Go further · Chapter 5 · 5b · A step deeper
How does a Bell test work, step by step?
The short answer (tap to open)
A Bell test sends entangled pairs to two labs, each choosing between two settings at random. For each of the four setting combinations you work out how strongly the results match, then combine the four into one score. Any pre-written plan scores 2 at most. Quantum theory predicts about 2.83, and experiments find it.
What are the ingredients?
Two labs, Alice's and Bob's. A source sends them entangled photon pairs. Each lab has two possible filter settings and picks one at random for every pair, after the photons have left the source. Each result is +1 (passed) or −1 (blocked).
How do you score it?
For each of the four combinations of settings, multiply the two results for every pair and average them. That average is the correlation: +1 if they always match, −1 if they always differ, 0 if there's no link. Then combine the four correlations, adding three and subtracting one:
S = C₁ + C₂ + C₃ − C₄
John Clauser, Michael Horne, Abner Shimony and Richard Holt showed in 1969 that any pre-written plan gives S between −2 and 2. Quantum theory, with the best settings (filters at 0° and 45° for Alice, 22.5° and 67.5° for Bob), predicts S ≈ 2.83.
What the test gives, in words
With entangled pairs and the best settings (Alice at 0° and 45°, Bob at 22.5° and 67.5°), each correlation is about 0.71 and S comes out at about 2.83. With pre-written instructions, every correlation is +1 or −1, and S is always 2 or −2, whatever the instructions say.
What are the loopholes, and how were they closed?
A clever enough plan could cheat if the experiment leaves gaps:
- Communication: if Alice's setting could reach Bob's lab before his measurement, the photons could coordinate. Fix: put the labs far apart and choose settings so fast that not even light could cross in time.
- Detection: if detectors miss many photons, a plan could hide in which ones the detectors catch. Fix: very efficient detectors, or atoms instead of photons.
- Setting choice: if the settings weren't truly independent of the source, the test fails (that's superdeterminism, page 6b). Fix: fast random number generators, and in 2016, 100,000 people typing choices, and in other tests the light of distant stars.
In 2015 three experiments closed the first two loopholes at once. The third can never be closed completely, only pushed back further.
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Four correlations, one score, one limit.
Plans stop at 2; nature reaches 2.83.