Copenhagen

To the Hampstead Theatre yesterday for Michael Frayn’s play Copenhagen. The basic premise of the action was a visit in 1941 to Neils Bohr in Copenhagen, paid by the German physicist Werner Heisenberg. Bohr was the acknowledged father of atomic theory, and Heisenberg had co-invented quantum mechanics; they had previously worked together in Copenhagen. It was the height of the war, Denmark was under German occupation, and Denmark’s Jews were soon to be deported to the camps. Bohr himself was half Jewish, and in 1943 would escape to the USA via Britain to work on the Manhattan Project. Heisenberg was an ‘Ayrian’ physicist working in Nazi Germany. Because he embraced ‘Jewish’ physics—most of the pioneers of atomic physics at Göttingen where he worked were Jews—he was called a ‘White Jew’ in Nazi circles. Nevertheless, the subsequent suspicion regarding his visit, yet unresolved in spite of numerous interviews with Bohr and Heisenberg after the war, and the recent emergence of previously unpublished letters from Heisenberg to his wife, is that Heisenberg was seeking knowledge of the Allies progress in the construction of an atomic bomb. The corollary being that had he suspected that they were working on such a device, he potentially, would have had the knowledge and motivation to build a Nazi bomb.
 
Quantum Mechanics—the basis of atomic theory—has the curious attribute that it produces results which agree with experimental observations to a quite astonishing degree of accuracy, while having no point of contact with the real world as understood by classical physics. As one of the greatest physicists of the modern age, Richard Feynmann observed, ‘Anyone who thinks they understand quantum mechanics, doesn’t understand quantum mechanics.’  Thus, anyone seeking to add quantum mechanics to a discussion of the mechanics of building an atomic bomb and presenting the result to a mainly non-technical theatre audience, is swimming in shark-infested waters indeed.
 
The play was a three-hander, with Bohr, Heisenberg, and Bohr’s wife Margrethe, who acted as a sort of narrator or Geek chorus. Furthermore, it was set in the future when they were all ‘safely dead’, so the action included mention of history’s interpretation of the meeting, their own memories of it, the evidence after the war of actual German progress towards atomic power, and the development by the allies and then use of, the bomb on Japan. Intermixed were discussions about aspects of atomic theory and quantum mechanics, together with the mechanics of how to make a bomb. A recurring theme was uncertainty; if non-scientists know anything about Heisenberg, it is that he formulated the famous Uncertainty Principle. One formulation of this, is that the better you know the position of a particle, the less you know about its velocity and vice versa. Furthermore, the very act of measuring something, changes it. The uncertainty principle spelled the death-knell of a purely deterministic, classical world. In the play, this idea counterpointed with the ‘uncertainty’ of Heisenberg’s motive for the meeting. 
 
Even with (or perhaps because of) my long ago background in physics, I was frequently confused; it was necessary to concentrate the entire time. The Times theatre critic gave the play four stars, and the audience at our performance seemed to be appreciative; I’m guessing that they were both overawed by the outpouring of complex and esoteric information. My wife said she thought her head would explode. Much was said without proper explanation, and in my view confused the issue. For example, Bohr was credited, and it was mentioned several times, with the invention of ‘complementarity’, (which I was unfamiliar with and does not appear in the Wikipedia page on Bohr). This refers to the wave/particle duality of light and matter. Hardly an ‘invention’, more the naming of phenomena that existed and had to be accepted. To clarify: experiments confirm, unequivocally, that light takes the form of waves. Other experiments, equally unambiguous, prove that it has the nature of particles. Furthermore, and stranger still, fundamental particles like electrons, can be diffracted; since diffraction only works with waves, electrons and by extension matter, can also behave either like a wave or a particle. In my view, the play confused the wave/particle duality—hardly if ever mentioned—with Heisenberg’s formulation of quantum mechanics using matrix algebra as opposed to Erwin Schrödinger’s wave mechanics. The two are totally different mathematically, but they produce the same answers. However matrix algebra is fiendishly difficult, and nowadays people mostly use wave mechanics for calculations.
 
Then there was the question of the possible manufacture of a bomb. An atomic bomb is frighteningly simple in concept. All you need is a lump of fissionable material—say uranium 235—larger that the so-called critical mass, and it will explode spontaneously. The simplest bomb, that used on Nagasaki, used a cannon to fire a piece of uranium that was below critical mass into another piece of uranium, also below critical mass. As they came together, critical mass was exceeded, and they spontaneously exploded. The difficult part is refining the uranium. Natural uranium contains less than 1% of the U235 isotope; the rest is mostly U238. The numbers refer to the number of protons and neutrons in the nucleus, so U238 is very slightly heavier than U235. Since isotopes are chemically identical, a physical separation technique sensitive to the 1% difference in mass must be used. The only method available in the 1940s was diffusion, and this only works with a gas. The uranium was reacted with fluorine to produce uranium hexafluoride, and the gas was passed through myriads of filters, using the fact that the rate of diffusion goes with the square root of the mass. Uranium containing around 95% of U235 is needed for bomb manufacture. The process is enormously longwinded, and enormously expensive, so absolute confidence in the calculation of the amount needed is essential before you start.
 
Heisenberg made the case that he and Germany had not been developing a bomb by saying that he had calculated the critical mass of uranium needed to be 1000 kg, and it would have taken decades to enrich that amount. The actual amount needed was only 20 kg, so he was out by a factor of fifty and Bohr chided him for that, but it did appear to show that he had decided that such a weapon was not possible. In which case, why the visit?
 
Such from the action on stage, the programme notes, and my own knowledge, was I able to glean from the play. But it was hard work, and I really did not enjoy it. What the rest of the audience made of it is difficult to fathom. Science can be presented successfully in a theatre—Stoppard can do it, but he interlaces the action with sparkling wit and repartee. There were very few laughs in Copenhagen, and I was somewhat relieved when it was over.