E=mc2 (19 page)
Authors: David Bodanis
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=mc
2
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=mc
2
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 c
2
— 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.
Cecilia Payne's work had helped show that our sun and all the other stars in the heavens are great E=mc
2
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=mc
2
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=mc
2
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.)
The problem of how stars manage to use helium as a further fuel in the giant E=mc
2
pumps, however, hadn't gone much further than where Payne's work and the direct follow-ups had left it in the 1920s. The heat of over 10-million-degrees at the center of our sun was able, barely, to squeeze the positive charges of four hydrogen nuclei together to make helium. To squeeze together those helium nuclei in a burning process to get larger elements, you'd need to get higher temperatures. But the universe was well surveyed.
Where could you find something hotter than the center of a star?
Hoyle's habit of putting things together in his own way now came to the fore. At the start of World War II he was sent to a radar research group, and in December 1944, after an information-sharing mission to the United States, he ended up waiting in Montreal for a rare flight back across the Atlantic.
He wandered around the city and beyond, and also picked up information about the British research group at Chalk River (about 100 miles from Ottawa). Although nobody told him anything official about the Manhattan Project, from the names he heard there—including several whose work he'd known at Cambridge before the war—he gradually deduced the basic stages of the top-secret project still going on at Los Alamos.
The easiest way to accumulate the raw material for a bomb, he already knew from reading accounts published before the war, was by cooking up plutonium in a reactor. He also knew that Britain had not tried building reactors. That meant, he concluded, that the specialists must have found some unsuspected problem with the plutonium route; probably with getting the ignition to operate fast enough. Now, though, seeing the specialists in Canada, including experts in the mathematics of explosions, he realized it must have been overcome.
Oppenheimer and Groves had barbed wire and armed guards and layers of security officers around the plutonium detonation group at Los Alamos. But that was no protection against a man who'd managed to outwit the stern educational establishment of village Yorkshire. By the time he was finally assigned a seat on a flight back, Hoyle had outlined what Oppenheimer's hundreds of specialists had proven. A substance such as plutonium that won't fully explode on its own will certainly crash apart its own atoms if it's squeezed inward abruptly enough. Implosion raises the pressure and temperature enough to do that.
Everyone in the bomb projects had thought of implosion as intensely localized; suitable only for plutonium spheres a few inches across. But why did it have to stay so small? Implosion was a powerful technique on Earth. Hoyle was used to following his thoughts anywhere. Why couldn't it apply in the stars?
If a star ever imploded, it too would get hotter. Instead of being below 20 million degrees, its center could reach—as Hoyle quickly computed—closer to 100 million degrees. That would be enough to squeeze even the larger nuclei of more massive elements together. Helium could be squeezed to create carbon. If the implosion went further, the star would get even hotter, and then heavier nuclei would be created: oxygen, silicon, sulfur, and the rest.
It all depended on a star's actually undergoing this inner collapse, but Hoyle
realized
there was a plausible reason this should happen. When a star was still at the relatively cool 20 million degrees, and capable only of burning hydrogen, the helium that was produced would build up like ash in a fireplace. When all the hydrogen was used up, that ash wouldn't be able to burn. The upper reaches of the star would no longer be pushed outward by the fires within. They would come crashing inward—just as in the Los Alamos bomb.
When a star implodes inward, that would raise its temperature to the 100 million degrees that is enough to ignite the helium ash. When
that
helium is used up, a further ash accumulates and the next stage occurs. The carbon can't burn at 100 million degrees, so now a further level of the star crashes down. The temperature gets higher, and the cycles go on. It's as if a multifloor building were slowly collapsing, as the struts holding up one floor after another suddenly buckle and break. E=mc
2
is central, for each level of burning—first the hydrogen, then the helium, then the carbon—gets its power from the conversion of mass into energy.
There were more details to come next, many contributed by Hoyle himself, but the idea taken from the atomic bomb had been central in solving the problem. Hoyle had simply switched the implosion process from the few pounds of plutonium laboriously collected on Earth, to a sphere of ultraboiling gas—a star—hundreds of thousands of miles wide, at immense distances away in space. He'd seen how stars can cook up the elements of life. When the larger of these stars used up their last possible fuel, it was also clear they'd have to break apart. Everything they had made would then pour out.
. . .
We tend to think of our planet as old, but when it was newly formed the heavens were already ancient; full of millions of these exploded giants. Their eruptions flung out silicon, and iron and even oxygen, to make the substance of Earth.
A large number of unstable elements such as uranium and thorium were created in the ancient stars' explosions as well, and when these elements floated over, becoming incorporated in the deep body of Earth, their continued explosions shot fragments of their nuclei at high velocity into the surrounding rock.
Along with the initial heat left over from the impacts of Earth's creation, the radioactive blastings from the uranium and similar heavy elements have kept our planet's depths from cooling. Their repeated multitudes of E=mc
2
bursts helped produce enough churning heat underneath the surface to make the thin continents on top roll forward, so shaping the surface of Earth.
In some places, sections of the thin crust were pushed crumpling into each other, producing the lifted ripples we call the Alps, Himalayas, or Andes. In other places, the churning heat pulled open gaps that we know by such names as San Francisco Bay, the Red Sea, and the Atlantic. These made excellent collection basins for the hydrogen that had also landed, and as that combined with oxygen, the result was oceans of sloshing water. Iron deep inside the planet sloshed in its own more stately fashion, driven by the daily spinning of the whole globe around its axis. That sent up invisibly streaking magnetic lines, of exactly the sort Michael Faraday described, and reproduced, in the basement of London's Royal Institution 4 billion years later. The result was an invisible network of magnetic force lines, far overhead, helping shield the self-assembling carbon molecules on the surface from some of the worst of the spraying radiation from outer space.
Volcanoes exploded upward—powered by the constant E=mc
2
derived heat beneath—and that led to something of a continuous conveyer belt from deep underground. Key trace elements were pushed up into the air, helping produce our fertile soil; great clouds of carbon dioxide were carried upward as well, creating a greenhouse effect in the young planet's atmosphere, and further ensuring the surface warmth needed for life. Where the frictional heat generated by the atoms blasting apart in accord with E=mc
2
was especially concentrated, deep-sea volcanoes could billow up even through thousands of feet of cold ocean water—which is how the Hawaiian islands lifted above the Pacific waves.
Fast-forward several billion years, and mobile chunks of carbon atoms emerged (in other words, us!) to wade through low-flying clouds of star-created oxygen, stir caffeine-dense liquids of Big Bang hydrogen atoms, and read about how they came to exist. For we live on a planet where E=mc
2
is constantly at work in the technology around us.
Atomic bombs were one of the first direct applications. At the start there were just a handful, laboriously created in the labs of the Manhattan Project, but soon there were many more, as a great infrastructure of factories and scholarships and research institutes became established after Hiroshima. Several hundred atomic or hydrogen bombs were built and ready by the end of the 1950s; today, even well after the Cold War, there are many thousands. To create them there were hundreds of open-air tests over the years, spraying immense gushes of radioactive particles into the stratosphere, there to float to every location on the planet; becoming a part of the bodies of every person alive.
Nuclear submarines were created, with radioactively exploding elements sequestered inside; pouring out heat that spun the turbines. They were fearsome weapons, yet thereby allowed a curious stability in the most dangerous phases of the Cold War. The previous generations of submarines, from World War II, had been unable to spend much time at battle stations. Cruising on the surface, World War II submarines might just manage to travel at the 12 mph of a person on a bicycle; taking the safer route, underwater, they moved at the 4 mph of a person walking. Once they'd crossed half the North Atlantic or the Pacific, they'd used up so much fuel that they quite soon had to engage in difficult wartime refueling, or turn around and trundle back. With nuclear-powered engines, it was different. Russian and American submarines could get into firing range, and then stay there for weeks or months on end— a dangerous standoff, but one at least making the other side very cautious about any moves that might provoke these hidden vessels to launch their missiles.
