  This paper furthers the long historical examination of and debate on the
foundations of quantum mechanics (QM) by presenting two local hidden variable
(LHV) rules in the context of the EPRB experiment which violate Bell's
inequality, but which are nevertheless local and deterministic under reasonable
definitions of the terms, and coincide approximately with the conventional QM
prediction. The theories are based on the general idea of probabilistic
detection of particles depending on an interaction of hidden variables within
the measuring device and particle, and relate mathematically to Fourier
analysis. The crucial discrepancy of variations in the hidden variable
distribution based on relative polarizer orientations is isolated which
invalidates assumptions in Bell-type theorems. The first theory can be analyzed
completely symbolically whereas the second was analyzed using numerical
methods. The properties of the second in particular are shown to be
approximately consistent with the reported results and uncertainties in all
three Aspect experiments. Variation in the total photon pairs detected over
orientations is shown to be a basic characteristic of these theories. Some
comments on the relevance of active vs. passive locality are made. Two sections
consider these ideas relative to energy conservation and the measurement
problem (collapse of the wavefunction). One section proposes new experiments.
