Abstract
In a previous article we proposed a new model for quantum gravity (QGR) and cosmology, dubbed SU(∞)-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent the SU(∞) symmetry group. In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the SU(∞) representing Hilbert spaces. Using quantum uncertainty relations, it is shown that the parameter space—the spacetime—has a 3+1 dimensional Lorentzian geometry. Here, after a review of SU(∞)-QGR, including a demonstration that its classical limit is Einstein gravity, we compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by the holographic principle and quantum entanglement. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. The hope is that this exercise provides a better understanding of gravity as a universal quantum force and clarifies the physical nature of the spacetime. We identify several common features among the studied models: the importance of 2D structures; the algebraic decomposition to tensor products; the special role of the SU(2) group in their formulation; the necessity of a quantum time as a relational observable. We discuss how these features can be considered as analogous in different models. We also show that they arise in SU(∞)-QGR without fine-tuning, additional assumptions, or restrictions.
Highlights
Introduction and ResultsSeveral fundamental questions about gravity and spacetime are not still answered by general relativity or by various attempts to find a consistent quantum description for gravitational interaction
One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent the SU(∞) symmetry group
From comparison of the SU(∞)-quantum gravity (QGR) proposal with some of other approaches to QGR, we recognized a series of similar aspects, symmetries, and structures, which despite their different roles and interpretations in different models, can be considered as analogous and common
Summary
Several fundamental questions about gravity and spacetime are not still answered by general relativity or by various attempts to find a consistent quantum description for gravitational interaction. We remind that the tensor product of Hilbert spaces of subsystems is important for gravitational interaction, and for meaningful definition of locality, quantum clocks, quantum information flow and relative entropy, renormalization flow, and holographic properties of states None of these concepts would make sense without mathematical and physical notion of distinguishable subsystems. SU(∞)-QGR is a fundamentally quantum model, in the sense that its axioms come from quantum physics and its formulation is not a quantized version of a classical model It does not include in its foundation, neither explicitly nor implicitly, a background spacetime or ingredients from Einstein general relativity, such as an entropy–area relation.
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