  We show that if a discrete quantum gravity is not classical, then it cannot
be generated by an isometric dynamics. In particular, we show that if the
quantum measure {\mu} (or equivalently the decoherence functional) is generated
by an isometric dynamics, then there is no in- terference between events so the
system describing evolving universes is classical. The result follows from a
forbidden configuration in the path space of causal sets.
