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Spacetime from Entanglement: The Emergence of Metric, Gravity, or Topology

This paper argues that the claim "spacetime emerges from entanglement" actually refers to three distinct phenomena—metric, gravitational dynamics, and topological connectivity—none of which fully satisfy the conditions for emergence because they rely on additional non-entanglement factors, with only gravitational dynamics qualifying as truly novel.

Original authors: Rasmus Jaksland

Published 2026-07-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Rasmus Jaksland

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, 3D hologram projected from a 2D screen. This is the wild idea behind a famous theory called AdS/CFT. In this setup, the "screen" (the boundary) is a world without gravity, while the "hologram" (the bulk) is our familiar universe filled with gravity and spacetime.

For a while, physicists have been buzzing with a catchy slogan: "Spacetime emerges from entanglement." It sounds like magic: if you take the quantum "knots" (entanglement) between particles on the screen, they magically weave together to create the fabric of space and time in the hologram.

But Rasmus Jaksland, a philosopher at Princeton, is here to tell us that this slogan is a bit like a menu that says "Delicious Meal" without telling you if you're getting soup, a steak, or a salad. He argues that behind this single, catchy phrase, there are actually three very different claims hiding, and they don't all stand up to the same scrutiny.

The Three Different "Meals" on the Menu

Jaksland breaks down the "spacetime from entanglement" idea into three distinct dishes:

The Shape of Space (The Metric): This is about the actual geometry—the distances and angles that make up the hologram. Some results suggest that if you know the entanglement on the screen, you can figure out the shape of the 3D world.
The Rules of the Game (Gravitational Dynamics): This is about how things move and interact. It's the idea that the laws of gravity (like Einstein's equations) are actually just a fancy way of describing how entanglement changes on the screen.
The Connection (Topology): This is about whether the hologram is one big piece or two separate islands. The idea here is that if the particles on the screen are "knotted" together, the hologram becomes a single, connected world. If they aren't, the hologram falls apart into disconnected chunks.

The Big Catch: You Need More Than Just "Knots"

Here is where the paper gets critical. Jaksland checks these claims against two strict rules that any "emergence" story must follow:

The Determination Rule: The starting ingredients must be enough to uniquely create the final dish.
The Novelty Rule: The final dish must be something totally new, not just a remix of the ingredients you started with.

The Verdict on the "Shape of Space" (Metric):
The paper argues that entanglement alone is not enough to build the shape of the hologram. To figure out the geometry, you also need to know the shape of the screen itself (the boundary metric).

The Analogy: Imagine trying to bake a cake (the hologram) using only a secret recipe of sugar knots (entanglement). Jaksland says, "Wait, you also need the cake pan!" The "cake pan" is the boundary metric.
The Problem: If you need the cake pan (a shape) to make the cake (a shape), then the cake isn't really "new" or "emergent" in a surprising way. It's just a shape made from another shape. The paper suggests that claiming the hologram's geometry emerges only from entanglement is misleading because it hides the fact that you're also using a pre-existing geometry as a base.

The Verdict on the "Rules of the Game" (Gravitational Dynamics):
This claim fares much better. The paper suggests that the dynamics (how gravity moves and changes) on the hologram side might actually be a genuine surprise.

The Analogy: The screen has no gravity at all; it's just a flat stage. But the hologram has gravity. If the way the entanglement wiggles and changes on the screen perfectly matches the way gravity moves in the hologram, that is a genuine "novelty." The hologram has a dynamic force (gravity) that the screen simply doesn't have.
The Catch: Even here, you need more than just entanglement. You need other data, like the energy of the particles on the screen. But once you include those, the "gravity" part feels like a true emergence because the screen itself is static and gravity-free.

The Verdict on the "Connection" (Topology):
This is the trickiest one. The idea is that entanglement stitches two separate islands into one big world.

The Problem: The paper points out that entanglement isn't the only thing needed. For example, the temperature of the system matters. You can have entangled particles, but if the temperature is too high, the hologram might still fall apart into two pieces.
The Mystery: We don't yet know exactly what other ingredients are needed to stitch the world together. Because we don't know the full list of ingredients, we can't be sure if the "connection" is truly new or just a logical combination of things we already knew were there.

The Final Takeaway

So, what's the real story? The paper doesn't say "Spacetime from Entanglement" is wrong, but it says we need to stop using it as a magic wand.

Be Specific: When scientists say "spacetime emerges," they might mean the shape, the rules, or the connections. These are three different things.
Check the Ingredients: Entanglement is a crucial ingredient, but it's rarely the only one. You almost always need the background shape of the universe (the boundary) to get started.
Don't Get Too Excited (Yet): If you need a pre-existing shape to make a new shape, it's not a huge metaphysical surprise. The most promising "surprise" is that the rules of gravity might emerge from the dance of entanglement, but even that requires a full set of ingredients we are still listing.

In short, the universe might be woven from quantum knots, but the loom we're weaving it on is still there, and we need to know exactly what's on that loom before we claim the tapestry appeared out of thin air.

Problem
The AdS/CFT correspondence has generated widespread claims in the physics literature that "spacetime emerges from entanglement," often citing the Hubeny-Rangamani-Takayanagi (HRT) formula as the primary evidence. However, the term "spacetime" is used ambiguously in these discussions, potentially conflating distinct spatiotemporal aspects. Furthermore, philosophical analyses of emergence in quantum gravity often rely on specific criteria—such as determination and novelty—that may not be satisfied by these claims if they are not scrutinized for their specific content. The paper addresses the lack of clarity regarding what specific aspect of spacetime (metric, dynamics, or topology) is claimed to emerge, and whether the proposed emergence bases (entanglement) are sufficient to satisfy necessary conditions for emergence, particularly when the implicit elements of the basis are made explicit.

Methodology
The paper employs a conceptual analysis of the AdS/CFT correspondence, focusing on the HRT formula and related results (e.g., the first law of entanglement entropy, thermofield double states). The methodology involves:

Disambiguation: Distinguishing between three specific claims often grouped under the umbrella of "spacetime from entanglement": the emergence of the bulk metric, the emergence of gravitational dynamics, and the emergence of topological connectivity.
Application of Emergence Criteria: Evaluating these three claims against two necessary conditions for emergence as defined in the philosophy of physics (following Crowther 2021):
- Determination: The emergence basis must uniquely determine the emergent.
- Novelty: The emergent must be qualitatively different from the emergence basis.
Contextual Analysis: Investigating the "emergence basis" for each claim to identify implicit elements (such as boundary metrics or specific state parameters) that are often omitted in general statements but are mathematically necessary for the derivation. The paper introduces the concept of "contrasting emergence claims," where the basis is partially implicit, to explain how physicists frame these results.

Key Contributions and Results

Distinction of Emergence Claims: The paper demonstrates that the literature contains three distinct emergence claims that are not interchangeable:
1. Metric Emergence: The claim that the bulk metric is determined by boundary entanglement entropies (e.g., Bao et al. 2019, 2021).
2. Gravitational Dynamics Emergence: The claim that the dynamical equations governing the metric (linearized Einstein equations) emerge from the dynamics of entanglement (e.g., Faulkner et al. 2014; Swingle 2018).
3. Topological Connectivity Emergence: The claim that the connectedness of the bulk manifold emerges from the entanglement of boundary degrees of freedom (e.g., Van Raamsdonk 2010a).
Analysis of the Metric Claim:
- Determination: The claim that the bulk metric emerges solely from entanglement fails the determination condition. To uniquely determine the bulk metric, one requires not only boundary entanglement entropies but also the induced metric on the boundary, the induced manifold, and the embedding of boundary regions.
- Novelty: When the emergence basis is fully furnished (including the boundary metric), the claim that the bulk metric emerges from it faces a novelty problem. Since both the emergent (bulk metric) and the basis (boundary metric) are metrics, they are not qualitatively different in the required sense. The results show that bulk geometric data are encoded in boundary geometric data, rather than a metric emerging from a pre-metrical structure.
Analysis of the Gravitational Dynamics Claim:
- Determination: Similar to the metric claim, determining gravitational dynamics requires more than just entanglement; it requires additional boundary data (e.g., energy density). Thus, it is also a "contrasting emergence claim."
- Novelty: This claim fares better regarding novelty. The CFT side lacks gravitational dynamics (the coupling of a metric to matter via dynamical equations), whereas the AdS side possesses them. Therefore, gravitational dynamics is novel compared to the fully furnished emergence basis, provided one accepts that the ontological model of the dynamics differs sufficiently between the two sides.
Analysis of the Topological Connectivity Claim:
- Determination: Entanglement is necessary but not sufficient for bulk connectivity. For instance, in the thermofield double state, entanglement exists, but if the temperature parameter is too high (large $\beta$ ), the dual spacetime becomes two disconnected thermal AdS spaces. Thus, entanglement alone does not determine connectivity; other parameters are required.
- Novelty: The novelty condition is ambiguous. While the global property of path-connectedness is new to the bulk (as the boundary manifold is disconnected), the local instances of path-connectedness within the boundary components already exist. If novelty requires the absence of the constituent relations in the basis, the claim may fail.

Significance
The paper argues that the broad slogan "spacetime emerges from entanglement" obscures significant differences in the plausibility and nature of the underlying claims. Its primary significance lies in three warnings for philosophers and physicists interpreting these results:

Ambiguity of Terminology: "Spacetime" refers to different aspects (metric, dynamics, topology) in different contexts, and these should not be conflated.
Implicit Basis: These are largely "contrasting emergence claims" where the emergence basis is left partially implicit. Making these implicit elements explicit is crucial for evaluating the claims.
Failure of Novelty: For the claim that the metric emerges from entanglement, the fully furnished basis includes a metric, potentially violating the novelty condition. This suggests that the results do not demonstrate the emergence of spacetime from a pre-geometric substrate, but rather the encoding of bulk geometry in boundary geometry. Only the emergence of gravitational dynamics appears to satisfy the novelty condition relative to the CFT basis.

The paper concludes that while these results point in similar directions, they cannot be grouped as evidence for a single, unanimous conclusion regarding the emergence of spacetime, and metaphysical conclusions regarding the non-fundamentality of spacetime must be drawn with caution regarding which specific aspect is being discussed.

The Three Different "Meals" on the Menu

The Big Catch: You Need More Than Just "Knots"

The Final Takeaway

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