have enough energy, that is, to climb in to the volcano from outside, and settle in the crater where the strong force dominates.

But tunnelling can work both ways. Because protons are also waves, they only have to come close enough together for their waves to overlap before the strong force does its work. So Gamow's tunneling process explains how the Sun generates heat.

In 1931, Gamow was called back to the USSR, where he was appointed Master of Research at the Academy of Sciences in Leningrad, and Professor of Physics at Leningrad University, at the tender age of 27. But his ebullient nature and independence of mind hardly suited him to a happy life under Stalin's regime, and when he was allowed to attend a scientific conference in Brussels in 1933 he seized the opportunity to stay away, moving to George Washington University in Washington DC, where he was Professor of Physics from 1934 to 1956, and then to the University of Colorado in Boulder, where he stayed until his death in 1968.

The idea of sticking protons together to make helium nuclei led Gamow to puzzle over the way particles must have interacted under the conditions of extreme heat and pressure in the Big Bang in which the Universe was born. In the 1930s, it became clear from observations of galaxies beyond the Milky Way that the Universe is expanding, with empty space between the galaxies stretching in a way predicted by the equations of Einstein's general theory of relativity.

Taking the theory and those observations at face value implied that the Universe started out from a hot, dense soup of particles -- protons, neutrons and electrons mingled together -- in the beginning. Very few people had that much faith in the equations or the observations in the 1930s and 1940s, but Gamow persisted in trying to explain how the stuff stars and galaxies are made of could have been cooked up by nuclear reactions from such a primeval particle soup.

Stars are essentially made of hydrogen (roughly 75 per cent) and helium (roughly 25 per cent). Everything else, including the elements such as carbon, oxygen and nitrogen that are so important for life, makes up less than 1 per cent of the visible mass of the Universe (astronomers now think that there are also vast quantities of so-called "dark matter" in the Universe, but this does not affect Gamow's discoveries about where star stuff comes from). The protons and electrons, combined together to make atoms, would provide the hydrogen. So the key problem is to manufacture helium.

In the 1940s, Gamow was joined at George Washington University by Ralph Alpher, a graduate student. He gave Alpher the task of working out the details of how helium could have been built up from protons and neutrons in the Big Bang.

All eminent scientists like to have graduate students to do such donkey work. But it was particularly important for Gamow to have someone to do the calculations for him, since although he was a brilliant physicist he was always hopeless at getting the details of his arithmetical calculations right, and had trouble adding up his bank statements. Together, they found that it was indeed possible to produce a mixture of 75 per cent hydrogen and 25 per cent helium out of the Big Bang, but that as the Universe expanded and thinned out the nuclear reactions would quickly come to a halt making it impossible to build up more complicated elements.

Gamow wasn't worried about this. After all, as he used to tell anyone who was interested, the theory explained where more than 99 per cent of the visible material in stars and galaxies came from, and that was good enough to be going on with. (In case you are wondering, the other elements are made inside stars; Fred Hoyle showed this in the 1950s.)

The detailed calculations formed part of Alpher's PhD thesis, which was submitted in 1948. They clearly deserved a wider audience, however, and Alpher and Gamow wrote a joint paper on the work for submission to the Physical Review. It was at this point that Gamow's sense of fun overcame him, and he perpetrated his most famous scientific joke. Without telling his friend Hans Bethe of his plan, he decided that it was "unfair to the Greek alphabet to have the article signed by Alpher and Gamow only, and so the name of Dr Hans A. Bethe (in absentia) was inserted in preparing the manuscript for print."{1} To Gamow's delight, and entirely by coincidence, the paper duly appeared in print on 1 April 1948, under the names Alpher, Bethe, Gamow. To this day, it is known as the "alpha, beta, gamma" paper. This is a suitable reflection of the fact that it deals with the beginning of the Universe, and also can be taken as referring to the contents of the paper, since helium nuclei are also known as alpha particles, beta ray is another term for electrons, and gamma rays are high energy photons (particles of light) involved in the nuclear reactions. It was the fate of those gamma rays that next caught the attention of Gamow and his students.

The calculations showed that the proportion of helium produced in the Big Bang depends on the temperature of the fireball in which the Universe was born. To match the observations that stars contain 25 per cent helium, Gamow's team had to set the temperature of the Big Bang rather precisely. But Einstein's equations then predict how the temperature of that radiation will fall as the Universe expands. Later in 1948, Alpher and another of Gamow's students, Robert Herman, published a paper in which they calculated that the temperature of this leftover radiation today must be about five degrees on the absolute, or Kelvin, scale -- that is, some -268 oC. The calculation is simple. In its modern form (updated slightly from 1948) it sets the temperature now, in Kelvin, as 1010 divided by the square root of the age of the Universe in seconds. One second after the moment of creation, the temperature was 10 billion degrees; after 100 seconds, it had already cooled to 1 billion degrees; and after an hour it was down to 170 million degrees. For comparison, the temperature at the heart of the Sun today is about 15 million degrees.

Gamow's team predicted, almost fifty years ago, that the Universe must be filled with radiation left over from the Big Bang, cooled all the way down to about 5 K. The radiation would be in the form of microwaves, just like those used in radar or in a microwave oven. In effect, the Universe is an "oven" with a temperature of a few K. Microwaves are in the radio part of the spectrum, and could be detected by radio telescopes. But radio astronomy was only just getting into its stride in the early 1950s, and Gamow didn't realise that it might actually be possible to measure this microwave background.

His own career soon took a new path, or he might have learned how much progress the radio astronomers were making and urged them to look for this background radiation.

In 1953, Francis Crick and James Watson, working in Cambridge, reported that they had discovered the structure of the molecule of life, the now-famous double helix of DNA. It soon became clear that the information carried by DNA -- the information which tells a fertilised egg how to grow to become a human being, and which tells each cell in that human being how to function -- is in the form of a genetic "code", spelled out on chemical units along the DNA double helix. But nobody knew how the code worked.

At the time, Gamow was visiting the Berkeley campus of the University of California, and, as he later recalled: I was walking through the corridor at the Radiation Lab, and there was Luis Alvarez going with Nature in his hand . . . he said "Look, what a wonderful article Watson and Crick have written." This was the first time that I saw it. And then I returned to Washington and started thinking about it.{2} Gamow was hooked. Scientific code-breaking was just the kind of thing to intrigue him, and he soon wrote to Watson and Crick, introducing himself and presenting some ideas about how the DNA code might be translated into action inside the cell. His first paper on the subject was published in 1954, and presented the key idea that hereditary properties could be characterised by a long number in digital form. This is exactly the way computers work, expressing everything in terms of binary numbers, long strings of 0s and 1s, and it was eventually confirmed that the DNA code does indeed work like this, but with four "digits" (like having the numbers 0, 1, 2, 3) instead of two. But it took a long time for the code to be cracked and read. Some of the key work was carried out in Paris, by Jacques Monod, Francois Jacob and their colleagues; but Gamow kept in touch with all of the researchers involved, contributing stimulating ideas to the debate. The code was finally cracked in 1961, and it is no coincidence that Crick and Watson received their Nobel Prize the following year.

By then, Gamow had almost forgotten his team's pioneering investigation of the temperature of the Universe. But in 1963 two young radio astronomers, Arno Penzias and Robert Wilson, began to puzzle over some strange "interference" they were getting with their telescope, a microwave detector built on Crawford Hill in New Jersey. The puzzle was that everywhere they pointed the telescope they found a persistent hiss of radio noise, corresponding to microwaves with a temperature of about 3 K. They tried everything to locate the source of the interference, even taking the whole antenna apart and cleaning off the pigeon droppings that had accumulated on it, then putting it back together. Nothing made any difference. It seemed that the Universe was filled with a background of microwave radiation. News of the discovery was published in 1964, and the radio noise was quickly explained by other researchers as the leftover radiation from the fireball of the Big Bang. By then, the work of Gamow and his team had been so neglected for so long that the first accounts failed to mention them, and the fact that they had predicted the existence of this radiation, at all. Understandably, this upset Gamow, Alpher and Herman greatly. But the omission was later rectified, and there is now no doubt in the mind of any astrophysicist that the radiation discovered by Penzias and Wilson accidentally in the early 1960s is the radiation predicted by Gamow's team in the 1940s.

The importance of the discovery cannot be over-emphasised. Before it was made, even the cosmologists did not really "believe" in the Big Bang -- and there were very few people who even called themselves cosmologists. They regarded cosmology rather like a great game of chess, in which they could work out theories and construct mathematical "models" of the Universe, with no expectation that the equations they scribbled on their blackboards actually described the real world.

The discovery of the background radiation changed all that. After 1964, those equations had to be taken seriously. With the realization that cosmology was indeed a real science, many physicists turned to its investigation, leading to the situation today, thirty years later, where the study of the Big Bang is possibly the most important branch of theoretical physics. As Steven Weinberg, one of those physicists who turned to cosmology after 1964, has summed up the situation: Gamow, Alpher and Herman deserve tremendous credit above all for being able to take the early universe seriously, for working out what known physical laws have to say about the first three minutes.{3}

Gamow died in 1968, ten years before the Nobel Committee gave their award for physics to Penzias and Wilson. Nobel Prizes are never awarded posthumously, but it would surely be right, on this occasion, to include the name of Dr George Gamow "in absentia". He had shown how the stars shine, almost single-handedly invented the Big Bang theory, and contributed to explaining the secret of life itself. The "ripples" discovered by COBE, and hailed in 1992 as "the greatest scientific discovery of all time" (by no less an authority than Stephen Hawking), are, in fact, just a secondary feature of the background radiation predicted by Gamow.

But his most enduring legacy is the series of books he wrote describing the mythical adventures of Mr Tompkins, a mild-mannered bank clerk who has vivid dreams in which he visits the world of the very small, inside the atom, and the world of the very large, the Universe itself. Although they first appeared in the 1940s, they still provide an excellent and entertaining guide to basic physics. Many readers seem to agree -- the collected edition was reprinted in England every single year during the 1980s, and has just been republished in English with a new foreword by Roger Penrose, one of the founding fathers of black hole theory.

The irony would probably have amused Gamow himself. Eminent scientists may have forgotten his seminal contribution to so much of twentieth century science; but generations of schoolchildren know him as a witty raconteur who explains science painlessly for beginners. Perhaps some things are more important than Nobel Prizes, after all.

Who is Stephen Hawking

and why are they making so much fuss about him, anyway?

John Gribbin

STEPHEN HAWKING has become a twentieth century icon, his image as familiar as that of Marilyn Monroe or Albert Einstein. He has reached the heady status of being famous for being famous -- the crippled genius who has written a book that has now been on the UK bestseller lists for more than five years. He has another book (a collection of scientific essays) coming out at the end of October, and will then probably be even more famous as the first scientist to have two books in the top ten at the same time.

But, like Monroe, Einstein, or the Beatles, Hawking's famousness does rest upon a secure foundation. He did do some dramatic and important work first, before he became an icon. The problem is, most of the people who have heard of Hawking the icon have only the haziest idea of what that work was all about. Fear not; the haze is about to clear. I am going to let you in on the secret of Hawking's scientific success.

The idea that the Universe was born in a singular event called the Big Bang, at a definite moment in time some 15 billion years ago, is now so familiar that it has become part of the stock in trade of stand up comedians. Thirty years ago, when Hawking was working for his PhD in Cambridge, this was an idea whose time had still not quite come. There were rival ideas about how the Universe came to be the way it is, and there was no direct evidence that the Big Bang itself had ever happened. All cosmologists knew for sure was that the Universe is expanding, with galaxies like our Milky Way moving apart from one another as the space between them stretches.

In the early 1960s, mathematical physicists also toyed with another great idea that they could not prove had any direct relevance to the Universe we live in. This was the concept of what are now known as black holes -- they were only given the name in 1969. According to the best laws of physics we know (Einstein's general theory of relativity), any dead star with more than about three times as much matter as there is in our Sun must collapse under its own weight, shrinking down literally to a mathematical point, a singularity. Living stars do not do this, because the heat generated in their interiors provides the pressure needed to hold them up against the inward pull of gravity. On its way to a singularity, the collapsing star becomes so dense that the gravitational pull at its surface becomes so strong that nothing, not even light, can escape. It disappears inside what is known as an event horizon. Nobody would ever be able to see what happened at the heart of the black hole; but Roger Penrose, then working at Birkbeck College in London (and later to share the best seller lists briefly with Hawking, with his book The Emperor's New Mind) proved that all the matter inside a black hole must collapse into the singular point, a point of infinite density at which the laws of physics break down.

Hawking's first major scientific contribution was to join forces with Penrose to turn this idea on its head. Collapsing things must form singularities, according to Penrose's work; now, they found that expanding things must come from singularities. In particular, they proved that the expansion of the Universe must have started from a point of infinite density where the laws of physics break down. At the same time, the Big Bang theory was being reinforced by the discovery of the now-famous cosmic background radiation, interpreted as the echo of the Big Bang itself. In the 1970s and since, supported by both theory (partly Hawking's theory) and observations, the Big Bang became the definitive description of the Universe.

For a time, Hawking left the universal studies to others, and concentrated on black holes. He found a curious feature of their behaviour, in which (according to theory -- nobody has yet seen a black hole) particles ought to "bubble off" from the event horizon. In effect, the energy of the intense gravitational field at the surface of the black hole is converted into mass (in line with Einstein's famous equation E = mc2) in the form of pairs of particles. One member of each pair falls in to the hole, while the other escapes. The activity gives every black hole a temperature, which depends only on its mass.

The calculations link relativity theory and quantum theory, the two great twentieth century physics ideas, with thermodynamics, the great nineteenth century physics idea. It was as surprising, as several physicists remarked, as opening up the bonnet of a modern sports car to find that it was powered by a Victorian steam engine. The discovery was esoteric, but it established Hawking's reputation among his peers. Meanwhile, as they used to say at the Saturday morning pictures, the cosmologists' view of the Universe was changing. At first, they had thought that the Big Bang was a unique event, and that the Universe was destined to expand forever. But over the past twenty years there has been increasing evidence, culminating with the ripples in the background radiation discovered last year by the COBE satellite, that this is not the case.

The only thing that can stop the expansion is gravity, and there is not enough matter in all the bright stars and galaxies to do the trick. But it now seems that the Universe actually contains ten to a hundred times more matter than we can see, in the form of dark objects. This is enough to ensure that the expansion will one day halt, and then reverse, crushing everything together again in a singularity -- the Omega Point.

Several cosmologists, including Hawing, have developed the idea that this means that the Universe is a black hole -- we are living inside an extremely large black hole, and will one day suffer the fate of any matter inside a black hole, as spelled out by Penrose thirty odd years ago. So cosmologists have recently puzzled over what happens at the singularity at the end of time, the Omega Point. The obvious guess is that the singularity that marks the death of our Universe marks the birth of another universal cycle, and this is born out by the mathematics.

But if one singularity can give birth to a Universe, why can't others? Specifically, what happens at the singularities that form inside black holes in our own Universe? According to some interpretations of the equations (and here I have to admit that not everyone agrees on this), the singularities could form their own baby universes. On this picture, stuff that falls into a black hole singularity is shunted sideways into another set of dimensions, its own spacetime. It sounds like science fiction, but it isn't really -- science fiction writers are never as imaginative as mathematical physicists.

The best way to picture what is going on is to imagine the expanding Universe as like the skin of an expanding balloon. When I was a child, my friends and I used to indulge in the rather disgusting habit of sucking the skin of a balloon to make a little bubble, that could be twisted at its base to retain its shape. Hawking's baby universes are rather like that, little bubbles on the surface of the expanding balloon, each expanding in their own right, still connected to the mother Universe by a "wormhole".

And, of course, the baby universes can have babies of their own, while our Universe may be the offspring of a black hole that formed in another spacetime. Very quickly, the picture in your mind comes to resemble a mass of expanding frogspawn, or the froth of a bubble bath being whipped up ever higher.

And that's why Stephen Hawking is regarded as a top-rank mathematical physicist. Because he helped to prove that the Universe was born in a Big Bang, because he found a way of combining relativity theory, quantum theory and thermodynamics to describe what goes on at the surface of a black hole, and because he has some extremely interesting ideas about how the Universe was born, and how it will end. Whatever anyone may tell you, though, he is not the greatest scientific thinker since Albert Einstein; that honour probably belongs to the late Richard Feynman. But that, as they also used to say at the Saturday morning pictures, is another story. I'll tell it to you another time.