measurement independence

Measurement independence is a quiet but crucial assumption sitting underneath every Bell test. It says that the choice of which measurement to perform — which way to orient a detector — is statistically independent of the hidden properties the particles carry before they are measured. In plain terms, the experimenters are free to choose their settings, and nature has not secretly arranged those choices to correlate with the particles.

This assumption matters because Bell's theorem only forces its dramatic conclusion if it holds. Bell showed that local hidden variables cannot reproduce quantum correlations; but the proof tacitly assumes the settings are freely chosen. If instead some common cause in the deep past fixed both the particles' properties and the experimenters' choices in a coordinated way, the correlations could be faked locally. This loophole is called superdeterminism.

Most physicists regard giving up measurement independence as a steep price — it would mean the universe conspires so thoroughly that even random number generators and distant quasar light, used to set detectors, are correlated with what is being measured. Such conspiracy would also undermine the basic logic of doing experiments at all. The assumption is therefore usually kept, and its honest status is that it is a reasonable but logically optional premise, not a proven fact.