E=mc2

by David Bodanis

  Because you were recommended by my family I have had your case investigated with special care and precision.

  I am glad that I can now inform you that I do not approve of the attack . . . and that I have taken measures against any further attack against you.

  I hope I shall see you in Berlin in the fall, in November or December, so that we may talk things over thoroughly man to man.

  With friendly greetings,

  Heil Hitler!

  Yours,

  H. Himmler

  P.S. I consider it, however, best if in the future you make a distinction for your audience between the results of scientific research and the personal and political attitude of the scientists involved.

  The P.S., it was understood, meant that Heisenberg could use Einstein's results on relativity and E=mc2, but he had to show he disavowed Einstein himself, and gave no support to the sort of liberal or internationalist views—such as supporting the League of Nations or speaking out against racism—that Einstein and other Jewish physicists had been known for taking.

  These terms weren't hard for Heisenberg to accept. In his teens he'd been active in the wandering clubs, where young Germans hiked for days or weeks at a time through wilderness areas, getting in contact with the true roots of their nation. Often, around the campfire, they'd talk of mystical heroes, and the way their country might regenerate in a hoped-for "Third" Reich, to be led—in the common phrasing of the time—by a sufficiently far-seeing leader, or Fuehrer. Many youngsters grew out of this, but well into his twenties Heisenberg remained drawn to the movement, despite mocking remarks from his more grown-up or liberal colleagues. During advanced university studies he'd regularly leave a seminar and meet up with a group of teenage boys, to lead them for a long walk and if possible a full night out in the woods, before racing back, by train, just in time for his next 9:00 A.M. lecture.

  When the German army's Weapons Bureau began work, in September, 1939—a month after Einstein's letter to FDR—Heisenberg was one of the first to volunteer to do anything that was needed. The Reich was already at war: its artillery and ground troops and air force and panzers successful in Poland. But there might well be greater enemies still to come. Heisenberg had always been an energetic worker, and now he surpassed himself. In December he delivered the first part of a comprehensive paper on how to construct a workable atomic bomb. In February, 1940, he had the full report done, and when a Berlin unit was set up to start building a reactor, in parallel with the work at his home university of Leipzig, he took command of both, regularly commuting between the two cities. It would have been tiring for most men, but Heisenberg was at the peak of his powers. He was still only in his thirties, a regular mountain-climber, a rugged horse rider, and active with two months' training each year in a mountain infantry unit, facing the Austrian border.

  The first tests were in Berlin, in an ordinary plank-walled building built on the wooded grounds not far from Meitner's old institute, under the cherry trees that bloomed so well in the warm, clear summer of 1940. To keep out the curious, the building was named "The Virus House." Heisenberg's first step was to load in enough uranium—far more than the fractions of an ounce Meitner had arranged for Hahn to try in 1938. Only a very few atoms had exploded apart then. The sample had been so thin that most of the neutrons that the atoms released simply sped off into the lab's empty air.

  Heisenberg ordered dozens of pounds of uranium. It wasn't hard to get, because the Reich's army had taken over Czechoslovakia a full year before invading Poland. Europe's largest uranium mines, which Marie Curie had once used, were at Joachimsthal there. The uranium was delivered. With the prestige of Heisenberg's name, the Weapons Bureau could ensure there were priority train shipments.

  Simply stacking together a large amount of uranium wouldn't get a reaction going. For a nucleus, as we saw, is a vanishingly tiny speck, deep in the empty spaces inside an atom. Most of the neutrons released by the first explosions would speed right past the nucleus, like an alien space probe hurtling through our solar system.

  Werner Heisenberg (seated third from right).

  He's wearing an armband in mourning for his father.

  AIP EMILIO SEGRE VISUAL ARCHIVES,

  PEIERLS COLLECTION

  The twist Fermi had found—that there was a great power in using slowed neutrons—could help solve this problem, and get a reaction to begin. Fast neutrons can be thought of as sleek, "streamlined" as they travel. But slow neutrons, as we've seen, can be thought of as more "wobbly"; more spread out. Even if their main body only comes close to one of the waiting nuclei, then part of the neutron—the "spread-out bit"—is likely to connect. What would have been a near miss of a nucleus if the neutron were coming in fast, becomes far more likely to be a "catch." When such a slow neutron gets caught or pulled in, circumstances are prepared for E=mc2 suddenly to operate: for the nucleus to wobble, then explode, letting out its great blasts of energy, and also, in the process, letting out a gush of extra neutrons, so that yet more atoms are hit, to wobble and explode apart in turn.

  Heisenberg searched for the right substance to produce that useful slowing of the neutrons. Anything that was dense with hydrogen would work to some extent, because the bumpings of neutrons against hydrogen tends to slow the neutrons down. That was why Fermi, back in 1934, had managed to get some effect even with ordinary water (H20) from the goldfish pond on the grounds of his institute. But when the first German teams tried spreading ordinary water around a uranium sample, although there were a few crackling reactions at the center of the sample, where the first uranium atoms broke apart, the neutrons that gushed out were still moving too fast to get the reaction to spread.

  Heisenberg needed a better moderator. He knew that around the time when Fermi had been working, a U.S. chemist, Harold C. Urey, had discovered that the water in all the world's oceans and lakes is not composed merely of H20. Mixed in with it is a variant molecule, slightly heavier. Instead of having ordinary hydrogen at the core, it has deuterium, which is very similar to hydrogen but weighs about twice as much. Aside from that it is the same as ordinary water—it's just as free-flowing, and transparent; it's part of our rain and ice and seas; we drink it all the time. But there's only one molecule of it for every 10,000 molecules of ordinary water, which is why "heavy water" had been overlooked before. (A large swimming pool has only about a drinking glass's worth spread within it.) But heavy water is superb at slowing down high-velocity neutrons. They smack into the heavier deuterium and start ricocheting, slowing with each bounce, and emerge a fraction of a second later, after several dozen ricochets, floating much slower than when they went in.

  German labs had accumulated only a few gallons of heavy water at first. This wasn't enough to be shared between Leipzig and Berlin. Heisenberg's sentiments were more with Leipzig, so it was in the basement of the physics institute there that the most important tests were prepared. As 1940 went on, the precious heavy water was poured in with the several pounds of stacked uranium. The mix of heavy water and uranium was packed into a tough spherical containment vessel, then dangled from a hoist while measuring devices were set up around it. Professors weren't supposed to get involved with the minutiae of experiments, but Heisenberg prided himself on his practical skills as much as on his theoretical gifts. He had built some of those measuring devices himself, with Robert Dopel, the main experimenter in charge.

  When the uranium and heavy water were in place, and the measuring devices set up closely around the container, the experiment was ready to begin. Gunpowder needs a match to start. Dynamite needs a blasting cap. For an atomic reaction, even one that's in uranium of too low a quality to lead to a full explosion, there has to be an initial source of emerging neutrons. Dopel had left a hole in the bottom of the containment vessel. The neutron source was a small amount of radioactive substance, similar to the one Chadwick had used. It was brought over, contained in a single long probe, and now, for the first time—in an experiment that began in February 1941—a
ll the working parts that could come together in a bomb were in place.

  When Dopel and Heisenberg gave the instructions, the probe would go in, and the first speeding neutrons would be let loose inside the uranium. A few of the uranium atoms would burst, flying apart much faster than anyone would have suspected before Meitner explained how E=mc2 was operating. Even more neutrons would spray out in the fast debris. They'd pass without much effect through the first layers of uranium atoms they hit, but when they reached the heavy water they'd be caught bouncing back and forth till they slowed down. When they reached the next layer of uranium metal they'd be wobbling so slowly, and so dispersedly, that they would be much more likely now to connect with the uranium nuclei, and especially the most fragile ones, and overload them, making them wobble, and tremble, and then explode apart in turn.

  Each one would be another crackling occurrence of E=mc2, in a sequence that Geiger counters would show building up faster and faster. In the first few millionths of a second—by Heisenberg's calculations—there would be perhaps 2,000 explosions. In the next millionths of a second there would be 4,000. Then 8,000, then 16,000, and so on. Doubling on that time scale rushes upward very quickly. If everything worked, there would be trillions of these minute explosions still in only a fraction of a second, and then hundreds of trillions, and the cascading effect would keep on going. It would be a "rip" in the ordinary fabric of matter, as all the energy that had been squeezed inside these atoms for billions of years now came out: there in the basement of the Leipzig institute; in this university run by officers appointed from Reich headquarters; with students proudly wearing the swastika in the classrooms above. To explode apart a billion atoms, you wouldn't need to set up an enormous laboratory, with a billion initiating neutron machines. Once a very few atoms started, the debris fragments they sent out—loaded with neutrons—would quickly start up the rest. This first uranium wasn't purified enough to produce a runaway reaction, but it would be a start.

  The professors gave the instruction. Dopel's assistant, Wilhelm Paschen, inserted the probe. It was early 1941. The initiating neutrons were inside the uranium! Everyone stared at the dials to record the result.

  And nothing happened.

  There wasn't enough uranium to get a reaction going. Heisenberg wasn't fazed, and simply ordered more, from the enterprising Berlin Auer company, which over the years had moved on from toothpaste, and was now a wholesale supplier of a whole range of uranium products. Its raw supplies were no problem, as Einstein had also warned in his letter to FDR. ("Germany has actually stopped the sale of uranium from the Czechoslovakia mines which she has taken over," Einstein had written, ". . . while the most important source of uranium is the Belgian Congo.") The Union Miniere in occupied Belgium had thousands of pounds stockpiled from those Congo mines. When the Joachimsthal stockpiles ran low, the Germans turned there next.

  Machining uranium into a usable form was hard, since it demands a lot of labor, plus the fine uranium dust that's produced is dangerous for the workers. But Heisenberg had a procurement organization to draw on that wasn't hindered by outmoded notions of human rights. Germany had many concentration camps, full of people who were soon to be killed anyway. Why shouldn't important projects get some advantage from them? As the war went on, Berlin Auer executives calmly bought female "slaves" from the Sachsenhausen concentration camp. They could be worked to prepare the uranium oxide the German project needed. Back in April 1940, Heisenberg had expressed his impatience at how long the first Auer shipments were taking. The administrative head of the army project assured him that Berlin Auer would have its work force operating at maximum speed. Supplies had started coming in that summer, and now in 1941, even more was quickly shipped.

  In autumn 1941 there were more promising tests, and finally, in spring 1942, the breakthrough happened. The containment vessel was pouring out neutrons: 13 percent more than the inserted source had pumped inside it to start with. The trapped energy that Einstein had first spoken of nearly 40 years before was now being released. It was as if a narrow funnel was stretching up from deep underground, and a thundering wind—the released energy—was blowing fast along it. Himmler's faith was justified. Heisenberg—triumphant—had managed to get the power of Einstein's equation to come roaring up, and appear in Nazi Germany.

  Einstein was getting hints of Heisenberg's success, for the director of the Kaiser Wilhelm Institute for Physics had been Dutch, and when he too was expelled, ending up in America, he shared with his new colleagues what he'd heard of the work at the Virus House and Leipzig.

  Einstein wrote another letter to FDR: "I have now learned that research in Germany is carried out in great secrecy and that it has been extended to another of the Kaiser Wilhelm Institutes, the Institute of Physics." But this time it seems that there wasn't even the courtesy of a reply. A white-haired foreigner is one thing, especially if he has a grand reputation in science. But tensions were rising as war got closer, and the FBI now saw reasons to discount anything he said. For Einstein was a socialist, and a Zionist—and he had even spoken out against excess profits for arms manufacturers. The FBI reported back to army intelligence that:

  In view of his radical background, this office would not recommend the employment of Dr. Einstein, on matters of a secret nature, without a very careful investigation, as it seems unlikely that a man of his background could, in such a short time, become a loyal American citizen.

  When the United States finally did get a serious atomic project started, it was helped through some skillful manipulations by impatient visitors from Britain. Mark Oliphant was another one of Rutherford's bright young men, and in the summer of 1941 he led a two-front assault. First he arrived in Washington, dangling the gift of the cavity magnetron—a key device for shrinking room-sized radar sets to a volume that could be crammed into an airplane, and also for greatly increasing accuracy. (This was when Oliphant discovered that Lyman J. Briggs, leader of the West's atomic research project, had locked the top-secret British results inside his safe.) Next, Oliphant traveled to Berkeley, where the physicist Ernest Lawrence worked.

  Lawrence was not especially bright as physicists go, but he loved machines, great big powerful machines, and his very simplicity—his directness of focus—allowed him to get them built. For example, Samuel Allison (working at the University of Chicago then) remembers that Briggs had "a tiny cube of uranium which he liked to keep on his desk and show to insiders. . . . Briggs used to say, (I want a whole pound of this,' . . . Lawrence would have said he wanted forty tons and got it."

  By the autumn of 1941 Briggs was out, and a group of more effective leaders including Lawrence was in, and by December—when Pearl Harbor brought the United States into the war—the project really took off. It came to be called the Manhattan Project, as part of the cover story that it was simply part of the Manhattan Engineering District.

  The refugees Briggs had scorned were indispensable. Eugene Wigner, for example, was a remarkably quiet, unassuming young Hungarian, who came from an equally quiet and unassuming family. When World War I had broken out, Eugene's father had stayed away from political discussions, pointing out, quite sensibly, that he was pretty sure the emperor was not going to be swayed by the views of the Wigner family. But this caution meant that when Eugene, a superb student, was facing university choices, the father had him take a practical engineering degree, as the odds on a career in theoretical physics succeeding were very slight.

  Wigner did succeed at physics, and after he was forced out of Europe in the 1930s, he ended up centrally involved in the American duplicate of Heisenberg's calculations, detailing how a reaction could begin. But his engineering training meant that he handled the subsequent steps far better than Heisenberg. What shape, for example, should the uranium be that would go inside a reactor? The most efficient possible design would be a sphere. That way the maximum number of neutrons would be deep in the center. Next best—if a sphere was too hard to cut accurately—would be an oval shape. After that
comes a cylinder, then a cube, and last, worst of all, would be to try building it with the uranium stretched out in flat sheets.

  For his Leipzig device, Heisenberg had chosen the flat sheets. The reason was simply that flat surfaces almost always have the easiest properties to compute, if you're advancing by pure theory. But engineers with enough practical experience are never restricted to pure theory. There are many informal tricks of the trade for how ovals and other shapes work. Wigner knew them, as did many other similarly cautious refugees, who'd also been advised by their families to take engineering degrees. Heisenberg did not. That was of central importance. Professors in general tend to be hierarchical, and pre-World War II German professors were at the peak of such confidence. As the war went on, a number of junior researchers in Germany found that Heisenberg had been mistaken in one engineering assumption or another. But Heisenberg almost always refused to listen; would angrily try to keep them from even daring to mention it.

  Even so, nobody could be confident the United States was going to win the race to make the bomb. America was just coming out of the Great Depression; much of its industrial base was still rusted and abandoned. When Heisenberg began his research for army ordnance, the Wehrmacht was the world's most powerful fighting force. It had entire army groups supplied with equipment that surpassed that of any other nation. The United States had an army that, if you included a lot of generation-old World War I artifacts, could just about supply two divisions, thus placing it below the tenth rank in the world, at about the level of Belgium.

  Germany also had the world's best engineers, and a strong university system—despite having expelled so many Jews—and above all, they had that head start: two precious years when Heisenberg and his colleagues had been working full out, while Briggs had mostly been musing at his desk. These were the quirks of fate that would influence who ended up using the equation first. E=mc2 was far from the pure reaches of Einstein's inked symbols now. The Allied effort would have to go faster.