Quantum entanglement

Two particles, a single fate

Entanglement is perhaps the most counter-intuitive phenomenon in all of physics. Two particles can be prepared in a shared state such that they form an inseparable whole: describing one without the other becomes impossible, even if they are separated by several kilometers.

A concrete example

Imagine two entangled particles whose spins are always opposite. Their shared state is written:

   |ψ⟩ = ( |0⟩_A |1⟩_B  +  |1⟩_A |0⟩_B ) / √2

This means: either A is 0 and B is 1, or A is 1 and B is 0 — the two possibilities in superposition. But never the two the same. Neither particle has a definite value before measurement; only their correlation is certain.

What happens upon measurement

   BEFORE :   A and B entangled, neither has a definite value
             (superposition of the pair)

   Alice measures A here  --------- ... 1000 km ... --------  Bob has B over there
        |                                                       |
        v                                                       v
   Alice gets 0  =========> INSTANTLY ==========>  B is fixed to 1
   (at random)                 Alice's measurement            (guaranteed)
                               determines B's state

The moment Alice measures her particle and gets (at random) 0, Bob's particle is instantly fixed to 1 — even if Bob is on the other side of the Earth. The two results are perfectly correlated, every time, whatever the distance.

"Spooky action at a distance"

Einstein hated this idea, which he called "spooky action at a distance" (spukhafte Fernwirkung). He thought the particles must possess hidden values from the start (like two gloves separated into two boxes: opening one reveals "left", so the other is "right").

But in 1964, John Bell showed that this hypothesis could be tested. The experiments (Aspect 1982, and many others since, crowned by the 2022 Nobel Prize) ruled against Einstein: there are no pre-existing hidden values. The correlation is far stronger than any "glove" explanation would allow. Entanglement is real.

The safeguard: no communication faster than light

Beware of a tempting misconception: can entanglement be used to transmit an instant message? No. Alice gets a random result (0 or 1) that she does not control. On his side, Bob also sees a string of random results. Only by comparing their lists, later, over a classical channel (telephone, limited by the speed of light) do they discover the correlation.

   Alice does not choose her result -> she cannot "send" anything
   Bob sees randomness until he has Alice's list
   -> no information travels faster than light

Entanglement creates extraordinary correlations, but it does not violate relativity.

In summary

Two entangled particles form a whole: neither has a definite value, only their correlation is certain. Measuring one instantly fixes the other, at any distance. Bell's experiments proved that this is not about pre-existing hidden values. But since the results are random and uncontrollable, entanglement does not allow communicating faster than light.