What is entanglement?

Imagine a pair of gloves. Someone puts one in a box for you and one in a box for a friend in Australia. You open yours and find a left glove. Instantly you know your friend has the right one. Nothing travelled anywhere. The answer was in the boxes all along.

The physicist John Bell had a friend, Reinhold Bertlmann, who always wore odd socks. See one pink sock and you know the other isn't pink. Bell used him as the example in a famous 1981 paper.

So two photons that always agree at the same angle might simply carry matching instructions from the moment the source made them: "if asked at this angle, pass." That's a perfectly ordinary explanation. To find out whether something deeper is going on, you have to ask at different angles.

Physicists call the photons entangled: made in one shared state, so that neither photon has a polarisation of its own, only a link to the other.

Quantum theory predicts how often the two labs agree when their filters sit at an angle to each other. At the same angle, always. At right angles, never. In between, the agreement falls off smoothly, following the same squared rule as chapter 2. At 30° apart they agree 75% of the time. At 60° apart, 25%.

In 1964 John Bell, a physicist at CERN, found a way to turn this into a sharp test. Here's a version of it, devised by the physicist David Mermin in 1981, that you can play.

That's the whole of Bell's idea. Pre-written instructions, however clever, are stuck above a limit. Quantum theory predicts results below it. So either quantum theory is wrong, or the photons don't carry pre-written instructions.

Experiments use a version called the CHSH test, after John Clauser, Michael Horne, Abner Shimony and Richard Holt (1969). Any plan scores at most 2. Quantum theory predicts up to about 2.83.

Many times, and quantum theory wins every time.

• 1972: Stuart Freedman and John Clauser in California made the first test. Quantum theory won.
• 1982: Alain Aspect's team in Paris switched the filter settings while the photons were in flight, so no signal between the labs could have coordinated them.
• 1998: Anton Zeilinger's team in Innsbruck put the labs 400 metres apart and chose the settings with fast random generators.
• 2015: three teams, in Delft, Vienna and Boulder, closed the last major gaps in the same experiments for the first time. Physicists call these the "loophole-free" tests.
• 2016: the Big Bell Test asked about 100,000 people around the world to type random numbers into a game, and labs used those keystrokes to choose their settings.
• 2017: China's Micius satellite sent entangled photons to ground stations 1,200 kilometres apart. The link held.

Aspect, Clauser and Zeilinger shared the 2022 Nobel Prize in Physics for this work. Optional page 5c tells Bell's own story: he did it as a side project.

It's tempting to think Lab A could turn its filter and make Lab B's results change. It can't, and you can check.

Each lab, on its own, sees pure randomness. The pattern only exists in the comparison. Since the comparison needs ordinary communication, nothing usable travels faster than light. Physicists call this the no-signalling rule. It holds in every interpretation.

Bell's theorem shows that you can't have all three of these together:

1. instructions the particles carry (or anything local to each lab) set the results;
2. nothing travels faster than light;
3. each lab chooses its setting freely, independent of how the source made the particles.

Experiments show nature breaks the combination. Which one gives way is where physicists disagree, and that's the heart of the interpretations in chapter 6.

In a 1947 letter to Max Born, Albert Einstein dismissed the idea as spukhafte Fernwirkung, "spooky action at a distance". Einstein, Boris Podolsky and Nathan Rosen had argued in 1935 that quantum theory must be incomplete, missing exactly the kind of pre-written instructions the game above allows. Bell turned their argument into a test, and the experiments came down against the instructions.

Entanglement is a resource, and three technologies depend on it.

• Quantum computers. A quantum computer of many qubits only beats ordinary computers if its qubits become entangled during the calculation. Chapter 7.
• Secure keys. In 1991 Artur Ekert showed how two people can use entangled pairs to share a secret key, and use Bell's test to check nobody listened in. Chapter 13.
• Teleportation and networks. Entanglement plus an ordinary message can move a quantum state from one place to another. It moves information, not matter, and never faster than light. Optional page 5a explains.