Cellular automaton for spinor gravity in four dimensions

TL;DR

This paper constructs a four-dimensional cellular automaton model of spinor gravity that exhibits local Lorentz symmetry exactly and emergent diffeomorphism symmetry in the continuum limit, providing insights into quantum gravity.

Contribution

It introduces a discrete automaton model of spinor gravity with exact Lorentz symmetry and emergent diffeomorphism symmetry, linking cellular automata to quantum gravity concepts.

Findings

Lorentz symmetry is exact at the discrete level.

Diffeomorphism symmetry emerges in the continuum limit.

Coarse graining leads to probabilistic evolution of configurations.

Abstract

Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four dimensions. Local Lorentz symmetry is exact on the discrete level and diffeomorphism symmetry emerges in the naive continuum limit. Our setting could serve as a model for quantum gravity if diffeomorphism symmetry is realized in the true continuum limit and suitable collective fields for vierbein and metric acquire nonvanishing expectation values. The discussion of this interesting specific model reveals may key qualitative features of the continuum limit for probabilistic cellular automata. This limit obtains for a very large number of cells if the probabilistic information is sufficiently smooth. It is associated to coarse graining. The automaton property that every bit configuration is updated at every discrete time step to precisely one new bit configuration does no longer hold on the coarse grained level. A coarse grained configuration of occupation numbers can evolve into many different configurations with certain probabilities. This characteristic feature of quantum field theories can come along with the emergence of continuous space-time symmetries.