Authors: Michael Frayn
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.