Episode 29 - The double slit

Tomlin Hawthorne

You're in a corridor. At the far end there's a wall with two doors in it, side by side. Beyond the doors is a large room.

Tomlin Hawthorne

With only the left door open, there's a particular spot in that room that you can walk to. No trouble.

Tomlin Hawthorne

With only the right door open, you can also get to that spot.

Tomlin Hawthorne

Now I open both doors.

Tomlin Hawthorne

Can you still get to the spot?

Tomlin Hawthorne

Of course you can. You've now got two ways of getting there where before you had one. Opening a second door can't possibly make a place harder to reach.

Tomlin Hawthorne

For you, that's true. For an electron, it's false. There are places an electron can reach when one door is open, and can't reach when two are. Open a second door, and you make some destinations impossible.

Tomlin Hawthorne

I'd like you to notice that this is not a mildly surprising fact. It's a violation of something that seems closer to logic than to physics. And it's been checked, over and over, for a hundred years. Today I'm going to show you the experiment. I can't explain it. Nobody can. But I can show you exactly what happens.

Tomlin Hawthorne

Last time you touched a guitar string lightly at its midpoint, and a third of the way along, and heard clear bell-like notes, and found that in between there's only a thud. Those are the patterns that fit. An atom works the same way, with an electron wave where the string is. That's why atoms have fixed energy levels, and why they don't collapse.

Tomlin Hawthorne

But I left something hanging. I said an electron is a wave. I said it earlier about light. And I've also said both of them are particles. I've been carrying both statements along as though that were fine. Today we stop pretending.

Tomlin Hawthorne

Richard Feynman opened his lectures on quantum mechanics with this experiment. He told his students that everything strange about the subject is in it, and that it is really the only mystery there is. And he was candid about what he could offer. He couldn't explain it. He could only describe, exactly, what happens.

Tomlin Hawthorne

In 2002 the magazine Physics World asked its readers to vote for the most beautiful experiment in the history of physics. This one won.

Tomlin Hawthorne

I'm going to present it as a play in three acts. In each act, I'll tell you the set-up, and I'd like you to predict the result before I say it.

Tomlin Hawthorne

The set is the same throughout. On the left, a source: something that fires things. In the middle, a wall, with two narrow vertical slits in it, close together. On the right, a screen that records where things land.

Tomlin Hawthorne

Act One. Bullets.

Tomlin Hawthorne

The source is a rather inaccurate machine gun, spraying bullets toward the wall. Most hit the wall and stop. Some go through one slit or the other and carry on to the screen, which is a thick board. After a while, we go and look at where the bullets are embedded.

Tomlin Hawthorne

Predict. What's the pattern?

Tomlin Hawthorne

Two bands. A cluster of bullets behind the left slit, and a cluster behind the right slit. If the slits are close, the two clusters overlap into one broad heap.

Tomlin Hawthorne

And if I'd done it with only the left slit open, I'd get a heap behind the left slit. Only the right, a heap behind the right. And with both open, I get exactly the sum of the two. Every bullet went through one slit or the other. Left-slit bullets plus right-slit bullets. Nothing could be more ordinary.

Tomlin Hawthorne

Remember that: with things, the result for two slits is the result for one, plus the result for the other.

Tomlin Hawthorne

Same set, but now it's a tank of water. The source is a paddle, bobbing up and down, sending out ripples. The wall has two gaps. The screen is a row of corks that bob to show how rough the water is at each point.

Tomlin Hawthorne

Predict.

Tomlin Hawthorne

You know this one, from episode ten. The ripples go through both gaps at once. On the far side, each gap acts as a new source, and two sets of ripples spread out and overlap. Where a crest from one meets a crest from the other, the water's twice as rough. Where a crest meets a trough, it's flat.

Tomlin Hawthorne

So along the screen, you get stripes. Rough, calm, rough, calm, rough. Lots of them, spread right across. Not two bands. Many.

Tomlin Hawthorne

And notice: there are calm places, where a cork doesn't move at all. If I blocked one gap, that cork would bob. Waves from the other gap would reach it. It's only when both gaps are open that it's still. Two lots of wave, adding up to none.

Tomlin Hawthorne

So with waves, the result for two slits is not the result for one plus the result for the other. There are places that get less with two than with one.

Tomlin Hawthorne

That's interference. It's the signature of a wave. It's how Thomas Young proved, in 1801, that light is one.

Tomlin Hawthorne

Two acts, two patterns. Things give you two heaps. Waves give you stripes.

Tomlin Hawthorne

Act Three. Electrons.

Tomlin Hawthorne

The source fires electrons. And you know what an electron is. It's a particle. It's the thing J. J. Thomson discovered. It has a definite mass and a definite charge. When it hits a detector, it makes one click, in one place. You never detect half an electron. You never get a click spread over two places.

Tomlin Hawthorne

The screen is coated so that each electron that lands makes a tiny flash, a single dot of light, exactly where it hit.

Tomlin Hawthorne

And I'm going to turn the source right down. So low that it sends out one electron at a time. One. Then a long gap. Then another. There's never more than a single electron in the apparatus.

Tomlin Hawthorne

Predict. After we've sent a few thousand electrons through, one by one, what's the pattern of dots on the screen?

Tomlin Hawthorne

Take your time with this one.

Tomlin Hawthorne

Here's what happens. There's a film of it, made in Japan in 1989 by a physicist called Akira Tonomura, and I'd urge you to watch it, because seeing it is different from being told.

Tomlin Hawthorne

The first electron goes through. A dot appears on the screen. One dot, in one place. A particle.

Tomlin Hawthorne

The second. Another dot, somewhere else. The third, somewhere else again. They seem to be landing at random. For the first few dozen, you'd say there's no pattern at all. Just a scatter.

Tomlin Hawthorne

Keep watching. A hundred dots. A thousand. And slowly, out of the scatter, a pattern forms. The dots are piling up in some places and avoiding others. Bands. Stripes. Many of them, spread right across the screen. Dense, sparse, dense, sparse.

Tomlin Hawthorne

It's the wave pattern. It's Act Two.

Tomlin Hawthorne

Built out of dots. Each of which arrived, like a bullet, in one place.

Tomlin Hawthorne

Let's go through what that means, slowly.

Tomlin Hawthorne

Each electron arrives as a single dot. So it's a particle.

Tomlin Hawthorne

The dots, collectively, form interference stripes. So something is behaving as a wave: going through both slits, and overlapping with itself on the far side.

Tomlin Hawthorne

But what? The electrons went through one at a time. There was only ever one in the machine. There was nothing else for it to interfere with. Each electron, somehow, on its own, did whatever produces interference. In some sense each one went through both slits.

Tomlin Hawthorne

And it gets worse. Because of the dark stripes.

Tomlin Hawthorne

There are places on the screen where no electrons land. Not ever. Now block the right-hand slit, and repeat the experiment. With only the left slit open, electrons do land in those places. Quite happily.

Tomlin Hawthorne

So here's a spot on the screen. With one slit open, electrons arrive there. With two slits open, they don't.

Tomlin Hawthorne

That's the two doors. Opening the second slit has prevented the electron from reaching somewhere it could reach before. If the electron is a little ball that goes through the left slit, how does it know whether the right slit, which it didn't go near, is open or shut?

Tomlin Hawthorne

You might try saying: all right, the electron isn't a little ball. It's a smeared-out wave, and it does go through both slits. Fine. But then why does it arrive as one sharp dot? Why don't we ever see half an electron at the left slit and half at the right?

Tomlin Hawthorne

So let's check. Let's catch it in the act.

Tomlin Hawthorne

We put a tiny detector beside the slits. Something that can tell us, for each electron, which slit it passed through. A little light shining across, say, so we see a glint as the electron goes by.

Tomlin Hawthorne

And we run the experiment again, one electron at a time.

Tomlin Hawthorne

What do the detectors say?

Tomlin Hawthorne

Every electron is seen at exactly one slit. Left. Right. Right. Left. Never both. Never half. Each electron goes through one slit or the other, like a perfectly well-behaved bullet.

Tomlin Hawthorne

Good. So now we know. They do go through just one. Then how do they make the stripes?

Tomlin Hawthorne

We look at the screen.

Tomlin Hawthorne

The stripes are gone.

Tomlin Hawthorne

Two heaps. One behind each slit. It's Act One. The bullet pattern.

Tomlin Hawthorne

Switch the detector off, change nothing else, run it again. The stripes come back.

Tomlin Hawthorne

I'll say that again, because it's the centre of this entire series. When we don't find out which slit each electron went through, they behave as though each went through both, and we get interference. When we do find out, they go through one or the other, and the interference disappears.

Tomlin Hawthorne

Now, the natural thought is: you disturbed it. You shone a light on the electron to see where it was, and the light knocked it about, and that jumbled the pattern. That was Heisenberg's first thought too. And it turns out to be wrong, or at least far too shallow. Physicists have spent decades designing ever gentler ways of marking the path, ways that provably don't jostle the particle at all. It makes no difference. What destroys the pattern isn't the disturbance.

Tomlin Hawthorne

It's the information.

Tomlin Hawthorne

If there is any record, anywhere in the universe, from which you could in principle work out which slit the electron went through, then no interference. It doesn't matter whether anyone reads the record. It doesn't matter whether a person is involved at all. If the path could be known, the electron takes one path. If the path can't be known, even in principle, it behaves as though it took both.

Tomlin Hawthorne

That's as far as the experiment goes, and it's as far as I can go. I told you I couldn't explain it.

Tomlin Hawthorne

What I can do is tell you how physicists calculate it, because the calculation works perfectly.

Tomlin Hawthorne

The theory says: associate with the electron a wave. Not a wave of water, or of anything material. A mathematical wave, called the wavefunction. It spreads out from the source. It goes through both slits. It overlaps and interferes on the far side, exactly like the ripples in the tank.

Tomlin Hawthorne

And then there's a rule. Where the wave is strong, the electron is likely to be found. Where the wave is weak, it's unlikely. Where the wave cancels to nothing, the electron never appears.

Tomlin Hawthorne

So the wave isn't the electron. The wave tells you the odds of where the electron will turn up. Between the source and the screen, the theory talks only about the wave. At the screen, a particle appears, in one place, chosen by chance, with the chances set by the wave.

Tomlin Hawthorne

That rule was added by a German physicist, Max Born, in 1926. Famously, the crucial part of it is in a footnote, added while the paper was in proof. He got a Nobel Prize for the footnote. He was, and I offer this purely for pleasure, the grandfather of Olivia Newton-John.

Tomlin Hawthorne

So that fog, in the last episode, round the nucleus of an atom? It's that. It's the wavefunction. It's a cloud of likelihood. Where it's thick, that's where you'd probably find the electron, if you looked.

Tomlin Hawthorne

And what's the electron doing when you're not looking? The theory doesn't say. It declines to answer. It gives you the wave, and the odds, and the dot. On the matter of what lies between, it's silent.

Tomlin Hawthorne

Is this just something peculiar about electrons? Something very small and flimsy? No. That's been tested too.

Tomlin Hawthorne

It works with single photons of light. It works with whole atoms. In 1999, a group in Vienna did it with a molecule made of sixty carbon atoms joined in the shape of a football. These are big, hot, solid objects, by atomic standards. One at a time, through a grating. Interference stripes. Twenty years later the same laboratory did it with molecules of two thousand atoms each.

Tomlin Hawthorne

Nobody has found a size at which it stops. It gets harder, for reasons we'll come to. But there's no known line above which things are just things.

Tomlin Hawthorne

The myth of the week has two heads, and I'd like to cut off both.

Tomlin Hawthorne

The first: that the electron splits in two, and half goes through each slit. It doesn't. Nobody has ever caught half an electron. Whenever you look, there's a whole one, in one place.

Tomlin Hawthorne

The second is the one you'll find in a certain kind of bookshop. That the experiment proves consciousness creates reality. That the electron behaves differently because a human mind is watching.

Tomlin Hawthorne

No. The word observation has done a lot of harm here. Nothing in the experiment requires a person. A detector with nobody reading it kills the pattern. A stray molecule of air that bumps into the electron and carries off a trace of where it was kills the pattern. What matters is whether the path has left a mark on something. That's strange enough. It doesn't need help.

Tomlin Hawthorne

And the question to take away. It's the one the experiment forces on you.

Tomlin Hawthorne

Between the source and the screen, what is the electron doing?

Tomlin Hawthorne

Not: what do we know about it. What is it doing? Did it go through the left slit? The right? Both? Neither?

Tomlin Hawthorne

Every one of those answers leads to a prediction that's contradicted by the experiment. It didn't go through just one, or we'd get two heaps. It didn't go through both as two halves, or we'd catch halves.

Tomlin Hawthorne

So is that a real question, which has an answer we haven't found? Or is it a badly formed question, like asking what's north of the North Pole? Niels Bohr thought the second. Einstein thought the first, and never stopped thinking it. We'll spend the next three episodes on their argument.

Tomlin Hawthorne

Your challenge. You can see interference with your own eyes this week, for the price of a cheap laser pointer.

Tomlin Hawthorne

In a dark room, shine the laser at a wall a few metres away. Now hold a single hair, one of your own will do, taut across the beam, right in front of the pointer.

Tomlin Hawthorne

Look at the spot on the wall. It's no longer a dot. It's a row of dashes, a line of bright spots with dark gaps between them, spread out sideways. Light going round the left side of the hair is interfering with light going round the right side.

Tomlin Hawthorne

Those dark gaps are places where light plus light makes dark. That's Young's experiment of 1801, with a hair. And everything I've described today is what happens when you turn the laser down so far that the light comes through one photon at a time, and the dashes still appear.

Tomlin Hawthorne

Next time. If an electron doesn't have a definite path, what else doesn't it have? A young German with hay fever, on a treeless island in the North Sea, finds out. And seventy years later a playwright turns it into the best drama ever written about science.