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Pré-Publication, Document De Travail Année : 2023

$SU(\infty)$-QGR: Emergence of Gravity in an Infinitely Divisible Quantum Universe

Résumé

$SU(\infty)$-QGR (SQGR) s a foundationally quantum approach to gravity. It assumes that Hilbert spaces of the Universe as a whole and its subsystems represent the symmetry group $SU(\infty)$. The Universe is divided to infinite number of subsystems based on an arbitrary finite rank symmetry group, which arises due to quantum fluctuations and clustering of states. After selection of two arbitrary subsystems as clock and reference observer, subsystems acquire a relative dynamics, and gravity emerges as a $SU(\infty)$ Yang-Mills quantum field theory, defined on the (3+1)-dimensional parameter space of Hilbert spaces of the subsystems. At classical limit, this observer is perceived as the spacetime. Consequently, SQGR explains both the dimension of and signature of spacetime. As a Yang-Mills model SQGR is renormalizable and despite prediction of a spin-1 field for gravity at quantum level, at low energies it is perceived as classical Einstein model. The aim of the present work is to make the foundation of SQGR more mathematically rigorous and fill the gaps in the construction of the model reported in earlier works. In particular, we show that the global $SU(\infty)$ symmetry manifests itself through the entanglement of every subsystem with the rest of the Universe. Moreover, we demonstrate irrelevance of the geometry of parameter space, which can be gauged out by a $SU(\infty)$ gauge transformation up to an irrelevant constant. Therefore, SQGR deviates from gauge-gravity duality models, because the perceived classical spacetime is neither quantized, nor considered to be noncommutative. On the other hand, using quantum uncertainty relations, we demonstrate that the classical spacetime and its perceived geometry present the average path of the ensemble of quantum states of subsystems in their parameter space. We also briefly discuss SQGR specific models for dark energy.

Dates et versions

hal-03952241 , version 1 (23-01-2023)

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Citer

Houri Ziaeepour. $SU(\infty)$-QGR: Emergence of Gravity in an Infinitely Divisible Quantum Universe. 2023. ⟨hal-03952241⟩
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