Comments on quantum gravity and entanglement

TL;DR

The paper argues that non-perturbative quantum gravity in holographic theories can be understood as a patchwork of conventional quantum systems, with spacetime geometry emerging from entanglement among their degrees of freedom. It connects geometric connectivity to quantum information measures like entanglement entropy and mutual information via the Ryu–Takayanagi prescription and thermofield-double constructions, and demonstrates how connected spacetimes can arise as quantum superpositions of disconnected patches. The discussion includes a concrete toy model mapping a harmonic oscillator to a spin chain to illustrate emergent radial directions and UV/IR relations, and emphasizes that highly entangled low-energy states are a hallmark of holographic duals. The work surveys the role of entanglement in glueing spacetime, the potential universality of entanglement-based geometry, and the conditions under which gravity-like dynamics may emerge from quantum degrees of freedom.

Abstract

In this note, we attempt to provide some insights into the structure of non-perturbative descriptions of quantum gravity using known examples of gauge-theory / gravity duality. We argue that in familiar examples, a quantum description of spacetime can be associated with a manifold-like structure in which particular patches of spacetime are associated with states or density matrices in specific quantum systems. We argue that quantum entanglement between microscopic degrees of freedom plays an essential role in the emergence of a dual spacetime from the nonperturbative degrees of freedom. In particular, in at least some cases, classically connected spacetimes may be understood as particular quantum superpositions of disconnected spacetimes.

Figures (13)

• Figure 1: Proposed mathematical structure of an asymptotically AdS quantum spacetime. For some choice of causal patches, we have a quantum systems associated to each patch and a set of maps between the spaces of states for the quantum system. For the example shown, a given spacetime can be associated with a state $| \Psi \rangle_A$ of the CFT on $S^d \times R$. This maps to a pure state of the CFT on $R^{d,1}$ associated with the Poincare patch $B$ and to mixed states of the CFTs on $H^d \times R$ associated with the smaller causal patches $C$ and $D$. See section 2 for details.
• Figure 2: Effect on geometry of decreasing entanglement between holographic degrees of freedom corresponding to $A$ and $B$: area separating corresponding spatial regions decreases while distance between points increases.
• Figure 3: Representative massive geodesic in Poincare-AdS spacetime.
• Figure 4: The same geodesic in the global spacetime. The full evolution in Poincare time corresponds to evolution for a finite proper time, the solid part of the complete geodesic (which extends to $\tau = \pm \infty$).
• Figure 5: Global AdS spacetime, showing the Poincare patch. This is the region inside the past and future light sheets emanating from a particular boundary point P, or the causal patch accessible to certain accelerated observers.