By implicitly assuming that all measurements occur simultaneously, Bell's Theorem only applied to local theories that violated Heisenberg's Uncertainty Principle. By explicitly introducing time into our derivation of Bell's theorem, an extra term related to the time-ordering of actual measurements is found to augment (i.e. weaken) the upper bound of the inequality. Since the same locality assumptions hold for this rederivation as for the original, we conclude that only {\em classical} measurement-order independent local hidden variable theories are constrained by Bell's inequality; time dependent, non-classical local theories (i.e. theories respecting Heisenberg's Uncertainty Principle) can satisfy this new bound while exceeding Bell's limit. Unconditional nonlocality is only expected to occur with Bell parameters between 22 and 4. This weakening of Bell's inequality is seen for the quantum Bell operator (squared) as an extra term involving the commutators of {\em local} measurement operators. We note that a factorizable second-quantized wavefunction can reproduce experimental measurements; because such wavefunctions allow local de Broglie-Bohm hidden variable modelling, we have another indication that violation of {\em Bell's} inequality does not require an acceptance of non-locality.
The celebrated inequalities of Bell are based on the assumption that local hidden parameters exist. When combined with conflicting experimental results these inequalities appear to prove that local hidden parameters cannot exist. This suggests to many that only instantaneous action at a distance can explain Einstein, Podolsky, Rosen (EPR) type of experiments. We show that Bell-type theories and proofs leading to the well-known inequalities completely exclude a large class of time dependencies in their considerations. Owing to the fact that the electrodynamics of moving bodies cannot be described by time-independent theories or models, we conclude that the Bell theorem cannot describe the physics of EPR experiments. We also show how hidden parameter theories that include time can obtain the quantum result.