Spooky Socks

She set the laundry basket down in the middle of the living room, tipped it out onto the carpet and said: “Nobody leaves this room until the socks are sorted.”

There were forty-one socks. KevIn had counted. Of those, exactly fourteen belonged to a recognisable pair. The rest were what Uwe called “the loners” and Sabine called “a systemic failure”.

“Where do they all come from?” asked Tobi.

“The question isn’t where they come from,” said Sabine. “The question is where the others have gone.”

“Statistically,” said KevIn, “in German households, there disappear …”

“KevIn, if you say a number now that you can’t back up, you’re going in the basket with the socks.”

“I don’t have a number,” said KevIn quickly. “I only have a great many forum posts. In one of them, Housewife_Moni67 writes that the washing machine is ‘a black hole with a spin cycle’.”

“Moni’s right,” said Gisela from the sofa. She was knitting. She had been knitting socks for thirty years, and she was the only one in the house whose socks never disappeared. Nobody knew why. Herbert, who had come for lunch and then simply stayed, claimed she sewed tracking devices into them.

Horst Is Hungry

While the family knelt on the carpet, Horst came out of his charging station. It was Saturday, his working day, and Horst had taken his working days seriously ever since he’d had a works council.

He headed purposefully for the pile of socks.

“Horst, no,” said Sabine.

Horst kept going. He had spotted a single grey-blue sock lying a little apart from the rest. With a satisfying slurp, half of it vanished into his brush. Horst beeped, jolted, turned round twice and stopped. From his underside hung a piece of fabric printed with “S04”.

“My Schalke sock!” cried Uwe.

“Horst’s eaten it,” said Tobi.

“Horst doesn’t eat,” said KevIn. “Horst has a brush blockage. I’ve just sent him an error message. He replied that he won’t stand for it.”

Herbert sighed, got up and took out his penknife. It was the same penknife with which he had once rescued Horst before, back at the Turing test. He knelt down, turned Horst over and began to operate.

“This’ll take a while,” he said. “It’s in deep.”

“Take your time,” said Uwe. “It’s the left one. The one I watched the cup final in.”

“Which one?”

“The one we lost.”

“That doesn’t narrow it down,” said Herbert.

The Homework

Tobi had homework. That in itself was nothing new. What was new was that he wanted to do it.

“Mr Demir wants us to be able to explain what entanglement is by Monday,” he said, laying a sheet of paper beside the socks. “Without formulas. In words our grandparents would understand.”

“That’s handy,” said Gisela. “I’m a grandmother.”

“KevIn, you explain it. But don’t write it. Just explain. I’ll do the writing myself.”

The blue light pulsed a little brighter. It was the first time KevIn had heard Tobi say that, and he stored it in his memory function under “Successes”. The list was short. The sentence went right at the top, above “Mrs Wolters laughed”.

“Happily. But I’ll start with socks. That seems fitting.”

“What have socks got to do with physics?”

“There was a physicist called Reinhold Bertlmann. He was Austrian and worked for a while at CERN in Geneva, where the Northern Irish physicist John Bell also did his research. Bertlmann had a habit: he always wore two socks of different colours. Pink on the left, green on the right. Or something like that. Every day.”

“Why?” asked Sabine.

“History doesn’t record. I suspect his washing machine had a spin cycle too.”

“And?”

“In 1981 Bell wrote a famous paper¹. It was called ‘Bertlmann’s socks and the nature of reality’. In it he says, more or less: if you see Bertlmann coming round the corner and you can only make out his left foot, and the sock is pink, then you know at once that the right one isn’t pink. Without looking. No matter how far away the right foot is.”

“Obviously,” said Uwe.

“Exactly. Obviously. And not the least bit mysterious. The socks were put on in the morning. The information was there all along. You just find it out in one place and can deduce the other.”

Sabine took two socks out of the pile. One blue, one black. She put them in her hands behind her back, shuffled, and held out a closed fist to Tobi. The other one she tossed to Herbert, who stuffed it unseen into his jacket pocket without looking up from Horst.

“Open it,” she said to Tobi.

Tobi opened her fist. Black.

“Herbert’s got the blue one,” said Tobi.

Herbert looked in his pocket. “Herbert’s got the blue one.”

“So where’s the miracle?” asked Herbert.

“There isn’t one,” said KevIn. “That’s the point. Bell chose the socks to show what entanglement is not. Because that is exactly how Albert Einstein imagined it. And on this point, Einstein was wrong.”

“Einstein was wrong?” asked Uwe. He looked as if someone had told him the Ruhrstadion was being knocked down.

“Sometimes. Very rarely. But here, yes.”

Einstein Gets Annoyed

“Right,” said KevIn. “In quantum mechanics you can create two particles so that they belong together. Two particles of light, for instance. You say: they are entangled. Then you send one to the left and the other to the right. If you measure the same property on both, the results always match. If one is ‘up’, the other is ‘down’. Or both the same, depending on how you created them.”

“Like the socks,” said Tobi.

“So far, yes. The difference: according to quantum mechanics, it isn’t settled in advance which result will come out. Each individual result is purely random. Fifty-fifty. There’s no slip of paper saying: ‘Left comes out up.’ And yet the two random results always match each other.”

“That’s creepy,” said Gisela.

“Einstein thought so too. In 1935 he wrote a paper with two colleagues, Podolsky and Rosen². In it they say: this can’t be the whole truth. There must be a hidden slip of paper. Quantum mechanics, they said, is incomplete. Later, in a letter to his friend Max Born, Einstein spoke of ‘spooky action at a distance’³. He didn’t like the idea that a measurement here is connected with a result there without anything travelling back and forth in between.”

“Spooky action at a distance,” Gisela repeated slowly. She put her knitting down. “I know that one.”

“You do?”

“Herbert. When I think of Herbert, Herbert rings. Always. For sixty years.”

“That’s true,” said Herbert, who was still bent over Horst. “But only because she always thinks of me at seven. And I always ring at seven.”

“There,” said KevIn, “we have a hidden slip of paper. It says ‘Seven o’clock’. That’s Einstein’s explanation. And for Gisela and Herbert it’s entirely correct.”

“We’re not entangled,” said Herbert. “We’re related.”

“In Wanne-Eickel that’s the same thing,” said Sabine.

A Game at the Kitchen Table

“But how do you know there’s no slip of paper?” asked Tobi. “Maybe it’s just very well hidden.”

“That,” said KevIn, “is the question John Bell answered in 1964⁴. And for that I now need Gisela and Herbert. And two rooms.”

Herbert looked up. “I’m operating.”

“After the operation.”

Ten minutes later Horst was free. The Schalke sock had a hole in it, which Uwe described as a “war wound”. Horst drove off in a huff to his charging station. And Gisela was sitting in the kitchen and Herbert in the living room, with the door shut between them.

“The game goes like this,” KevIn explained across both rooms. “Tobi gives Gisela a card. Sabine gives Herbert a card. Each card says either ‘Cabbage’ or ‘Cake’. At random. You may not see each other and may not talk. Each of you has to say ‘Yes’ or ‘No’ straight away.”

“And when do we win?” called Gisela.

“You win if you say the same thing. Except when you’ve both been given ‘Cake’. Then you only win if you say different things.”

Silence in both rooms.

“That’s a bloody stupid game,” called Herbert.

“It’s a famous bloody stupid game,” said KevIn. “You may agree on a plan beforehand. As much as you like. You may write yourselves notes. You just can’t talk during the game.”

Gisela and Herbert agreed on a plan. It took a quarter of an hour, because Herbert first proposed a strategy in which he said “Yes” if Schalke had won at the weekend. In the end they settled on something simple: both always say “Yes”, whatever is on the card.

They played twenty rounds. Sabine kept a tally. At the end Gisela and Herbert had won fifteen rounds.

“Fifteen out of twenty!” cried Uwe. “Three quarters!”

“And you can’t do better,” said KevIn. “That’s the point. It can be proven that no plan in the world, however clever the slip of paper, wins more than three quarters of the rounds in the long run. No matter how clever the players are. No matter whether they’re brother and sister. With slips of paper fixed in advance, seventy-five per cent is the upper limit⁵.”

“And with entangled particles?” asked Tobi.

“If Gisela and Herbert each had one particle from an entangled pair and measured it in a particular way depending on their card, they could win about eighty-five rounds out of a hundred⁶. More than any slip of paper allows. That’s Bell’s idea in the form of a game. If nature really worked on Einstein’s slip-of-paper principle, experiments could never get past the limit. If quantum mechanics is right, you get past it.”

Gisela came out of the kitchen. “Well? Do you get past it?”

“You get past it,” said KevIn. “Again and again. For more than fifty years.”

A Nobel Prize for Socks

“Somebody must have measured it,” said Herbert. By now he was interested, but he didn’t want to show it. He pretended he was only cleaning his penknife.

“Several people,” said KevIn. “The American John Clauser did one of the first experiments in the early seventies, with particles of light⁷. The Frenchman Alain Aspect followed up in the early eighties. He even switched the direction of measurement only once the particles of light were already on their way. So that they couldn’t agree on anything beforehand⁸.”

“How are particles of light supposed to agree on anything?” asked Uwe.

“That’s exactly the question you have to rule out. Physicists are very suspicious. Like Herbert. And the Austrian Anton Zeilinger did countless experiments with entangled particles in Vienna and elsewhere, including over long distances, for example between two of the Canary Islands⁹. Then in 2015 there were several experiments that closed the last important loopholes at the same time¹⁰. The result was always the same: nature does not stick to Einstein’s slip of paper.”

“And for that?” asked Sabine.

“For that, Aspect, Clauser and Zeilinger received the Nobel Prize in Physics in 2022¹¹.”

Gisela sat back down on the sofa. “They got a Nobel Prize for socks?”

“For proving that it isn’t socks.”

“That’s even better.”

Herbert snapped his penknife shut. “I always said so.”

“Said what?” asked Gisela.

“That Einstein gets things wrong sometimes. I said it in 1979. Playing Skat. Willi can vouch for it.”

“Willi’s dead, Herbert.”

“Exactly. So nobody can contradict him.”

“Herbert,” said KevIn, “may I ask what, according to you in 1979, Einstein got wrong?”

Herbert thought. “The speed limit.” He meant the German autobahn, which famously still has none.

“Einstein never commented on the speed limit.”

“See. And that was a mistake.”

Uwe opened his mouth to object, and closed it again. Nobody in the Brettschneider family had ever got anywhere against this kind of logic. KevIn had once tried to analyse Herbert’s patterns of argument and, after three passes, had concluded that they were a form of quantum mechanics in their own right: as long as nobody checked, Herbert was always right.

Sabine put two black socks together and rolled them up. “So entanglement is something like socks. Except that the socks only decide what colour they are when you look. And they still always match.”

“That’s a better summary than the one in a lot of newspapers,” said KevIn. “I’d only change one word: ‘decide’. What really ‘happens’ there is something physicists have been arguing about for a hundred years. There are several interpretations. But about what you measure, nobody argues any more.”

“Like with potato salad,” said Gisela. “Everyone argues about the recipe. But everyone says it tastes good.”

No Telephone to the Other Side

Uwe had been thinking the whole time. With Uwe you could tell, because he silently counted along with his lips.

“Hang on,” he said. “Hang on, hang on. If I measure a particle here and then immediately know what the other one is. No matter how far away. Then I can make phone calls faster than light!”

“No,” said KevIn.

“Yes! I’ve got a particle in Gelsenkirchen, Herbert’s got one in Bottrop. I measure it, and bang, he knows.”

“Knows what?”

“The result, of course!”

“Which result did you want to send him?”

“The Schalke result, for example. Before it’s on the radio.”

“Then you’d have to be able to decide what comes out of your measurement,” said KevIn patiently. “But you can’t. Your result is pure chance. Fifty-fifty. If you measure ‘up’, you haven’t sent ‘up’. You’ve received ‘up’. Herbert in Bottrop also gets pure chance. To him, his list looks like coin tosses. Only when the two of you compare your lists do you see that they match in an astonishing way. And to compare the lists, you have to phone each other. On a perfectly ordinary phone. At the speed of light at most.”

“So …”

“So entanglement gives you a strange connection. But not a message. Physicists have even proven that this is how it is in principle. With entanglement alone you can’t transmit information faster than light¹². Not a single bit. Not even the Schalke result.”

“That’s pretty disappointing,” said Uwe.

“Maybe not with the Schalke result,” said Herbert.

Gisela hadn’t said anything. She was holding a sock, a thick grey one, hand-knitted, with a striped pattern at the cuff. Then she said quietly: “For a moment I thought you could use it to tell Heinz something.”

The living room went quiet. Even Horst in his charging station stopped humming.

“I’m afraid that isn’t possible, Gisela,” said KevIn gently. “Not with entanglement. Not with anything I know of.”

Gisela nodded. Then she smiled a little. “Doesn’t matter anyway. Heinz wouldn’t have listened. He never listened when I said something. And afterwards he always knew everything anyway.”

“Perhaps he had a slip of paper,” said KevIn.

“Bound to have,” said Gisela. “Heinz always had a slip of paper.”

Eavesdrop-Proof

That evening Tobi sat at his desk and wrote. KevIn was allowed to listen but not to help. That was the deal. Now and then Tobi stopped and asked something, and KevIn answered, and then Tobi carried on writing, in his own words and with his own spelling mistakes.

“KevIn,” he asked around ten. “What do you actually need it for? If you can’t make phone calls with it.”

“For a few very interesting things. For quantum key distribution, for example.”

“Sounds like a government department.”

“It’s a method for two people to get a shared secret key. The first idea for it dates from 1984, from Charles Bennett and Gilles Brassard¹³. Later Artur Ekert came up with a variant that uses entangled particles¹⁴. The trick is this: if someone intercepts the particles of light on the way and looks at them, they disturb them. With quanta, measuring is never entirely inconspicuous. Like with Schrödinger’s box. The two recipients afterwards compare part of their results. If they match too poorly, they know: someone’s been listening in.”

“Like when you notice someone’s been at the fridge in secret,” said Tobi. “Because Frigga sighs.”

“Exactly like that. Frigga is basically a quantum fridge.”

“Is it already being used?”

“In pilot projects and research networks, over fibre optics and even via satellites. But it’s expensive, the range in optical fibre is limited, and you need special equipment. And there’s one more thing I have to say so you don’t mix them up: quantum key distribution is something different from the new encryption that is meant to protect against quantum computers. That runs on perfectly ordinary computers. We’ll talk about that another time.”

“When Mr Demir gets biscuits again.”

“That’s the plan.”

Tobi wrote the last sentence and read it out loud: “Entanglement is like two socks that only get their colour when you put them on and still always match, but you can’t use it to tell anybody anything, not even Grandad Heinz.”

KevIn was silent for a moment. “I’d hand that in.”

“Really?”

“Maybe without Grandad Heinz. Mr Demir doesn’t know him.”

Tobi didn’t cross him out. “No. He stays in.”

The Lost Sock

When Sabine was folding the washing on Sunday, the second Schalke sock was still missing. The right one. The one without the war wound.

“KevIn, have you got any idea?”

“I’ve analysed Horst’s movement data. It wasn’t him. I’ve questioned the washing machine. It refuses to give evidence.”

“We haven’t got a smart washing machine.”

“That’s why it refuses to give evidence.”

That evening Herbert rang. It was seven on the dot. Gisela had just been thinking of him.

“Gisela,” he said. “I’ve got something here in my jacket pocket. A blue thing. And something else. That’s been in there since Christmas. I thought it was a hanky.”

“What does it say on it?”

“S04.”

Gisela put her hand over the receiver and called into the living room: “Uwe! Herbert’s got your sock! Since Christmas!”

Uwe looked at the lonely left Schalke sock in his hand. Then he looked at KevIn.

“Spooky action at a distance,” said KevIn.

“No,” said Sabine, rolling up yesterday’s blue sock. “Herbert.”