Spacetime from Entanglement — Geometry as Quantum Information

Entanglement doesn’t just correlate particles — it may stitch space itself. Break the entanglement between two regions of a quantum system, and the space between them pinches off. In 2010, Mark van Raamsdonk showed that cutting entanglement in a boundary quantum field theory literally severs the geometry of its gravitational dual. Space isn’t a stage. It’s a web of quantum links — and if you remove the links, the stage collapses.

The case: how entanglement builds geometry

In the AdS/CFT correspondence, a quantum field theory without gravity (on the boundary) encodes a theory of gravity in a higher-dimensional curved spacetime (the bulk). In 2010, van Raamsdonk demonstrated that the amount of entanglement in the boundary state controls the connectivity of the bulk. His key setup: two copies of a CFT in a thermofield double state,

|TFD⟩ = Σ_n e^{-βE_n/2} |n⟩_L |n⟩_R

This state is maximally entangled and dual to an eternal anti-de Sitter (AdS) black hole — a two-sided wormhole connecting two exterior universes. Reduce the entanglement by tuning the temperature or perturbing the state, and the wormhole stretches, thins, and eventually pinches off into two disconnected spacetimes. No entanglement, no bridge.

The Ryu-Takayanagi formula makes this precise: the entanglement entropy S(A) of a boundary region A equals the area of the minimal bulk surface γ_A that divides the corresponding bulk region:

S(A) = Area(γ_A) / (4G_N)

This is not an analogy. It is a mathematical equivalence in the duality. Geometry becomes a proxy for quantum correlation. Each Planck area (ℓₚ² ≈ 2.6×10⁻⁶⁶ cm²) on γ_A contributes roughly one qubit of entanglement.

Specific examples: tensor networks and ER=EPR

MERA (2009): Brian Swingle observed that the multi-scale entanglement renormalization ansatz (MERA), developed by Guifré Vidal for condensed matter systems, has a network geometry identical to a discrete slice of AdS space. The depth of the network maps to the radial direction in AdS — energy scale becomes radial distance. MERA isn’t just a computational tool; it’s a toy universe where spacetime is the circuit layout needed to build a quantum state.

HaPPY code (2015): Pastawski, Yoshida, Harlow, and Preskill built tensor networks where bulk points are encoded in boundary regions via quantum error correction. A bulk qubit can be reconstructed from any boundary region larger than half the total — exactly the threshold for a quantum error-correcting code. This means: local bulk geometry is protected by global boundary entanglement.

ER=EPR (2013): Maldacena and Susskind conjectured that every entangled pair — whether electrons, photons, or Hawking radiation quanta — is connected by a Planck-scale, non-traversable wormhole. The EPR paradox (quantum entanglement) and the ER bridge (geometric connection) are not coincidental; they are dual descriptions. In 2024, this was elevated to an operational theorem in the LOCC framework: simulating entanglement between two agents requires a wormhole-like geometric structure in the dual gravitational description. The entanglement isn’t like a bridge. It is the bridge.

What’s contested

The hard question: does this mean spacetime is literally emergent in our universe — or is this just a property of highly symmetric models like AdS/CFT?

AdS space is not our universe. Ours is asymptotically de Sitter, not anti-de Sitter, and lacks a timelike boundary where a CFT could live. While similar entanglement-geometry links appear in de Sitter models (e.g., 2024 calculations of complexity in the Bunch-Davies vacuum), there is no full duality analogous to AdS/CFT. The precise mechanism by which 3D space emerges from entanglement in flat or expanding spacetime remains undefined.

Another open issue: causality. If spacetime emerges from entanglement, how do causal relations — which appear fundamental in relativity — arise from quantum correlations that are acausal by nature? Current tensor network models reproduce spatial geometry but struggle with time evolution and dynamical gravity. The emergence of causal structure is not yet understood.

Why this has to do with other realms

This idea — that a geometric reality is encoded in lower-dimensional information — appears in systems with no physics in common. Consider dest bagan: more than 3,000 Buddhist temples were built in a grid across 40 km² of dry plain between the 9th and 13th centuries. No central plan survives. Yet the system self-organized into a stable, navigable spatial structure through local ritual and economic rules. Like the bulk geometry in AdS/CFT, Bagan’s spatial order emerges not from a master map but from repeated, entangled decisions. The city, too, is encoded in its social “boundary theory.” Both cases suggest: structure can be non-local, and space can be a consensus.

An open question

If a region of space can dissolve when entanglement vanishes, could we — even in principle — detect the moment a microscopic volume of space ceases to exist? What instrument would register that?

Key sources

Van Raamsdonk, M. (2010) — "Building up spacetime with quantum entanglement" — reinterprets entanglement as the foundation of spatial connectivity.
Ryu, S. and Takayanagi, T. (2006) — “Holographic derivation of entanglement entropy” — the original RT formula.
Maldacena, J. and Susskind, L. (2013) — “Cool horizons for entangled black holes” — introduces ER=EPR.
Swingle, B. (2009–2012) — foundational work linking MERA to AdS geometry.
Pastawski, F. et al. (2015) — HaPPY tensor networks as holographic codes.
Harlow, D. (2018) — “TASI lectures on the emergence of bulk physics” — review (to verify: exact year may vary by publication).

Abhishek