E=mc2

by David Bodanis

  Meitner had first really come to know her nephew when he'd been an eager science student in Berlin a decade before. They'd often played piano duets together, even though she had trouble keeping up. (Though they'd have fun, translating Allegro ma non tanto as "Fast, but not auntie.")

  Now Robert was a grown man, and a promising physicist, working at Niels Bohr's institute in Denmark. The first night, arriving late, he was in no condition for discussing science. The next morning, when he came down to the ground-floor restaurant at their hotel, he found his aunt puzzling over Hahn's letter. The barium they had added was showing such persistent radioactivity— so much spraying out of energy streams—that she and the researchers in Berlin couldn't help but wonder why. Had it somehow been created that way during the Berlin experiments?

  Frisch suggested that it was just a mistake in Hahn's experiment, but his aunt waved that aside. Hahn was no genius, but he was a good chemist. Other labs made mistakes. Not hers. Frisch didn't take much convincing. He knew she was right.

  They stayed at the breakfast table while Frisch ate, talking it over. The experiment that Meitner had suggested to the Berlin crew could be explained if the uranium atom had somehow split apart. A barium nucleus is about half the size of a uranium nucleus. What if the barium they were detecting was simply one of the big halves that had resulted? But by everything nuclear physics had been showing—all the work from Rutherford on up—that should be impossible. There are over 200 particles inside a uranium nucleus, all those protons and neutrons. They were stuck together with what is known as the strong nuclear force, an exceptionally powerful nuclear glue. How could a single incoming neutron break through every one of those bonds, to tear off a huge chunk? You don't throw a simple pebble at a large boulder and expect the boulder to break in half.

  They finished breakfast, then went for a walk in the snow. Their hotel wasn't far from a forest. Frisch put on skis, and offered to help his aunt with a pair for herself, but she declined ("Lise Meitner made good her claim," Frisch wrote, "that she could walk just as fast without").

  No one had ever chipped off more than a fragment from a nucleus. They were confused. Even if an incoming neutron had hit some sort of weak point, how could dozens of protons be pulled off in one impact? The nucleus wasn't built like a rocky cliff that could break in half. It was supposed to remain intact for billions of years.

  Where could the energy to suddenly tear it apart come from?

  Meitner had first met Einstein at a conference in Salzburg, in 1909. They were almost exactly the same age, and Einstein was already famous. At the conference he recapped his 1905 findings. To find that energy could appear out of disappearing mass was "so overwhelmingly new and surprising," Meitner recounted decades later, "that to this day I remember the lecture very well."

  Now, in the snow with her nephew, she stopped by a tree trunk, and they settled down to work it out. The most recent model of the nucleus was due to Niels Bohr, the kindly soft-spoken Dane who was her nephew's employer. Instead of looking at the nucleus as a rigid metal, some stiffened collection of ball bearings welded tight, Bohr viewed it more as a liquid drop.

  A water drop is always on the verge of bursting apart, due to the weight inside it. That near-bursting weight is like the crackling electric charges between the protons in a nucleus. All the protons push against each other. (That's what two positive charges will always do.) But a water drop stays together, most of the time, because it also has a lot of rubbery surface tension on the top. That is like the glue-taut strong force that clusters the protons together, despite all the electricity trying to push them apart.

  In a small nucleus, such as that of carbon or lead, the gluing strong force is so great that it doesn't matter that there's a lot of electrical power hidden away inside, trying to push the protons apart. It won't win. But in a big nucleus, a really huge one such as that of uranium, could the extra neutrons tip the balance?

  Meitner and her nephew weren't physicists for nothing. They had paper with them, and pencils, and in the cold of the Swedish forest, this Christmas Eve, they took them out and began calculating. What if it turned out that the uranium nucleus was so big, and so crammed with extra neutrons spacing apart the protons in there, that even before you started artificially pushing extra neutrons in, it was already in a pretty precarious state? That would be as if the uranium nucleus were a water droplet that already was stretched apart as far as it could go before bursting. Into that overstuffed nucleus, one more plump neutron was then inserted.

  Meitner started to draw the wobbles. She drew as well as she played the piano. Frisch took a pencil from her, politely, and did the sketches. The single extra neutron that came in made the nucleus begin to stretch in the middle. It was like taking a water balloon, and squeezing it in the middle. The two ends bulge out. If you're lucky, the rubber of the balloon will hold, and the water won't burst out. But keep on with it. Squeeze in some more, and when the balloon spreads sideways, let go until it rebounds back toward the center and then squeeze in the opposite way. Keep on repeating. Eventually the balloon will burst. Get your timing right, and you don't even have to squeeze very hard. Each time the water balloon is rebounding back, you just let it reach its maximum rebound, and then—as with pumping on a swing—you give it a further squeeze to speed it on its way into yet another rubber-stretching contortion.

  In the uranium nucleus, that's what the incoming neutrons had been doing. The reason Hahn had so much trouble classifying what he saw was that he'd been convinced adding neutrons would only make a substance heavier. But, in fact, he'd cracked the uranium in half.

  It was a crucial insight, if true, but they'd have to check it. To start with, they knew that the electricity of the protons within the nucleus could now be available to make the bits fly apart. In the units by which physicists keep count, that's about 200 MeV—200 million electron volts. Frisch and Meitner worked that out mostly in their heads. But would Einstein's 1905 equation prove that there really was that amount of energy available inside to send the nucleus roaring apart? Frisch takes up the story:

  Fortunately [my aunt] remembered how to compute the masses of nuclei . . . and in that way she worked out that the two nuclei formed by the division of a uranium nucleus would be lighter than the original uranium nucleus, by about one-fifth the mass of a proton. Now whenever mass disappears, energy is created, according to Einstein's formula E=mc2. . . .

  But how much energy would that be? One-fifth of a proton is a preposterously tiny speck of matter. The dot over a letter / has many more protons than there are stars in our galaxy. Yet the "disappearance" of that fifth of a proton—this subvisible speck—has to be enough to generate 200 MeV of energy. In Berkeley, California, a building-sized magnet was being planned that might, when charged with more electricity than the whole city of Berkeley ordinarily used, power up a particle to 100 MeV of energy. And now this speck was supposed to produce even more.

  It would seem impossible—except for the immense size of c2. The world of mass, and the world of energy, are linked by that frantically widening bridge. From our perspective, the fragment of a proton slips across the roadway of that "=" sign: transforming; growing.

  Growing.

  They had crossed a river on their walk out from Kungalv, but it was frozen. The village was too far away to hear any market noises. Meitner did the calculation. Frisch remembered later: "One-fifth of a proton mass was just equivalent to 200 MeV. So here was the source for that energy; it all fitted!"

  The atom was open. Everyone had been wrong before. The way in wasn't by blasting harder and harder fragments at it. One woman, and her nephew, quiet in the midday snow, had now seen that. You didn't even have to supply the power for a uranium atom to explode. Just get enough extra neutrons in there to start it off. Then it would start jiggling, more and more wildly, until the strong forces that held it together gave way, and the electricity inside made the fragments fly apart. This explosion powered itself.

  Meitner and h
er nephew considered their science politically neutral, so they prepared their discovery for publication. It had to be named, and Frisch was reminded of how bacteria divide. Back in Copenhagen he asked a visiting American biologist at Bohr's institute for the right word in English. The label fission, accordingly, to describe how atomic nuclei divide, was introduced in his ensuing paper. Hahn had already published the Berlin findings, with minimal credit to Meitner, and soon began a nearly quarter-century-long campaign to pretend that all the credit was really his own.

  The thirty-year quest was over. In the decades since Einstein's equation first appeared in 1905, physicists had shown how the atom could be opened, and the compressed and frozen energy that E=mc2 spoke about let out. They'd found the nucleus, and a particle called the neutron that could get in and out of the nucleus pretty easily (especially if one used the trick of sending it in slowly), and they'd found that when extra neutrons were pushed into overstuffed atoms such as uranium, the whole nucleus wobbled, and trembled, and then exploded.

  What Meitner had realized was that this could occur because of the way the powerful electricity within the nucleus was held in by the springs or glue of the strong nuclear force. When an extra neutron made the nucleus start wobbling, those springs gave way, and the inner parts flew apart with wild energy. If you checked all the weights before and after, you'd find that the bits flying apart "weighed" less than when they were still held together in the nucleus. That "disappeared" mass was what powered their high-velocity escape. For it hadn't truly disappeared. The deep insights behind the equation had guaranteed that it would simply become apparent in the form of energy, getting the powerful c2 boost to magnify it (in units of mph2) by nearly 450,000,000,000,000,000 times.

  It was an ominous finding, for in theory anyone could use it to start cracking apart nuclei, those central cores of atoms, and letting out these great blasts of energy. In any other era, the next steps might have taken place slowly, with the first atomic bomb only appearing some time in the 1960s or 1970s. But in 1939, the world had just begun its largest war ever.

  The race was on to see in which country the equation's power would emerge first.

  PART 4

  Adulthood

  Germany's Turn I0

  By 1939, Einstein was far from being the unknown young man whose father had to beg a Leipzig professor to give him a job. His work in relativity had made him the most famous scientist in the world. He had been Berlin's leading professor, and when anti-Jewish mobs and politicians had made it impossible to stay there, he went to America, in 1933, taking up a position at the new Institute for Advanced Study in Princeton, New Jersey.

  When Einstein heard of Meitner's results and how other research teams were beginning to extend it, colleagues were able to get one of the president's own confidants to carry a personal letter direct to the White House.

  F. D. Roosevelt,

  President of the United States,

  White House

  Washington, D.C.

  Sir:

  Some recent work . . . which has been communicated to me in manuscript, leads me to expect that the element uranium may be turned into a new and important source of energy in the immediate future. Certain aspects of the situation which has arisen seem to call for watchfulness and, if necessary, quick action on the part of the Administration. . . .

  This new phenomenon would . . . lead to the construction of bombs, and it is conceivable—though much less certain—that extremely powerful bombs of a new type may thus be constructed. A single bomb of this type, carried by boat and exploded in a port, might well destroy the whole port together with some of the surrounding territory. . . .

  Yours very truly,

  Albert Einstein

  Unfortunately, it met with this reply:

  THE WHITEHOUSE

  WASHINGTON

  October 19,1939

  My dear Professor,

  I want to thank you for your recent letter and the most interesting and important enclosure.

  I found this data of such import that I have convened a board. . . . Please accept my sincere thanks.

  Very sincerely yours,

  Franklin Roosevelt

  Even someone who'd only been in America for a few years, as Einstein had, would understand that "most interesting" was a brush-off. Presidents are constantly sent impractical ideas. There's an obligation to be polite when the sender is famous, but FDR and his colleagues did not believe a bomb could possibly destroy a whole port.

  Albert Einstein

  IMAGE SELECT/ART RESOURCE, NEW YORK

  The letter was shuttled away from FDR's desk, and ended up in the hands of Lyman J. Briggs, the easygoing, pipe-smoking director of the federal government's Bureau of Standards. He would be responsible for all U.S. atomic bomb development.

  In the long history of governments assigning the wrong man to a job—and there have been some choice ones—this is one of the choicest. Briggs had entered government service during the administration of Grover Cleveland, in 1897, before the Spanish-American war. He was a man of the past, comfortable with that time when everything had seemed easier, and America had been safe. He wanted to keep it that way.

  In April 1940, Meitner's nephew, Robert Frisch, then in England, was beginning to convince the British authorities that a practical bomb could be built. A top-secret memo carrying the news was later rushed to Washington. By then there had been massive battles throughout Europe; panzer armies had overrun ever more countries. But you couldn't trick Lyman J. Briggs. That darn-foolish Brit report could be a danger if it ever got out. He locked it in his safe.

  Germany's bureaucrats, even scientifically untrained ones, took the opposite view of history. What good was the recent past? It had only led to the sellout at the end of World War I, the corruption of the Weimar Republic, inflation, and then unemployment. The beckoning future would be better. That's why there was such belief in new roads, new cars, new machines—and new conquests. The latest laboratory speculations also promised something new and powerful. Joseph Goebbels later noted in his diary: "I received a report about the latest developments in German science. Research in the realm of atomic destruction has now proceeded to a point where . . . tremendous destruction, it is claimed, can be wrought with a minimum of effort. . . . It is essential that we be ahead of everybody. . . ."

  And they had just the man for the job.

  In the summer of 1937, early in the month of July, Werner Heisenberg was on top of the world. He was the world's greatest living physicist after Einstein, famous for his work in quantum mechanics and the Uncertainty Principle. He had just been married, and now was returning after an extended honeymoon to the old family apartment in Hamburg, where his mother still lived, and the old five-foot-long electrically operated battleship he'd made as a teenager was still on display. He had a pleasant phone call to make, for he'd also been appointed to a senior position at the same university department where he'd earned his own Ph.D., as the wonder of the German academic establishment almost fifteen years earlier. He dialed the university's rector from his mother's phone.

  Heisenberg had a way of standing with shoulders squared straight, in a state of alert excitement, whenever he was pleased. The call went through, but the rector told him there was a serious problem. An elderly physicist, Johannes Stark, had convinced the weekly magazine of the SS to run an anonymous article saying that Heisenberg wasn't sufficiently patriotic, that he had worked with the Jews, didn't have the proper pro-German spirit, etc.

  This was the sort of public attack that often preceded a late-night arrest and then deportation to a concentration camp. Heisenberg was scared, but also furious. They were picking on the wrong man! It's true he'd worked with Jewish physicists, but Bohr and Einstein and the great physicist Wolfgang Pauli and so many others were Jewish or partly Jewish that he'd had no choice. Despite that he'd always stood up for his country in public discussions, defending Hitler's actions; he'd always faithfully rejected job offers from top foreign
universities.

  Heisenberg tried enlisting closest friends to help, but that had no effect. Soon he was brought for questioning to the basement of SS headquarters at Prinz-Albert-Strasse in Berlin, where the walls were uncovered cement, and the mocking sign "Breathe deeply and calmly" was up. (He wasn't beaten, and one of the interrogators had taken a Ph.D. at Leipzig for which Heisenberg was an examiner, but his wife later said he had nightmares about it for years.) Only when there were no signs of the SS attack letting Lip did he enlist one more ally, the woman who was closest to him of all: his mother.

  The Heisenbergs were from the educated middle class, and so were the Himmlers, and Heisenberg's mother had known Heinrich Himmler's mother from the time they were young. In August, Mrs. Heisenberg went to see Mrs. Himmler, in her small but very clean apartment, where fresh flowers were always placed in front of the crucifix, and she passed along a letter from her son.

  At first Mrs. Himmler didn't want to bother her son by delivering it, but as Heisenberg later recalled, his mother played the trump card: " (Oh, you know, Mrs. Himmler, we mothers know nothing about politics— neither your son's nor mine. But we know that we have to care for our boys. That is why I have come to you.' And she understood that."

  It worked.

  [From the office of the director of the SS]

  Very Esteemed Herr Professor Heisenberg!

  Only today can I answer your letter of July 21,1937, in which you direct yourself to me because of the article of Professor Stark. . . .