Two photons fly apart to Alice and Bob, who each measure polarization at an angle they pick. Each result alone is a coin flip. Together they agree more often than any pre-arranged plan could manage.
Each dot is your measured agreement rate at one angle difference. Sweep Bob's polarizer to fill in the curve.
Alice randomly picks 0° or 45°, Bob randomly picks 22.5° or 67.5°, for 20,000 pairs. Score each setting by how much results agree (+1 all agree, −1 all disagree), then combine: S = E(0°,22.5°) + E(45°,22.5°) + E(45°,67.5°) − E(0°,67.5°). Any theory where photons carry instructions from the source scores at most 2.
| Alice, Bob | Quantum E | Hidden-instr. E |
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Press the button to run both universes side by side.
A polarizer lets a photon through or blocks it. For one photon on its own, it's always 50/50. For an entangled pair, if Alice and Bob set the same angle they always agree. Set them 90° apart and they always disagree. In between, quantum mechanics says they agree with probability cos²(angle difference).
The "hidden instructions" universe is Einstein's hope: each pair leaves the source carrying a shared secret, say a preferred angle, and each photon just follows it. That plan can match the 0° and 90° cases perfectly, but in between it can only manage a straight line.
John Bell proved in 1964 that no theory with local hidden instructions can score above 2. Experiments starting with Clauser (1972) and Aspect (1982), and loophole-free tests in 2015, keep getting about 2.8. Nature is not running on hidden instructions.
It still can't be used to send a message: Bob's own results are pure coin flips whatever Alice does. The correlation only shows up when they compare notes.
Entanglement can't send a message by itself, but correlations that no hidden-instruction plan can fake turn out to be a resource. These are the uses being built now.
In entanglement-based quantum key distribution, Alice and Bob turn their matching results into a shared secret key. Any spy who intercepts the photons has to measure them, which breaks the correlations, and a Bell test shows it. China's Micius satellite shared entangled photons between ground stations 1,200 km apart in 2017.
In the demo: equal angles give perfectly matching tapes, a ready-made shared key.If a Bell test scores above 2, the results cannot have been written in advance, so they are provably unpredictable. NIST and the University of Colorado run a public randomness beacon built on this idea, useful for lotteries, audits and fair selection.
In the demo: each tape on its own is a fair coin no one could have scripted.A quantum computer's power comes from qubits that are entangled with each other, so the machine works on correlations that no list of classical values can describe. Quantum error correction also uses entanglement to spread one qubit's information across many.
In the demo: the cos² curve is the extra correlation classical bits can't reach.Using a shared entangled pair plus an ordinary message, a quantum state can be moved from one place to another without sending the particle itself. First shown in 1997, it is the basis for quantum repeaters that would link quantum computers into a network.
In the demo: the effect only appears once Alice and Bob compare notes.Independent atoms in a clock each add their own random noise. Entangling them lets the noise partly cancel, so the clock ticks more precisely than the limit for independent atoms. The same idea is being used to sharpen magnetic and gravity sensors.
In the demo: correlated results are more predictable as a group than as individuals.Bell tests turned a philosophical argument into an experiment. The 2015 loophole-free tests in Delft, Vienna and Boulder, and the 2022 Nobel Prize for Aspect, Clauser and Zeilinger, settled that nature does not run on local hidden instructions.
In the demo: press Run the Bell test and you have repeated their analysis.