Entanglement

Two particles with no individual properties and one shared one. Einstein used it in 1935 to argue that quantum mechanics must be incomplete, and the argument was careful, valid, and answerable by experiment — though nobody realised that for thirty years.

1935 – 196418 min

By the end you should be able to

Say precisely what makes a state entangled rather than merely correlated
Reconstruct the EPR argument and identify its premises
Explain why entanglement cannot be used to send a message

I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.
Erwin Schrödingerintroducing the term "entanglement", 1935

Schrödinger coined the word in 1935 — Verschränkung in the original, which carries more the sense of folding or interleaving than the English suggests — in direct response to the EPR paper. And he was not paying a compliment. He was identifying what he took to be the theory's central defect: that it predicts states of affairs which, on any ordinary reading, do not make sense. The cat appears in the same paper. It is a nice historical irony that the term now used to name quantum mechanics' most celebrated resource was introduced by someone trying to point out that something had gone badly wrong.

Watch the pairs with the detectors aligned. Then look at what either detector sees on its own.

Loading the detectors…

With both detectors at the same angle the results are always opposite — every pair, without exception. And each detector alone reports up half the time, indistinguishable from a fair coin. Two streams of perfect randomness that agree perfectly with each other.

There is an obvious explanation, and it deserves to be taken seriously because the entire argument turns on it. Suppose each pair leaves the source carrying instructions. This one says up, that one says down, fixed at the moment of creation. Send them to opposite ends of the country. Of course the results are anti-correlated: they were arranged that way before either particle left. This is a pair of gloves in two boxes. Open the box in Glasgow, find a left glove, and you know instantly that the box in Bristol contains a right one. Nothing travelled. Nothing was influenced. You simply learned something that was already the case. Bell later put it in terms of a colleague at CERN, Reinhold Bertlmann, who always wore socks of two different colours. See one pink sock and you know at once the other is not pink. There is no mystery, and no physicist would write a paper about it. So is entanglement just gloves? That is the question, and until 1964 it looked unanswerable.

You might think

Einstein rejected quantum mechanics because he could not accept randomness.

Actually

The dice remark is real, but it is not the core of his objection here, and the EPR paper is not about probability at all. His actual concern was locality — the principle that what happens in one place cannot instantly affect what is true somewhere else. He wrote to Born that what he could not accept was the idea that a system’s real state depends on what is done to another system spatially separated from it. Notably, Einstein disliked the EPR paper itself: Podolsky drafted it and submitted it without showing him the final text, and Einstein complained to Schrödinger that the main point had been "buried by erudition". His own later formulations are much clearer, and they are about separability, not about God and dice.

It cannot carry a message

One thing about entanglement is not a matter of interpretation, and it is worth nailing down before the next two lessons. Alice sees exactly 50/50, whatever Bob does. Whatever angle he sets, whether he measures at all, whether he has even received his particle — every statistic available on Alice's side is identical. The simulation computes this by summing the joint probabilities rather than asserting it, and it comes out at exactly ½ for every pair of settings. So Bob cannot signal to Alice. The correlations are only visible when the two records are brought together and compared, and that comparison requires an ordinary message travelling at or below light speed. This is a theorem — the no-communication theorem — and it holds for every entangled state, not just this one. Whatever is going on, it does not permit faster-than-light messaging. Relativity is not violated in the way a first reading suggests. Whether something subtler is going on is the subject of the rest of this act.

Compare the two curves — and note carefully where they touch.

Loading the detectors…

Quantum mechanics gives −cos θ. The red curve is a real local hidden-variable model, computed rather than sketched: each particle carries instructions decided at the source, with no influence between the wings. The two agree exactly at 0°, 90° and 180° — the settings anyone naturally tries — and differ only in between.

Why nobody found this for thirty years

The reason is visible in the sim, and it is not that physicists were incurious. A local hidden-variable model — gloves, instructions, elements of reality — reproduces quantum mechanics exactly at: - 0° (aligned): perfect anti-correlation. Both theories. - 90° (perpendicular): no correlation at all. Both theories. - 180° (opposed): perfect correlation. Both theories. Those are precisely the settings anyone would try. They are the ones with obvious physical meaning, the ones you would use to check that your apparatus works, and the ones that appear in every discussion of EPR from 1935 onwards. The theories separate only at the angles in between — and there was no reason whatever to suppose that something decisive was hiding at 45°. So the disagreement looked untestable, and therefore metaphysical. Bohr published a reply to EPR in the same year, in the same journal, under the same title; it is famously difficult to follow, and Bohr himself later described the passage as unclear. It was nonetheless widely taken to have settled matters, which is unusual for an argument few could restate. Most physicists concluded there was nothing to measure and went back to work — and the theory worked, so this was not unreasonable.

The experiment

Perfect anti-correlation at matched settings

Established in principle by EPR 1935; first realised with photon polarisation by Wu and Shaknov, 1950 · 1950 · Columbia University

The question: Do entangled pairs actually exhibit the perfect correlations the singlet state predicts — or is the state a mathematical fiction with no laboratory realisation?
The apparatus: Positron annihilation in a copper source produces two gamma rays travelling in opposite directions, polarisation-entangled by conservation of angular momentum. Their relative polarisation was measured by Compton scattering from anthracene, with the scattered rays detected in coincidence — polarisation of hard gammas cannot be measured with a polariser, so the asymmetry of Compton scattering is used as a proxy.

Theory predicted

For an entangled pair, the ratio of perpendicular to parallel scattering coincidences should reach about 2.0 at the optimal scattering angle; for unpolarised or independently polarised gammas it would be 1.0.

They measured

A ratio of 2.04 ± 0.08, consistent with the quantum prediction and inconsistent with independent emission.

How sure could they be? About 4%, sufficient to confirm entangled correlations exist but nowhere near sufficient to test locality — the experiment measures only at matched settings, where local hidden-variable models agree with quantum mechanics anyway. Wu and Shaknov were not testing EPR and did not frame it that way.

Why it mattered

It establishes that entangled pairs are producible and behave as predicted, which is the necessary groundwork. It says nothing about whether the correlations require non-locality — precisely because it probes only the settings where both theories agree. Fourteen years later Bell would show which settings to use instead, and this 1950 data was among the first things re-examined in that light.

1935EPR argue quantum mechanics is incomplete. Bohr replies; Schrödinger coins "entanglement".
1935Einstein complains to Schrödinger that Podolsky buried the point in erudition.
1950Wu and Shaknov produce entangled gamma pairs and confirm the correlations at matched settings.
1952Bohm reformulates EPR in terms of spin, which is the version everyone now uses.
1964Bell shows the disagreement is experimentally decidable.

Where this leaves us

The EPR argument is valid. Its premises are: that perfect prediction without disturbance implies an element of reality, and that distant events cannot instantly influence one another. From those, quantum mechanics is incomplete. So either the theory is incomplete, or one of those premises is false. For thirty years that looked like a matter of taste. The two positions agreed on every measurement anyone was making, because everyone measured at the settings where they agree. Then in 1964 John Bell — an Irish physicist at CERN, employed to design accelerators, who worked on foundations in his spare time and called it his hobby — proved that it is not a matter of taste. He showed that any theory in which particles carry properties decided in advance, with no influence passing between distant wings, must satisfy a specific numerical inequality. And that quantum mechanics predicts a number that breaks it. Not a philosophical difference. A measurable one. Bell was a realist by temperament, sympathetic to Einstein, and fully expected experiments to come out on Einstein's side.