How to Make an Apple Pie from Scratch

by Harry Cliff

  But unlike a firework, Lemaître’s primeval atom didn’t explode into a space that already existed—the explosion was space. Before the firework, all of space was squashed down inside the primeval atom, and afterward, it was space itself that expanded. There was no center to Lemaître’s firework—the explosion happened everywhere in the universe at the same time. Everywhere was inside the primeval atom and the primeval atom was everywhere. It’s true that almost every galaxy in the sky is rushing away from us, but at the same time they aren’t actually moving through space. It’s the space in between that’s getting bigger, carrying every galaxy farther and farther apart as if they were sitting on the surface of some vast inflating balloon.

  Although the firework universe made Lemaître something of a public celebrity, it’s fair to say that his theory didn’t meet with universal acclaim in the scientific community. Many were dismayed by the idea of a moment of creation, specifically the possible role it might leave for a creator. Arthur Eddington, who had a huge amount of respect for his talented former student, called the idea “repugnant.” However, Einstein, who had been troubled for some time by his attempts to maintain a static universe, was won over, describing Lemaître’s theory as “the most beautiful and satisfactory explanation of creation to which I have ever listened.”

  The trouble was that Lemaître’s theory was just one of many possible ways of describing the evolution of the universe. By the 1930s, all such cosmological models were based on the powerful framework provided by Einstein’s general theory of relativity. This jewel-like theory was Einstein’s masterpiece, an elegant and highly mathematical reimagination of what we mean by space, time, and gravity. General relativity made it possible to write down a single equation describing the size, shape, and evolution of the entire universe, effectively creating the modern science of cosmology, the study of the universe as a whole. However, there wasn’t one unique equation, there were many, each describing a different universe with a different history and a different future. Lemaître’s firework universe was just one of these, and while it explained why almost every galaxy appears to be rushing away from us, there were other theories that could do the same thing without the need for a philosophically troubling moment of creation.

  For the most part, such high-minded cosmological debates remained the preserve of devotees of general relativity, among them Einstein, Lemaître, and Eddington. However, in the late 1930s nuclear physicists started to take an interest in Lemaître’s firework universe, not as a way of solving problems in astronomy per se, but as a way to unlock the origin of the chemical elements. At the time, the stars weren’t thought to be hot enough to make the heavy elements, but there was one place that certainly would have been: the ultimate thermonuclear oven at the dawn of time.

  FLASH-FRIED HELIUM

  There isn’t any one person to credit with the idea of the big bang. The theory came together slowly in fits and starts, the work of many hands. That said, one person who did a lot to get the whole thing going was George Gamow.

  Gamow never planned to come up with a theory of how the universe began. He was led to the big bang almost by accident during his quest to unlock the origins of the elements, a line of research that goes all the way back to his lively coffee-fueled discussions with Fritz Houtermans in the summer of 1928. Gamow was well equipped to come to grips with the universe as a whole. As a young student in Petrograd he had learned general relativity from one of its all-time greats, the Russian physicist and mathematician Alexander Friedmann, who had been the first person to use Einstein’s theory to write down an equation describing an expanding universe.

  When Hans Bethe had argued in 1939 that the stars weren’t hot enough to fuse elements beyond helium, Gamow began to wonder if the beginning of the expanding universe might have had the right conditions to do the job. Unlike many of his colleagues, Gamow found himself shut out from research on atomic bombs during the Second World War. Perhaps the U.S. authorities were worried by his Russian roots, or maybe it was just his rambunctious personality and love of a good story told over a martini or three. In any case, he was left with plenty of time to develop his ideas, and by the end of the war he had the skeleton of a theory.

  Gamow’s big bang started with a universe that was incredibly small and dense, filled with a cold but fantastically thick soup of neutrons, packing a metric ton into every cubic centimeter. The universe then expanded, following an equation discovered by Friedmann and Lemaître, increasing in size by a factor of ten in a little over a second. As space expanded, the neutrons fused together, or “coagulated” as Gamow put it, to form larger nuclei made of neutrons. At the same time, some of the neutrons decayed into protons, converting these neutron-only nuclei into ones made of both protons and neutrons, and eventually all the familiar chemical elements.

  Gamow’s scheme was unbelievably ambitious: his goal was to make every single chemical element in one almighty explosion at the dawn of time. To have any chance of being right it would need to accurately reproduce the relative amounts of each element as we find them in the world around us. Fortunately, just before the war the Swiss-Norwegian geochemist Victor Goldschmidt had published the results of a wide-ranging survey of the abundances of the elements based on collated measurements of rocks, meteorites, and the spectra of starlight. Goldschmidt’s data was an archeological treasure trove capturing the entire cosmic history of the elements. If Gamow’s big bang could replicate Goldschmidt’s data, then he would be onto a winner.

  Gamow may have had a fantastic imagination, but he didn’t have much enthusiasm for the hard work of calculating the detailed consequences of his wild ideas. Instead, he gave the problem of predicting how much of each element should be made in his big bang to his PhD student, Ralph Alpher. Alpher was a bit of a novice when it came to nuclear physics but had been bounced into the area after he discovered to his dismay that the thesis topic he had spent a year working on had already been published by another physicist.*2 At the time, Gamow was working out on a bit of a limb, and so at least, Alpher thought, he would be relatively free from competition.

  During his PhD studies, Alpher was pulling a forty-hour week on military research at the Johns Hopkins Applied Physics Lab and moonlighting with Gamow on physics after hours at George Washington University. They would meet to discuss progress at Gamow’s favorite Washington restaurant, Little Vienna, where Alpher would snatch a bite to eat between jobs while the hard-drinking Gamow knocked back martini after martini. Alpher was soon having more sober discussions with his neighbor at Johns Hopkins, Robert Herman, who was fascinated by Alpher and Gamow’s theory and soon joined them as a collaborator.

  The big breakthrough came when Alpher happened to hear a talk given by the physicist Donald Hughes about his experimental work firing neutrons at various elements. Hughes was interested in how different materials would fare in the harsh environment of a nuclear reactor and so had been bombarding as many elements with neutrons as he could get his hands on. Alpher immediately realized that Hughes’s data was exactly what he needed.

  Comparing Hughes’s neutron data with Goldschmidt’s element abundances, Alpher noticed a pattern. Elements that had a high tendency to gobble up neutrons tended to be rarer, and vice versa, which makes sense if you think about it a bit. An element that’s good at swallowing neutrons would have gotten converted into heavier elements during Gamow’s big bang, leaving relatively little of the original element. On the other hand, an element that’s unlikely to absorb a neutron will tend to hang around once it’s been made, leading to a higher abundance. It was only indicative, but it seemed to suggest that Gamow was onto something.

  Alpher completed his PhD dissertation in the summer of 1948. Along the way, he and Herman had realized that Gamow’s original assumption of a cold neutron soup was wrong. Instead, the early universe would have been dominated not by neutrons but by light and would have been so ferociously hot that any e
lements that formed in the first few minutes would be immediately smashed apart again by collisions with high-energy photons. In the refined model, the cosmic cooking process only kicked in when the universe had been expanding for around five minutes and cooled down to a billion degrees.

  However, neutrons only live for an average of fifteen minutes before decaying into protons, electrons, and neutrinos, and so many of them would have died off during those first five minutes. As result, the first nuclear reactions would have involved a proton and a neutron fusing together to make the heavy isotope of hydrogen known as deuterium. Once some deuterium had been cooked, it could then swallow another neutron or proton to make either tritium (a heavy isotope of hydrogen made of one proton and two neutrons) or helium-3 (two protons and one neutron). These could then fuse to make helium-4, which could then swallow more neutrons until eventually you’d made all the elements in the periodic table. To his delight, when Alpher calculated the abundances of the elements predicted by the big bang, his result matched Goldschmidt’s data rather well.

  When Alpher and Gamow published an outline of the theory in the spring of 1948 it caused a media sensation. An article written by a local journalist got syndicated all over the country, with The Washington Post reporting that “The World Began in Five Minutes.” Gamow, in typical Gamowy style, put it rather more colorfully: “The elements were produced in less time than it takes to cook a dish of duck and roast potatoes.”

  Several journalists seized on the symmetry between the creative thermonuclear explosion of the big bang and the destructive explosion of a nuclear weapon. Others strayed into religious territory, causing Alpher to receive several letters from concerned Christians offering prayers for his soul, even though he had been careful to avoid any mention of God. Such was the media frenzy that when Alpher made his oral defense of his PhD, around three hundred people crowded into the room at George Washington University to listen in on how the universe began.

  Over the next few years, Alpher and Herman forged ahead, developing the big bang into a proper, quantitative scientific theory. However, the whole project soon hit the rocks. One rather embarrassing issue that had been bubbling away for almost two decades concerned the age of the universe. Cosmologists could use Hubble’s measurement of how fast the universe was expanding to rewind the clock and figure out how far back in time the big bang was supposed to have happened. The answer came out at around 2 billion years, an inconveniently short figure given that radiometric dating suggested that the Earth was more than 4 billion years old. How could the universe be younger than the Earth?

  Not a small problem, I’m sure you’d agree, but Gamow wasn’t deterred. In 1949 he showed that a bit of judicious fiddling with the cosmological equations could lengthen the age of the universe as much as you liked. However, this involved some pretty shameless jiggery-pokery, which Einstein among others was seriously unhappy with.

  An even more serious flaw in the Alpher-Gamow-Herman theory was the same issue that the stellar physicists had been struggling with: the fact that there were no stable nuclei with masses 5 or 8. Once you’d made helium-4 in the big bang you hit a dead end. Adding another neutron or fusing two helium nuclei together both got you nowhere. Alpher, Herman, and a number of other physicists including the great Italian Enrico Fermi tried in vain to find a route over the mass gap, but every time they thought they’d managed to erect a rickety bridge to the heavier elements, the whole thing came crashing down.

  With the big bang theory seemingly on its last legs, one of its chief opponents, Fred Hoyle, was more than happy to put the boot in. Driven by a deep aversion to the idea of a moment of creation, he and his collaborators across the Atlantic in Cambridge, Hermann Bondi and Thomas Gold, had been developing a radical alternative history of the universe, the steady state, arguing that the universe has always been here, always will be, and despite the endless cycle of stellar birth and death, is unchanging.

  The problem was, how can you have an expanding universe that always looks the same? The solution was hit upon by Gold—the spontaneous creation of matter. As the universe expands and the galaxies fly farther and farther apart, Gold suggested that atoms could be constantly popping into existence to fill in the gaps. This new matter would eventually clump together to form new stars and galaxies as the old ones age and fade away, keeping the universe looking the same indefinitely.

  It was a pretty mad idea at first glance. For one thing, having matter appear out of nowhere violates the conservation of energy. But on the other hand, you only really needed a very small amount of matter creation to keep the universe steady, “about one atom every century in a volume equal to the Empire State Building,” as Hoyle vividly put it.

  With Gamow and his colleagues struggling to “make” the heavy elements in the big bang, the steady state won a major victory in 1957 when Hoyle, Fowler, and the Burbidges published their tour-de-force paper on how stars cook the chemical elements, the one familiarly known as B2FH. At a stroke, the big bang’s original raison d’être had been shot to pieces. There was no need for a big bang to make the heavy elements; the stars could do it just fine on their own, thank you very much.

  And yet, and yet. Even as the steady state seemed to be in the ascendency, portents of its downfall were beginning to appear in the heavens. Improved measurements of the expansion of space had been gradually lengthening the age of the universe, until by 1958 it had grown to as much as 13 billion years, far older than the oldest rocks found on Earth. Meanwhile new measurements of X-rays and radio waves from deep space challenged some of the basic tenets of the steady state, to the point that even some of its advocates began to abandon it.

  Another problem that had been strangely ignored when B2FH came out was the thorny issue of helium. Helium is the second most abundant element in the universe, making up 25 percent of the total mass of all atoms compared to 75 percent for hydrogen and just a tiny sprinkling of heavier elements. Everything else—the carbon in our bones, the oxygen we breathe, the iron in our blood, the edible gold leaf on top of our apple pie—is just a light dusting of icing sugar on a vast hydrogen-helium cake. However, since stars make helium and all the other elements together, there is no way that they could have made such huge quantities of helium and yet so little of all the rest. Assuming that all matter started out as hydrogen, then most of the helium in the universe must have come from somewhere else. But where?

  Hoyle, whose faith in the steady state bordered on fanatical, tried to get around the problem by proposing the existence of gigantic “black stars,” enormous objects thousands or even millions of times heavier than the Sun, conveniently hidden from view inside giant clouds of gas. Thanks to their gigantic sizes, these megastars would go through a series of violent explosions and collapses, sort of like mini big bangs in their own right, generating temperatures of tens of billions of degrees in their cores and fusing vast amounts of hydrogen into helium. Unfortunately for Hoyle, there was zero evidence that these black stars really exist in the universe, and many of his colleagues saw it as a desperate attempt to salvage a dying theory.

  On the other hand, it seemed that the big bang might fit the bill. Despite not being able to make the heavy elements, the theory had no trouble at all with making helium. The question was, how much helium would you expect to get fused in a hot big bang, and, crucially, does this match what we see in the universe around us?

  To answer this question, we need to go right back to the first few minutes of the universe’s history, to a time when all of space was filled with a blazing plasma of particles. Today, our universe is dominated by matter—gas, dust, stars, and dark matter*3 scattered across an otherwise empty void—but back then it was ruled by light. You might even say that the universe was made of light. The matter particles, the protons, neutrons, and electrons that would go on to make up everything we see around us, were little more than froth riding on a furious ocean of photons.
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  In the first few minutes, this primordial light was so fierce that a single photon carried enough energy to smash an atomic nucleus to pieces. As a result, almost no nuclei could form. If a proton and a neutron managed to fuse to make deuterium, then they were instantly blown apart again by a collision with a high-energy photon. However, in these first few minutes the universe was expanding extremely rapidly, and as it expanded, it cooled. After about three minutes the cosmic oven had cooled to a few billion degrees and photons no longer had enough oomph to destroy a deuterium nucleus. Suddenly, the amount of deuterium in the universe skyrocketed, and the cosmic cooking process roared into action.

  In little more than a minute, a blizzard of nuclear reactions converted deuterium into tritium and helium-3, and then into helium-4. After about a hundred seconds, almost all the available neutrons had been consumed and it was all over. A few nuclear reactions carried on at a fairly desultory rate for the next little while, but just twenty minutes after the big bang the cosmic oven grew too cool, thermonuclear cooking came to an end, and the amount of helium in the universe was set.

  But how much helium? Remarkably, the answer depends on a single ratio: the number of neutrons for every proton at the moment nuclear fusion gets going. Since almost all the neutrons end up getting converted into helium, and helium contains two neutrons and two protons, this simple ratio tells us precisely how much helium gets made. And the number of neutrons depends crucially on what happened in the very first second.

  During the first second of cosmic time, the energy of particles in the primordial fireball is so high that neutrons and protons were continually being converted into each other by collisions with high-energy particles. At first, the reactions that convert protons to neutrons ran at the same rate as the opposite reactions converting neutrons back into protons. Equality reigned.