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Argh - yes it can. Bell explicitly have a pretty trivial one in one of his early papers. QM cannot be explained by a non-contextual hidden variables model. (The simplest physical version of contextuality is locality - so as Bell showed you cannot explain quantum theory with a local hidden variables model).

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Let's not break causality by observing non-local hidden variables.

Presumably talking to the wind here as this thread is old, but nonlocal hidden variables do not break causality! This can be seen explicitly in Bell's trivial model, where the state of a system is just the regular quantum state plus a uniform random number between 0 and 1 (hidden). Or put it this way, if this model "breaks causality" then so does regular non-relativistic quantum theory.

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