Discrete Quantum Gravity is not Isometric
Discrete quantum gravity, isometric dynamics
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 µ (or equivalently the decoherence functional) is generated by an isometric dynamics, then there is no interference between events so the system describing evolving universes is classical. The result follows from a forbidden configuration in the path space of causal sets.
Gudder, S. (2011). Discrete quantum gravity is not isometric. Mathematics Preprint Series. Retrieved from https://digitalcommons.du.edu/math_preprints/34