Copenhagen

by Michael Frayn

  Bohr I never shot Hendrik Casimir.

  Heisenberg You told me you did.

  Bohr It was George Gamow. I shot George Gamow. You don’t know—it was long after your time.

  Heisenberg Bohr, you shot Hendrik Casimir.

  Bohr Gamow, Gamow. Because he insisted that it was always quicker to act than to react. To make a decision to do something rather than respond to someone else’s doing it.

  Heisenberg And for that you shot him?

  Bohr It was him! He went out and bought a pair of pistols! He puts one in his pocket, I put one in mine, and we get on with the day’s work. Hours go by, and we’re arguing ferociously about—I can’t remember—our problems with the nitrogen nucleus, I expect—when suddenly Gamow reaches into his pocket …

  Heisenberg Cap-pistols.

  Bohr Cap-pistols, yes. Of course.

  Heisenberg Margrethe was looking a little worried.

  Margrethe No—a little surprised. At the turn of events.

  Bohr Now you remember how quick he was.

  Heisenberg Casimir?

  Bohr Gamow.

  Heisenberg Not as quick as me.

  Bohr Of course not. But compared with me.

  Heisenberg A fast neutron. However, or so you’re going to tell me …

  Bohr However, yes, before his gun is even out of his pocket …

  Heisenberg You’ve drafted your reply.

  Margrethe I’ve typed it out.

  Heisenberg You’ve checked it with Klein.

  Margrethe I’ve retyped it.

  Heisenberg You’ve submitted it to Pauli in Hamburg.

  Margrethe I’ve retyped it again.

  Bohr Before his gun is even out of his pocket, mine is in my hand.

  Heisenberg And poor Casimir has been blasted out of existence.

  Bohr Except that it was Gamow.

  Heisenberg It was Casimir! He told me!

  Bohr Yes, well, one of the two.

  Heisenberg Both of them simultaneously alive and dead in our memories.

  Bohr Like a pair of Schrödinger cats. Where were we?

  Heisenberg Skiing. Or music. That’s another thing that decides everything for you. I play the piano and the way seems to open in front of me—all I have to do is follow. That’s how I had my one success with women. At a musical evening at the Bückings in Leipzig—we’ve assembled a piano trio. 1937, just when all my troubles with the … when my troubles are coming to a head. We’re playing the Beethoven G major. We finish the scherzo, and I look up from the piano to see if the others are ready to start the final presto. And in that instant I catch a glimpse of a young woman sitting at the side of the room. Just the briefest glimpse, but of course at once I’ve carried her off to Bayrischzell, we’re engaged, we’re married, etc—the usual hopeless romantic fantasies. Then off we go into the presto, and it’s terrifyingly fast—so fast there’s no time to be afraid. And suddenly everything in the world seems easy. We reach the end and I just carry on ski-ing. Get myself introduced to the young woman—see her home—and, yes, a week later I’ve carried her off to Bayrischzell—another week and we’re engaged—three months and we’re married. All on the sheer momentum of that presto!

  Bohr You were saying you felt isolated. But you do have a companion, after all.

  Heisenberg Music?

  Bohr Elisabeth!

  Heisenberg Oh. Yes. Though, what with the children, and so on … I’ve always envied the way you and Margrethe manage to talk about everything. Your work. Your problems. Me, no doubt.

  Bohr I was formed by nature to be a mathematically curious entity: not one but half of two.

  Heisenberg Mathematics becomes very odd when you apply it to people. One plus one can add up to so many different sums …

  Margrethe Silence. What’s he thinking about now? His life? Or ours?

  Bohr So many things we think about at the same time. Our lives and our physics.

  Margrethe All the things that come into our heads out of nowhere.

  Bohr Our private consolations. Our private agonies.

  Heisenberg Silence. And of course they’re thinking about their children again.

  Margrethe The same bright things. The same dark things. Back and back they come.

  Heisenberg Their four children living, and their two children dead.

  Margrethe Harald. Lying alone in that ward.

  Bohr She’s thinking about Christian and Harald.

  Heisenberg The two lost boys. Harald …

  Bohr All those years alone in that terrible ward.

  Heisenberg And Christian. The firstborn. The eldest son.

  Bohr And once again I see those same few moments that I see every day.

  Heisenberg Those short moments on the boat, when the tiller slams over in the heavy sea, and Christian is falling.

  Bohr If I hadn’t let him take the helm …

  Heisenberg Those long moments in the water.

  Bohr Those endless moments in the water.

  Heisenberg When he’s struggling towards the lifebuoy.

  Bohr So near to touching it.

  Margrethe I’m at Tisvilde. I look up from my work. There’s Niels in the doorway, silently watching me. He turns his head away, and I know at once what’s happened.

  Bohr So near, so near! So slight a thing!

  Heisenberg Again and again the tiller slams over. Again and again …

  Margrethe Niels turns his head away …

  Bohr Christian reaches for the lifebuoy …

  Heisenberg But about some things even they never speak.

  Bohr About some things even we only think.

  Margrethe Because there’s nothing to be said.

  Bohr Well … perhaps we should be warm enough. You suggested a stroll.

  Heisenberg In fact the weather is remarkably warm.

  Bohr We shan’t be long.

  Heisenberg A week at most.

  Bohr What—our great hike through Zealand?

  Heisenberg We went to Elsinore. I often think about what you said there.

  Bohr You don’t mind, my love? Half-an-hour?

  Heisenberg An hour, perhaps. No, the whole appearance of Elsinore, you said, was changed by our knowing that Hamlet had lived there. Every dark corner there reminds us of the darkness inside the human soul …

  Margrethe So, they’re walking again. He’s done it. And if they’re walking they’re talking. Talking in a rather different way, no doubt—I’ve typed out so much in my time about how differently particles behave when they’re unobserved … I knew Niels would never hold out if they could just get through the first few minutes. If only out of curiosity .… Now they’re started an hour will mean two, of course, perhaps three .… The first thing they ever did was to go for a walk together. At Göttingen, after that lecture. Niels immediately went to look for the presumptuous young man who’d queried his mathematics, and swept him off for a tramp in the country. Walk—talk—make his acquaintance. And when Heisenberg arrived here to work for him, off they go again, on their great tour of Zealand. A lot of this century’s physics they did in the open air. Strolling around the forest paths at Tisvilde. Going down to the beach with the children. Heisenberg holding Christian’s hand. Yes, and every evening in Copenhagen, after dinner, they’d walk round Faelled Park behind the Institute, or out along Langelinie into the harbour. Walk, and talk. Long, long before walls had ears … But this time, in 1941, their walk takes a different course. Ten minutes after they set out … they’re back! I’ve scarcely had the table cleared when there’s Niels in the doorway. I see at once how upset he is—he can’t look me in the eye.

  Bohr Heisenberg wants to say goodbye. He’s leaving.

  Margrethe He won’t look at me, either.

  Heisenberg Thank you. A delightful evening. Almost like old times. So kind of you.

  Margrethe You’ll have some coffee? A glass of something?

  Heisenberg I have to get back and prepare for my lecture.

  Margrethe But you�
��ll come and see us again before you leave?

  Bohr He has a great deal to do.

  Margrethe It’s like the worst moments of 1927 all over again, when Niels came back from Norway and first read Heisenberg’s uncertainty paper. Something they both seemed to have forgotten about earlier in the evening, though I hadn’t. Perhaps they’ve both suddenly remembered that time. Only from the look on their faces something even worse has happened.

  Heisenberg Forgive me if I’ve done or said anything that …

  Bohr Yes, yes.

  Heisenberg It meant a great deal to me, being here with you both again. More perhaps than you realise.

  Margrethe It was a pleasure for us. Our love to Elisabeth.

  Bohr Of course.

  Margrethe And the children.

  Heisenberg Perhaps, when this war is over .… If we’re all spared .… Goodbye.

  Margrethe Politics?

  Bohr Physics. He’s not right, though. How can he be right? John Wheeler and I …

  Margrethe A breath of air as we talk, why not?

  Bohr A breath of air?

  Margrethe A turn around the garden. Healthier than staying indoors, perhaps.

  Bohr Oh. Yes.

  Margrethe For everyone concerned.

  Bohr Yes. Thank you .… How can he possibly be right? Wheeler and I went through the whole thing in 1939.

  Margrethe What did he say?

  Bohr Nothing. I don’t know. I was too angry to take it in.

  Margrethe Something about fission?

  Bohr What happens in fission? You fire a neutron at a uranium nucleus, it splits, and it releases energy.

  Margrethe A huge amount of energy. Yes?

  Bohr About enough to move a speck of dust. But it also releases two or three more neutrons. Each of which has the chance of splitting another nucleus.

  Margrethe So then those two or three split nuclei each release energy in their turn?

  Bohr And two or three more neutrons.

  Heisenberg You start a trickle of snow sliding as you ski. The trickle becomes a snowball …

  Bohr An ever-widening chain of split nuclei forks through the uranium, doubling and quadrupling in millionths of a second from one generation to the next. First two splits, let’s say for simplicity. Then two squared, two cubed, two to the fourth, two to the fifth, two to the sixth …

  Heisenberg The thunder of the gathering avalanche echoes from all the surrounding mountains …

  Bohr Until eventually, after, let’s say, eighty generations, 280 specks of dust have been moved. 280 is a number with 24 noughts. Enough specks of dust to constitute a city, and all who live in it.

  Heisenberg But there is a catch.

  Bohr There is a catch, thank God. Natural uranium consists of two different isotopes, U-238 and U-235. Less than one per cent of it is U-235, and this tiny fraction is the only part of it that’s fissionable by fast neutrons.

  Heisenberg This was Bohr’s great insight. Another of his amazing intuitions. It came to him when he was at Princeton in 1939, walking across the campus with Wheeler. A characteristic Bohr moment—I wish I’d been there to enjoy it. Five minutes deep silence as they walked, then: ‘Now hear this—I have understood everything.’

  Bohr In fact it’s a double catch. 238 is not only impossible to fission by fast neutrons—it also absorbs them. So, very soon after the chain reaction starts, there aren’t enough fast neutrons left to fission the 235.

  Heisenberg And the chain stops.

  Bohr Now, you can fission the 235 with slow neutrons as well. But then the chain reaction occurs more slowly than the uranium blows itself apart.

  Heisenberg So again the chain stops.

  Bohr What all this means is that an explosive chain reaction will never occur in natural uranium. To make an explosion you will have to separate out pure 235. And to make the chain long enough for a large explosion …

  Heisenberg Eighty generations, let’s say …

  Bohr … you would need many tons of it. And it’s extremely difficult to separate.

  Heisenberg Tantalisingly difficult.

  Bohr Mercifully difficult. The best estimates, when I was in America in 1939, were that to produce even one gram of U-235 would take 26,000 years. By which time, surely, this war will be over. So he’s wrong, you see, he’s wrong! Or could I be wrong? Could I have miscalculated? Let me see .… What are the absorption rates for fast neutrons in 238? What’s the mean free path of slow neutrons in 235 …?

  Margrethe But what exactly had Heisenberg said? That’s what everyone wanted to know, then and forever after.

  Bohr It’s what the British wanted to know, as soon as Chadwick managed to get in touch with me. What exactly did Heisenberg say?

  Heisenberg And what exactly did Bohr reply? That was of course the first thing my colleagues asked me when I got back to Germany.

  Margrethe What did Heisenberg tell Niels—what did Niels reply? The person who wanted to know most of all was Heisenberg himself.

  Bohr You mean when he came back to Copenhagen after the war, in 1947?

  Margrethe Escorted this time not by unseen agents of the Gestapo, but by a very conspicuous minder from British intelligence.

  Bohr I think he wanted various things.

  Margrethe Two things. Food-parcels …

  Bohr For his family in Germany. They were on the verge of starvation.

  Margrethe And for you to agree what you’d said to each other in 1941.

  Bohr The conversation went wrong almost as fast as it did before.

  Margrethe You couldn’t even agree where you’d walked that night.

  Heisenberg Where we walked? Faelled Park, of course. Where we went so often in the old days.

  Margrethe But Faelled Park is behind the Institute, four kilometres away from where we live!

  Heisenberg I can see the drift of autumn leaves under the street-lamps next to the bandstand.

  Bohr Yes, because you remember it as October!

  Margrethe And it was September.

  Bohr No fallen leaves!

  Margrethe And it was 1941. No street-lamps!

  Bohr I thought we hadn’t got any further than my study. What I can see is the drift of papers under the reading-lamp on my desk.

  Heisenberg We must have been outside! What I was going to say was treasonable. If I’d been overheard I’d have been executed.

  Margrethe So what was this mysterious thing you said?

  Heisenberg There’s no mystery about it. There never was any mystery. I remember it absolutely clearly, because my life was at stake, and I chose my words very carefully. I simply asked you if as a physicist one had the moral right to work on the practical exploitation of atomic energy. Yes?

  Bohr I don’t recall.

  Heisenberg You don’t recall, no, because you immediately became alarmed. You stopped dead in your tracks.

  Bohr I was horrified.

  Heisenberg Horrified. Good, you remember that. You stood there gazing at me, horrified.

  Bohr Because the implication was obvious. That you were working on it.

  Heisenberg And you jumped to the conclusion that I was trying to provide Hitler with nuclear weapons.

  Bohr And you were!

  Heisenberg No! A reactor! That’s what we were trying to build! A machine to produce power! To generate electricity, to drive ships!

  Bohr You didn’t say anything about a reactor.

  Heisenberg I didn’t say anything about anything! Not in so many words. I couldn’t! I’d no idea how much could be overheard. How much you’d repeat to others.

  Bohr But then I asked you if you actually thought that uranium fission could be used for the construction of weapons.

  Heisenberg Ah! It’s coming back!

  Bohr And I clearly remember what you replied.

  Heisenberg I said I now knew that it could be.

  Bohr This is what really horrified me.

  Heisenberg Because you’d always been confident that weapons wo
uld need 235, and that we could never separate enough of it.

  Bohr A reactor—yes, maybe, because there it’s not going to blow itself apart. You can keep the chain reaction going with slow neutrons in natural uranium.

  Heisenberg What we’d realised, though, was that if we could once get the reactor going …

  Bohr The 238 in the natural uranium would absorb the fast neutrons …

  Heisenberg Exactly as you predicted in 1939—everything we were doing was based on that fundamental insight of yours. The 238 would absorb the fast neutrons. And would be transformed by them into a new element altogether.

  Bohr Neptunium. Which would decay in its turn into another new element …

  Heisenberg At least as fissile as the 235 that we couldn’t separate …

  Margrethe Plutonium.

  Heisenberg Plutonium.

  Bohr I should have worked it out for myself.

  Heisenberg If we could build a reactor we could build bombs. That’s what had brought me to Copenhagen. But none of this could I say. And at this point you stopped listening. The bomb had already gone off inside your head. I realised we were heading back towards the house. Our walk was over. Our one chance to talk had gone forever.

  Bohr Because I’d grasped the central point already. That one way or another you saw the possibility of supplying Hitler with nuclear weapons.

  Heisenberg You grasped at least four different central points, all of them wrong. You told Rozental that I’d tried to pick your brains about fission. You told Weisskopf that I’d asked you what you knew about the Allied nuclear programme. Chadwick thought I was hoping to persuade you that there was no German programme. But then you seem to have told some people that I’d tried to recruit you to work on it!

  Bohr Very well. Let’s start all over again from the beginning. No Gestapo in the shadows this time. No British intelligence officer. No one watching us at all.

  Margrethe Only me.

  Bohr Only Margrethe. We’re going to make the whole thing clear to Margrethe. You know how strongly I believe that we don’t do science for ourselves, that we do it so we can explain to others …

  Heisenberg In plain language.

  Bohr In plain language. Not your view, I know—you’d be happy to describe what you were up to purely in differential equations if you could—but for Margrethe’s sake …

  Heisenberg Plain language.