E=mc2

by David Bodanis

  Roosevelt's letter of October 19, 1939, in Einstein on Peace, ed. Otto Nathan and Heinz Norden (New York: Simon & Schuster, 1960), p. 297.

  "I received a report. . .": This diary entry jumps ahead from the main narrative; Goebbels made it in 1942, after the February meeting where Heisenberg made a powerful presentation to a number of Nazi officials, explaining how easily one could proceed with a bomb.

  . . . he'd always faithfully rejected the job offers . . . : See, David Cassidy, Uncertainty: The Life and Science of Werner Heisenberg (New York: Freeman, 1992), pp. 412-14.

  . . . his wife later said he had nightmares . . . : Ibid., p. 390.

  "Oh, you know, Mrs. Himmler . . .": Alan Beyerchen, Scientists Under Hitler (New Haven, Conn.: Yale University Press, 1977), pp. 159-60. The interview with Beyerchen took place 34 years after the events; possibly Heisenberg's playing up his mother's naïveté.

  "Very Esteemed Herr Professor . . .": The letter is reproduced in Samuel Goudsmit, Alsos: The Failure in German Science (London: Sigma Books, 1947), p. 119.

  What would have been a near miss . . . : This is the operation of the famous Uncertainty Principle, which had been worked out largely by Heisenberg in the mid-1920s. It's an odd effect—but central to how E = mc2 came to finally be removed from the laboratory, and turned into such an overpowering force on Earth. It's also, like E = mc2, one of those immensely powerful equations that can be written out in a brief space; in its essence it's simply ?x.?v?h. The ?x is the inexactitude in measuring where a particle is, and ?v is the inexactitude in measuring the velocity at which it's moving. (The symbol "h" is the extremely small figure known as Planck's constant.)

  What the ? in the equation says is that reality's accuracy has a little seesaw or teeter-totter built into it. If you start measuring a particle's location more accurately, then you'll start measuring its velocity less accurately, and vice versa. When one goes up, the other goes down.

  This has no direct effect on the large objects around us in ordinary life, but on the micro level, and in what Heisenberg was trying to do in 1940, it's crucial. If you slow down a neutron that you're propelling at a target, then you'll be able to measure its velocity more accurately than you could before. By the "teeter-totter" of the Uncertainty Principle, however, this means you won't be able to measure its location as accurately. In symbols, as the ?v gets less, the ?x gets bigger.

  That might seem just a matter of clever words, but—as with the curios of relativity in our earlier chapters—it really does come true. Because Ax is larger, there's a greater spread in our possibility of specifying the neutron's location. That means its interaction with the target changes. For what is a fruitful definition of an incoming object's size? Simply how likely it is that it'll contact the nucleus it's being shot at.

  It can be irritating to think that this is as good a definition of "size" as one can get, but again, think of the way that in special relativity there was no objective background or "true" time within which events could be placed. To feel that there is a "true" size that can be measured is, indeed, in itself a violation of the Uncertainty Principle. Thus a baseball glove or cricket glove allows you to catch balls which otherwise you would have missed: the size of your hand has effectively increased, due to the extra webbing. But if a viewer knew very little about the game, and just caught a quick blur of the catch on a TV screen, it would be just as plausible for the viewer to conclude that it was the ball that had enlarged, and that this was why fielders could suddenly make such spectacular catches.

  With the Uncertainty Principle, there's no way of getting past that blur. The incoming neutron has slowed down, the likelihood of there being a "catch" has gone up— and that's as much explanation as we're going to get of why the target has "become" larger. (In real life the Principle is probabilistic, and the effective "widening" only applies to a sequence of neutrons being shot out.)

  The Uncertainty Principle was fundamental to how E=mc2 was released, for it was used in many other calculations needed to construct a bomb. (The electrons in an atom, for example, can't be going too fast—they'd fly away, otherwise—but that constraint on their speed means there's a decreased detail available for any calculations about their actual location within an atom.)

  "Germany has actually stopped the sale . . .": The letter is widely quoted. See, e.g., Einstein: A Centenary Volume, ed. A. P. French, p. 191.

  But Heisenberg had a procurement organization . . .: Much of the timing is clarified in Mark Walker's German National Socialism and the quest for nuclear power 1939-1949 (Cambridge: Cambridge University Press, 1989); see especially pp. 132-3. It was in 1943 that the women were "bought" from Sachsenhausen; at the same time, Russian prisoners of war were being used in other aspects of the bomb project (they were forced to work, for example, on Bagge's isotope sluice). Late in the war, when parts of the Kaiser Wilhelm Institute for Physics was being relocated to the Hechingen area, Heisenberg was informed that Polish slave labor would be available.

  . . . female "slaves": With the passage of time, it is easy to forget what attitudes the individuals who worked in Germany during the war were accepting; what words like bought and slave actually meant. There are tens of thousands of pages in the Nuremberg Trial documentation; on November 15, 1947, the New York Herald Tribune reported the firsthand testimony behind just one:

  Nuremberg, November 14,1947 (A.P.) A French witness testified today that the I. G Farben combine purchased 150 women from the Oswiecim [Auschwitz] concentration camp>after complaining about a price 0/200 marks (then $80.00) each, and killed all of them in experiments with a soporific drug.

  The witness was Gregoire M. Afrine. He told the American military tribunal trying 23 Farben directors on war crimes charges that he was employed as an interpreter by the Russians after they overran the Oswiecim camp in January 1945 and found a number of letters there. Among the letters, he said, were some addressed from Farben s "Bayer"plant to the Nazi commandant of the camp. These excerpts were offered in evidence:

  1. In contemplation of experiments with a new soporific drug we would appreciate your procuring for us a number of women.

  2. We received your answer but consider the price of 200 marks a woman excessive. We propose to pay not more than iyo marks a head. If agreeable, we will take possession of the women. We need approximately 150.

  3. We acknowledge your accord. Prepare for us 150 women in the best possible condition, and as soon asyou advise us you are ready we will take charge of them.

  4. Received the order ofiyo women. Despite their emaciated condition, they were found satisfactory. We shall keep you posted on developments concerning the experiment.

  5. The tests were made. All subjects died. We shall contact you shortly on the subject of a new load.

  Heisenberg had expressed his impatience . . . : On Heisenberg's sense of urgency, see, e.g., Cassidy, Uncertainty, pp. 428-89.

  "I have now learned that research . . .": Einstein on Peace, Otto Nathan and Hans Norden (New York: Schocken, 1968), p. 299.

  ". . . this office would not recommend the employment of Dr. Einstein . . .": Richard A. Schwartz, "Einstein and the War Department," Isis, 80, 302 (June 1989), pp. 282-83.

  Lawrence was not especially bright . . . : Again, as with Hahn, brightness is a relative matter. Lawrence understood his own limitations—"You've got to practically crucify yourself if you're going to amount to anything" he'd explained to an assistant when he was first teaching at Berkeley (in Nuel Phar Davis, Lawrence and Oppenheimer, London: Jonathan Cape, 1969, p. 16)—and, in part, as a result Lawrence was exceptionally keen on tracking outside developments which he could incorporate for his own work. His great success was improving a Norwegian's method for accelerating charged particles—it was the basis of the cyclotron, and ultimately what won him his Nobel Prize. Such anxious "borrowing" is central to one sort of successful lab: See Kealey's Economic Laws of Scientific Research in the Guide to Further Reading for Chapters 8 and 9.

  "a tiny cube
of uranium . . .": Davis, Lawrence and Oppenheimer, p. 99.

  . . . a practical engineering degree . . . : Wigner, Recollections of Eugene P. Wigner (New York: Plenum Press, 1992), pp. 59-62. The caution was widespread: even the intellectually awesome von Neumann took a chemical engineering qualification along with his doctorate in mathematics summa cum laude. Einstein also kept involved in practical inventions—a better electrical current monitor; an improved refrigerator—in part for similar reasons.

  What shape . . . should the uranium be . . . : The points are presented on p. 40 of Jeremy Bernstein's introduction to his Hitler's Uranium Club. Bernstein's work has been central to my understanding of German work on the bomb; I've drawn on it throughout these chapters. Note that when other teams in Germany showed that cubes were in fact the more efficient shape, Heisenberg resisted their findings till most of the war was over—much like his suppression of the views of German researchers who argued for moderators other than the heavy water he preferred.

  . . . flat surfaces . . . have the easiest properties to compute . . . : It's a common weakness. The F-117 Stealth fighter, for example, has sharp angular lines not because they're especially aerodynamic—they're not—but because the 1970s computers that were used to analyze its properties couldn't handle anything more rounded. See Ben Rich and Leo Janos, Skunk Works: A Personal Memoir of My Years at Lockheed (Boston: Little, Brown, 1994), p. 21.

  The United States had an army . . . below the tenth rank . . . : How much a backwater America still was—both intellectually, and militarily—in the late 1930s is often overlooked. If anything, it was the U.S. experience in running such administrative/military efforts as the Manhattan Project that contributed to the triumphantly confident postwar view.

  11. Norway

  . . . already was a perfectly sound heavy water factory . . . [in] Norway: It was actually a fertilizer factory, attached to a large hydroelectric installation. When hydrogen and oxygen are separated to make fertilizer, it's easy to accumulate heavy hydrogen. The heavy water was built up from that.

  It was a fateful decision . . . : Academic families in pre-1945 Germany were often among the most nationalistic, identifying easily with the militarily-proud Berlin government. Many of these families saw Germany's rise as dependent on such "heroic" moves as the attacks on Denmark and Austria in the 1860s and on France in 1870, and the invasion of Belgium in 1914.

  When those expansions collapsed in 1918 the feeling of being trapped simply got stronger. There were constant reminders: When Heisenberg was dominating the world's physics establishment with his 1920s work in quantum mechanics, French occupation troops—often of the lowest quality—were still on his nation's soil. The result was a querulous, resentful tone in much of the country's elite— and so a burst of satisfaction, when finally, in the first successful years from 1936 on, the long-delayed expansion could begin again.

  "democracy can't develop sufficient energy . . .": Cassidy, Uncertainty, p. 473; indeed all of Chapter 24 are recommended. See also, e.g., Abraham Pais, Neils Bohr's Times (Oxford: Oxford University Press, 1991), p. 483 as well as Walker, German National Socialism, pp. 113-115.

  "It fell to me . . .": R. V Jones, "Thicker than Water," in Chemistry and Industry, August 26,1967, p. 1422.

  "Halfway down we sighted our objective . . .": Knut Haukelid, Skis Against the Atom (London: William Kimber, 1954; revised 1973, London: Fontana), p. 68.

  "Where trees grow, a man can make his way": Ibid., p. 65.

  12. America's Turn

  [Ernest Lawrence's] personnel skills made Heisenberg look considerate . . . : Which does not mean that Lawrence's managerial style couldn't produce benefits in another fashion. For Lawrence ended up collecting students who prospered in his sort of environment. Many of them stole from each other, or snipped out each other's names from original copies of experimental results, yet the Berkeley lab was never strictly immoral. It was "amoral"— and that's very different. Many of its members simply raced in any way possible to fulfill what the outside world wanted. If prestige in medicine came from finding tools to cure disease, then that's what they would back-stab to achieve.

  When E = mc2 and associated technologies opened up a range of new opportunities, Lawrence's squabbling young men became some of the main controllers of the "spigot" carrying those new powers into our world. They supplied the improved medical tracers to de Hevesy and his colleagues; they worked on improved devices for practical X-ray focusing, for radiotherapy in cancer, and much else. After the war the atomic bomb project opened a gushing well—of grants, contacts; technical knowledge—and Lawrence's men simply happened to be very experienced at pressing to the front of whatever well they saw. An entire book could be written on the interplay between the ethical and practical issues involved.

  America's own physics establishment had been so weak . . . : But this was changing fast. For the way returning postdoctoral fellows seeded prime universities in the U.S., see Daniel J. Kevles, The Physicists: The History of a Scientific Community in Modern America (Cambridge, Mass.: Harvard University Press, 1995); especially Chapter 14.

  "In July 1939, Lawrence . . .": Emilio Segre, A Mind Always in Motion (Berkeley: University of California Press, 1994), pp. 147-48.

  . . . factories thousands of feet long . . . able to filter toxic uranium clouds: And this—not the space program—is where Teflon got its first commercial use. The pumps controlling the Tennessee factory filters needed sealants that would be immune to the highly reactive vapor. Substances where fluorine atoms wrap protectively around carbon chains are ideal; the resultant polytetrafluoroethylene is what later became shortened to Teflon. Eventually it was realized that a substance that toxic uranium clouds weren't going to stick to would have little problem with the frying pan residues of ordinary suburban kitchens. When the same polytetrafluoroethylene is stretched to form a membrane, Goretex is the result.

  "He said he appeared not to believe in the eventual success . . .": Peter Goodchild, /. Robert Oppenheimer: Shat-terer of Worlds (New York: Fromm, 1985), p. 80.

  "It won't be any trouble . . .": Alice Kimball Smith's 1976 interview with Nedelsky, in Robert Oppenheimer: Letters and Recollections, ed. A. K. Smith and Charles Weiner, (Palo Alto: Stanford University Press, 1995), p. 149.

  One team . . . was simply trying to pull out the most explosive component of natural uranium: This is the famous U235, which forms a bit under 1 percent of ordinary uranium, whose main ores are the calmer U238. One way to remember the difference is that you can hold 50 pounds of U238 in your cupped hands, and only feel a slight warmth, but if you ever found two separate 25-pound chunks of U235 and decided to bring them together, the best details your next of kin could hope to get would have to be supplied by CNN helicopter-borne camera crews, using extreme telephoto lenses to get pictures of the blast site and crater.

  A more humdrum way to remember the difference between these two types of uranium is by focusing on the nature of even and odd numbers. Since U238 has 238 particles in its nucleus, everything inside that nucleus is "paired off: an incoming neutron isn't going to have any loose partner to affect easily. But since U235 has an odd number of 235 particles in its nucleus, that means there are 46 pairs of protons and 71 pairs of neutrons—and one extra neutron. That's the vulnerable one. When a fresh neutron arrives from the outer world, it easily reacts with the spare neutron; the result is now 46 tightly bound pairs of protons and 72 tightly bound pairs of neutrons. When a nucleus is configured in this "tighter" way, it's much easier for potentially fissile segments to shoot out. Why that happens— and how it produces a lower energy barrier—is at the heart of practical atomic engineering.

  Although . . . there were exceptions . . . : The Du Pont engineers who constructed the setting for the Hanford reactor core knew little of atomic physics, but they did know the basic engineering principle that something's always going to go wrong, and you need to allow extra architectural space for the fixes. When the first full running of the reactor slowed due to
xenon building up as a by-product of the reaction, they had left enough extra space—following Wheeler's earlier suggestion—that it was easy to increase the amount of uranium used without tearing apart and rebuilding the reactors. The extra uranium's power more than made up for the xenon. See John Archibald Wheeler, Geons, Black Holes, and Quantum Foam (New York: Norton, 1998), pp. 55-59.

  . . . a ball of plutonium . . . low-density: The phrase low-density is of course relative; it's still far denser than lead. The significant point is that it's not dense enough to self-ignite.

  "It stinks!": Nuel Phar Davis, Lawrence and Oppenheimer (London: Jonathan Cape, 1969), p. 216.

  Teller was vain enough . . . : Teller's private project was the hydrogen bomb, a device far more powerful than what could be built out of uranium. The fact that Oppenheimer later had doubts about its necessity was one of the reasons a petulant Teller testified against Oppenheimer in post-war loyalty hearings.

  "All that day Serber amused herself. . . ": Serber, The Los Alamos Primer (Berkeley: University of California Press, 1992), p. 32. From the same page: "I remember someone at Los Alamos saying that he could order a bucket of diamonds and it would go through Purchasing without a question, whereas if he ordered a typewriter he would need . . . to get a priority number and submit a certificate of need."

  "It is possible . . .": Richard Rhodes, The Making of the Atomic Bomb (New York: Simon & Schuster, 1986), pp. 511-12. I've added the layout of addressee and date.

  Even a few pounds . . . uninhabitable for years: What could Germany have plausibly achieved? Probably not an entire bomb, but a reactor using carbon dioxide as a moderator rather than heavy water had been strongly pushed by Paul Harteck, the physical chemist based in Hamburg. It would have been easy to construct with the uranium supplies and engineering skills Germany had; the large amounts of highly radioactive substance produced would have been simple to mount on a V-i or V-2. Note that Otto Skorzeny seems to have proposed launching a radioactive weapon from a submarine to explode in New York. Coming from ordinary staff planners, that proposal could have been discounted, but Skorzeny was the man who'd organized and led the glider-borne assault that snatched Mussolini from an "impregnable" mountain prison in 1943. Certainly Nazi submarines could easily reach the East Coast of the United States, and occasional ones had been equipped to launch small planes.