Models for Discrete Quantum Gravity

Rodolfo Gambini, Rafael A. Porto, Jorge A. Pullin

Abishev Medeu, Berkimbayev Daulet

Caner Ateş

Stephen D. H. Hsu

Quantum gravitational effects suggest a minimal length, or spacetime interval, of order of the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is that quantum states with norm below some very small threshold do not exist. The exclusion of what Everett referred to as maverick branches is necessary for the emergence of the Born Rule in no collapse quantum mechanics. We discuss this in the context of quantum gravity, showing that discrete models (such as simplicial or lattice quantum gravity) indeed suggest a discrete Hilbert space with minimum norm. These considerations are related to the ultimate level of fine-graining found in decoherent histories (of spacetime geometry plus matter fields) produced by quantum gravity.

Dean P. Rickles, Xerxes D. Arsiwalla, Hatem Elshatlawy

Roman V. Buniy, Stephen D. H. Hsu, A. Zee

We show that discretization of spacetime naturally suggests discretization of Hilbert space itself. Specifically, in a universe with a minimal length (for example, due to quantum gravity), no experiment can exclude the possibility that Hilbert space is discrete. We give some simple examples involving qubits and the Schrödinger wavefunction, and discuss implications for quantum information and quantum gravity.