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

The Sorkin-Johnston State in a Patch of the Trousers Spacetime