The Magicians

by Marcus Chown

  ‡ The electromagnetic force between a proton and an electron in a hydrogen atom is ten thousand billion billion billion billion times stronger than the gravitational force between them.

  § In fact, to incorporate both in his equation, Dirac was forced to use matrices with four columns with four numbers in each, which would later become known as the ‘gamma matrices’.

  ¶ The fact that each negative-energy state is filled when it contains just one electron is important. If any number of electrons could pile into a single negative-energy state, there would be no way they could ever be ‘filled up’ and stop normal electrons falling into them and making matter unstable. However, quantum theory permits the existence of two distinct types of particle: those with half-integer spin and those with integer spin. The minimum possible quantity, or ‘quantum’, of spin is half of a certain quantity. Particles with half-integer spin, known as ‘fermions’, have the property of being hugely antisocial and need to be one to each quantum state, while the latter, known as ‘bosons’, are extremely gregarious and happy to pile in together into a single state. Electrons, it turns out, are fermions.

  4

  Goldilocks universe

  The nitrogen in our DNA, the calcium in our teeth, the iron in our blood, the carbon in our apple pies were made in the interiors of collapsing stars.

  We are made of starstuff.

  CARL SAGAN

  As we look out into the Universe and identify the many accidents of physics and astronomy that have worked together to our benefit, it almost seems as if the Universe must have known that we were coming.

  FREEMAN DYSON

  Kellogg Radiation Laboratory, Pasadena, California, February 1953

  The man sitting across the desk was talking utter garbage. Willy Fowler knew this because he was an experimental nuclear physicist, and nobody in the world could do what this guy was claiming he could do: predict the precise energy state of a complex atomic nucleus. It was a ‘many body’ system, in which numerous protons and neutrons buzzed about each other like a swarm of submicroscopic bees. Theorists’ capabilities were limited to predicting the exact behaviour of a ‘two-body’ system, such as an electron circling a proton in a hydrogen atom or the Moon travelling in its orbit around the Earth.

  Nevertheless, here in Fowler’s office in Caltech’s Kellogg Radiation Laboratory, a bespectacled Limey astronomer was claiming that he could do what no nuclear physicist in the world could do. And what was even more outrageous was that his prediction was based not on any consideration of nuclear physics but on an argument the likes of which Fowler had never before heard. ‘The universe contains carbon,’ he was sure he had heard Fred Hoyle say, ‘and therefore a carbon nucleus must have an energy state of exactly 7.65 megaelectronvolts.’*

  Hoyle told Fowler he was convinced that the cores, or ‘nuclei’, of all atoms had been assembled from nuclei of the simplest atom, hydrogen, inside stars that had lived and died before the Sun and the Earth were born. It was, by necessity, a multi-stage process. The first step involved four hydrogen nuclei somehow coming together and forming a nucleus of the second-lightest atom, helium.† The second step was for two helium nuclei to stick together to make a nucleus of beryllium. The problem was that beryllium was unstable and, within a billion-billionth of a second of forming, fell apart. The route to building up heavier atomic nuclei such as oxygen, calcium and sodium appeared well and truly blocked.

  Hoyle claimed there was a way to leapfrog the troublesome beryllium barrier. His scheme, as far as Fowler could tell, required the existence of a high-energy ‘excited’ state of a carbon nucleus at precisely 7.65 megaelectronvolts above its normal ‘ground’ state.

  Fowler would later recount that his first impression of Hoyle was of someone who had gone a ‘long way off his mental compass bearings’.1 However, working in the shadow of the Mount Wilson 100-inch telescope with which Edwin Hubble had discovered that the universe was expanding in 1929 had made him a nuclear physicist who was tolerant of astronomical ideas. Not showing Hoyle the door would prove to be the smartest career move he ever made.

  It was highly probable that Hoyle was wrong, but Fowler adhered to the experimenter’s maxim: never close your mind to the unexpected. He called the members of his small research group into his office and made the British astronomer repeat his argument. ‘Is there any chance’, asked Hoyle, ‘that experiments could have missed a 7.65 MeV state of carbon?’

  Much of the technical discussion that ensued went well over Hoyle’s head, but eventually there was a consensus among Fowler’s group. If the state had some very special properties, it was just about conceivable that it could have been missed. Hoyle looked around the assembled faces hopefully, but Fowler shook his head. He had too much work on to carry out an experiment to test Hoyle’s outlandish claim. ‘Anyone else?’ asked Fowler. There was one person. Ward Whaling was a Texan who had recently arrived at Caltech from Rice University in Houston. Turning to Hoyle, he said, ‘I’ll do it. I’ll look for your energy state.’

  *

  Hoyle’s prediction had had a long period of gestation. It had all begun in the autumn of 1944, when he was a theorist working in England on the development of radar for the war effort. He had been delegated to attend a conference at the end of November in Washington DC. Getting there involved a perilous crossing of the Atlantic, zigzagging to avoid the deadly U-boats. In fact, he had been so worried that, prior to boarding the RMS Aquitania at Greenock in Scotland, Hoyle had taken out life insurance at Lloyd’s – he had a wife, Barbara, and two young children – and visited his parents in Yorkshire, in case it was the last time he ever saw them. But after ten tedious days at sea along with ten thousand American troops who were returning home, he arrived in the New World.

  The bright lights and abundance of New York City were overwhelming after five years of blackouts and rationing in England. Astonished, Hoyle wandered the streets in what seemed to him a ‘fairyland’, before taking the train south from Pennsylvania Station. In Washington DC, he checked in with the British Embassy and picked up a generous allowance. There were three days to fill before the start of the conference, so he decided to head north to Princeton and see astronomer Henry Norris Russell, famous for his groundbreaking classification of stars in the Hertzsprung–Russell diagram.

  Hoyle’s interest in astronomy had come about by accident. At Cambridge in 1938–9, he had been the student of Paul Dirac. The story was that the quantum theorist had not wanted a student and Hoyle had not wanted a supervisor, but the pair had been thrust together as a joke by a mischievous faculty member. The famously taciturn Dirac had nevertheless given Hoyle one piece of useful advice. In his view, all the low-hanging fruit of fundamental physics had been picked during the quantum revolution of the 1920s and 1930s. If Hoyle wanted to do important work, he should therefore look for interesting problems in another scientific field.

  Hoyle decided to pursue either astronomy or biology, and was luckily saved the trouble of having to choose. Tasked with the responsibility of inviting speakers for a student society, he approached the Cambridge astronomer Ray Lyttleton, who enthused about a particular stellar problem he was working on. Hoyle’s interest was immediately piqued. He began collaborating with Lyttleton, and became an astronomer by default.

  Hoyle’s meeting with Russell at Princeton went well, but it proved more important in terms of what it led to. This would involve assembling a jigsaw puzzle of information gathered from many different sources, illustrating the often chaotic way in which science is done.

  On learning that Hoyle would be heading to California after the conference in Washington to visit the US naval headquarters in San Diego, Russell urged him to visit the Mount Wilson Observatory, just north of Los Angeles. He even wrote a letter of introduction to Walter Adams, the observatory’s director.

  When he got to California, Hoyle went to meet Adams, who immediately sent him up the mountain to spend the weekend at the giant 100-inch Hooker Telescope, the bigges
t in the world. It was a wonderful opportunity to see the astronomers at work, but it was what happened when the weekend was over that proved crucial. A keen hiker, Hoyle decided to walk down the mountain and was met by Walter Baade in Altadena, the city in the San Gabriel foothills just above Pasadena. The German–American astronomer was classified as an ‘enemy alien’ and had been barred from military service, which left him in the enviable position of having unlimited access to the world’s biggest telescope while the lights of Los Angeles below were under wartime blackout.

  Baade, a scarily clumsy driver despite being a first-class telescope observer, drove Hoyle to his office at Santa Barbara Street. The pair spent a stimulating afternoon discussing the latest developments in astronomy, which culminated in Hoyle leaving with copies of some papers on ‘supernovae’, prodigiously violent exploding stars that had been discovered by Baade and his Swiss–American colleague Fritz Zwicky. Had Hoyle read the papers immediately they might have meant little to him, but by a turn of fate he did not look at them until he was back in England, by which time he had learnt something that would not only yield a key insight about supernovae but would change the course of his scientific life.

  Hoyle had to head to Montréal to hitch a ride on a giant Liberator or Flying Fortress bomber that could fly him nonstop across the Atlantic to Prestwick, near Glasgow. However, bad weather delayed his departure for several days, and while he was waiting he bumped into two physicists he knew from back home. It was an open secret in Cambridge that Nick Kemmer, who had been a student of Wolfgang Pauli, and Maurice Pryce had been recruited by Tube Alloys, the British project to build an atomic bomb.

  The idea was to exploit ‘nuclear fission’, which had been discovered in Berlin by Otto Frisch, Lise Meitner and Fritz Strassmann on the eve of the Second World War. An unstable heavy nucleus was prone to splitting into two, or ‘fissioning’, and in the process spitting out several energetic neutrons. These could trigger the splitting of further nuclei, raising the possibility of a ‘nuclear chain reaction’ that would unleash a vast amount of nuclear energy explosively.

  Hoyle knew that two different nuclei were capable of fission – a rare ‘isotope’ of uranium known as uranium-235, and a man-made nucleus, first created in 1940, known as plutonium-239. Making plutonium in sufficient quantities for a bomb would require building a nuclear reactor, or ‘pile’. Britain, under bombardment by the Luftwaffe, lacked the resources to follow both routes to a bomb and so had plumped for concentrating uranium- 235, a painstakingly slow process that was being carried out at Chalk River, near Montréal. Hoyle took the fact that Kemmer and Pryce were in Canada to mean that sufficient uranium-235 had been accumulated.

  As he waited for the weather over Montréal to improve, Hoyle began to wonder about a rumour he had heard that a team consisting of some of the best physicists from America and Europe had been assembled at a secret location in the southwest of the US. It puzzled him; he had thought that it would be easy to create an explosion with uranium-235 by simply slamming together two pieces that in combination exceeded the ‘critical mass’ necessary to trigger a runaway nuclear chain reaction. The existence of the large team could mean only that for plutonium things were not as simple as that, which would explain why Britain had chosen what he had thought was the more difficult route to develop a bomb.

  Clearly, something must prevent two subcritical masses of plutonium from merging, and the only thing Hoyle could think of was the fission of plutonium itself. As two lumps approached each other, he reasoned, fission must generate heat so rapidly that it pushed the pieces apart before a runaway chain reaction could catch hold. If he was right, it would mean that the scientists would have to find a way to force together the pieces of plutonium. As he mused on how they might do that, he realised that the best way would be to cause a spherical shell of plutonium to implode by surrounding it with conventional explosives. Imagining the scenario, he immediately saw a problem: the required implosion would occur only if the shockwave from the explosives was perfectly spherically symmetric, but such a shockwave would be incredibly difficult to engineer. Now he understood why it had been necessary to assemble the high-powered team.

  Hoyle’s musings were a distant memory when, back in England over Christmas, he finally had time to read Walter Baade’s papers on supernovae.2 The energy released in such a stellar cataclysm was staggering; typically, a supernova outshone an entire galaxy of several hundred billion stars. As he wondered about the energy source, Hoyle realised that only one thing was capable of powering such a detonation: gravity.

  If a slate tile falls off the roof of a house, the gravity of the Earth accelerates it so that it hits the ground at high speed. Physicists say that its ‘gravitational potential energy’ – that is, the energy it possesses by virtue of its location in a gravitational field – is converted into another form: energy of motion. Similarly, if the core of a star shrinks, it is as if the gravity of the star accelerates countless quadrillion slates and their gravitational potential energy is converted into other forms of energy, such as heat. Paradoxically, in a supernova, it is the implosion of the core of a star that drives the explosion of its outer regions into space.

  At this point, Hoyle began to put together the jigsaw pieces he had acquired in the US. Just as the implosion of plutonium in a bomb would trigger nuclear reactions, so too would the implosion of the core of a star. The nuclear reactions in each case were entirely different, but that did not matter; the idea that implosion would lead to nuclear reactions was like a light-bulb going on in Hoyle’s head.3 In the inferno of a supernova explosion, those nuclear reactions could potentially forge nature’s chemical elements.

  The catastrophic shrinkage of the core of the star would be triggered when the core exhausted its fuel and was no longer able to generate the heat needed to stop it being crushed by gravity. Hoyle imagined a frenzy of element-building nuclear reactions going on in the outer envelope of a dying star, driven by the tremendous heat liberated by the shrinkage. Thrust into space by the explosion, the elements would enrich clouds of interstellar gas and dust and, when those clouds fragmented under gravity, would become incorporated into new generations of stars and planets. If Hoyle was right, supernovae were the furnaces in which the elements that make up our bodies were forged.

  There are ninety-two naturally occurring elements, ranging from hydrogen, the lightest, all the way to uranium, the heaviest. It had once been thought that they had all been put in the universe on day one by a Creator, but in the first half of the twentieth century, the idea had arisen that they had actually been made. Scientists had noticed that the abundance or scarcity of each element was related to the nuclear properties of its atoms. For instance, an element whose nuclei were more tightly bound than nuclei of slightly lighter or slightly heavier elements was also more abundant than them, which was a strong hint that nuclear processes had played a key role in the creation of the elements.

  The obvious possibility was that the universe had started out with nuclei of the lightest element, hydrogen, and that nuclei of all the heavier elements had been assembled inside stars subsequently, by the repeated sticking together of this basic nuclear building block. In fact, a key discovery Baade made under the blacked-out skies above Los Angeles was that the Milky Way contains two distinct populations of stars. In the ‘spiral arms’, where the Sun orbits, are hot blue stars with a relatively high concentration of heavy elements, and in the centre of the galaxy are cool red stars with a low concentration.‡ As would later be shown, the blue ‘Population I’ stars are young and the red ‘Population II’ stars are old, their heavy-element concentrations revealing that heavier elements have become more common as the galaxy has aged, exactly as would be expected if heavy elements are built up inside stars over time.4

  The building of ever-bigger nuclei is not easy because it requires forcing together ever more protons, and like charges repel each other ferociously. The only way the repulsion can be overcome is by the slamming togeth
er of nuclei at ever-greater speeds, which, since temperature is a measure of microscopic motion, is synonymous with ever-greater temperature. In fact, the building of heavy elements requires the existence of a furnace at a temperature of many billions of degrees.

  It was the belief that the interiors of stars could never attain such mind-bogglingly high temperatures that caused the American physicist George Gamow to search for an alternative furnace for forging the elements and claim that a hot Big Bang fitted the bill. But in 1944, reading Baade’s papers, Hoyle saw an opportunity to demonstrate that there was no need to look for an alternative furnace; if he was right, the interiors of stars could reach temperatures at least a thousand times as great as the ten million degrees or so at the heart of the Sun.

  The sequence of nuclear reactions that built up the elements inside stars was likely to be complex, and Hoyle did not have the slightest idea of its details. However, the beauty of a supernova, he realised, was that the inferno was so preposterously dense and hot that the details did not matter. In the ensuing submicroscopic frenzy, nuclei would constantly form and break apart, and a balance would be reached in which the processes of creation and destruction perfectly matched. Such a balance depended only on how tightly bound each nucleus was, and in such a state of ‘statistical thermodynamic equilibrium’, the relative abundances of the elements would become fixed and unchanging. In the jargon, they would ‘freeze out’.

  All Hoyle needed to know was the abundances of different elements and how tightly bound were their nuclei. Unfortunately, his radar work had left him in the West Sussex countryside, with no access to data of this kind. Then, in March 1945, his research took him to Cambridge, where he ran into Otto Frisch. The Austrian physicist had recently returned from the US, where he had been working with the team developing the atomic bomb at Los Alamos in New Mexico. Frisch, it turned out, had exactly what Hoyle wanted: from the drawer in his desk, he pulled out a table of nuclear data, painstakingly compiled by the German nuclear physicist Josef Mattauch.