The modal interpretation of quantum mechanics allows one to keep the standard
classical definition of realism intact. That is, variables have a definite
status for all time and a measurement only tells us which value it had.
However, at present modal dynamics are only applicable to situations that are
described in the orthodox theory by projective measures. In this paper we
extend modal dynamics to include positive operator measures (POMs). That is,
for example, rather than using a complete set of orthogonal projectors, we can
use an overcomplete set of nonorthogonal projectors. We derive the conditions
under which Bell's stochastic modal dynamics for projective measures reduce to
deterministic dynamics, showing (incidentally) that Brown and Hiley's
generalization of Bohmian mechanics [quant-ph/0005026, (2000)] cannot be thus
derived. We then show how {\em deterministic} dynamics for positive operators
can also be derived. As a simple case, we consider a Harmonic oscillator, and
the overcomplete set of coherent state projectors (i.e. the Husimi POM). We
show that the modal dynamics for this POM in the classical limit correspond to
the classical dynamics, even for the nonclassical number state ∣n⟩. This
is in contrast to the Bohmian dynamics, which for energy eigenstates, the
dynamics are always non-classical.Comment: 14 page
