  It was shown by Bell that no local hidden variable model is compatible with
quantum mechanics. If, instead, one permits the hidden variables to be entirely
non-local, then any quantum mechanical predictions can be recovered. In this
paper, we consider general hidden variable models which can have both local and
non-local parts. We then show the existence of (experimentally verifiable)
quantum correlations that are incompatible with any hidden variable model
having a non-trivial local part, such as the model proposed by Leggett.
