E=mc2

by David Bodanis

  This was a disheartening result. Uranium could pour out energy in accord with E=mc2, because the uranium nucleus is so large and overstuffed that it barely holds together. Iron is different. Its nucleus is one of the most perfect and most stable imaginable. A sphere made of iron—even if it was molten or gaseous or ionized iron—could not pour out heat for thousands of millions of years.

  Suddenly the vision of using E=mc2 and related equations to explain the whole universe was blocked. Astronomers could just look past the top of the atmosphere, to the great spaces and waiting suns beyond us, and wonder.

  The individual who broke that barrier—letting E=mc2 slip the surly bonds of Earth—was a young Englishwoman named Cecilia Payne, who loved seeing how far her mind could take her. Unfortunately, the first teachers she found at Cambridge when she entered in 1919 had no interest in such explorations. She switched majors, and then switched again, which led to her reading up on astronomy, and when Payne decided on anything, the effects were impressive. She terrified the night assistant at the university's telescope her first night there, after she'd been reading for only a few days. He "fled down the stairs," she recalled, "gasping: 'There's a woman out there asking questions.'" But she wasn't put off, and a few weeks later she described another such incident: "I bicycled up to the Solar Physics Observatory with a question in my mind. I found a young man, his fair hair tumbling over his eyes, sitting astride the roof of one of the buildings, repairing it. CI have come to ask,' I shouted up at him, 'why the Stark effect is not observed in stellar spectra.'"

  This time her subject did not flee. He was an astronomer himself, Edward Milne, and they became friends. Payne tried to pull her arts student friends into her astronomical excitements, and even though they might not have understood much of what she was saying, she was the sort of person others like being around. Her rooms at Newnham College were almost always crowded. A friend wrote: ". . . when safely lying on her back on the floor (she despises armchairs), she will talk of all things under the sun, from ethics to a new theory of making cocoa."

  Cecilia Payne

  THE PRINCIPAL AND FELLOWS OF NEWNHAM COLLEGE, CAMBRIDGE, ENGLAND

  Rutherford was teaching at Cambridge by then, but didn't know what to do with Payne. With men he was bluff and friendly, but with women he was bluff and pretty much a thug. He was cruel to her at lectures, trying to get all the male students to laugh at this one female in their midst. It didn't stop her from going—she could hold her own with his best students in tutorials— but even forty years later, retired from her professorship at Harvard, she remembered the rows of braying young men, nervously trying to do what their teacher expected of them.

  But Arthur Eddington, a quiet Quaker, was also at the university, and he was happy to take her on as a tutorial student. Although his reserve never lifted—tea with students was generally in the presence of his elderly unmarried sister—the twenty-year-old Payne picked up Eddington's barely stated awe at the potential power of pure thought.

  He liked to show how creatures who lived on a planet entirely shrouded in cloud would be able to deduce the main features of the unseen universe above them. There would have to be glowing spheres out there, he imagined them reasoning, for the original gas clouds floating in space would gradually form dense enough clumps to start nuclear reactions inside and light up—they would become suns. These glowing spheres would be dense enough to pull planets swinging around them. If the beings on the mythical planet ever did find that a sudden wind had blown an opening in their clouds, when they looked up they'd see a universe of glowing stars, with circling planets, just as they'd expected.

  It was exhilarating to think that someone on Earth might solve the problem of how to deal with all the iron in the sun, and so be able actually to work out Eddington's vision. When Eddington first assigned Payne a problem on stellar interiors, which might at least start to achieve this, "the problem haunted me day and night. I recall a vivid dream that I was at the center of [the giant star] Betelgeuse, and that, as seen from there, the solution was perfectly plain; but it did not seem so in the light of day."

  But even with this kind man's backing, a woman couldn't do graduate work in this field in England, so she went to Harvard, and there blossomed even more. She switched from her heavy woolen clothing to the lighter fashions of 1920s America; she found a thesis adviser, Harlow Shapley, an up-and-coming astrophysicist; she loved the liberty she found in the student dorms, and the fresh topics in the university seminars. She was bursting with enthusiasm.

  And that could have blocked everything. Raw enthusiasm is dangerous for young researchers. If you're excited by a new field—keen to join in with what your professors and fellow students are doing—that usually means you'll be trying to fit in with their approaches. But students whose work stands out usually have had some reason to avoid this, and keep a critical distance. Einstein didn't especially respect his Zurich professors: most, he thought, were drudges, who never questioned the foundations of their teaching. Faraday couldn't be content with explanations that left out the inner feelings of his religion; Lavoisier was offended at the vague, inexact chemistry handed down by his predecessors. For Payne, some of her needed distance came from getting to know her fun fellow Ivy League students a little better. Shortly after arriving: "I expressed to a friend that I liked one of the other girls in the House where I lived at Radcliffe College. She was shocked: 'But she's a Jew!' was her comment. This frankly puzzled me. . . . I found the same attitude towards those of African descent."

  She also got a glimpse of what was going on in the back rooms at the Observatory. In 1923, the word computer did not mean an electrical machine. It meant people whose sole job was to compute. At Harvard, it was applied to ranks of slump-shouldered spinsters in those back rooms. A few of them had once had first-rate scientific talent ("I always wanted to learn the calculus," one said, "but [the director] did not wish it"), yet that was usually long since crushed out of them, as they were kept busy measuring star locations, or cataloging volumes of previous results. If they got married they could be fired; if they complained of their low salaries, they would be fired as well.

  Lise Meitner had had her problems in getting started in research in Berlin, but there was nothing like this desolate, life-crushing sexism. A few of the Harvard "computers," in several decades of bent-back work, succeeded in measuring over 100,000 spectral lines. But what it meant, or how it fit in with the latest developments in physics, was almost always not for them to understand.

  Payne was not going to be pushed into their ranks. Spectroscope readings can be ambiguous where they overlap. Payne began to wonder how much the way her professors broke them apart depended on what they already had in mind. For example, let the reader note the following letters very well, and then try to read them:

  n o t e

  v e r y

  o n e w

  e l l g

  e t i t

  It's not easy. But if you start reading it instead as "Not everyone . . . " then it leaps out. What Cecilia Payne decided on, there in 1920s Boston, was a Ph.D. project that would let her confirm and further develop a new theory about how to build up spectroscope interpretations. Her work was more complicated than our example above, for spectroscope lines from the sun will always include fragments of several elements; there are distortions from the great temperature as well.

  An analogy can show what Payne did. If astronomers are convinced there's going to be lots of iron in the sun (which seemed fair for there was so much iron on Earth and in asteroids), there'd be only one way to read an ambiguous string of lines from a spectroscope. If they came out, for example, as:

  t h e y s a i d i r o n a g a i e n

  you'd parse it to read:

  t h e y s a i d I r o n a g a i e n

  and there'd be no need to worry too much about the odd spelling of agaien. The extra e could be a fault in the spectroscope, or some odd reaction on the sun, or just a fragment that was slipped in from some other eleme
nt. There's always something that doesn't fit. But Payne kept an open mind. What if it was really trying to communicate:

  t H e y s a i d i r o n a g a i e n

  She went through the spectroscope lines over and over again, checking for these ambiguities. Everyone had boosted the lines one way, to make it read as if they were for iron. But it wasn't too much of a stretch to boost them differently, so that they read hydrogen, not iron.

  Even before Payne finished her doctorate, her results began to spread in gossip among astrophysicists. While the old explanation of the spectroscope data had been that the sun was two-thirds iron or more, this young woman's interpretation was that it was over 90 percent hydrogen, with most of the rest being the nearly as lightweight helium. If she was right, it would change what was understood about how stars burn. Iron is so stable that no one could imagine it transformed through E=mc2 to generate heat in our Sun. But who knew what hydrogen might do?

  The old guard knew. Hydrogen would do nothing. It wasn't there, it couldn't be there; their careers—all their detailed calculations, and the power and patronage that stemmed from it—depended on iron being what was in the sun. After all, hadn't this female only picked up the spectroscopic lines from the sun's outer atmosphere, rather than its deep interior? Maybe her readings were simply confused by the temperature shifts or chemical mixes there. Her thesis adviser declared her wrong, and then his old thesis adviser, the imperious Henry Norris Russell, declared her wrong, and against him there was very little recourse. Russell was an exceptionally pompous man, who would never accept he could be wrong—and he also controlled most grants and job appointments in astronomy on the East Coast.

  For a while Payne tried to fight it anyway: repeating her evidence; showing the way her hydrogen interpretation was just as plausible in the spectroscope lines as the iron ones; even more, the way new insights—the latest in European theoretical physics—were suggesting a way hydrogen really could power the sun. It didn't matter. She even tried reaching out to Eddington, but he withdrew, possibly out of conviction, possibly out of caution before Russell—or possibly just from a middle-aged bachelor's fear of a young woman turning to him with emotion. Her friend from her student days at the Cambridge Solar Physics Observatory, the young fair-haired Edward Milne, was by now an established astronomer, and did try to help, but he didn't have enough power. Letters were exchanged between Payne and Russell, but if she wanted to get her research accepted she'd have to recant. In her own published thesis she had to insert the humiliating line: "The enormous abundance [of hydrogen] . . . is almost certainly not real."

  A few years later, though, and the full power of Payne's work became clear, for independent research by other teams backed her spectroscope reinterpretations. She was vindicated, and her professors were shown to have been wrong.

  . . .

  Although Payne's teachers never really apologized, and tried to hold down her career as long as they could, the way was now open to applying E=mc2 to explain the fires of the sun. She had shown that the right fuel was floating up in space; that the sun and all the stars we see actually are great E=mc2 pumping stations. They seem to squeeze hydrogen mass entirely out of existence. But in fact they're simply squeezing it along the equals sign of the equation, so that what had appeared as mass, now bursts into the form of billowing, explosive energy. Several researchers made starts on the details, but the main work was done by Hans Bethe, the same man who later co-wrote that 1943 memo to Oppenheimer about the ongoing German threat.

  Down on Earth, the many hydrogen atoms in our atmosphere just fly past each other. Even if crushed under a mountain of rock, they won't really stick to each other. But trapped near the center of the sun, under thousands of miles of weighty substance overhead, hydrogen nuclei can be squeezed close enough together that they will, in time, join together, to become the element helium.

  If this were all that happened, it wouldn't be very important. But each time four nuclei of hydrogen get squeezed together, Bethe and the others now showed that they follow the potent, subatomic arithmetic of the sort Meitner and her nephew Frisch worked on that afternoon in the Swedish snow. The mass of the four hydrogen nuclei can be written as 1+1+1+1. But when they join together as helium, their sum is not equal to 4! Measure a helium nucleus very carefully, and it's about 0.7 percent less, or just 3.993 units of weight. That missing 0.7 percent comes out as roaring energy.

  It seems like an insignificant fraction, but the sun is many thousands of times the size of Earth, and the hydrogen in this tremendous volume is available as fuel. The bomb over Japan had destroyed an entire city, simply from sucking several ounces of uranium out of existence, and transforming it into glowing energy. The reason the sun is so much more powerful is that it pumps 4 million tons of hydrogen into pure energy each second. One could see our sun's explosions clearly from the star Alpha Centauri, separated from us by 24 trillion miles of space; and from unimagined planets around stars far along the spiral arm of our galaxy as well.

  The sun did that much pumping yesterday when you woke up—4 million tons of hydrogen "squeezed" along Einstein's 1905 equation from the mass side to the energy side, getting multiplied by the huge figure of c2— and it was pouring out that much energy at dawn over Paris five centuries ago, and when Mohammed first took refuge in Medina, and when the Han Dynasty was established in China. Energy from millions of disappearing tons was roaring overhead each second when the dinosaurs lived: Earth has been nurtured, and warmed, and protected, by this same raging fire as long as it has been in orbit.

  I5 Creating the Earth

  Cecilia Payne's work had helped show that our sun and all the other stars in the heavens are great E=mc2 pumping stations. But on its own, hydrogen-burning could easily have led to a sterile, dead universe. Early in the universe's history, there would have been great blazings as the hydrogen stars created their helium. But the original hydrogen fuel would eventually have used itself up, and the fires explained by E=mc2 would have gradually died down, leaving only giant floating ash heaps of used helium. Nothing else would have ever been created.

  To create the universe we do know, there had to be some device for building the carbon and oxygen and silicon and all the other elements that planets and life depend on. These elements are larger and more complex than what a simple hydrogen-to-helium combustion machine could ever produce.

  Payne had been independent enough to challenge the consensus that stars were made of iron, and this had allowed the first stage of insight: showing that there actually was enough hydrogen in the stars above our atmosphere to allow the energy-spraying sequence of I + I + I + I= not quite 4.00 to occur, thereby sustaining their fires. But with the production of helium, it stopped. Who would be cockily independent enough to go further, and show how E=mc2 could operate to create the ordinary elements of our planet and daily life as well?

  In 1923, when Payne arrived at Harvard, a seven-year-old Yorkshire lad was found by his local truant officer to have been spending most of the past year at the local cinema. Even though young Fred Hoyle explained most forcefully that it had been good for his education—he'd taught himself to read by following the subtitles—he was forced, against his will, back to school. It would be this young boy's work that ultimately solved the next major step in how the sun burns.

  About one year after Hoyle returned to school, his class was assigned to collect wildflowers. Back in the classroom the teacher read out the list of flowers, describing one as having five petals. Hoyle examined the sample he'd collected, now in his hand. It had six petals. This was curious. If it had been a petal less than described, that would have been understandable, he might have torn one off in carrying it. But how could there be more? He was puzzling over it, and vaguely heard a strident voice, and then: "The blow was delivered flat-handed across the ear," he wrote, " . . . the one in which I was to become deaf in later life. Since, moreover, I wasn't expecting it at all, I had no opportunity to flinch by the half inch or so that would have reduced
the impulsive pressure on my drum and middle ear."

  It took a few minutes for Hoyle to recover, but then he left the school, and back at home explained to his mother what had happened: "I pointed out, I'd given the school system a tryout over three years, and, if you didn't know something was no good after three years, what did you know?"

  Fred Hoyle

  AIP EMILIO SEGRE VISUAL ARCHIVES, PHYSICS TODAY COLLECTION

  His mother pretty much agreed, and so did his father, who had survived two years as a machine gunner on the Western Front by disobeying the less than brilliant orders from his upper-class officers to test-fire his guns at ten-minute intervals (which would have given his squad's exact location to German assault teams). Fred Hoyle got yet another year off. "Each morning, I ate breakfast and started off from home, just as if I were going to school. But it was to the factories and workshops of Bingley that I went. There were mills with clacking and thundering looms. There were blacksmiths and carpenters Everybody seemed amused to answer my questions."

  In time he was railroaded back to school, where a few kind teachers saw his talent, and helped with scholarships. He ended up studying mathematics and then astrophysics at the University of Cambridge, and he did so well that the intensely private Paul Dirac took him on as a student, which was unheard of, and he even had tea with Payne's old supervisor Eddington—though as there were rumors of some sort of intellectual "disgrace" she had run into at Harvard, Payne's name was now barely mentioned. (History had been rewritten: Henry Norris Russell and the others now implied they'd "always" known that plenty of hydrogen was available in the sun.)