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Bell's theoremtheorem

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Entangled particles behave as if connected by an invisible thread. Measuring one instantly determines the state of the other, no matter how far apart they are. Bell's theorem proves that this is not a trick: no prearranged plan can explain such correlation without faster-than-light interaction.

How it works

Bell inequalities are tested on pairs of photons. Entangled photons fly apart, and in remote laboratories their polarization is measured at different angles. Statistical analysis of correlations shows whether they exceed the classical limit. If so, it means the particles truly interact non-locally. This forms the basis of quantum cryptography — an eavesdropper cannot listen in without being detected because they would disrupt the correlations.

💡 Imagine two suspects who give identical answers during interrogation, even without conspiring. If they had prearranged, the correlation of their answers could not exceed a certain limit — Bell's inequality. Experiments show this limit is violated.
|E(a,b) - E(a,b')| + |E(a',b) + E(a',b')| \leq 2
E(a,b) is the expectation value of the product of the measurement outcomes (±1) for analyzer orientations a and b; a, a', b, b' are different measurement directions for the two particles. Violation of the inequality means that the predictions of quantum mechanics cannot be reproduced by a local realistic theory.
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Discovered by
Abner ShimonyAlain AspectAnton ZeilingerArtur EkertDaniel GreenbergerJohn Clauser
Related concepts
quantum entanglementwave functionQuantum superpositionHilbert space
Related laws
Heisenberg uncertainty principlesuperposition principlespin–statistics theorem

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