However, in the strong coupling limit of QGR spacetime/gravity and matter may be indistinguishable. A priori, the same concept can be applied to QGR. In QFTs without gravity, subsystems are particles /fields or their collections. Indeed, we will see later in this work that some QGR models struggle to find a naturally factorized-tensor product-Hilbert space in which each factor can be considered as presenting the Hilbert space of a subsystem. This concept has special importance for gravity, because as far as we know from general relativity, it is a universal force, coupling everything to the rest of the Universe. In addition, progress in quantum information has highlighted the crucial role of the division of the Universe in parts-subsystems-and thereby, the necessity for a proper mathematical definition of what can be considered as a distinguishable quantum (sub)system. They are sometimes called Quantum First models in the literature . In the last decade or so progress in quantum information theory has motivated the construction of QGR models which are not based on the quantization of a classical theory. We also show that they arise in S U ( ∞ )-QGR without fine-tuning, additional assumptions, or restrictions. We discuss how these features can be considered as analogous in different models. 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 S U ( 2 ) group in their formulation the necessity of a quantum time as a relational observable. 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. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. Here, after a review of S U ( ∞ )-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. Using quantum uncertainty relations, it is shown that the parameter space-the spacetime-has a 3+1 dimensional Lorentzian geometry. In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the S U ( ∞ ) representing Hilbert spaces. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent the S U ( ∞ ) symmetry group. In a previous article we proposed a new model for quantum gravity (QGR) and cosmology, dubbed S U ( ∞ )-QGR.
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