A Minimal Model for Quantum Gravity

TL;DR

This paper proposes a minimal, discrete quantum gravity model using a quantum computer framework with N qubits on a fuzzy sphere, aligning with key principles like Lorentz invariance and holography, and describing black hole area quantization.

Contribution

It introduces a minimal quantum gravity model based on quantum computing concepts, linking fuzzy spheres, spin networks, and black hole spectra in a novel way.

Findings

Model is discrete, parameter-free, and Lorentz invariant.

Realizes the Holographic Principle naturally.

Provides a discrete, non-uniform area spectrum for quantum black holes.

Abstract

We argue that the model of a quantum computer with N qubits on a quantum space background, which is a fuzzy sphere with n=2^N elementary cells, can be viewed as the minimal model for Quantum Gravity. In fact, it is discrete, has no free parameters, is Lorentz invariant, naturally realizes the Holographic Principle, and defines a subset of punctures of spin networks' edges of Loop Quantum Gravity labelled by spins j=2^(N-1)-1/2. In this model, the discrete area spectrum of the cells, which is not equally spaced, is given in units of the minimal area of Loop Quantum Gravity (for j=1/2), and provides a discrete emission spectrum for quantum black holes. When the black hole emits one string of N bits encoded in one of the n cells, its horizon area decreases of an amount equal to the area of one cell.