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Spacetime from Entanglement — Geometry as Quantum Information

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Spacetime from Entanglement — Geometry as Quantum Information

The most radical proposal in modern physics: spacetime is not fundamental. It emerges from quantum entanglement. Cut the entanglement between two regions and space tears apart. Stitch it back and space reconnects. The geometry of the universe may be a derived property of quantum information — an output, not an input.

Confidence: established (Ryu-Takayanagi formula connects geometry to entanglement); established (ER=EPR as a conjecture with much supporting evidence); theoretical (spacetime as fully emergent from entanglement); speculative (precise mechanism in our universe)

Van Raamsdonk’s Thought Experiment (2010)

Mark van Raamsdonk published a remarkably simple but profound argument in 2010. Consider two copies of a CFT in a thermofield double (TFD) state:

|TFD⟩ = Σ_n e^{-βEn/2} |n⟩_L |n⟩_R

This state is maximally entangled between the two copies. In the bulk, this corresponds to an eternal AdS black hole — a two-sided wormhole (Einstein-Rosen bridge) with each copy living on one boundary.

Now: Gradually decrease the entanglement. What happens to the bulk?

  • Maximum entanglement → connected wormhole geometry (two sides linked)
  • Partial entanglement → thinner, stretched wormhole geometry
  • Zero entanglement → disconnected spacetime (the wormhole severs; the two bulks become two separate universes)

The conclusion: entanglement holds space together. Without quantum entanglement between boundary degrees of freedom, there is no bulk spacetime connecting them. Geometry is entanglement, written geometrically.

The paper literally ends: “Perhaps it is not unimaginable that in the future, we will be able to say more precisely that the atoms of spacetime are entanglement degrees of freedom of the underlying quantum system, that the glue holding spacetime together is entanglement.”

ER=EPR (Maldacena and Susskind, 2013)

Juan Maldacena and Leonard Susskind conjectured in 2013 that two entangled particles are always connected by an Einstein-Rosen (ER) bridge — a microscopic, non-traversable wormhole. The notation “ER=EPR” conflates:

  • ER: Einstein-Rosen bridge (wormhole)
  • EPR: Einstein-Podolsky-Rosen entanglement

The conjecture: these are two descriptions of the same thing. Every entangled pair — electron spins, photons in a Bell test, Hawking radiation quanta — is connected by a Planck-scale wormhole. What we call quantum entanglement is, geometrically, a microscopic wormhole.

Why This Matters for the Firewall Paradox

ER=EPR provides a possible escape from the AMPS firewall paradox. If an infalling observer is entangled with the outgoing Hawking radiation, and ER=EPR holds, then the observer and the radiation are connected by a (non-traversable) microscopic ER bridge. The “drama” at the horizon is avoided because the seemingly incompatible entanglements are actually consistent via the geometric ER bridge structure.

Status (2024-2026)

ER=EPR has matured from a conjecture to something approaching a theorem in specific contexts:

  • Operational theorem (2024): Published in Physics Letters B, ER=EPR has been proven as an operational theorem in the two-agent, LOCC (local operations, classical communication) setting. In this protocol, entanglement between systems is operationally equivalent to having a non-traversable wormhole between them.
  • Algebraic formulation (MIT, 2024): “Algebraic ER=EPR and Complexity Transfer” (JHEP 2024) associates bulk spacetime connectivity/disconnectivity with operator algebraic structure in the GN→0 limit. Both the amount and structure of entanglement matter.
  • Non-local gravitational energy (2025): arXiv:2512.05022 shows that entanglement-induced ER bridges are compatible with ER=EPR’s non-traversability requirement and absence of macroscopic throat.
  • SYK duality (2025): In SYK models, quenched and annealed disorder-averaged correlators are dual to zero-throat wormhole contractions versus EPR pairs — an exact equivalence at the level of specific observables.

Tensor Networks — Geometry as Entanglement Structure

A more concrete realization of spacetime-from-entanglement comes from tensor networks. The boundary CFT state can be represented as a tensor network — a circuit of quantum operations. The structure of this network maps to the geometry of the bulk.

MERA (Multi-Scale Entanglement Renormalization Ansatz)

The MERA tensor network, originally developed for condensed matter physics by Guifré Vidal, builds a quantum state layer by layer, with each layer representing a different length scale. Brian Swingle (2009-2012) noticed that the network structure of MERA is identical to the hyperbolic geometry of AdS space — the network’s “depth” maps to the AdS radial direction (energy scale).

This suggests: AdS geometry is the optimal tensor network for compressing quantum information in a CFT. The space itself is the compression algorithm.

HaPPY Tensor Networks — Holographic Error Correction (2015)

Pastawski, Yoshida, Harlow, and Preskill (HaPPY, 2015) constructed explicit tensor network models that reproduce the Ryu-Takayanagi formula exactly and simultaneously function as quantum error-correcting codes. See concept-holographic-error-correction for detailed treatment. The key finding: bulk information is encoded redundantly in the boundary, such that any small piece of the boundary doesn’t have enough information to reconstruct the bulk — this is exactly the structure of an error-correcting code.

Complexity and Spacetime Growth

Susskind and collaborators (2014-ongoing) proposed that the computational complexity of the CFT state corresponds to the volume of the Einstein-Rosen bridge connecting two copies. An old black hole has a very long ER bridge inside — and the boundary quantum state requires exponentially complex operations to prepare. “Complexity = Volume” (or the later “Complexity = Action” conjecture) translates computational complexity into spacetime geometry.

Recent (2024): Circuit complexity calculations for the Bunch-Davies vacuum in de Sitter space suggest that spacetime emergence from horizon-scale TFD entanglement is a universal property for spacetimes with horizons — not just AdS black holes.

What “Emergent” Actually Means

Calling spacetime “emergent” from entanglement means:

  • The quantum system (CFT) is the fundamental level of description
  • Spacetime geometry is a derived property — it appears when the system is in certain states with particular entanglement structures
  • In different entanglement configurations, there might be no geometric description at all
  • Changing entanglement changes geometry — “quantum surgery” on entanglement is literal surgery on spacetime topology

This is deeply non-intuitive. It implies that space, as we experience it, is more like a convenient description of information relations than a primary substance.

Key Facts

  • Van Raamsdonk (2010): “Building up spacetime with quantum entanglement” — the decisive conceptual paper
  • Maldacena-Susskind (2013): ER=EPR conjecture
  • The Ryu-Takayanagi formula: S(A) = Area(γ_A)/(4G_N) is the geometric fingerprint of entanglement in the bulk
  • MERA → AdS geometry: tensor network structure = hyperbolic bulk geometry (Swingle 2009)
  • Complexity = Volume conjecture: computational complexity of boundary state = ER bridge volume
  • If two parties destroy all entanglement between them, spacetime between their regions disconnects (van Raamsdonk)
  • Planck-scale ER bridges connecting entangled particles are non-traversable (no faster-than-light signaling)
  • The entanglement entropy of the radiation in a black hole determines the causal structure of the spacetime interior (island formula)

The Deeper Implication — What Is Space?

If spacetime is emergent from entanglement, several questions become urgent:

1. What is the “pre-geometric” substrate? The CFT has no gravity, no geometry, no spacetime in the ordinary sense. It’s just quantum fields in flat space. The bulk AdS space emerges from its dynamics. What is the physical interpretation of this? Possibly: the underlying degrees of freedom are not local — they don’t live at points in space — and locality is an approximate, emergent concept.

2. Does spacetime have atoms? If entropy scales with area (Bekenstein-Hawking), and area is quantized in Planck units, each Planck area encodes one bit. Spacetime may be “pixelated” at the Planck scale — a holographic bitmap. The “atoms” of space are information bits.

3. What breaks down at singularities? Classical GR predicts singularities inside black holes where spacetime “breaks down.” In the emergent picture, singularities may correspond to regions of the dual quantum system where classical description fails — perhaps where entanglement entropy diverges or where the quantum state transitions between phases. The singularity is not where space tears; it’s where the quantum description becomes non-geometric.

4. Does this resolve the measurement problem? Quantum mechanics has the measurement problem: how does observation collapse a wave function? If spacetime itself is built from entanglement, and entanglement is what quantum mechanics describes, perhaps the measurement problem and the quantum gravity problem are two sides of the same coin. Some researchers (e.g., Penrose) have suggested gravitational decoherence as the collapse mechanism. ER=EPR and emergent spacetime suggest a deeper connection.

Cross-Realm Surprise

The idea that a complex structure (3D spacetime) is entirely determined by a simpler structure (2D entanglement pattern) appears in completely different contexts:

  • concept-distributed-cognition: emergent collective behavior from simple individual rules — no “central” spacetime, just correlated agents
  • concept-mycelium-networks: the “wood wide web” — complex forest-scale behavior emerging from local fungal connections
  • concept-fabric-as-data: 3D woven structure encoding 2D pattern data (quipu, Jacquard) — lower-dimensional encoding of higher-dimensional structure

The holographic principle is convergent evolution of information compression, playing out at the level of the universe itself.

See Also

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