How to Make an Apple Pie from Scratch

by Harry Cliff

  Unfortunately, giving that particular problem to that particular student turned out to be a big mistake. About two-thirds of the way through, the student got fed up and threw in the towel. Having myself ridden the three-year roller coaster of loneliness, confusion, and frustration that is the modern PhD, during which a friend and I frequently fantasized about running off to start a bakery, I can totally sympathize. The problem was that according to Cambridge’s rather archaic rules, Hoyle had gifted the problem to the student irrevocably and couldn’t work on it himself unless the student canceled his PhD registration.

  Unfortunately for Hoyle, five and a half thousand miles away in sunny California, Hans Bethe’s young postdoc Ed Salpeter was thinking about the very same problem. Salpeter had taken a sabbatical from Cornell in Upstate New York to spend the summer of 1951 working at the California Institute of Technology’s Kellogg Radiation Lab with Willy Fowler, a burly extrovert from Ohio. Fowler had already made his name as the father of experimental astrophysics by using particle accelerators to recreate the reactions that power the Sun and stars in the lab. Salpeter, on the other hand, was a theorist in desperate need of data. In particular, he needed to know the precise energy of the beryllium-8 nucleus. He couldn’t have come to a better place.

  As luck would have it, Fowler’s team had already made just the measurement Salpeter needed. Shortly after the war they had used their proton accelerator to knock chunks out of beryllium-9 nuclei, briefly creating beryllium-8, which immediately fell apart into two helium nuclei. Adding up the energies of the two helium nuclei that came whizzing out of the collision, Fowler was able to make an accurate measurement of beryllium-8’s energy. To Salpeter’s delight, it had almost precisely the right value to massively boost the rate of the triple-alpha process. What’s more, it became clear to Salpeter that the fusion of helium into carbon-12 could take place at much lower temperatures than previously thought, a couple of hundred million degrees instead of billions of degrees.

  Back in Cambridge, Hoyle read Salpeter’s paper on helium fusion with growing frustration. You can almost picture him banging his fist on his desk and cursing Cambridge’s out-of-date regulations. He had been well and truly gazumped by the dynamic duo of Salpeter and Fowler. However, rather than throw his hands up in despair, Hoyle channeled his anger into a renewed determination that would soon bear fruit.

  In late 1952, he got an invitation to spend the following spring lecturing at Caltech. Swapping the gloom and rationing of postwar Britain for the sun-drenched orange groves of Southern California was an enticing prospect, and what’s more Hoyle had already gotten a taste for the good life during his trip to the United States in 1944. While preparing for his lectures Hoyle went back over Salpeter’s reaction and began to realize that there was something seriously wrong.

  Once carbon-12 had been made inside a star, it would almost immediately smack into another helium nucleus to create oxygen-16. That’s not a problem in itself—after all, oxygen is an important ingredient of the universe—but the trouble was that the reaction would go so fast that almost no carbon would be left over to make living things (or indeed apple pies). The fact that Hoyle, a carbon-based life-form, was able to worry about such matters suggested that there must be some other process at work that stopped all the carbon from being burnt up.

  The solution that Hoyle hit upon was both brilliant and fantastically audacious. He realized that carbon-12 could only have formed inside stars if its nucleus had a very specific property.

  Now, just like electrons in atoms, protons and neutrons inside atomic nuclei can exist in a wide variety of different states, known as energy levels. You can think of these energy levels as like the rooms in a large multistory hotel. When the nucleus is in its lowest energy state, the protons and neutrons fill up the rooms nearest the ground floor, only taking up residence in the higher floors if there are no spaces left downstairs. However, if you smack a nucleus hard, perhaps by firing a gamma ray at it, the protons and neutrons get thrown into an excited state—perhaps in the analogy there’s a fire in reception and all the residents run upstairs in a mad panic and end up in rooms on higher floors. Anyway, in a nucleus, there are a well-defined set of these excited states, which are determined by the forces between the protons and neutrons and the laws of quantum mechanics.

  Hoyle realized that if there was an excited state in carbon-12 with the same energy as a typical collision between a beryllium-8 and a helium nucleus inside a star, then the rate of carbon-12 production would get a big boost, more than compensating for the later reaction to make oxygen-16. He was even able to calculate the energy of this special state—it needed to be very close to 7.65 MeV.*4

  By the time Hoyle arrived at Caltech, he was itching to talk to Willy Fowler about his special carbon state. But when he tried to buttonhole him at a cocktail party arranged in Hoyle’s honor, Fowler refused to talk shop, leaving Hoyle to make small talk with the rest of the Caltech faculty. However, Hoyle was a man on a mission, and the next day he burst into Fowler’s office without so much as a by-your-leave, demanding that they drop what they were doing and use their particle accelerator to look for his predicted excited state.

  Fowler was skeptical to say the least. Here was a funny little man with a strange accent making wild claims that he could predict energy levels in atomic nuclei, a feat that even the best nuclear theorists of the time couldn’t pull off. Hoyle’s claim was clearly ludicrous, he obviously knew nothing about nuclear physics, and, besides, they had already measured the energy levels of carbon-12 and found no sign of the state that Hoyle appeared to be obsessed with. Fowler gave him the brush-off, but Hoyle just would not let it rest, eventually managing to peel off one of the junior postdocs, Ward Whaling, and persuade him it was worth taking a second look.

  Doing the experiment was a serious undertaking. Aside from the usual technical challenges that go along with creating nuclear reactions in a lab, just to get the experiment set up Whaling and his colleagues had to maneuver a spectrometer weighing several tons down a narrow corridor, rolling it along on a bed made up of hundreds of tennis balls, while a group of undergraduates frantically ferried the balls from the back to the front. The experiment itself took place in a dark half basement of the Kellogg Lab, with Hoyle watching on anxiously amid electrical cables and whirring machinery. He later wrote that he had felt like an accused criminal on trial, except unlike a criminal he didn’t know whether he was innocent or guilty.

  Days of nervous waiting passed without result, as Hoyle repeatedly descended into the hot, cramped basement, emerging with relief into the Californian air at the end of each day. He was acutely aware of how silly he would end up looking if he had set Whaling and his team on a wild-goose chase. However, after about two weeks of painstaking work, Whaling gave him the extraordinary verdict: they had found Hoyle’s excited state of carbon-12 exactly where he said it must be. Everyone, including Hoyle, was stunned. Fowler in particular, who had been extremely dubious about the pushy little man from England, was so blown away by Hoyle’s achievement that he arranged to spend the following year across the pond working with him in Cambridge.

  Hoyle returned home on a wave of euphoria. When Whaling published the results a few months later, he put Hoyle’s name first on the paper, a remarkable tribute considering he hadn’t actually gotten his hands dirty doing the experiment. Once he had come back down to earth, Hoyle was left in awe at the precarious state of affairs that made the existence of life in the universe possible. Apart from the special life-giving state of carbon-12, he realized that if oxygen-16 had had a similar state, with an energy of 7.19 MeV, then all the carbon produced inside a star would immediately get converted into oxygen. When he consulted oxygen-16’s nuclear properties he found a state perilously close to the danger zone, at 7.12 MeV. Likewise, if beryllium-8 had been stable instead of immediately falling apart into two helium nuclei, then helium burning would be so violent
that stars would blow themselves to smithereens long before they could fuse a decent quantity of carbon, or indeed any of the other heavy elements.

  Life in the universe seems to be balanced on a knife edge. Shift any of the states in beryllium, carbon, or oxygen just a whisker in the wrong direction and you end up with a carbon-free universe, one with no life, or at least not life as we know it. It’s as if some great cosmic tinkerer has carefully arranged their subtle nuclear properties so that enough of these atoms could get forged inside stars, sprayed out across the cosmos, and then, by a series of random accidents over billions of years, come together to form walking, talking collections of atoms that spend at least some of their time wondering about how they got there. Nuclear physics, in other words, seems to be fine-tuned for life.

  If you find all this a bit unsettling, you’re in good company. Fine-tuning is one of the most controversial topics in modern physics, and it’s not difficult to see why. Once you accept the premise you’re led almost inevitably to some pretty nonscientific ideas: gods, multiverses, giant cosmic simulations, and more besides. (This whole issue will come back with a vengeance later on.)

  Putting any existential angst aside for now, we’ve reached a big moment on our quest to make an apple pie from scratch. At long last we’ve found the recipes for two of the main products of my garage experimentation. First of all:

  THE RECIPE FOR CARBON— THE TRIPLE-ALPHA PROCESS

  Step 1: Deep inside a star, smack two helium nuclei together to form a highly unstable beryllium-8 nucleus.

  Step 2: Quickly now, and by quickly I mean in around one ten-thousandth of a trillionth of a second, fire in another helium nucleus and cross your fingers.

  Step 3: If you’re very lucky, that helium nucleus will fuse with the beryllium-8 before it can spontaneously disintegrate, producing a nucleus of carbon-12 in Fred Hoyle’s special excited state.

  Step 4: Time to cross your fingers again. Some of the time, that excited carbon-12 nucleus will just fall apart again, leaving the three helium nuclei you started with. But with a bit more luck, the excited state will instead de-excite by firing out two gamma rays, leaving us with a newly minted nucleus of good old carbon-12.

  Using this recipe, we can leap across the yawning gaps in the periodic table at masses 5 and 8, taking us all the way from helium at mass 4 to carbon at mass 12. With that previously impassable chasm behind us, the way is open to fuse all the chemical elements from carbon to uranium. Just ahead of us is the next stop, oxygen-16, and the way to get there is remarkably straightforward:

  THE RECIPE FOR OXYGEN— THE ALPHA PROCESS

  Step 1: Take a freshly baked carbon-12 nucleus and smack it with a helium-4 nucleus.

  Step 2: Voilà! Oxygen-16 (plus a bit of leftover nuclear energy in the form of a gamma ray).

  With these two recipes in hand, we can at last make two of the main ingredients of our apple pie. Of course we still haven’t figured out the precise details of how and where these reactions actually happen. While Hoyle had good reason to suspect that carbon and oxygen were made inside stars that had exhausted their supply of hydrogen, the story of how and why this happens is complex, dramatic, and unerringly beautiful. And what’s more, the stellar origins of the chemical elements are far from settled. Across the world, astronomers still continue to ponder and probe the deepest reaches of the cosmos in search of the stellar ovens in which the ingredients of our world were made.

  THE LIVES OF THE STARS

  Perched on a high outcrop of the Sacramento Mountains, amid fragrant pines and firs, are the white domes of the Apache Point Observatory. To the west, the ridge plunges through thick forest to the Tularosa Basin a mile below and the dazzling gypsum dunes of the White Sands National Park. In the mid-nineteenth century this was the Old West of legend, where Apache tribes ruled over a wide fertile valley, until they were displaced by American cattle ranchers who overgrazed the land and turned it into an arid desert. Today, large tracts of this corner of New Mexico lie within a U.S. military firing range, and across the mountains to the northwest is where the world’s first atomic bomb was detonated in July 1945.

  The telescopes of Apache Point are trained on far more distant and far more potent nuclear fires. From this commanding vantage point high in the mountains, astronomers survey light from hundreds of thousands of stars spread across the Milky Way in an attempt to unravel the evolutionary history of our galaxy and the origins of the chemical elements.

  From my motel in Alamogordo, I had taken the road east, climbing from the desert floor into the mountains, past the cutesy village of Cloudcroft and onward and upward through woods of tall conifers. As I approached the observatory, a sign warned me that cars shouldn’t drive up at night—the glare of headlights is the last thing astronomers need to contend with when stargazing.

  It was midafternoon when I pulled up in front of the single-story operations building. I was there to meet Karen Kinemuchi, one of Apache Point’s professional observers who had generously agreed to let me accompany her during the coming night shift. I found her on the platform of the huge 2.5-meter Sloan Telescope, which hangs perilously over a sheer drop to the mountainside below, where she was debugging an electrical glitch with a colleague.

  She greeted me with a smile and a handshake and gestured with undisguised pride toward the spectacular view over the basin to the San Andres Mountains beyond. It certainly was an incredible spot to do your day job. After a few moments soaking in the view, I made my opening conversational gambit, which being British, was naturally about the weather. The Sun was shining, but there was a layer of hazy cloud to the southwest, which had been building through the afternoon despite forecasts for a sunny day and a clear night. Karen didn’t seem too concerned though; the telescope scans the sky in infrared light and can see through this kind of cloud cover with ease as long as it doesn’t get too thick. In any case, we could check the radar map when we got to the control room.

  My visit to Apache Point had been inspired by a Skype call I’d had with another astronomer a few weeks earlier. Jennifer Johnson, professor of astronomy at Ohio State University, uses data from the Sloan Telescope to try to understand how different stellar processes forge the ninety or so naturally occurring elements in the periodic table. It’s a story that’s captivating and complex in equal parts, and despite all the progress since Ed Salpeter, Fred Hoyle, and Ward Whaling unlocked the recipe for carbon in the early 1950s, it’s a story that’s still being written.

  Sitting in her office in Columbus, Ohio, surrounded by books and astronomical ephemera, Jennifer had cheerily talked me through our state-of-the-art understanding of where the chemical elements come from, often breaking into a smile or a laugh when she arrived at some particularly thorny challenge that was exercising her and her colleagues. The foundations of her subject, which is known as “stellar nucleosynthesis”—literally the cooking of atomic nuclei in stars—can be traced all the way back to Hoyle’s visit to Caltech in 1953. Bowled over by Hoyle’s magician-like prediction about the origins of carbon, the nuclear physicist and head of the Kellogg Radiation Lab, Willy Fowler, had spent the following year in Cambridge. There he met the astronomical power couple Margaret and Geoffrey Burbidge, who with Hoyle made up a formidable four-person team.

  In 1957, their partnership resulted in one of the most significant papers in the history of astrophysics. Known colloquially as B2FH after its four authors, the paper is a nuclear cookbook, laying out an intricate web of reactions that could create almost every element in nature in a variety of different stellar ovens. However, the key difference between the stars and ordinary kitchen ovens is that their power comes from the nuclear cooking process itself, and it’s the changing chemical composition of a star’s interior that ultimately shapes its evolution, from its birth as a cloud of collapsing dust and gas to its spectacular death throes.

  According to
B2FH there is no single place in the universe where all the chemical elements are made. Instead there is a range of different stellar furnaces, each of which enriches interstellar space with different chemical elements; small stars like our Sun that die by slowly shedding their outer layers, giant stars that blow themselves apart in spectacular supernova explosions, and white dwarfs, dead stellar husks that can detonate violently when they gobble up too much gas from a companion.

  Jennifer’s mission is to try to weave together all these different processes to create a complete picture of the origins of the elements. In the course of her research, she has produced a beautiful color-coded version of the periodic table, where each chemical element is shaded depending on where we currently think it comes from. The array of different colors scattered across the table, with many elements shaded in more than one color, gives an impression of the long, varied, and interconnected evolutionary histories of the stuff from which we are made.

  But before we get into some hard-core stellar physics, let’s take a step back and consider how we know anything about the stars at all. In 1835, the French philosopher Auguste Comte declared that we would never know what stars were made from. Now, saying that we’ll never know something is really just asking for trouble—you can only ever be proved wrong—but on the other hand it wasn’t an unreasonable statement given how stupendously far away the stars are. You can’t exactly pop over to one and take a sample. But in just a couple of decades poor old Comte got oeuf all over his face thanks to the unexpected arrival of a revolutionary new technique: spectroscopy.

  Spectroscopy emerged from the crucial discovery that different chemical elements absorb and emit specific colors, or more technically frequencies, of light. If you studied chemistry at school you may have gotten to throw powdered metals into a Bunsen flame, creating a brief, vivid burst of color. Strontium, for example, turns the flame crimson, while copper produces a lurid green. The color of a firework comes from the same effect. The set of frequencies that a given element absorbs and emits are specific to that element, representing a unique fingerprint that can be used to detect its presence in a Bunsen flame, a firework, or indeed in the fiery atmosphere of a distant star.*5