  The machinery of quantum mechanics is fully capable of describing a single
realistic world. Here we discuss the converse: in spite of appearances, and
indeed numerous claims to the contrary, any quantum mechanical model can be
mimicked, up to any finite accuracy, by a completely classical system of
equations. An implication of this observation is that Bell's theorem is not
applicable in the cases considered. This is explained by scrutinising Bell's
assumptions concerning causality, retrocausality, statistical (in-)dependence,
and his fear of `conspiracy' (there is no conspiracy in the language used to
describe the deterministic models). The most crucial mechanism for the counter
intuitive Bell/CHSH violation is the fact that, regardless the settings chosen
by Alice and Bob, the initial state of the system should be a realistic one.
The potential importance of our construction in model building is discussed.
