  If the Lagrangian of nature respects parity invariance then there are two
distinct possibilities: either parity is unbroken by the vacuum or it is
spontaneously broken. We examine the two simplest phenomenologically consistent
gauge models which have unbroken and spontaneously broken parity symmetries,
respectively. These two models have a Lagrangian of the same form, but a
different parameter range is chosen in the Higgs potential. They both predict
the existence of dark matter and can explain the MACHO events. However, the
models predict quite different neutrino physics. Although both have light
mirror (effectively sterile) neutrinos, the ordinary-mirror neutrino mixing
angles are unobservably tiny in the broken parity case. The minimal broken
parity model therefore cannot simultaneously explain the solar, atmospheric and
LSND data. By contrast, the unbroken parity version can explain all of the
neutrino anomalies. Furthermore, we argue that the unbroken case provides the
most natural explanation of the neutrino physics anomalies (irrespective of
whether evidence from the LSND experiment is included) because of its
characteristic maximal mixing prediction.
