Chapter 03 · The Nature of Space and Time/Emergent Spacetime & Gravity

Holographic Spacetime

1997 / 2010 · Juan Maldacena, Mark Van Raamsdonk, Shinsei Ryu, Tadashi Takayanagi, Leonard Susskind

A higher-dimensional spacetime with gravity is exactly described by a lower-dimensional quantum theory on its boundary. Geometry emerges from entanglement.

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In one sentence

Spacetime geometry emerges from quantum entanglement in a lower-dimensional theory without gravity, as established by AdS/CFT in anti-de Sitter space. Whether this generalizes to our de Sitter universe is an open question.

The claim

Maldacena's 1997 discovery of AdS/CFT showed that a string-theory description of gravity in anti-de Sitter space (a spacetime with negative curvature) is mathematically equivalent to a quantum field theory without gravity living on its boundary. In the boundary theory there is no spacetime geometry; the geometry only appears when you reorganize the boundary-theory data into bulk variables. This is an exact mathematical duality, not an approximation.

Van Raamsdonk extended this with a striking observation in 2010: the bulk spacetime can be sliced open by removing entanglement between two halves of the boundary theory. As entanglement decreases, the bulk geometry literally falls apart, and the two halves become more and more spatially disconnected. Ryu and Takayanagi made this precise in 2006: the area of a minimal surface in the bulk that separates two regions is proportional to the entanglement entropy between those regions in the boundary. Geometry emerges from entanglement patterns.

Two important caveats. AdS/CFT is exact only in anti-de Sitter space; our universe is approximately de Sitter (positive curvature), and generalizing holographic emergence to de Sitter is an active research program with no clean exact duality yet despite 25 years of work. The ER=EPR conjecture (Maldacena and Susskind, 2013) takes the entanglement-geometry connection further by claiming entangled particles are connected by microscopic wormholes, but it is primarily a conjecture that rephrases known relationships between entanglement and wormhole geometry rather than a testable theory in its own right.

The family stance

Spacetime is not fundamental. It emerges from a deeper structure: entanglement patterns, thermodynamic relations on horizons, or discrete causal ordering. None of these has been confirmed; each makes some testable predictions but most operate at conceptual or structural levels.

Predictions

AdS/CFT predicts precise relationships between strongly coupled QFT correlators (e.g., quark-gluon plasma viscosity, condensed matter analogs) and gravitational dynamics in AdS bulk
If holographic emergence generalizes to cosmological de Sitter spacetime, specific structural imprints should appear in cosmological correlators beyond standard inflation predictions
Quantum error correction codes that reconstruct bulk from boundary make precise claims about which boundary degrees of freedom encode which bulk regions, testable in lattice realizations

Evidence

AdS/CFT itself is an exact mathematical duality used as a computational tool in high-energy theory (e.g., quark-gluon plasma viscosity bounds, holographic condensed matter)
Ryu-Takayanagi entanglement-area relation has been verified in many holographic computations and generalized to entanglement wedge reconstruction
Quantum error correction provides a precise framework for how boundary information encodes bulk regions, with explicit toy models (HaPPY codes, random tensor networks)
ER=EPR has driven technical progress on wormholes, traversable wormhole protocols (Gao-Jafferis-Wall 2017), and quantum complexity

Counterpoints

AdS/CFT is exact only in anti-de Sitter spacetime; our universe is de Sitter, and de Sitter holography is unsolved despite multiple programs (dS/CFT, swampland, FRW holography)
The 'holographic emergence' claim is tightly tied to special backgrounds; whether it tells us anything about real cosmology is contested
ER=EPR is largely conceptual: it rephrases known relationships between entanglement and geometry rather than producing distinctive empirical predictions
Holography provides many dualities but no unique emergent description of our specific universe

Variants in this family

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▸Go deeperTechnical detail with proper terminology

AdS/CFT specifically: type IIB string theory on AdS5 x S^5 (anti-de Sitter spacetime in five dimensions times a 5-sphere) is dual to N=4 supersymmetric Yang-Mills on the AdS5 boundary. Both sides are exactly computable in matched large-N / strong-coupling limits; the duality is checked at the level of correlators, anomalies, and operator spectra.

Ryu-Takayanagi formula: S(A) = Area(γ_A) / (4 G_N), where γ_A is the minimal-area surface in the bulk anchored on the boundary of region A. This is the classical limit of the more general entanglement wedge reconstruction framework.

ER=EPR: Maldacena and Susskind 2013 observed that two entangled black holes in AdS are described by a single bulk geometry with an Einstein-Rosen bridge (non-traversable wormhole) connecting them. The conjecture extends this: any entangled pair has a wormhole-like geometric connection at some level, however microscopic.

de Sitter status: dS/CFT (Strominger 2001 and follow-ups), the de Sitter swampland program, FRW holography, holographic cosmology, multiple research programs exist; none has produced a clean exact duality analogous to AdS/CFT. Most contemporary work on emergent spacetime is forced to use AdS as a calculational arena and argue by analogy about de Sitter.