Spacetime from Entanglement

If "it from bit" is right, the most ambitious test of the idea would be spacetime itself. Can the very stage on which physics happens emerge from quantum information? Over the past two decades, a remarkable line of research has begun to suggest that the answer may be yes — at least in certain theoretical settings.

A clue from holography

The AdS/CFT correspondence, proposed by Juan Maldacena in 1997, describes certain gravitational universes (with a particular negatively curved geometry) as exactly equivalent to ordinary quantum theories without gravity, living on their boundary. In 2006, Shinsei Ryu and Tadashi Takayanagi discovered a strikingly simple dictionary entry: the amount of entanglement between regions of the boundary theory is given by the area of a surface in the bulk geometry. Entanglement on one side; geometry on the other.

Disentangle, and space tears apart

Mark Van Raamsdonk pushed the idea in a short, influential 2010 essay. If geometry is encoded in entanglement, then reducing the entanglement between two halves of the boundary should pull the corresponding regions of space apart — and removing it entirely should disconnect them. Connectedness of space, on this view, is a manifestation of quantum entanglement. In his phrase, spacetime is "built up" from it.

ER = EPR

In 2013 Juan Maldacena and Leonard Susskind proposed an even bolder link. "ER" refers to Einstein–Rosen bridges — wormholes connecting distant regions of space. "EPR" refers to the Einstein–Podolsky–Rosen paper, the founding document of entanglement. Their conjecture: these are two descriptions of the same thing. Two entangled black holes are connected by a wormhole, and perhaps, in some highly quantum sense, any entangled pair is connected by a microscopic one.

Networks of information

Tensor networks — tools developed to describe entangled states of many particles — turned out to reproduce key features of these geometries, with the network's structure playing the role of space. Since 2015, much of this work has been pursued under the banner "It from Qubit," a deliberate echo of Wheeler.

Honest caveats

• The sharpest results hold in anti-de Sitter space, which is not the universe we live in. Extending them to our expanding, positively curved cosmos is an open problem.
• ER = EPR is a conjecture, not an established result.
• Even in the best-understood cases, entanglement alone does not appear to be the full story; other quantum-information quantities, such as complexity, may also be needed.

Why it matters for the observer question

If spacetime emerges from entanglement, then the questions of these notes converge. The relational, information-theoretic picture of quantum mechanics and the emergence of classical reality would extend all the way down to the arena of physics itself. Space would not be a container in which observers and information live; it would be one of the things that information, through its patterns of correlation, brings into being. That convergence — between the foundations of quantum theory and the origin of spacetime — is the horizon my research is aimed at.

Further reading: S. Ryu & T. Takayanagi, "Holographic Derivation of Entanglement Entropy from AdS/CFT" (2006); M. Van Raamsdonk, "Building up spacetime with quantum entanglement" (2010); J. Maldacena & L. Susskind, "Cool horizons for entangled black holes" (2013).