  We consider the dynamics of the Sorkin-Johnston (SJ) state for a massless
scalar field in two dimensions. We conduct a study of the renormalized
stress-tensor by a subtraction procedure, and compare the results with those of
the conformal vacuum, with an important contribution from correction term. We
find a large trace anomaly and compute backreaction effects to two dimensional
(Liouville) gravity. We find a natural interpretation for the mirror behavior
of the SJ state described in previous works.
