Entanglement is arguably the most intriguing phenomenon in quantum physics , the one that departs the furthest from our common-sense expectations.

Entanglement is possibly the most intriguing phenomenon in quantum physics, the one that departs furthest from our *common-sense* expectations . To understand it, and consider its importance, we have to do a little history.

Quantum entanglement was discovered *on paper* by Einstein, Podolsky, and Rosen in 1935 ; and it seems so absurd that they both claimed that it was proof that quantum physics must be wrong, or at least incomplete. Yet the *absurd phenomenon is real, as *2022 Nobel laureates in physics John Clauser, Alain Aspect, and Anton Zeilinger demonstrated in the lab .

## What is quantum entanglement?

Let’s think of any particle, for example, an electron. An electron has several physical properties: its mass, its electric charge, and its spin .

The spin of a particle is its intrinsic spin. We can think of it as if the particle were a miniature planet rotating around an axis. It is usually represented by an arrow pointing in the forward direction of a screw rotating in the same way as the particle. In the case of Earth, it would be an arrow along the Earth’s axis of rotation and pointing up (toward the North Star). Using quantum physics notation, the two basic spin states are | ↑ ⟩ (spin pointing up) and | ↓ ⟩ (pointing down):

Suppose now that we have two particles (electron 1 and electron 2), both with the spin pointing up. Your status is | ↑ ⟩₁ | ↑ ⟩₂:

Analogously we could consider a state with both spins pointing down, | ↓⟩₁ | ↓ ⟩₂ .

Now, according to quantum physics, the system of the two electrons could be in a superposition of both states:

```
| ↑ ⟩₁ | ↑ ⟩₂ + | ↓ ⟩₁ | ↓ ⟩₂
```

In this situation the two possibilities coexist: the two spins pointing up and both pointing down. It is what is called an entangled state, in which it is not possible to attribute a definite spin state to any of the electrons. If we measure the spin of particle 1, we can obtain ↑ or ↓ with a probability of 50%. And the same if we choose to measure the spin of electron 2.

Now comes the key point. Suppose we measure the spin of electron 1 and get ↑. Then the state is no longer a superposition, since the possibility ↓ is automatically excluded. Therefore, only one of the terms of the above superposition survives, namely the first term, | ↑ ⟩₁| ↑ ⟩₂ :

```
| ↑ ⟩₁| ↑ ⟩₂ + | ↓ ⟩₁| ↓ ⟩₂ ⎯→ | ↑ ⟩₁| ↑ ⟩₂
```

This change of state, just by being observed, is called state collapse , and it is a postulate of quantum mechanics in its most orthodox formulation.

The important point is that now the spin of the second electron can no longer be ↑ or ↓ with a probability of 50%. It is now ↑ with a probability of 100%. And yet we have not acted on it in any way.

## What disgusted Einstein

Somehow, what has happened to electron 1 has instantly influenced the state of electron 2. And that mysterious influence has been transmitted *without any physical support* (electromagnetic waves or something like that). Furthermore, the particles could be millions of kilometers apart and the effect is produced in exactly the same way. It looks like a kind of telepathy between the states of the two electrons. And this is what deeply disgusted Einstein, since it seems to contradict the theory of relativity, according to which no physical influence can be transmitted faster than light.

Despite its depth, Einstein et al.’s paper had little impact on the scientific community. Most physicists considered these disquisitions to be Byzantine discussions. For practical purposes, everything was similar to a more conventional or “classical” situation, in which we *would ignore* if the electrons have (both) the spin up or down. And by measuring the spin of one of them, we get out of doubt about the spin of the other.

There would be no transmission of information. There would only be ignorance on our part of the *true* spin state of the electrons *from the start* .

## Bell’s inequalities

However, in 1964, the Irish physicist John Bell (the true hero of this story, and yet never received the Nobel Prize) proved that things are not the same as the classical analogue, in other words, that the phenomenon of entanglement could be demonstrated experimentally . The key to Bell’s idea is to use many pairs of particles and allow the observers of each electron (called Alice and Bob in scientific jargon) to measure spin, not just in the vertical direction, but in other directions as well.

Bell showed that the measures of Alice (say a₁, a₂, a₃, etc.) and Bob’s (b₁, b₂, b₃, etc.) can be mathematically combined in a certain way, such that *if nature is classical* (ie , the physical magnitudes are well defined and there is no instantaneous transmission of information), the value of this combination must necessarily be less than or equal to 2.

```
Naturaleza clásica ⟹ f(a₁, a₂,… ; b₁, b₂,…) ≤ 2
```

This is what is called Bell’s inequalities (there are other equivalent ways of expressing them). Furthermore, Bell showed that in an entangled quantum state these inequalities are violated.

```
Física cuántica ⟹ f(a₁, a₂,… ; b₁, b₂,…) > 2
```

So now it was going to be possible to decide experimentally between the two alternatives.

## the first experiments

This is where the award-winning researchers come in, as they pioneered experiments that tested Bell’s inequalities. And the verdict of nature has been clear: Bell’s inequalities are violated , and moreover they do so in the proportion predicted by quantum physics. So quantum theory has passed the test of experiment with flying colors and, more importantly, even if quantum physics is one day superseded by a more perfect theory, it will still be *non-classical* , since Bell’s inequalities are experimentally violated. .

These contributions have an extraordinary intellectual depth, since they show us something very deep and strange about the intimate mechanisms of nature. In addition, they have been the basis for the development of technologies with fabulous potential, such as teleportation , cryptography and quantum computing.

*Alberto Casas González , Research Professor, Institute of Theoretical Physics (IFT – UAM – CSIC)*

*This article was originally published on The Conversation . Read the original .*