Problem
Two entangled photons have correlated polarisations. Measured with parallel polarizers, they always give the same outcome. Why is this correlation not enough to conclude that the polarisation was predetermined? Argue by citing Bell’s inequalities and the Aspect experiments.
Solution
The “naive” explanation (hidden variables). The fact that two photons always give the same outcome with parallel polarizers could easily be explained by supposing that each photon carries an “instruction” fixed at the origin: an identical predetermined polarisation for the two. This is the local hidden variables hypothesis: the correlation would be like that of two gloves sent in different boxes — if one is left-handed, the other is certainly right-handed, with nothing mysterious about it.
Why the parallel case alone does not decide. With parallel polarizers both theories — quantum and hidden variables — predict perfect correlation. The two models are indistinguishable in that configuration: perfect correlation by itself neither proves nor rules out predetermination.
Bell’s idea. Bell (1964) showed that if the two photons are measured with polarizers at different angles (not only parallel), the two theories predict quantitatively different correlations. Every local hidden variable theory must satisfy an inequality (Bell / CHSH) that limits how strong the correlations can be. Quantum mechanics predicts correlations that violate that inequality for certain choices of angles.
Aspect’s verdict. Alain Aspect’s experiments (1981–1982), and later the “loophole-free” tests of 2015, measure exactly these correlations at multiple angles and find a violation of Bell’s inequalities, in agreement with the quantum prediction.
Conclusion. The observed correlation does not arise from locally predetermined polarisations: no local hidden variable theory can reproduce the data. The properties were not defined before the measurement, and the correlations between the two photons are non-local in Bell’s sense. Nature is genuinely quantum, not a hidden clockwork.
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Topics: Fisica quantistica Concepts: Entanglement · Polarizzazione e legge di Malus