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Heisenberg in Copenhagen: An Exchange

To the Editors:

I wish to address myself to some of the technical issues that Thomas Powers brings up in connection with his response to Paul Lawrence Rose’s letter concerning Heisenberg’s wartime visit to Copenhagen [NYR, October 19, 2000]. I am in disagreement with both Powers’s and Rose’s analysis of the reasons for this meeting and have come to believe that we may never fully know the answer, although we will know more when the letter that Bohr wrote to Heisenberg, but never sent, is released in 2012—the fiftieth anniversary of Bohr’s death. Nonetheless we can get the technical details straight, which Powers has not done.

It is totally wrong to say, as Powers does, that the “random walk” method of estimating the critical mass, which Heisenberg first used at Farm Hall, is a “shorthand way.” It is an entirely incorrect way. Picture a sphere of uranium undergoing fission. In each fission roughly two neutrons are produced. The sphere must be large enough so that more neutrons are created in the fission than diffuse through its surface. The equation that determines this balance has one term that refers to the diffusion and another that refers to the buildup of the fission neutrons. What Heisenberg did was in essence to leave out this term. He later included it in a lecture he gave at Farm Hall and got more or less the correct answer.

There is no evidence that he or anyone else in the German project did this calculation correctly during the war.1 In June of 1942 Heisenberg was asked how much uranium a nuclear bomb would use that could destroy London. If one kilogram of uranium could be completely fissioned it would produce an explosion equal to about twenty thousand tons of TNT; about the size of the Hiroshima bomb. This would correspond to a sphere of uranium with a radius of a little over two centimeters—a ping- pong ball. But in a real bomb only about 2 percent of the uranium is fissioned so that about a hundred kilograms of uranium are needed, which corresponds to a radius of about eight and a half centimeters. At Farm Hall Heisenberg did not seem to have a clear idea of the efficiency question, so it is totally unclear to me what he had in mind when, in 1942, he apparently indicated that it was the shape of a pineapple. Powers also refers to Heisenberg’s discussion of “tampers”—material wrapped around the bomb to enhance the explosive effect. In Farm Hall Heisenberg was clearly thinking like a reactor physicist here. Tampers in bombs have very different requirements.

Finally I would like to comment on the famous drawing which Bohr presented at Los Alamos on December 31, 1943. I am responsible for bringing this matter to light in a profile of Hans Bethe I wrote for The New Yorker.2 Both Powers and Rose are persuaded that Heisenberg transmitted this drawing—which turned out to be a design for a reactor—directly to Bohr in Copenhagen. They insist on this despite the fact that Bohr’s son Aage, who was Bohr’s confidant at the time, has insisted that this did not happen. Of the drawing Bethe wrote me, “I am positive that there was a drawing. Niels Bohr presented it to us, and both Teller and I immediately said, ‘This is a drawing of a reactor, not of a bomb.’…Whether the drawing was actually due Heisenberg [sic] or was made by Bohr from memory I cannot tell….” I contacted every living person who was at that meeting and none of them could tell either. I think that Aage Bohr is right and that the drawing came to his father from someone else in the project—there were other visitors to Copenhagen—and not from Heisenberg.

Jeremy Bernstein

Aspen, Colorado

To the Editors:

The evidence for and against Heisenberg’s having made a serious calculation of the critical mass of an atomic bomb is, as Thomas Powers says in his reply to Paul Lawrence Rose’s letter, complex. There is a brief summary of it in my postscript to the published text of Copenhagen, together with my reasons for dissenting from Powers (and Rose), and for reaching the conclusion presented in the play (that he didn’t make it). If I’m mistaken about this, however, and Heisenberg did make it, then the bulk of the evidence seems to me to support Powers’s view that by one means or another he got the answer about right and not Rose’s that he got it totally wrong.

Some of Professor Rose’s other points I find a little mystifying. He says that Heisenberg’s trip to Copenhagen was “an intelligence foray…with the purpose of ascertaining how far the Allied project had progressed….” This suggestion is fully explored in the play, and indeed my Heisenberg entirely accepts that it was so. Professor Rose suggests that I “fantasize” Heisenberg’s fear that he was in danger of his life from the Gestapo for talking to Bohr. I can’t claim the credit for any fantasy here, I’m afraid. My Heisenberg is merely paraphrasing what the real Heisenberg claims in his memoirs: “I did not broach the dangerous subject until we took our evening walk. Since I had reason to think that Niels was being watched by German agents, I spoke with the utmost circumspection.”

Rose claims that the notion that Heisenberg “would say anything treasonous to Bohr is hardly credible.” But he also claims that an additional purpose of his conversation was “establishing whether a nuclear weapon was scientifically feasible.” Since Heisenberg knew that Bohr regarded atomic weapons as a practical impossibility in any remotely imaginable time-scale, I don’t understand how he could plausibly have done this unless, as he claims in his memoirs, he had at the very least “hinted that it was now possible in principle to build atom bombs”; and I don’t understand how any such hint, made to an enemy alien by someone working on a secret military program, could have failed to be treasonous.

Michael Frayn


Thomas Powers replies:

My chief worry, whenever I find myself arguing about Heisenberg in print, is that readers who happen by won’t understand what the dispute is about. At the heart of it, in my view, is an anomaly—why American

intelligence officers, in the closing months of the Second World War, discovered that not only was there no German atomic bomb, but there had not even been a big effort to build one.

This came as a surprise to the American Alsos mission at the time and it is still hard to explain. Fission had been discovered in Germany, scientists there had access to uranium ore and a Norwegian heavy water

plant, and the German military actively supported research into the feasibility of building a bomb virtually from the first day of hostilities in September 1939, a full two years before the American government took a serious interest. In a letter written to me a few years back the Italian physicist Ugo Fano described a party at the Ann Arbor, Michigan, home of Samuel Goudsmit, scientific director of the Alsos mission, in late August 1939. There two Nobel Prize–winning physicists, Werner Heisenberg, soon to return to Germany, and Enrico Fermi, a refugee from Mussolini’s Italy, were both honored guests. “At that party,” Fano writes, “[Edoardo] Amaldi drew me aside to point out its humor: ‘See Fermi, see Heisenberg, sitting in that corner. Everyone in this room expects a big war and the two of them to lead fission work on opposite sides, but nobody says!’” (Letter of September 18, 1993) Within a month Heisenberg had in effect been drafted to do theoretical work on bomb physics and he soon wrote two papers which were the basis of further German research during the war.

But the German military’s early interest in atomic bombs had died by the turn of the year 1941–1942 and in February the research effort was handed over to the Ministry of Education, where it languished till the end of the war. When an important official initiative is abandoned there usually remains a substantial paper record explaining the reasons for the turnabout, but not in this case. The only clear statement of the matter comes after the fact—from Albert Speer, Hitler’s newly appointed minister for economic mobilization, who described in his memoirs a meeting with Heisenberg and other German physicists in June 1942, when Heisenberg convinced him that developing atomic weapons was too big, too expensive, and too uncertain for Germany in wartime (Albert Speer, Inside the Third Reich, Macmillan, 1970, pp. 225ff).

That’s it—there is no other body of official paper to point to which might explain why the army dropped a program in which it had showed such a lively early interest. All the rest of the argument—not just Jeremy Bernstein’s letter above, but a shelf of books and numerous scholarly articles—finds its focus in the question which arises from the anomaly: Why did Heisenberg tell officials that a bomb was too difficult for Germany in wartime? Was he simply trying to save Germany a lot of wasted effort, or was he actively trying to hinder the development of atomic bombs?

This question should not have been difficult to answer. Heisenberg’s old friends among the Allies, many of whom had gone to Los Alamos to work on the American bomb, might have simply asked him, and my guess is that he would have answered pretty straightforwardly. But they didn’t ask, and when Heisenberg offered a tentative explanation after the war in an article in the British scientific journal Nature, he was roundly attacked. Soon he quit trying to explain himself, leaving it to historians to puzzle out what happened. To do this we must take into account all evidence of what Heisenberg did and said during the war, and in the end we must come to some conclusion about what he intended. There is really no way around this task; so far as we know the German interest in atomic bombs withered under Heisenberg’s emphasis on the difficulties, and his influence can-not be fairly judged until his motives are understood.

This brings me to Jeremy Bernstein’s letter, the latest in a series of exchanges between us on this matter, both privately and in print, going back ten years. He makes two points. The first is that I have failed to

understand how Heisenberg said he had calculated the critical mass of a bomb in a lecture delivered in August 1945 to fellow German scientists incarcerated by the British at Farm Hall in England. I warned readers at the time that I am no physicist and won’t attempt to sort out the “random walk” business here. It would be simpler to cite my source—an account by the British chief of scientific intelligence during the war, R.V. Jones, who described in print his discussion of Heisenberg’s Farm Hall lecture with his principal adviser on bomb questions, Charles Frank. Jones began with his memory of what Heisenberg had said:

Each of the last nuclei to explode [at the end of 80 generations of fission] would be on the average a distance away equal to a “drunkard’s walk” of 80 steps each equal to the mean distance that a neutron would travel in the uranium before striking another nucleus. Since this vital distance was thought to be a few centimeters, say 8 or 9, the final, nuclei would be 8 or 9 times the square root of 80, or about 80 centimeters away. This should be the radius of the bomb, giving a mass of about 40 tons.

When Frank read this account, he wrote Jones a letter amending it slightly:

As I remember it, Heisenberg gave just the calculation you quote, except that my memory says he reached the answer 5 tons…. He gave this calculation at the beginning of an elegant colloquium, delivered the day after they heard about Hiroshima, in which he used a rather polished version of diffusion-and-multiplication theory (which he was no doubt familiar with from their pile work) to arrive at an answer for critical mass of the order of 1 or a few kilograms. He gave the crude and faulty calculation at the beginning, as the way they had worked it out before, and I think he said it was the way he had worked it out, and I think he said it was the estimate he gave at the 1940 conference about what was to be done with nuclear fission in relation to the war. I think he said he had done the revised calculation overnight, and I think that the whole style of the lecture implied that he was presenting a result and argument new to him and to his audience. [Emphasis in original. R.V. Jones, Introduction to Alsos by Samuel A. Goudsmit, second edition, Tomash Publishers/American Institute of Physics, 1988, pp. xv–xvi.]

Bernstein interprets Heisenberg’s remarks, available to us since the 1992 release of the Farm Hall tapes recorded by British intelligence during the war, to mean that Heisenberg failed to calculate the critical mass of an atomic bomb earlier in the war. Because fissionable material is extremely difficult and expensive to manufacture, the amount of it necessary for a bomb—the “critical mass”—is by far the most important technical question to be asked before embarking on a bomb program. A figure on the order of tons would have made building a bomb impossible for any nation at the time, the United States included. From his interpretation of Heisenberg’s remarks on this point Bernstein concludes there was no German bomb, and no German bomb program, as the result of “simple incompetence”—the phrase he used in an article in the May 1999 issue of Commentary. In his letter he writes, “There is no evidence that he [Heisenberg] or anyone else in the German project did this calculation correctly during the war,” but in fact there is such evidence—in the Farm Hall discussion recorded on the night after Hiroshima, Otto Hahn, one of the ten German scientists, protested Heisenberg’s claim that huge amounts of fissionable uranium were required for a bomb. “But tell me why you used to tell me that one needed 50 kilograms of ‘235’ in order to do anything. Now you say one needs two tons.” (I am quoting Jeremy Bernstein’s extensively footnoted edition of Hitler’s Uranium Club: The Secret Recordings at Farm Hall, p. 118.

The German physicist Manfred von Ardenne confirms in his memoirs, as he did to me personally in an interview in 1989, that Hahn told him in 1940 that critical mass would be on the order of kilograms, not tons, citing Heisenberg as his source. The fact that Heisenberg had calculated a roughly correct value for critical mass is also demonstrated by his answer to a question during the June 1942 conference in Berlin with Albert Speer. In a letter to Samuel Goudsmit of October 3, 1948, Heisenberg wrote: “General Field Marshall Milch asked me approximately how large a bomb would be, of which the action was sufficient to destroy a large city. I answered at that time, that the bomb, that is the essentially active part, would have been about the size of a pineapple.” (Goudsmit papers, American Institute of Physics) The “essentially active part” of a bomb is called the core. Erich Bagge, who was also present at the meeting with Speer, told interviewers, including me, that Heisenberg had shaped his hands in the air to suggest an object about the size of a “football.” Anyone wondering just how big the core of a bomb might be should consult Picturing the Bomb: Photographs from the

Secret World of the Manhattan Project, by Rachel Fermi and Esther Samra (Abrams, 1995). On the back cover, and again on page 201, are photographs of Harold Agnew holding the core of the plutonium bomb which destroyed Nagasaki. It is about the size of a pineapple, a large honeydew melon, or a soccer ball.

Bernstein’s remark about tampers is opaque to me. He seems not to understand the purpose of a tamper in making a bomb. Heisenberg did, a fact which strongly indicates he had been thinking in a sophisticated way about bomb design.

There is much additional evidence that Heisenberg understood roughly how a bomb could be made, and that he was worried about what he knew. His visit to see his old friend Niels Bohr in Copenhagen in September 1941 makes this clear. He was given permission to make the trip by the German Foreign Office, without which no German civilian was allowed to travel during the war, but no evidence has ever surfaced to suggest that Heisenberg made the trip as part of some official mission. By his own account he went to discuss the possibility of atomic bombs, and by Bohr’s account, fragmentary as it is, Heisenberg told him the Germans were embarked on a bomb program and tried to discuss it further before an angry Bohr cut him off. Figuring out what happened at that meeting—the subject of Michael Frayn’s play Copenhagen—goes beyond the points raised by Bernstein here, but the fact of it offers important evidence that Heisenberg had his own agenda. Telling Bohr about the bomb program was obviously a major breach of German security regulations, as Frayn points out in his letter, and drawing for Bohr a sketch of a reactor only compounded the offense. I first learned of this sketch in Bernstein’s book Hans Bethe: Prophet of Energy, in which he writes:

In October [actually September] of 1941, Heisenberg, of his own initiative, made a visit to Copenhagen to see Bohr. The reason for this visit is not clear. It occurred just after Heisenberg had become certain that—in principle, at least—a bomb could be made. Perhaps he wanted to reach some understanding with Bohr that neither side could make a bomb, or perhaps he had some more devious intent. In any case, he succeeded only in convincing Bohr that the Germans were on the verge of making a bomb. He gave Bohr a drawing, of which Bethe said, “Later on, at Los Alamos, this drawing was transmitted to us by Bohr. It was clearly a drawing of a reactor, but when we saw it our conclusion was that these Germans were totally crazy—did they want to throw a reactor down on London?” In retrospect the Germans were not crazy at all. They knew perfectly well what to do with a reactor…. [pp. 77–78]

Later on I also had extensive discussions about this drawing with Bethe, who reproduced it for me in a drawing from memory—the original sketch having been lost. On the last day of 1943 at Los Alamos this sketch, and Bohr’s memory of what Heisenberg had told him two years earlier, became the subject of a day-long conference to determine whether the Germans were on the verge of making a bomb. Bohr by that time had convinced himself that Heisenberg might be planning some sort of weapon using slow neutrons but Bethe, Edward Teller, and others wrote up a paper, submitted to General Leslie Groves, dismissing Bohr’s theory as unworkable. The point here is that Bohr had been personally escorted to New Mexico by Groves, that an urgent conference was held to consider Bohr’s views within a day of his arrival, and that the subject of the conference was the sketch and Bohr’s extrapolation of what he thought Heisenberg had been trying to tell him about bomb design. My own view is that Heisenberg, finding Bohr in 1941 initially skeptical that anyone could build a bomb, drew the sketch in order to explain the manufacture of a new fissionable element (plutonium) as a way of convincing Bohr that the practical difficulties were not as great as he had hoped. (The sketch Bethe drew for me on September 23, 1989, of the sketch Heisenberg gave him is reproduced on this page.)

But now Bernstein has reversed himself; he no longer believes what Bethe told him in the late 1970s—that Bohr said this sketch had been drawn for him by Heisenberg. Bernstein attributes his change of mind to a denial by Bohr’s son, Aage, that Heisenberg ever drew such a sketch. I first learned of the sketch from Bernstein, and I believe he first learned of the younger Bohr’s denial from me, since I cited it in my 1993 book, Heisenberg’s War. The younger Bohr accompanied his father to Los Alamos and acted as his confidential secretary; why his memory of the sketch differs from Bethe’s I do not know, and it is apparent that Bernstein does not know either. For this reason Bernstein’s newfound doubts about the sketch strike me as odd and insubstantial. He interviewed Bethe repeatedly over a period of two years and got to know him well, I am sure. But the intimacy and trust established over this long period were somehow overthrown by whatever it was that Aage Bohr told Bernstein in “a message” which was “conveyed” by the late Abraham Pais. What could the younger Bohr have “conveyed” that was so convincing? Until I hear something with a little meat to it I’m going to continue to rely on the version of events Bethe gave to me, which went beyond, but in no way contradicts, what he told Bernstein. He mentioned it often in letters, and on November 27, 1991, he explicitly confirmed my understanding of the facts—that Bohr told Bethe that the sketch had been drawn for him by Heisenberg, and that he “told us about the sketch in the big group in Oppenheimer’s office on December 31.”

With or without the sketch the story is essentially the same—that Heisenberg had told Bohr about German efforts to build a bomb, and that Bohr had come up with a theory of how they might be going about it—a theory dismissed by the scientists at Los Alamos, not without resistance from the stubborn Bohr. The episode is important for what it tells us about Heisenberg’s frame of mind, and the fact that he sought out Bohr, told him bombs were possible, and wanted to discuss the matter further is strong evidence that there was more on his mind than trying to help Hitler win the war.

Explaining the “failure” of the German bomb program by the “simple incompetence” of Werner Heisenberg, one (along with Einstein and Niels Bohr) of the three greatest physicists of the twentieth century, strikes me as the conclusion of a man who is not really looking very hard. Something about Heisenberg’s wartime role clearly interests Bernstein; he continues to write about it, and he has gone to a lot of trouble to annotate the Farm Hall transcripts. But what he writes seems prompted by a kind of anxiety that Heisenberg is going to get away with something if Bernstein lets his guard down. In a decade of nibbling at the edges of the controversy he does not appear to me ever to have become genuinely curious about what happened, which I take to be the natural starting point. If he would step back, take a cleansing breath, and attack the whole question from the other end—by asking why the German military so quickly dropped a bomb program it had eagerly taken up—he would discover how difficult it is to identify an internal critic or opponent of the effort, with the exception of Heisenberg, who told the authorities it was too big, too expensive, and too uncertain for Germany in wartime. Maybe Bernstein would find something new and important; maybe not. But he would be dealing with the question that matters.

  1. 1

    A reader who would like more detail can consult The Los Alamos Primer by Robert Serber (University of California Press, 1992) or my Hitler’s Uranium Club (Copernicus, 2000).

  2. 2

    See my article “What Did Heisenberg Tell Bohr About the Bomb?” Scientific American, May 1995, p. 92.

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