Copenhagen

Act Two

Heisenberg It was the very beginning of spring. The first time I came to Copenhagen, in 1924. March: raw, blustery northern weather. But every now and then the sun would come out and leave that first marvellous warmth of the year on your skin. That first breath of returning life.

Bohr You were twenty-two. So I must have been … Thirty-eight.

Bohr Almost the same age as you were when you came in 1941.

Heisenberg So what do we do?

Bohr Put on our boots and rucksacks …

Heisenberg Take the tram to the end of the line …

Bohr And start walking!

Heisenberg Northwards to Elsinore.

Bohr If you walk you talk.

Heisenberg Then westwards to Tisvilde.

Bohr And back by way of Hillerød.

Heisenberg Walking, talking, for a hundred miles.

Bohr After which we talked more or less non-stop for the next three years.

Heisenberg We’d split a bottle of wine over dinner in your flat at the Institute.

Bohr Then I’d come up to your room …

Heisenberg That terrible little room in the servants’ quarters in the attic.

Bohr And we’d talk on into the small hours.

Heisenberg How, though?

Bohr How?

Heisenberg How did we talk? In Danish?

Bohr In German, surely.

Heisenberg I lectured in Danish. I had to give my first colloquium when I’d only been here for ten weeks.

Bohr I remember it. Your Danish was already excellent.

Heisenberg No. You did a terrible thing to me. Half-an-hour before it started you said casually, Oh, I think we’ll speak English today.

Bohr But when you explained …?

Heisenberg Explain to the Pope? I didn’t dare. That excellent Danish you heard was my first attempt at English.

Bohr My dear Heisenberg! On our own together, though? My love, do you recall?

Margrethe What language you spoke when I wasn’t there? You think I had microphones hidden?

Bohr No, no — but patience, my love, patience!

Margrethe Patience?

Bohr You sounded a little sharp.

Margrethe Not at all.

Bohr We have to follow the threads right back to the beginning of the maze.

Margrethe I’m watching every step.

Bohr You didn’t mind? I hope.

Margrethe Mind?

Bohr Being left at home?

Margrethe While you went off on your hike? Of course not. Why should I have minded? You had to get out of the house. Two new sons arriving on top of each other would be rather a lot for any man to put up with.

Bohr Two new sons?

Margrethe Heisenberg.

Bohr Yes, yes.

Margrethe And our own son.

Bohr Aage?

Margrethe Ernest!

Bohr 1924—of course — Ernest.

Margrethe Number five. Yes?

Bohr Yes, yes, yes. And if it was March, you’re right — he couldn’t have been much more than …

Margrethe One week.

Bohr One week? One week, yes. And you really didn’t mind?

Margrethe Not at all. I was pleased you had an excuse to get away. And you always went off hiking with your new assistants. You went off with Kramers, when he arrived in 1916.

Bohr Yes, when I suppose Christian was still only …

Margrethe One week.

Bohr Yes.… Yes.… I almost killed Kramers, you know.

Heisenberg Not with a cap-pistol?

Bohr With a mine. On our walk.

Heisenberg Oh, the mine. Yes, you told me, on ours. Never mind Kramers — you almost killed yourself!

Bohr A mine washed up in the shallows …

Heisenberg And of course at once they compete to throw stones at it. What were you thinking of?

Bohr I’ve no idea.

Heisenberg A touch of Elsinore there, perhaps.

Bohr Elsinore?

Heisenberg The darkness inside the human soul.

Bohr You did something just as idiotic.

Heisenberg I did?

Bohr With Dirac in Japan. You climbed a pagoda.

Heisenberg Oh, the pagoda.

Bohr Then balanced on the pinnacle. According to Dirac. On one foot. In a high wind. I’m glad I wasn’t there.

Heisenberg Elsinore, I confess.

Bohr Elsinore, certainly.

Heisenberg I was jealous of Kramers, you know.

Bohr His Eminence. Isn’t that what you called him?

Heisenberg Because that’s what he was. Your leading cardinal. Your favourite son. Till I arrived on the scene.

Margrethe He was a wonderful cellist.

Bohr He was a wonderful everything.

Heisenberg Far too wonderful.

Margrethe I liked him.

Heisenberg I was terrified of him. When I first started at the Institute. I was terrified of all of them. All the boy wonders you had here — they were all so brilliant and accomplished. But Kramers was the heir apparent. All the rest of us had to work in the general study hall. Kramers had the private office next to yours, like the electron on the inmost orbit around the nucleus. And he didn’t think much of my physics. He insisted you could explain everything about the atom by classical mechanics.

Bohr Well, he was wrong.

Margrethe And very soon the private office was vacant.

Bohr And there was another electron on the inmost orbit.

Heisenberg Yes, and for three years we lived inside the atom.

Bohr With other electrons on the outer orbits around us all over Europe.

Heisenberg Max Born and Pascual Jordan in Göttingen.

Bohr Yes, but Schrödinger in Zurich, Fermi in Rome.

Heisenberg Chadwick and Dirac in England.

Bohr Joliot and de Broglie in Paris.

Heisenberg Gamow and Landau in Russia.

Bohr Everyone in and out of each other’s departments.

Heisenberg Papers and drafts of papers on every international mail-train.

Bohr You remember when Goudsmit and Uhlenbeck did spin?

Heisenberg There’s this one last variable in the quantum state of the atom that no one can make sense of. The last hurdle …

Bohr And these two crazy Dutchmen go back to a ridiculous idea that electrons can spin in different ways.

Heisenberg And of course the first thing that everyone wants to know is, What line is Copenhagen going to take?

Bohr I’m on my way to Leiden, as it happens.

Heisenberg And it turns into a papal progress! The train stops on the way at Hamburg …

Bohr Pauli and Stern are waiting on the platform to ask me what I think about spin.

Heisenberg You tell them it’s wrong.

Bohr No, I tell them it’s very …

Heisenberg Interesting.

Bohr I think that is precisely the word I choose.

Heisenberg Then the train pulls into Leiden.

Bohr And I’m met at the barrier by Einstein and Ehrenfest. And I change my mind because Einstein — Einstein, you see? — I’m the Pope — he’s God — because Einstein has made a relativistic analysis, and it resolves all my doubts.

Heisenberg Meanwhile I’m standing in for Max Born at Göttingen, so you make a detour there on your way home.

Bohr And you and Jordan meet me at the station.

Heisenberg Same question: what do you think of spin?

Bohr And when the train stops at Berlin there’s Pauli on the platform.

Heisenberg Wolfgang Pauli, who never gets out of bed if he can possibly avoid it …

Bohr And who’s already met me once at Hamburg on the journey out …

Heisenberg He’s travelled all the way from Hamburg to Berlin purely in order to see you for the second time round …

Bohr And find out how my ideas on spin have developed en route.

Heisenberg Oh, those years! Those amazing years! Those three short years!

Bohr From 1924 to 1927.

Heisenberg From when I arrived in Copenhagen to work with you …

Bohr To when you departed, to take up your chair at Leipzig.

Heisenberg Three years of raw, bracing northern springtime.

Bohr At the end of which we had quantum mechanics, we had uncertainty …

Heisenberg We had complementarity …

Bohr We had the whole Copenhagen Interpretation.

Heisenberg Europe in all its glory again. A new Enlightenment, with Germany back in her rightful place at the heart of it. And who led the way for everyone else?

Margrethe You and Niels.

Heisenberg Well, we did.

Bohr We did.

Margrethe And that’s what you were trying to get back to in 1941?

Heisenberg To something we did in those three years.… Something we said, something we thought.… I keep almost seeing it out of the corner of my eye as we talk! Something about the way we worked. Something about the way we did all those things …

Bohr Together.

Heisenberg Together. Yes, together.

Margrethe No.

Bohr No? What do you mean, no?

Margrethe Not together. You didn’t do any of those things together.

Bohr Yes, we did. Of course we did.

Margrethe No, you didn’t. Every single one of them you did when you were apart. You first worked out quantum mechanics on Heligoland.

Heisenberg Well, it was summer by then. I had my hay fever.

Margrethe And on Heligoland, on your own, on a rocky bare island in the middle of the North Sea, you said there was nothing to distract you …

Heisenberg My head began to clear, and I had this very sharp picture of what atomic physics ought to be like. I suddenly realised that we had to limit it to the measurements we could actually make, to what we could actually observe. We can’t see the electrons inside the atom …

Margrethe Any more than Niels can see the thoughts in your head, or you the thoughts in Niels’s.

Heisenberg All we can see are the effects that the electrons produce, on the light that they reflect …

Bohr But the difficulties you were trying to resolve were the ones we’d explored together, over dinner in the flat, on the beach at Tisvilde.

Heisenberg Of course. But I remember the evening when the mathematics first began to chime with the principle.

Margrethe On Heligoland.

Heisenberg On Heligoland.

Margrethe On your own.

Heisenberg It was terribly laborious — I didn’t understand matrix calculus then … I get so excited I keep making mistakes. But by three in the morning I’ve got it. I seem to be looking through the surface of atomic phenomena into a strangely beautiful interior world. A world of pure mathematical structures. I’m too excited to sleep. I go down to the southern end of the island. There’s a rock jutting out into the sea that I’ve been longing to climb. I get up it in the half-light before the dawn, and lie on top, gazing out to sea.

Margrethe On your own.

Heisenberg On my own. And yes — I was happy.

Margrethe Happier than you were back here with us all in Copenhagen the following winter.

Heisenberg What, with all the Schrödinger nonsense?

Bohr Nonsense? Come, come. Schrödinger’s wave formulation?

Margrethe Yes, suddenly everyone’s turned their backs on your wonderful new matrix mechanics.

Heisenberg No one can understand it.

Margrethe And they can understand Schrödinger’s wave mechanics.

Heisenberg Because they’d learnt it in school! We’re going backwards to classical physics! And when I’m a little cautious about accepting it …

Bohr A little cautious? Not to criticise, but …

Margrethe … You described it as repulsive!

Heisenberg I said the physical implications were repulsive. Schrödinger said my mathematics were repulsive.

Bohr I seem to recall you used the word … well, I won’t repeat it in mixed company.

Heisenberg In private. But by that time people had gone crazy.

Margrethe They thought you were simply jealous.

Heisenberg Someone even suggested some bizarre kind of intellectual snobbery. You got extremely excited.

Bohr On your behalf.

Heisenberg You invited Schrödinger here …

Bohr To have a calm debate about our differences.

Heisenberg And you fell on him like a madman. You meet him at the station — of course — and you pitch into him before he’s even got his bags off the train. Then you go on at him from first thing in the morning until last thing at night.

Bohr I go on? He goes on!

Heisenberg Because you won’t make the least concession!

Bohr Nor will he!

Heisenberg You made him ill! He had to retire to bed to get away from you!

Bohr He had a slight feverish cold.

Heisenberg Margrethe had to nurse him!

Margrethe I dosed him with tea and cake to keep his strength up.

Heisenberg Yes, while you pursued him even into the sickroom! Sat on his bed and hammered away at him!

Bohr Perfectly politely.

Heisenberg You were the Pope and the Holy Office and the Inquisition all rolled into one! And then, and then, after Schrödinger had fled back to Zürich — and this I will never forget, Bohr, this I will never let you forget — you started to take his side! You turned on me!

Bohr Because you’d gone mad by this time! You’d become fanatical! You were refusing to allow wave theory any place in quantum mechanics at all!

Heisenberg You’d completely turned your coat!

Bohr I said wave mechanics and matrix mechanics were simply alternative tools.

Heisenberg Something you’re always accusing me of. ‘If it works it works.’ Never mind what it means.

Bohr Of course I mind what it means.

Heisenberg What it means in language.

Bohr In plain language, yes.

Heisenberg What something means is what it means in mathematics.

Bohr You think that so long as the mathematics works out, the sense doesn’t matter.

Heisenberg Mathematics is sense! That’s what sense is!

Bohr But in the end, in the end, remember, we have to be able to explain it all to Margrethe!

Margrethe Explain it to me? You couldn’t even explain it to each other! You went on arguing into the small hours every night! You both got so angry!

Bohr We also both got completely exhausted.

Margrethe It was the cloud chamber that finished you.

Bohr Yes, because if you detach an electron from an atom, and send it through a cloud chamber, you can see the track it leaves.

Heisenberg And it’s a scandal. There shouldn’t be a track!

Margrethe According to your quantum mechanics.

Heisenberg There isn’t a track! No orbits! No tracks or trajectories! Only external effects!

Margrethe Only there the track is. I’ve seen it myself, as clear as the wake left by a passing ship.

Bohr It was a fascinating paradox.

Heisenberg You actually loved the paradoxes, that’s your problem. You revelled in the contradictions.

Bohr Yes, and you’ve never been able to understand the suggestiveness of paradox and contradiction. That’s your problem. You live and breathe paradox and contradiction, but you can no more see the beauty of them than the fish can see the beauty of the water.

Heisenberg I sometimes felt as if I was trapped in a kind of windowless hell. You don’t realise how aggressive you are. Prowling up and down the room as if you’re going to eat someone — and I can guess who it’s going to be.

Bohr That’s the way we did the physics, though.

Margrethe No. No! In the end you did it on your own again! Even you! You went off skiing in Norway.

Bohr I had to get away from it all!

Margrethe And you worked out complementarity in Norway, on your own.

Heisenberg The speed he skis at he had to do something to keep the blood going round. It was either physics or frostbite.

Bohr Yes, and you stayed behind in Copenhagen …

Heisenberg And started to think at last.

Margrethe You’re a lot better off apart, you two.

Heisenberg Having him out of town was as liberating as getting away from my hay fever on Heligoland.

Margrethe I shouldn’t let you sit anywhere near each other, if I were the teacher.

Heisenberg And that’s when I did uncertainty. Walking round Faelled Park on my own one horrible raw February night. It’s very late, and as soon as I’ve turned off into the park I’m completely alone in the darkness. I start to think about what you’d see, if you could train a telescope on me from the mountains of Norway. You’d see me by the street-lamps on the Blegdamsvej, then nothing as I vanished into the darkness, then another glimpse of me as I passed the lamp-post in front of the bandstand. And that’s what we see in the cloud chamber. Not a continuous track but a series of glimpses — a series of collisions between the passing electron and various molecules of water vapour.… Or think of you, on your great papal progress to Leiden in 1925. What did Margrethe see of that, at home here in Copenhagen? A picture postcard from Hamburg, perhaps. Then one from Leiden. One from Göttingen. One from Berlin. Because what we see in the cloud chamber are not even the collisions themselves, but the water-droplets that condense around them, as big as cities around a traveller — no, vastly bigger still, relatively — complete countries — Germany … Holland … Germany again. There is no track, there are no precise addresses; only a vague list of countries visited. I don’t know why we hadn’t thought of it before, except that we were too busy arguing to think at all.

Bohr You seem to have given up on all forms of discussion. By the time I get back from Norway I find you’ve done a draft of your uncertainty paper and you’ve already sent it for publication!

Margrethe And an even worse battle begins.

Bohr My dear good Heisenberg, it’s not open behaviour to rush a first draft into print before we’ve discussed it together! It’s not the way we work!

Heisenberg No, the way we work is that you hound me from first thing in the morning till last thing at night! The way we work is that you drive me mad!

Bohr Yes, because the paper contains a fundamental error.

Margrethe And here we go again.

Heisenberg No, but I show him the strangest truth about the universe that any of us has stumbled on since relativity — that you can never know everything about the whereabouts of a particle, or anything else, even Bohr now, as he prowls up and down the room in that maddening way of his, because we can’t observe it without introducing some new element into the situation, a molecule of water vapour for it to hit, or a piece of light — things which have an energy of their own, and which therefore have an effect on what they hit. A small one, admittedly, in the case of Bohr …

Bohr Yes, if you know where I am with the kind of accuracy we’re talking about when we’re dealing with particles, you can still measure my velocity to within — what …?

Heisenberg Something like a billionth of a billionth of a kilometre per second. The theoretical point remains, though, that you have no absolutely determinate situation in the world, which among other things lays waste to the idea of causality, the whole foundation of science — because if you don’t know how things are today you certainly can’t know how they’re going to be tomorrow. I shatter the objective universe around you — and all you can say is that there’s an error in the formulation!

Bohr There is!

Margrethe Tea, anyone? Cake?

Heisenberg Listen, in my paper what we’re trying to locate is not a free electron off on its travels through a cloud chamber, but an electron when it’s at home, moving around inside an atom …

Bohr And the uncertainty arises not, as you claim, through its indeterminate recoil when it’s hit by an incoming photon …

Heisenberg Plain language, plain language!

Bohr This is plain language.

Heisenberg Listen …

Bohr The language of classical mechanics.

Heisenberg Listen! Copenhagen is an atom. Margrethe is its nucleus. About right, the scale? Ten thousand to one?

Bohr Yes, yes.

Heisenberg Now, Bohr’s an electron. He’s wandering about the city somewhere in the darkness, no one knows where. He’s here, he’s there, he’s everywhere and nowhere. Up in Faelled Park, down at Carlsberg. Passing City Hall, out by the harbour. I’m a photon. A quantum of light. I’m despatched into the darkness to find Bohr. And I succeed, because I manage to collide with him.… But what’s happened? Look — he’s been slowed down, he’s been deflected! He’s no longer doing exactly what he was so maddeningly doing when I walked into him!

Bohr But, Heisenberg, Heisenberg! You also have been deflected! If people can see what’s happened to you, to their piece of light, then they can work out what must have happened to me! The trouble is knowing what’s happened to you! Because to understand how people see you we have to treat you not just as a particle, but as a wave. I have to use not only your particle mechanics, I have to use the Schrödinger wave function.

Heisenberg I know — I put it in a postscript to my paper.

Bohr Everyone remembers the paper — no one remembers the postscript. But the question is fundamental. Particles are things, complete in themselves. Waves are disturbances in something else.

Heisenberg I know. Complementarity. It’s in the postscript.

Bohr They’re either one thing or the other. They can’t be both. We have to choose one way of seeing them or the other. But as soon as we do we can’t know everything about them.

Heisenberg And off he goes into orbit again. Incidentally exemplifying another application of complementarity. Exactly where you go as you ramble around is of course completely determined by your genes and the various physical forces acting on you. But it’s also completely determined by your own entirely inscrutable whims from one moment to the next. So we can’t completely understand your behaviour without seeing it both ways at once, and that’s impossible. Which means that your extraordinary peregrinations are not fully objective aspects of the universe. They exist only partially, through the efforts of me or Margrethe, as our minds shift endlessly back and forth between the two approaches.

Bohr You’ve never absolutely and totally accepted complementarity, have you?

Heisenberg Yes! Absolutely and totally! I defended it at the Como Conference in 1927! I have adhered to it ever afterwards with religious fervour! You convinced me. I humbly accepted your criticisms.

Bohr Not before you’d said some deeply wounding things.

Heisenberg Good God, at one point you literally reduced me to tears!

Bohr Forgive me, but I diagnosed them as tears of frustration and rage.

Heisenberg I was having a tantrum?

Bohr I have brought up children of my own.

Heisenberg And what about Margrethe? Was she having a tantrum? Klein told me you reduced her to tears after I’d gone, making her type out your endless redraftings of the complementarity paper.

Bohr I don’t recall that.

Margrethe I do.

Heisenberg We had to drag Pauli out of bed in Hamburg once again to come to Copenhagen and negotiate peace.

Bohr He succeeded. We ended up with a treaty. Uncertainty and complementarity became the two central tenets of the Copenhagen Interpretation of Quantum Mechanics.

Heisenberg A political compromise, of course, like most treaties.

Bohr You see? Somewhere inside you there are still secret reservations.

Heisenberg Not at all — it works. That’s what matters. It works, it works, it works!

Bohr It works, yes. But it’s more important than that. Because you see what we did in those three years, Heisenberg? Not to exaggerate, but we turned the world inside out! Yes, listen, now it comes, now it comes.… We put man back at the centre of the universe. Throughout history we keep finding ourselves displaced. We keep exiling ourselves to the periphery of things. First we turn ourselves into a mere adjunct of God’s unknowable purposes, tiny figures kneeling in the great cathedral of creation. And no sooner have we recovered ourselves in the Renaissance, no sooner has man become, as Protagoras proclaimed him, the measure of all things, than we’re pushed aside again by the products of our own reasoning! We’re dwarfed again as physicists build the great new cathedrals for us to wonder at — the laws of classical mechanics that predate us from the beginning of eternity, that will survive us to eternity’s end, that exist whether we exist or not. Until we come to the beginning of the twentieth century, and we’re suddenly forced to rise from our knees again.

Heisenberg It starts with Einstein.

Bohr It starts with Einstein. He shows that measurement — measurement, on which the whole possibility of science depends — measurement is not an impersonal event that occurs with impartial universality. It’s a human act, carried out from a specific point of view in time and space, from the one particular viewpoint of a possible observer. Then, here in Copenhagen in those three years in the mid-twenties we discover that there is no precisely determinable objective universe. That the universe exists only as a series of approximations. Only within the limits determined by our relationship with it. Only through the understanding lodged inside the human head.

Margrethe So this man you’ve put at the centre of the universe — is it you, or is it Heisenberg?

Bohr Now, now, my love.

Margrethe Yes, but it makes a difference.

Bohr Either of us. Both of us. Yourself. All of us.

Margrethe If it’s Heisenberg at the centre of the universe, then the one bit of the universe that he can’t see is Heisenberg.

Heisenberg So …

Margrethe So it’s no good asking him why he came to Copenhagen in 1941. He doesn’t know!

Heisenberg I thought for a moment just then I caught a glimpse of it.

Margrethe Then you turned to look.

Heisenberg And away it went.

Margrethe Complementarity again. Yes?

Bohr Yes, yes.

Margrethe I’ve typed it out often enough. If you’re doing something you have to concentrate on you can’t also be thinking about doing it, and if you’re thinking about doing it then you can’t actually be doing it. Yes?

Heisenberg Swerve left, swerve right, or think about it and die.

Bohr But after you’ve done it …

Margrethe You look back and make a guess, just like the rest of us. Only a worse guess, because you didn’t see yourself doing it, and we did. Forgive me, but you don’t even know why you did uncertainty in the first place.

Bohr Whereas if you’re the one at the centre of the universe …

Margrethe Then I can tell you that it was because you wanted to drop a bomb on Schrödinger.

Heisenberg I wanted to show he was wrong, certainly.

Margrethe And Schrödinger was winning the war. When the Leipzig chair first became vacant that autumn he was short-listed for it and you weren’t. You needed a wonderful new weapon.

Bohr Not to criticise, Margrethe, but you have a tendency to make everything personal.

Margrethe Because everything is personal! You’ve just read us all a lecture about it! You know how much Heisenberg wanted a chair. You know the pressure he was under from his family. I’m sorry, but you want to make everything seem heroically abstract and logical. And when you tell the story, yes, it all falls into place, it all has a beginning and a middle and an end. But I was there, and when I remember what it was like I’m there still, and I look around me and what I see isn’t a story! It’s confusion and rage and jealousy and tears and no one knowing what things mean or which way they’re going to go.

Heisenberg All the same, it works, it works.

Margrethe Yes, it works wonderfully. Within three months of publishing your uncertainty paper you’re offered Leipzig.

Heisenberg I didn’t mean that.

Margrethe Not to mention somewhere else and somewhere else.

Heisenberg Halle and Munich and Zürich.

Bohr And various American universities.

Heisenberg But I didn’t mean that.

Margrethe And when you take up your chair at Leipzig you’re how old?

Heisenberg Twenty-six.

Bohr The youngest full professor in Germany.

Heisenberg I mean the Copenhagen Interpretation. The Copenhagen Interpretation works. However we got there, by whatever combination of high principles and low calculation, of most painfully hard thought and most painfully childish tears, it works. It goes on working.

Margrethe Yes, and why did you both accept the Interpretation in the end? Was it really because you wanted to re-establish humanism?

Bohr Of course not. It was because it was the only way to explain what the experimenters had observed.

Margrethe Or was it because now you were becoming a professor you wanted a solidly established doctrine to teach? Because you wanted to have your new ideas publicly endorsed by the head of the church in Copenhagen? And perhaps Niels agreed to endorse them in return for your accepting his doctrines. For recognising him as head of the church. And if you want to know why you came to Copenhagen in 1941 I’ll tell you that as well. You’re right — there’s no great mystery about it. You came to show yourself off to us.

Bohr Margrethe!

Margrethe No! When he first came in 1924 he was a humble assistant lecturer from a humiliated nation, grateful to have a job. Now here you are, back in triumph — the leading scientist in a nation that’s conquered most of Europe. You’ve come to show us how well you’ve done in life.

Bohr This is so unlike you!

Margrethe I’m sorry, but isn’t that really why he’s here? Because he’s burning to let us know that he’s in charge of some vital piece of secret research. And that even so he’s preserved a lofty moral independence. Preserved it so famously that he’s being watched by the Gestapo. Preserved it so successfully that he’s now also got a wonderfully important moral dilemma to face.

Bohr Yes, well, now you’re simply working yourself up.

Margrethe A chain reaction. You tell one painful truth and it leads to two more. And as you frankly admit, you’re going to go back and continue doing precisely what you were doing before, whatever Niels tells you.

Heisenberg Yes.

Margrethe Because you wouldn’t dream of giving up such a wonderful opportunity for research.

Heisenberg Not if I can possibly help it.

Margrethe Also you want to demonstrate to the Nazis how useful theoretical physics can be. You want to save the honour of German science. You want to be there to reestablish it in all its glory as soon as the war’s over.

Heisenberg All the same, I don’t tell Speer that the reactor …

Margrethe … will produce plutonium, no, because you’re afraid of what will happen if the Nazis commit huge resources, and you fail to deliver the bombs. Please don’t try to tell us that you’re a hero of the resistance.

Heisenberg I’ve never claimed to be a hero.

Margrethe Your talent is for skiing too fast for anyone to see where you are. For always being in more than one position at a time, like one of your particles.

Heisenberg I can only say that it worked. Unlike most of the gestures made by heroes of the resistance. It worked! I know what you think. You think I should have joined the plot against Hitler, and got myself hanged like the others.

Bohr Of course not.

Heisenberg You don’t say it, because there are some things that can’t be said. But you think it.

Bohr No.

Heisenberg What would it have achieved? What would it have achieved if you’d dived in after Christian, and drowned as well? But that’s another thing that can’t be said.

Bohr Only thought.

Heisenberg Yes. I’m sorry.

Bohr And rethought. Every day.

Heisenberg You had to be held back, I know.

Margrethe Whereas you held yourself back.

Heisenberg Better to stay on the boat, though, and fetch it about. Better to remain alive, and throw the lifebuoy. Surely!

Bohr Perhaps. Perhaps not.

Heisenberg Better. Better.

Margrethe Really it is ridiculous. You reasoned your way, both of you, with such astonishing delicacy and precision into the tiny world of the atom. Now it turns out that everything depends upon these really rather large objects on our shoulders. And what’s going on in there is …

Heisenberg Elsinore.

Margrethe Elsinore, yes.

Heisenberg And you may be right. I was afraid of what would happen. I was conscious of being on the winning side … So many explanations for everything I did! So many of them sitting round the lunch-table! Somewhere at the head of the table, I think, is the real reason I came to Copenhagen. Again I turn to look.… And for a moment I almost see its face. Then next time I look the chair at the head of the table is completely empty. There’s no reason at all. I didn’t tell Speer simply because I didn’t think of it. I came to Copenhagen simply because I did think of it. A million things we might do or might not do every day. A million decisions that make themselves. Why didn’t you kill me?

Bohr Why didn’t I …?

Heisenberg Kill me. Murder me. That evening in 1941. Here we are, walking back towards the house, and you’ve just leapt to the conclusion that I’m going to arm Hitler with nuclear weapons. You’ll surely take any reasonable steps to prevent it happening.

Bohr By murdering you?

Heisenberg We’re in the middle of a war. I’m an enemy. There’s nothing odd or immoral about killing enemies.

Bohr I should fetch out my cap-pistol?

Heisenberg You won’t need your cap-pistol. You won’t even need a mine. You can do it without any loud bangs, without any blood, without any spectacle of suffering. As cleanly as a bomb-aimer pressing his release three thousand metres above the earth. You simply wait till I’ve gone. Then you sit quietly down in your favourite armchair here and repeat aloud to Margrethe, in front of our unseen audience, what I’ve just told you. I shall be dead almost as soon as poor Casimir. A lot sooner than Gamow.

Bohr My dear Heisenberg, the suggestion is of course …

Heisenberg Most interesting. So interesting that it never even occurred to you. Complementarity, once again. I’m your enemy; I’m also your friend. I’m a danger to mankind; I’m also your guest. I’m a particle; I’m also a wave. We have one set of obligations to the world in general, and we have other sets, never to be reconciled, to our fellow-countrymen, to our neighbours, to our friends, to our family, to our children. We have to go through not two slits at the same time but twenty-two. All we can do is to look afterwards, and see what happened.

Margrethe I’ll tell you another reason why you did uncertainty: you have a natural affinity for it.

Heisenberg Well, I must cut a gratifyingly chastened figure when I return in 1947. Crawling on my hands and knees again. My nation back in ruins.

Margrethe Not really. You’re demonstrating that once more you personally have come out on top.

Heisenberg Begging for food parcels?

Margrethe Established in Göttingen under British protection, in charge of post-war German science.

Heisenberg That first year in Göttingen I slept on straw.

Margrethe Elisabeth said you had a most charming house thereafter.

Heisenberg I was given it by the British.

Margrethe Your new foster-parents. Who’d confiscated it from someone else.

Bohr Enough, my love, enough.

Margrethe No, I’ve kept my thoughts to myself for all these years. But it’s maddening to have this clever son forever dancing about in front of our eyes, forever demanding our approval, forever struggling to shock us, forever begging to be told what the limits to his freedom are, if only so that he can go out and transgress them! I’m sorry, but really.… On your hands and knees? It’s my dear, good, kind husband who’s on his hands and knees! Literally. Crawling down to the beach in the darkness in 1943, fleeing like a thief in the night from his own homeland to escape being murdered. The protection of the German Embassy that you boasted about didn’t last for long. We were incorporated into the Reich.

Heisenberg I warned you in 1941. You wouldn’t listen. At least Bohr got across to Sweden.

Margrethe And even as the fishing-boat was taking him across the Sound two freighters were arriving in the harbour to ship the entire Jewish population of Denmark eastwards. That great darkness inside the human soul was flooding out to engulf us all.

Heisenberg I did try to warn you.

Margrethe Yes, and where are you? Shut away in a cave like a savage, trying to conjure an evil spirit out of a hole in the ground. That’s what it came down to in the end, all that shining springtime in the 1920s, that’s what it produced — a more efficient machine for killing people.

Bohr It breaks my heart every time I think of it.

Heisenberg It broke all our hearts.

Margrethe And this wonderful machine may yet kill every man, woman, and child in the world. And if we really are the centre of the universe, if we really are all that’s keeping it in being, what will be left?

Bohr Darkness. Total and final darkness.

Margrethe Even the questions that haunt us will at last be extinguished. Even the ghosts will die.

Heisenberg I can only say that I didn’t do it. I didn’t build the bomb.

Margrethe No, and why didn’t you? I’ll tell you that, too. It’s the simplest reason of all. Because you couldn’t. You didn’t understand the physics.

Heisenberg That’s what Goudsmit said.

Margrethe And Goudsmit knew. He was one of your magic circle. He and Uhlenbeck were the ones who did spin.

Heisenberg All the same, he had no idea of what I did or didn’t understand about a bomb.

Margrethe He tracked you down across Europe for Allied Intelligence. He interrogated you after you were captured.

Heisenberg He blamed me, of course. His parents died in Auschwitz. He thought I should have done something to save them. I don’t know what. So many hands stretching up from the darkness for a lifeline, and no lifeline that could ever reach them …

Margrethe He said you didn’t understand the crucial difference between a reactor and a bomb.

Heisenberg I understood very clearly. I simply didn’t tell the others.

Margrethe Ah.

Heisenberg I understood, though.

Margrethe But secretly.

Heisenberg You can check if you don’t believe me.

Margrethe There’s evidence, for once?

Heisenberg It was all most carefully recorded.

Margrethe Witnesses, even?

Heisenberg Unimpeachable witnesses.

Margrethe Who wrote it down?

Heisenberg Who recorded it and transcribed it.

Margrethe Even though you didn’t tell anyone?

Heisenberg I told one person. I told Otto Hahn. That terrible night at Farm Hall, after we’d heard the news. Somewhere in the small hours, after everyone had finally gone to bed, and we were alone together. I gave him a reasonably good account of how the bomb had worked.

Margrethe After the event.

Heisenberg After the event. Yes. When it didn’t matter any more. All the things Goudsmit said I didn’t understand. Fast neutrons in 235. The plutonium option. A reflective shell to reduce neutron escape. Even the method of triggering it.

Bohr The critical mass. That was the most important thing. The amount of material you needed to establish the chain-reaction. Did you tell him the critical mass?

Heisenberg I gave him a figure, yes. You can look it up! Because that was the other secret of the house-party. Diebner asked me when we first arrived if I thought there were hidden microphones. I laughed. I told him the British were far too old-fashioned to know about Gestapo methods. I underestimated them. They had microphones everywhere — they were recording everything. Look it up! Everything we said. Everything we went through that terrible night. Everything I told Hahn alone in the small hours.

Bohr But the critical mass. You gave him a figure. What was the figure you gave him?

Heisenberg I forget.

Bohr Heisenberg …

Heisenberg It’s all on the record. You can see for yourself.

Bohr The figure for the Hiroshima bomb …

Heisenberg Was fifty kilograms.

Bohr So that was the figure you gave Hahn? Fifty kilograms?

Heisenberg I said about a ton.

Bohr About a ton? A thousand kilograms? Heisenberg, I believe I am at last beginning to understand something.

Heisenberg The one thing I was wrong about.

Bohr You were twenty times over.

Heisenberg The one thing.

Bohr But, Heisenberg, your mathematics, your mathematics! How could they have been so far out?

Heisenberg They weren’t. As soon as I calculated the diffusion I got it just about right.

Bohr As soon as you calculated it?

Heisenberg I gave everyone a seminar on it a week later. It’s in the record! Look it up!

Bohr You mean … you hadn’t calculated it before? You hadn’t done the diffusion equation?

Heisenberg There was no need to.

Bohr No need to?

Heisenberg The calculation had already been done.

Bohr Done by whom?

Heisenberg By Perrin and Flügge in 1939.

Bohr By Perrin and Flügge? But, my dear Heisenberg, that was for natural uranium. Wheeler and I showed that it was only the 235 that fissioned.

Heisenberg Your great paper. The basis of everything we did.

Bohr So you needed to calculate the figure for pure 235.

Heisenberg Obviously.

Bohr And you didn’t?

Heisenberg I didn’t.

Bohr And that’s why you were so confident you couldn’t do it until you had the plutonium. Because you spent the entire war believing that it would take not a few kilograms of 235, but a ton or more. And to make a ton of 235 in any plausible time …

Heisenberg Would have needed something like two hundred million separator units. It was plainly unimaginable.

Bohr If you’d realised you had to produce only a few kilograms …

Heisenberg Even to make a single kilogram would need something like two hundred thousand units.

Bohr But two hundred million is one thing; two hundred thousand is another. You might just possibly have imagined setting up two hundred thousand.

Heisenberg Just possibly.

Bohr The Americans did imagine it.

Heisenberg Because Otto Frisch and Rudolf Peierls actually did the calculation. They solved the diffusion equation.

Bohr Frisch was my old assistant.

Heisenberg Peierls was my old pupil.

Bohr An Austrian and a German.

Heisenberg So they should have been making their calculation for us, at the Kaiser Wilhelm Institute in Berlin. But instead they made it at the University of Birmingham, in England.

Margrethe Because they were Jews.

Heisenberg There’s something almost mathematically elegant about that.

Bohr They also started with Perrin and Flügge.

Heisenberg They also thought it would take tons. They also thought it was unimaginable.

Bohr Until one day …

Heisenberg They did the calculation.

Bohr They discovered just how fast the chain reaction would go.

Heisenberg And therefore how little material you’d need.

Bohr They said slightly over half a kilogram.

Heisenberg About the size of a tennis ball.

Bohr They were wrong, of course.

Heisenberg They were a hundred times under.

Bohr Which made it seem a hundred times more imaginable than it actually was.

Heisenberg Whereas I left it seeming twenty times less imaginable.

Bohr So all your agonising in Copenhagen about plutonium was beside the point. You could have done it without ever building the reactor. You could have done it with 235 all the time.

Heisenberg Almost certainly not.

Bohr Just possibly, though.

Heisenberg Just possibly.

Bohr And that question you’d settled long before you arrived in Copenhagen. Simply by failing to try the diffusion equation.

Heisenberg Such a tiny failure.

Bohr But the consequences went branching out over the years, doubling and redoubling.

Heisenberg Until they were large enough to save a city. Which city? Any of the cities that we never dropped our bomb on.

Bohr London, presumably, if you’d had it in time. If the Americans had already entered the war, and the Allies had begun to liberate Europe, then …

Heisenberg Who knows? Paris as well. Amsterdam. Perhaps Copenhagen.

Bohr So, Heisenberg, tell us this one simple thing: why didn’t you do the calculation?

Heisenberg The question is why Frisch and Peierls did do it. It was a stupid waste of time. However much 235 it turned out to be, it was obviously going to be more than anyone could imagine producing.

Bohr Except that it wasn’t!

Heisenberg Except that it wasn’t.

Bohr So why …?

Heisenberg I don’t know! I don’t know why I didn’t do it! Because I never thought of it! Because it didn’t occur to me! Because I assumed it wasn’t worth doing!

Bohr Assumed? Assumed? You never assumed things! That’s how you got uncertainty, because you rejected our assumptions! You calculated, Heisenberg! You calculated everything! The first thing you did with a problem was the mathematics!

Heisenberg You should have been there to slow me down.

Bohr Yes, you wouldn’t have got away with it if I’d been standing over you.

Heisenberg Though in fact you made exactly the same assumption! You thought there was no danger for exactly the same reason as I did! Why didn’t you calculate it?

Bohr Why didn’t I calculate it?

Heisenberg Tell us why you didn’t calculate it and we’ll know why I didn’t!

Bohr It’s obvious why I didn’t!

Heisenberg Go on.

Margrethe Because he wasn’t trying to build a bomb!

Heisenberg Yes. Thank you. Because he wasn’t trying to build a bomb. I imagine it was the same with me. Because I wasn’t trying to build a bomb. Thank you.

Bohr So, you bluffed yourself, the way I did at poker with the straight I never had. But in that case …

Heisenberg Why did I come to Copenhagen? Yes, why did I come …?

Bohr One more draft, yes? One final draft!

Heisenberg And once again I crunch over the familiar gravel to the Bohrs’ front door, and tug at the familiar bell-pull. Why have I come? I know perfectly well. Know so well that I’ve no need to ask myself. Until once again the heavy front door opens.

Bohr He stands on the doorstep blinking in the sudden flood of light from the house. Until this instant his thoughts have been everywhere and nowhere, like unobserved particles, through all the slits in the diffraction grating simultaneously. Now they have to be observed and specified.

Heisenberg And at once the clear purposes inside my head lose all definite shape. The light falls on them and they scatter.

Bohr My dear Heisenberg!

Heisenberg My dear Bohr!

Bohr Come in, come in …

Heisenberg How difficult it is to see even what’s in front of one’s eyes. All we possess is the present, and the present endlessly dissolves into the past. Bohr has gone even as I turn to see Margrethe.

Margrethe Niels is right. You look older.

Bohr I believe you had some personal trouble.

Heisenberg Margrethe slips into history even as I turn back to Bohr. And yet how much more difficult still it is to catch the slightest glimpse of what’s behind one’s eyes. Here I am at the centre of the universe, and yet all I can see are two smiles that don’t belong to me.

Margrethe How is Elisabeth? How are the children?

Heisenberg Very well. They send their love, of course … I can feel a third smile in the room, very close to me. Could it be the one I suddenly see for a moment in the mirror there? And is the awkward stranger wearing it in any way connected with this presence that I can feel in the room? This all-enveloping, unobserved presence?

Margrethe I watch the two smiles in the room, one awkward and ingratiating, the other rapidly fading from incautious warmth to bare politeness. There’s also a third smile in the room, I know, unchangingly courteous, I hope, and unchangingly guarded.

Heisenberg You’ve managed to get some skiing?

Bohr I glance at Margrethe, and for a moment I see what she can see and I can’t — myself, and the smile vanishing from my face as poor Heisenberg blunders on.

Heisenberg I look at the two of them looking at me, and for a moment I see the third person in the room as clearly as I see them. Their importunate guest, stumbling from one crass and unwelcome thoughtfulness to the next.

Bohr I look at him looking at me, anxiously, pleadingly, urging me back to the old days, and I see what he sees. And yes — now it comes, now it comes — there’s someone missing from the room. He sees me. He sees Margrethe. He doesn’t see himself.

Heisenberg Two thousand million people in the world, and the one who has to decide their fate is the only one who’s always hidden from me.

Bohr You suggested a stroll.

Heisenberg You remember Elsinore? The darkness inside the human soul …?

Bohr And out we go. Out under the autumn trees. Through the blacked-out streets.

Heisenberg Now there’s no one in the world except Bohr and the invisible other. Who is he, this all-enveloping presence in the darkness?

Margrethe The flying particle wanders the darkness, no one knows where. It’s here, it’s there, it’s everywhere and nowhere.

Bohr With careful casualness he begins to ask the question he’s prepared.

Heisenberg Does one as a physicist have the moral right to work on the practical exploitation of atomic energy?

Margrethe The great collision.

Bohr I stop. He stops …

Margrethe This is how they work.

Heisenberg He gazes at me, horrified.

Margrethe Now at last he knows where he is and what he’s doing.

Heisenberg He turns away.

Margrethe And even as the moment of collision begins it’s over.

Bohr Already we’re hurrying back towards the house.

Margrethe Already they’re both flying away from each other into the darkness again.

Heisenberg Our conversation’s over.

Bohr Our great partnership.

Heisenberg All our friendship.

Margrethe And everything about him becomes as uncertain as it was before.

Bohr Unless … yes … a thought-experiment.… Let’s suppose for a moment that I don’t go flying off into the night. Let’s see what happens if instead I remember the paternal role I’m supposed to play. If I stop, and control my anger, and turn to him. And ask him why.

Heisenberg Why?

Bohr Why are you confident that it’s going to be so reassuringly difficult to build a bomb with 235? Is it because you’ve done the calculation?

Heisenberg The calculation?

Bohr Of the diffusion in 235. No. It’s because you haven’t calculated it. You haven’t considered calculating it. You hadn’t consciously realised there was a calculation to be made.

Heisenberg And of course now I have realised. In fact it wouldn’t be all that difficult. Let’s see.… The scattering cross-section’s about 6 × 10⁻²⁴, so the mean free path would be … Hold on …

Bohr And suddenly a very different and very terrible new world begins to take shape …

Margrethe That was the last and greatest demand that Heisenberg made on his friendship with you. To be understood when he couldn’t understand himself. And that was the last and greatest act of friendship for Heisenberg that you performed in return. To leave him misunderstood.

Heisenberg Yes. Perhaps I should thank you.

Bohr Perhaps you should.

Margrethe Anyway, it was the end of the story.

Bohr Though perhaps there was also something I should thank you for. That summer night in 1943, when I escaped across the Sound in the fishing-boat, and the freighters arrived from Germany …

Margrethe What’s that to do with Heisenberg?

Bohr When the ships arrived on the Wednesday there were eight thousand Jews in Denmark to be arrested and crammed into their holds. On the Friday evening, at the start of the Sabbath, when the SS began their round-up, there was scarcely a Jew to be found.

Margrethe They’d all been hidden in churches and hospitals, in people’s homes and country cottages.

Bohr But how was that possible? — Because we’d been tipped off by someone in the German Embassy.

Heisenberg Georg Duckwitz, their shipping specialist.

Bohr Your man?

Heisenberg One of them.

Bohr He was a remarkable informant. He told us the day before the freighters arrived — the very day that Hitler issued the order. He gave us the exact time that the SS would move.

Margrethe It was the Resistance who got them out of their hiding-places and smuggled them across the Sound.

Bohr For a handful of us in one fishing smack to get past the German patrol-boats was remarkable enough. For a whole armada to get past, with the best part of eight thousand people on board, was like the Red Sea parting.

Margrethe I thought there were no German patrol-boats that night?

Bohr No — the whole squadron had suddenly been reported unseaworthy.

Heisenberg How they got away with it I can’t imagine.

Bohr Duckwitz again?

Heisenberg He also went to Stockholm and asked the Swedish Government to accept everyone.

Bohr So perhaps I should thank you.

Heisenberg For what?

Bohr My life. All our lives.

Heisenberg Nothing to do with me by that time. I regret to say.

Bohr But after I’d gone you came back to Copenhagen.

Heisenberg To make sure that our people didn’t take over the Institute in your absence.

Bohr I’ve never thanked you for that, either.

Heisenberg You know they offered me your cyclotron?

Bohr You could have separated a little 235 with it.

Heisenberg Meanwhile you were going on from Sweden to Los Alamos.

Bohr To play my small but helpful part in the deaths of a hundred thousand people.

Margrethe Niels, you did nothing wrong!

Bohr Didn’t I?

Heisenberg Of course not. You were a good man, from first to last, and no one could ever say otherwise. Whereas I …

Bohr Whereas you, my dear Heisenberg, never managed to contribute to the death of one single solitary person in all your life.

Margrethe Well, yes.

Heisenberg Did I?

Margrethe One. Or so you told us. The poor fellow you guarded overnight, when you were a boy in Munich, while he was waiting to be shot in the morning.

Bohr All right then, one. One single soul on his conscience, to set against all the others.

Margrethe But that one single soul was emperor of the universe, no less than each of us. Until the morning came.

Heisenberg No, when the morning came I persuaded them to let him go.

Bohr Heisenberg, I have to say — if people are to be measured strictly in terms of observable quantities …

Heisenberg Then we should need a strange new quantum ethics. There’d be a place in heaven for me. And another one for the SS man I met on my way home from Haigerloch. That was the end of my war. The Allied troops were closing in; there was nothing more we could do. Elisabeth and the children had taken refuge in a village in Bavaria, so I went to see them before I was captured. I had to go by bicycle — there were no trains or road transport by that time — and I had to travel by night and sleep under a hedge by day, because all through the daylight hours the skies were full of Allied planes, scouring the roads for anything that moved. A man on a bicycle would have been the biggest target left in Germany. Three days and three nights I travelled. Out of Württemberg, down through the Swabian Jura and the first foothills of the Alps. Across my ruined homeland. Was this what I’d chosen for it? This endless rubble? This perpetual smoke in the sky? These hungry faces? Was this my doing? And all the desperate people on the roads. The most desperate of all were the SS. Bands of fanatics with nothing left to lose, roaming around shooting deserters out of hand, hanging them from roadside trees. The second night, and suddenly there it is — the terrible familiar black tunic emerging from the twilight in front of me. On his lips as I stop — the one terrible familiar word. ‘Deserter,’ he says. He sounds as exhausted as I am. I give him the travel order I’ve written for myself. But there’s hardly enough light in the sky to read by, and he’s too weary to bother. He begins to open his holster instead. He’s going to shoot me because it’s simply less labour. And suddenly I’m thinking very quickly and clearly — it’s like skiing, or that night on Heligoland, or the one in Faelled Park. What comes into my mind this time is the pack of American cigarettes I’ve got in my pocket. And already it’s in my hand — I’m holding it out to him. The most desperate solution to a problem yet. I wait while he stands there looking at it, trying to make it out, trying to think, his left hand holding my useless piece of paper, his right on the fastening of the holster. There are two simple words in large print on the pack: Lucky Strike. He closes the holster, and takes the cigarettes instead.… It had worked, it had worked! Like all the other solutions to all the other problems. For twenty cigarettes he let me live. And on I went. Three days and three nights. Past the weeping children, the lost and hungry children, drafted to fight, then abandoned by their commanders. Past the starving slave-labourers walking home to France, to Poland, to Estonia. Through Gammertingen and Biberach and Memmingen. Mindelheim, Kaufbeuren, and Schöngau. Across my beloved homeland. My ruined and dishonoured and beloved homeland.

Bohr My dear Heisenberg! My dear friend!

Margrethe Silence. The silence we always in the end return to.

Heisenberg And of course I know what they’re thinking about.

Margrethe All those lost children on the road.

Bohr Heisenberg wandering the world like a lost child himself.

Margrethe Our own lost children.

Heisenberg And over goes the tiller once again.

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

Margrethe He stands in the doorway, watching me, then he turns his head away …

Heisenberg And once again away he goes, into the dark waters.

Bohr Before we can lay our hands on anything, our life’s over.

Heisenberg Before we can glimpse who or what we are, we’re gone and laid to dust.

Bohr Settled among all the dust we raised.

Margrethe And sooner or later there will come a time when all our children are laid to dust, and all our children’s children.

Bohr When no more decisions, great or small, are ever made again. When there’s no more uncertainty, because there’s no more knowledge.

Margrethe And when all our eyes are closed, when even the ghosts have gone, what will be left of our beloved world? Our ruined and dishonoured and beloved world?

Heisenberg But in the meanwhile, in this most precious meanwhile, there it is. The trees in Faelled Park. Gammertingen and Biberach and Mindelheim. Our children and our children’s children. Preserved, just possibly, by that one short moment in Copenhagen. By some event that will never quite be located or defined. By that final core of uncertainty at the heart of things.