Scrutable

... we see the need to correct an unfortunate mistake in the Editorial, which is the statement: “One route out of this paradox could be an undetected, so-called hidden variable associated with both particles that underlies the correlated behaviour. However, John Stewart Bell proved that such an approach cannot explain the quantum mechanical outcomes. Any theory that uses hidden variables still requires non-local physics.”

This passage reflects a common misconception that Bell’s theorem proves that hidden variable theories reproducing quantum mechanics require non-local physics. In fact, locally causal completions of quantum mechanics are possible, if they violate the assumption that the hidden variables do not in any way depend on measurement settings.

There is no independent evidence that this assumption — commonly known as statistical independence — is fulfilled for quantum systems. As a consequence, the observed violations of Bell’s inequality can be said to show that maintaining local causality requires violating statistical independence. We wish to stress that this is not merely an issue of interpretation. The statistical independence assumption is mathematically necessary for the formulation of Bell-type inequalities.

Types of local hidden variables theories that violate statistical independence include those that are superdeterministic, retrocausal and supermeasured...