[Paper Review] Comments on quantum gravity and entanglement

Mark Van Raamsdonk|arXiv (Cornell University)|Jul 17, 2009

Black Holes and Theoretical PhysicsPhysics and Astronomy38 references159 citations

TL;DR

This paper argues that quantum entanglement between microscopic degrees of freedom is essential for the emergence of spacetime in holographic quantum gravity. Using gauge-theory/gravity duality, it shows that spacetime geometry arises from entangled quantum states in a non-perturbative framework, with entanglement linking disconnected regions into a connected spacetime, and proposes that entanglement structure may directly encode geometric properties.

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.

Motivation & Objective

• To understand how spacetime geometry emerges from non-perturbative quantum gravity using known examples of gauge-theory/gravity duality.
• To investigate the role of quantum entanglement in connecting spacetime regions and forming a coherent spacetime manifold.
• To explore whether the Hilbert space structure of quantum systems can describe global spacetime through patchwise quantum descriptions.
• To examine whether entanglement measures can have direct geometric interpretations in quantum gravity.

Proposed method

• Analyzes known examples of gauge-theory/gravity duality, particularly AdS/CFT, to study how spacetime arises from quantum systems.
• Maps states and density matrices in conformal field theories (CFTs) to different causal patches of spacetime, using isomorphisms and non-injective maps between Hilbert spaces.
• Uses toy models of spin chains and harmonic oscillators to study the emergence of radial direction in spacetime from quantum energy spectra.
• Examines the density of states in large-N gauge theories, showing exponential growth consistent with macroscopic spacetime emergence.
• Applies quantum information concepts—such as reduced density matrices and entanglement eigenvalues—to three-qubit systems to explore geometric encoding of entanglement.
• Investigates the condition under which eigenvalues of single-site density matrices form a valid triangle, suggesting a geometric interpretation of entanglement.

Experimental results

Research questions

• RQ1 How does spacetime geometry emerge from non-perturbative quantum gravity in holographic dualities?
• RQ2 What is the precise role of quantum entanglement in connecting classically disconnected spacetime regions into a single, connected spacetime?
• RQ3 Can the structure of quantum entanglement in a CFT fully encode the geometry of the dual spacetime?
• RQ4 Under what conditions does a quantum system's energy spectrum give rise to a macroscopic radial direction in emergent spacetime?
• RQ5 Can entanglement measures such as eigenvalues of reduced density matrices be interpreted as geometric invariants?

Key findings

• In holographic dualities, a single spacetime can be described as a quantum superposition of disconnected spacetime regions, with entanglement linking them into a connected geometry.
• Spacetime regions correspond to quantum states or density matrices in specific quantum systems, with different causal patches mapped to different CFTs (e.g., S^d×R, R^{d,1}, H^d×R).
• Entanglement between degrees of freedom in the boundary CFT is essential for the emergence of a connected spacetime; decreasing entanglement reduces the spatial separation between regions.
• The exponential growth of the density of states in large-N gauge theories (e.g., ρ(E) ∼ e^{cE}) is necessary for a macroscopic radial direction to emerge from a quantum system with a reasonable energy scale range.
• For three-qubit systems, the entanglement structure is completely encoded in the eigenvalues of single-spin density matrices, which form a triangle if and only if a valid quantum state exists.
• For n-qubit systems, the entanglement structure is constrained by polygonal inequalities on the eigenvalues of reduced density matrices, suggesting a general geometric interpretation of entanglement.