  A quantum scalar field in a patch of a fixed, topology-changing, $1+1$
dimensional "trousers" spacetime is studied using the Sorkin-Johnston
formalism. The isometry group of the patch is the dihedral group, the symmetry
group of the square. The theory is shown to be pathological in a way that can
be interpreted as the topology change giving rise to a divergent energy, in
agreement with previous results. In contrast to previous results, it is shown
that the infinite energy is localised not only on the future light cone of the
topology changing singularity, but also on the past cone, due to the time
reversal symmetry of the Sorkin-Johnston state.
