  Do diffusive non-Markovian stochastic Schr\"odinger equations (SSEs) for open
quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A
66, 012108 (2002)] we investigated this question using the orthodox
interpretation of quantum mechanics. We found that the solution of a
non-Markovian SSE represents the state the system would be in at that time if a
measurement was performed on the environment at that time, and yielded a
particular result. However, the linking of solutions at different times to make
a trajectory is, we concluded, a fiction. In this paper we investigate this
question using the modal (hidden variable) interpretation of quantum mechanics.
We find that the noise function $z(t)$ appearing in the non-Markovian SSE can
be interpreted as a hidden variable for the environment. That is, some chosen
property (beable) of the environment has a definite value $z(t)$ even in the
absence of measurement on the environment. The non-Markovian SSE gives the
evolution of the state of the system ``conditioned'' on this environment hidden
variable. We present the theory for diffusive non-Markovian SSEs that have as
their Markovian limit SSEs corresponding to homodyne and heterodyne detection,
as well as one which has no Markovian limit.
