  Theories which have fundamental information destruction or decoherence are
motivated by the black hole information paradox where one appears to have pure
states evolving into mixed states. However such theories have either violated
conservation laws, or are highly non-local. Here, we show that the tension
between conservation laws and locality can be circumvented by constructing a
relational theory of information destruction. In terms of conservation laws, we
derive a generalisation of Noether's theorem for general theories, and show
that symmetries imply a strong restriction on the type of evolution
permissable. With respect to locality, we distinguish violations of causality
from the creation or destruction of space-like seperated correlations. We show
that violations of causality need not occur in a relational framework, although
one can have situations where correlations decay faster than one might
otherwise expect or can be created over spatial distances. This creation or
destruction of correlations cannot be used to signal superluminally, and thus
no violation of causality occurs. We prove that theories with information
destruction can be made time-symmetric, thus impossing no arrow of time.
