Episode 31 - Entanglement

Tomlin Hawthorne

I take a pair of gloves. I put the left one in a box and the right one in another box, and I shuffle the boxes so that even I don't know which is which. I post one to London and one to Sydney.

Tomlin Hawthorne

A friend in London opens her box. It's the left glove.

Tomlin Hawthorne

At that instant, she knows what's in the box in Sydney, ten thousand miles away. She knows it faster than light could carry the news.

Tomlin Hawthorne

Is that spooky?

Tomlin Hawthorne

No. Of course not. Nothing travelled. The glove in Sydney was a right glove all along. It was a right glove in the post. She hasn't changed anything by opening her box. She's just found out something that was already so.

Tomlin Hawthorne

Albert Einstein was certain that the quantum world works like those gloves. Niels Bohr said it doesn't. For thirty years nobody could see how you'd tell. And then a man from Belfast showed that you can tell, by counting. Today we do the counting. You'll need nothing but your fingers, and at the end of it you'll have proved, for yourself, that the world is not made of gloves.

Tomlin Hawthorne

Last time you played a note for two seconds, and then for a hundredth of a second, and heard the pitch disappear into a click. A wave can't be sharp in both ways at once. That's the uncertainty principle. And we left Einstein writing to a friend that God does not play dice.

Tomlin Hawthorne

People sometimes imagine that Einstein, by then, was a grand old man who'd lost touch. That's unfair. He understood quantum mechanics as well as anyone alive. He'd helped invent it. His objection wasn't that it was wrong. It predicted everything correctly. His objection was that it couldn't be the whole story. And in 1935 he found what he thought was the proof. Today's question is his. Can two things far apart behave as one?

Tomlin Hawthorne

Princeton, New Jersey, May 1935. Einstein has been in America for a year and a half, a refugee. He's fifty-six. With two younger colleagues, Boris Podolsky and Nathan Rosen, he's written a four-page paper with a title that's a question: can quantum-mechanical description of physical reality be considered complete?

Tomlin Hawthorne

Podolsky, without telling Einstein, tipped off the press. And on the fourth of May the New York Times ran a headline: Einstein Attacks Quantum Theory. Einstein was furious, and never spoke to Podolsky again. He didn't much like the way the paper was written, either. He thought the main point had been buried. So let me give you the main point.

Tomlin Hawthorne

It's possible to produce two particles together, in a single event, in such a way that they share one quantum state. Say an atom gives off two photons at once, flying apart in opposite directions. The theory describes the pair with a single wavefunction. Schrödinger, reading the paper, gave this a name: he called the two particles entangled.

Tomlin Hawthorne

Here's what that means in practice. Each photon has a property, call it its polarisation, that you can measure in various ways. And the theory says two things about an entangled pair.

Tomlin Hawthorne

First: before you measure, neither photon has a definite value. Each is in a superposition, like the electron at the two slits. If you measure one, the result is pure chance, fifty-fifty.

Tomlin Hawthorne

Second: the two results are linked. If you make the same measurement on both, you'll always get matching answers. Always. However far apart they are.

Tomlin Hawthorne

Now put those together, as Einstein did. I measure my photon here. The outcome is random; it wasn't settled in advance. And at that moment, the outcome for yours, on the far side of the galaxy, becomes settled too. It'll match mine.

Tomlin Hawthorne

So either my measurement here reached out and instantly fixed something over there, faster than light. Which Einstein, of all people, wasn't going to accept. He called it spooky action at a distance.

Tomlin Hawthorne

Or, and this was his real point, the outcomes were settled all along. The photons were carrying the answers with them from the start, like gloves in boxes. And if that's so, then quantum mechanics, which says there's nothing definite there until you measure, is leaving something out. It's incomplete. There are hidden facts that the theory doesn't describe.

Tomlin Hawthorne

It's a superb argument. Bohr dropped everything for six weeks to answer it. His reply has the same title as Einstein's paper, and it is, to be honest, very hard to follow. The gist was that you can't talk about a particle's properties apart from the whole experimental arrangement used to measure them.

Tomlin Hawthorne

And the physics community listened to both, and shrugged. Whether the answers were there in advance or not, the predictions were the same. It seemed like a question about how you prefer to talk. Philosophy. Not something you could test. A young physicist who showed too much interest in it was liable to be told it was bad for his career.

Tomlin Hawthorne

Einstein died in 1955, still sure. Bohr died in 1962. The night before, he'd drawn a diagram on his blackboard. It was of one of Einstein's thought experiments. He was still arguing.

Tomlin Hawthorne

John Stewart Bell was born in Belfast in 1928, into a working-class Protestant family. His father had left school at eight. His brothers left at fourteen. John was the one who stayed on, with his mother's backing, got a job as a laboratory technician at the university, and was taken up by the professors there, who lent him books and let him sit in on lectures.

Tomlin Hawthorne

By the 1960s he was a respected theorist at CERN, the big European laboratory in Geneva. He designed particle accelerators. That was his day job, and he was very good at it. He had a red beard, a strong Ulster accent, and was a vegetarian by conviction. And he had a private obsession that he kept quiet about. He thought the founders of quantum mechanics had been slippery about what it meant, and that Einstein had been right to complain.

Tomlin Hawthorne

In 1964 he was on a year's leave in America. He wrote a short paper and sent it to a brand new journal called Physics, which had the unusual policy of paying its authors rather than charging them. It folded after four years. For some time, hardly anyone read the paper.

Tomlin Hawthorne

What it showed is that Einstein's view and Bohr's view are not just two ways of talking. They predict different numbers. You can tell them apart.

Tomlin Hawthorne

The key was to stop asking what happens when you make the same measurement on both particles. The gloves can explain that. Bell asked what happens when you make different measurements.

Tomlin Hawthorne

I'm going to give you the version worked out by an American physicist, David Mermin, because it needs no mathematics at all. It needs counting up to nine. Stay with me. This is the hardest five minutes in the series and, I think, the most rewarding.

Tomlin Hawthorne

Here's the equipment. In the middle of a room there's a box with a button. Each time you press it, it sends out two particles, one to the left and one to the right.

Tomlin Hawthorne

At the far left there's a detector. At the far right, another. The detectors aren't connected to each other or to the box in any way.

Tomlin Hawthorne

Each detector has a switch with three positions. One, two, three. And each has two lamps on top: a red and a green. When a particle arrives, the detector flashes one of them. Red or green. That's all it ever does.

Tomlin Hawthorne

Before each run, we set each switch, at random, to one, two or three. Separately. Then we press the button, and note what each detector flashed.

Tomlin Hawthorne

We do this thousands of times. And we find two facts.

Tomlin Hawthorne

Fact one. Whenever the two switches happen to be at the same setting, both at one, or both at two, or both at three, the two detectors flash the same colour. Every single time. Sometimes both red, sometimes both green, at random. But always the same as each other.

Tomlin Hawthorne

Now think like Einstein. How can that be? The detectors aren't in contact. The particles aren't in contact once they've left. And yet they always agree.

Tomlin Hawthorne

There's only one sensible explanation. The particles must be carrying instructions. Each one leaves the box with a little card that says what colour to flash for each switch setting. And the two particles in a pair carry the same card.

Tomlin Hawthorne

And the card has to cover all three settings. Because the particle doesn't know which way the switch will be set when it arrives. So a card might say: if the switch is at one, flash red. If two, flash red. If three, flash green. Call that card red-red-green.

Tomlin Hawthorne

That's the glove theory. The answers are written down in advance. It explains fact one perfectly. And notice, it's not one theory among many. If you want to explain perfect agreement between two things that aren't communicating, it's hard to think of anything else.

Tomlin Hawthorne

Now. Let's work out what the glove theory predicts for all the runs, including the ones where the switches are set differently.

Tomlin Hawthorne

How many kinds of card are there? Some cards say the same colour three times: red-red-red, or green-green-green. With a card like that, the detectors flash the same colour whatever the switches are doing. They agree a hundred per cent of the time.

Tomlin Hawthorne

All the other cards are mixed. Two of one colour and one of the other. Like red-red-green. Let's count how often the detectors agree with that card.

Tomlin Hawthorne

There are three settings on the left and three on the right. Three times three: nine possible combinations of switches. All equally likely. Let's go through them.

Tomlin Hawthorne

The card says red for one, red for two, green for three.

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Left at one, right at one. Red and red. Same.

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Left at one, right at two. Red and red. Same.

Tomlin Hawthorne

Left at two, right at one. Red, red. Same.

Tomlin Hawthorne

Left at two, right at two. Same.

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Left at three, right at three. Green and green. Same.

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That's five.

Tomlin Hawthorne

The other four combinations all have one switch at three and the other at one or two. So one flashes green and the other red. Different.

Tomlin Hawthorne

So with a mixed card, the detectors agree in five cases out of nine.

Tomlin Hawthorne

And with a same-three-times card, nine out of nine.

Tomlin Hawthorne

So whatever mixture of cards the box is sending out, whatever cunning scheme it uses, the detectors must flash the same colour at least five times in every nine. At least fifty-five and a half per cent of the time. It can be more. It can't be less.

Tomlin Hawthorne

That's the glove prediction. That's Bell's inequality. You've just derived it.

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Fifty per cent.

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Fifty is less than fifty-five and a half.

Tomlin Hawthorne

That's it. That's the whole thing. There is no set of instruction cards, none, that can agree every time the switches match and only half the time overall. We just counted. The least you can possibly get is five in nine.

Tomlin Hawthorne

So there are no cards. The particles are not carrying the answers. The colour your particle flashes was not settled before it arrived. And yet, when the switches match, it always agrees with its partner, across the room, or across a continent.

Tomlin Hawthorne

Quantum mechanics predicts exactly fifty per cent. The glove theory says it's impossible. And they can be told apart by standing in a laboratory with a notebook, counting flashes.

Tomlin Hawthorne

Bell had turned a question in metaphysics, are there definite facts when nobody's looking, into something you can measure. People sometimes call it experimental philosophy.

Tomlin Hawthorne

The first was John Clauser, in California, in 1972. He was a young researcher who'd come across Bell's paper and was sure, as it happens, that Einstein would be proved right. His superiors told him he was wasting his time. He built the apparatus largely out of scavenged parts. And quantum mechanics won.

Tomlin Hawthorne

There was a possible way out. Perhaps the detectors were somehow signalling to each other, at or below the speed of light, about how their switches were set. So in 1982 a French physicist, Alain Aspect, did it again, changing the switch settings while the particles were already in flight, too late for any signal to pass between them. Before he started, he'd gone to Geneva to ask Bell whether it was worth doing. Bell's first question was: do you have a permanent job? Quantum mechanics won again.

Tomlin Hawthorne

More loopholes were closed one by one. In 2015 a team in the Netherlands did a version with the two detectors more than a kilometre apart, which shut the last of them at once.

Tomlin Hawthorne

In 2022, Clauser, Aspect and an Austrian, Anton Zeilinger, shared the Nobel Prize.

Tomlin Hawthorne

Bell wasn't there. He'd died suddenly, of a stroke, in 1990, at sixty-two. It's said that he'd been nominated that year and didn't know.

Tomlin Hawthorne

So what does it mean? Let me be careful, because this is where people run off in all directions.

Tomlin Hawthorne

The glove theory rested on two assumptions. One: that things have definite properties whether or not anyone measures them. Physicists call that realism. Two: that what happens here can't instantly affect what happens over there. That's called locality.

Tomlin Hawthorne

Together, those two give you the five in nine. Nature gives fifty per cent. So at least one of them is false.

Tomlin Hawthorne

Either the particles don't have definite properties before they're measured. Or there's some kind of connection between distant places that doesn't weaken with distance and doesn't take time. Or both. Which one you give up depends on how you interpret the theory, and that's next episode.

Tomlin Hawthorne

But the comfortable picture, the one in which the world is made of separate objects, each with its own properties, each affected only by what's nearby, is gone. It isn't a matter of taste. It's been ruled out by experiment.

Tomlin Hawthorne

Einstein was wrong. But I'd say he was wrong in the most valuable way anyone ever has been. He was the one who saw that this was the heart of it. Everyone else was shrugging.

Tomlin Hawthorne

Now, what it doesn't mean. You cannot use this to send a message. I'd love to tell you otherwise. But think about what the person at the left-hand detector sees. A random string of reds and greens. And the person on the right: a random string of reds and greens. Neither can control what colour comes up. Neither can tell, from their own lights, what the other one's doing. The pattern, the fifty per cent, only shows up when they get together afterwards and compare notebooks. And the notebooks have to travel the ordinary way.

Tomlin Hawthorne

So Einstein's speed limit survives. Something is connected, in a way we don't have a good picture of. But no signal passes. Nature has arranged things so that the link can't be used to send so much as a single bit, as though it wanted the strangeness to be there and to be of no use at all.

Tomlin Hawthorne

The myth of the week comes in soft focus. That quantum entanglement shows everything in the universe is connected. That it explains telepathy, or healing at a distance, or why you thought of your sister just before she rang.

Tomlin Hawthorne

It shows that two particles, prepared together with great care and kept isolated from everything else, produce correlated results in a way gloves can't. That's a narrow, precise claim. And it's much stranger than the mystical version, because it's true.

Tomlin Hawthorne

And the question to take away is Einstein's own. A colleague of his, Abraham Pais, remembered a walk in Princeton, around 1950. Einstein suddenly stopped, turned to him, and asked whether he really believed that the Moon exists only when he looks at it.

Tomlin Hawthorne

He meant it as a challenge. Surely, surely, things are there when nobody's looking.

Tomlin Hawthorne

After Bell, what's the honest answer? The Moon is big and warm and constantly being struck by sunlight, so by the argument from last time, it's being measured by its surroundings all the time. Fine. But an electron? A photon? Is there a fact about it when nothing has recorded one?

Tomlin Hawthorne

And a question for the philosopher in you. What is it for something to be real? Does it mean having properties independently of everything else? If that's what real means, the experiments say that at least some things aren't.

Tomlin Hawthorne

Your challenge is to do Bell's theorem yourself. Take a sheet of paper. Write down a mixed card. Green-red-green, say. Then make a grid, three by three: left switch across the top, right switch down the side. In each of the nine boxes, write same or different.

Tomlin Hawthorne

Count the sames. You'll get five.

Tomlin Hawthorne

Try another mixed card. Five again. Try all six mixed cards if you like. It's always five. Then remember that nature gives four and a half.

Tomlin Hawthorne

It'll take you ten minutes. And you'll have personally checked the argument that won the 2022 Nobel Prize in Physics.

Tomlin Hawthorne

Next time. We've now got a theory that works flawlessly and that seems to say something impossible. So what is it telling us? Physicists have been arguing about that for a century, there are at least five serious answers, and they can't all be right. You're unusually well qualified for this one. It's a problem of interpretation.