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In the last episode (read here), we arrived at Einstein’s dilemma.

Either:

or

For 29 years, this remained a philosophical debate. The first possibility — that distant objects could be correlated instantaneously — seemed almost impossible to accept. Yet no one knew which of these options was actually correct. Einstein believed the first option must be wrong and bet that the second one, hidden variables, was the true explanation.

Then, in 1964, a scientist named John Stuart Bell came up with an idea to determine which of these possibilities actually occurs in nature. Einstein and Bohr had debated the issue extensively, but neither of them had proposed a concrete way to test whether entanglement — or long-distance correlations — were even possible.

Bell’s genius was that he solved this problem in an incredibly simple and elegant way — far simpler than anyone had imagined.

He invented a simple game that could experimentally decide between the two views.

That game is called the CHSH game.

The CHSH game was discussed in episode #24 (read here) involves three participants: a referee, Alice, and Bob.

The referee runs the game. Alice and Bob are teammates, but they are placed far away from each other in separate rooms. Once the game begins, they are not allowed to communicate in any way.

Before the game starts, Alice and Bob are allowed to discuss a strategy, but once the round begins, they are completely isolated.

So in three cases the outputs must match, and in one case they must differ.

Alice and Bob can agree on any strategy before the game begins. But once the round starts, they cannot communicate, so each player’s answer can only depend on the bit they receive.

As shown in episode #24, no matter what strategy they choose, they cannot win every round.

The best possible success rate is: 75% of the rounds. Since each case occurs with equal probability, the maximum average success rate is 3 out of 4 rounds, or 75%.

Any theory where outcomes are predetermined and local must obey this bound.
This limit is called a Bell inequality.

John Bell realized something remarkable.

If quantum mechanics really allows the kind of non-local correlations Einstein was worried about—where two distant particles behave in a coordinated way—then Alice and Bob could use those correlations to play the same game more successfully.

Here’s the basic idea: If you take two spins that are correlated, like the ones we discussed in the last episode, they will produce the same outcome whenever measured along the same direction, no matter how far apart they are. In other words, if both spins are measured in the same way, their results tend to match. It’s as if one spin “knows” what happened to the other and produces a correlated outcome.

Now, if we repeat this experiment using quantum spins and achieve a success rate higher than 75%, it indicates that the spins are somehow correlated even over large distances. On the other hand, if using a quantum strategy we still get a success rate of 75% or lower, it suggests there is no long-distance correlation, supporting Einstein’s claim that quantum mechanics is incomplete. This gives us a concrete method to test whether long-distance correlations are possible.

Interestingly, John Bell, who shared Einstein’s skepticism about quantum mechanics—designed his famous inequality in such a way that if it is violated, it disproves the idea of local hidden variables. Only if the inequality holds would Einstein’s notion of local realism remain valid.

Let us see how it can be implemented in real life!

To implement the quantum strategy, Alice and Bob share two correlated spins (see the last episode). Instead of sending ordinary answers, Alice and Bob each measure the spins and send the measurement outcome. If the spins are up, they send 1; if the spins are down, they send 0.

The bit they receive from the referee tells them which direction to measure.

Alice chooses between two directions:

Bob also has two choices, but his directions lie halfway between Alice’s:

After each measurement, the result is either spin up or spin down along that axis.
They convert this result into a bit and send it back as their answer.

For the corelated spin pair, the relationship between Alice’s result and Bob’s result depends only on the angle between their measurement directions.

Very roughly:

So by carefully choosing the angles, Alice and Bob can control how likely their answers are to match or differ.

This is the crucial trick.

Look at the four possible cases of the game.

In first three of the cases, the angle between Alice and Bob’s measurements is 45°.
With entangled particles, this makes their answers usually come out the same, which is exactly what the game requires. The figure below shows the most probable outcomes. Whether the spins are up or down, they are always aligned. As a result, Alice and Bob obtain the same measurement result, and therefore they send the same answer back to the referee.

In the fourth case, the angle between their measurements is 135°. So their spin results will be opposite most of the times, so if Alice gets up, bob gets down or vice versa as shown below.

But according to the rules of the game, this is exactly what is needed. In the last case, you need to send different answers.

Scientists conducted exactly this experiment. Everyone including John Bell was expecting that we would get less than 75% but when the experiment is performed, it is about 85% success. It is one of the most shocking results in the history of physics.

In the original words of John Bell himself:

“For me, it is so reasonable to assume that the photons in those experiments carry with them programs, which have been correlated in advance, telling them how to behave. This is so rational that I think that when Einstein saw that, and the others refused to see it, he was the rational man. The other people, although history has justified them, were burying their heads in the sand… So for me, it is a pity that Einstein's idea doesn't work. The reasonable thing just doesn't work.”

Everyone understood the mathematics, but no one could intuitively explain how two spins could remain correlated even when they are very far apart. At first, many scientists thought the experiments might not have been performed correctly. However, as more experiments were carried out over the years, the results became even stronger and more precise, consistently confirming the predictions of quantum mechanics.

For their groundbreaking work on these experiments, Alain Aspect, John F. Clauser, and Anton Zeilinger were awarded the Nobel Prize in Physics in 2022.

Below is the official statement from the Nobel Prize organization:

These experiments showed that Quantum Entanglement is real, yet we still do not know how it works. This is the universe’s greatest puzzle!