$\mathbf {SU(\infty)}$-QGR Quantumania: Everything, Everywhere, All At Once

TL;DR

This paper introduces a quantum framework for the universe based on infinite mutually commuting observables, leading to a novel perspective on gravity as an emergent Yang-Mills theory within an $SU( olinebreak ext{(} olinebreak ext{infinity)} olinebreak)$ symmetry context.

Contribution

It proposes a new quantum model of the universe with infinite symmetries, where gravity emerges from internal symmetries and quantum fluctuations induce a division into interacting subsystems.

Findings

Universe modeled as static, topological with continuous parameters

Quantum fluctuations lead to clustering and internal symmetries

Gravity emerges as an $SU( ext{infinity})$ Yang-Mills theory

Abstract

$SU(\infty)$-QGR is a quantum approach to Universe and gravity. Its main assumption is infinite mutually commuting observables in the Universe, leading to representation of $SU(\infty)$ by its Hilbert spaces and those of its subsystems. The Universe as a whole is static, topological, and characterized by two continuous parameters. Nonetheless, quantum fluctuations induce clustering and finite rank internal symmetries, which approximately divide the Universe to infinite interacting subsystems. Their Hilbert space depends on an additional dimensionful parameter, and selection of a subsystem as clock induces a relative dynamics, with $SU(\infty)$ sector as gravity. The Lagrangian defined on the (3+1)-dimensional parameter space is Yang-Mills for both symmetries. When quantumness of gravity is undetectable, it is perceived as curvature of an effective spacetime.