  Bell's theorem is purported to demonstrate the impossibility of a local
"hidden variable" theory underpinning quantum mechanics. It relies on the
well-known assumption of `locality', and also on a little-examined assumption
called `statistical independence' (SI). Violations of this assumption have
variously been thought to suggest "backward causation", a "conspiracy" on the
part of nature, or the denial of "free will". It will be shown here that these
are spurious worries, and that denial of SI simply implies nonlocal correlation
between spacelike degrees of freedom. Lorentz-invariant theories in which SI
does not hold are easily constructed: two are exhibited here. It is
conjectured, on this basis, that quantum-mechanical phenomena may be modeled by
a local theory after all.
