  Bell's inequalities rely on the assumption of measurement independence,
namely that the probabilities of adopting configurations of hidden variables
describing a system prior to measurement are independent of the choice of
physical property that will be measured. Weakening this assumption can change
the inequalities to accommodate experimental data. We illustrate this by
considering quantum measurement to be the dynamical evolution of hidden
variables to attractors in their phase space that correspond to eigenstates of
system observables. The probabilities of adopting configurations of these
variables prior to measurement then depend on the choice of physical property
measured by virtue of the boundary conditions acting on the dynamics. Allowing
for such measurement dependence raises the upper limit of the CHSH parameter in
Bell's analysis of an entangled pair of spin half particles subjected to
measurement of spin components along various axes, whilst maintaining local
interactions. We demonstrate how this can emerge and illustrate the relaxed
upper limit using a simple toy model of dynamical quantum measurement. The
conditioning of the hidden variable probability distribution on the chosen
measurement settings can persist far back in time in certain situations, a
memory that could explain the correlations exhibited in an entangled quantum
system.
