Copenhagen

by Michael Frayn

  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.