Discrete Quantum Gravity Is Not Isometric

TL;DR

This paper demonstrates that non-classical discrete quantum gravity models cannot be derived from isometric dynamics, implying that such models inherently involve interference effects and are fundamentally non-classical.

Contribution

It establishes a fundamental link between isometric dynamics and classicality in discrete quantum gravity, showing non-isometric models must exhibit quantum interference.

Findings

Isometric dynamics implies classical behavior with no interference.

Non-classical models cannot be generated by isometric dynamics.

Forbidden configurations in causal set path space prevent non-classical models from being isometric.

Abstract

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.