  By implicitly assuming that all possible Bell-measurements occur
simultaneously, all proofs of Bell's Theorem violate Heisenberg's Uncertainty
Principle. This assumption is made in the original form of Bell's inequality,
in Wigner's probability inequalities, and in the ``nonlocality without
inequalities'' arguments. The introduction of time into derivations of these
variants of Bell's theorem results in extra terms related to the time order of
the measurements used in constructing correlation coefficients. Since the same
locality assumptions are made in the Heisenberg-compliant derivations of this
paper, only time-independent classical local hidden variable theories are
forbidden by violations of the original Bell inequalities; time-dependent
quantum local hidden variable theories can satisfy this new bound and agree
with experiment. We further point out that factorizable wavefunctions have been
used to describe some EPR experiments and can be used to describe others. These
will generate local de Broglie-Bohm trajectories in the description of the
data. This second, independent, line of argument also shows that violation of
Bell's inequality is only evidence that Heisenberg's Uncertainty Principle
cannot be ignored.
