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

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Pith's one-line read "Spacetime from entanglement" in AdS/CFT hides three different claims; only gravitational dynamics stays novel once the full emergence basis is filled in.

desk verdict Clean three-way split of the 'spacetime from entanglement' slogan; only dynamics survives novelty once the full basis is restored. read the letter →

arxiv 2607.09823 v1 pith:6375AMX2 submitted 2026-07-10 physics.hist-ph gr-qchep-th

Rasmus Jaksland This is my paper · ORCID
classification physics.hist-phgr-qchep-th
keywords AdS/CFTspacetimeemergenceentanglementHRTformulagravitationaldynamicsmetricreconstructiontopologicalconnectivitynoveltycondition
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Physicists often say spacetime emerges from entanglement in the AdS/CFT correspondence. This paper shows that those slogans actually cover three separate claims: that the bulk metric is fixed by boundary entanglement, that bulk gravitational dynamics is fixed by entanglement dynamics, and that bulk topological connectivity arises from entanglement. None of the three claims meets a basic determination requirement if the emergence basis is only entanglement; extra boundary data are always required. Once those extra ingredients are included, the metric claim and the connectivity claim look less novel, because the basis already contains a metric or path-connectivity. Only the claim that gravitational dynamics emerges remains cleanly novel relative to its full basis. The result matters because it stops people from treating disparate holographic results as one unanimous argument that spacetime is non-fundamental.

What carries the argument

Contrasting emergence claims interpreted through Crowther’s determination (at least supervenience) and novelty conditions. The Hubeny–Rangamani–Takayanagi formula supplies the concrete link between boundary entanglement entropies and bulk areas, but the surrounding boundary data (induced metric, energy densities, manifold structure) must still be supplied before determination holds.

What would settle it

A concrete holographic construction in which the bulk metric (or bulk path-connectivity) is uniquely fixed by boundary entanglement data alone, without any use of the induced boundary metric or of pre-existing path relations on the boundary.

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Extended reading notes

Core claim

Behind the slogan that spacetime emerges from entanglement in AdS/CFT sit three distinct claims (bulk metric, gravitational dynamics, topological connectivity). None of them is determined by entanglement alone. When the missing boundary ingredients are restored, only gravitational dynamics is novel with respect to the completed emergence basis; the metric claim already presupposes a boundary metric, and the connectivity claim appears to presuppose connectivity.

Load-bearing premise

That the right way to judge these physicists’ emergence talk is by Crowther’s determination-plus-novelty conditions, with determination understood as at least supervenience.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

0 major / 4 minor

Summary. The paper argues that the slogan “spacetime emerges from entanglement” in AdS/CFT conceals three distinct claims—emergence of the bulk metric (via HRT + Bao et al. Jacobi reconstruction), of gravitational dynamics (via the first law of entanglement and linearized Einstein equations), and of topological connectivity (via van Raamsdonk’s thermofield-double argument). Using Crowther’s determination (at least supervenience) and novelty conditions, it shows that none of the three is determined by boundary entanglement alone; once the full emergence basis is restored (boundary metric/extrinsic curvature for the metric claim; CFT energy for dynamics; unspecified further data for connectivity), only gravitational dynamics remains clearly novel relative to that basis. Metric and connectivity claims are therefore at best “contrasting” emergence claims whose novelty is questionable.

Significance. If the analysis holds, it supplies a precise, literature-grounded disambiguation that philosophers and physicists interested in the metaphysical upshot of holographic entanglement must respect: the three results cannot be pooled as evidence for a single “spacetime-from-entanglement” thesis, and only the dynamics claim survives the standard determination-plus-novelty filter once implicit boundary data are made explicit. The reconstructions of Bao et al. (2019/2021), Faulkner et al. (2014)/Swingle–Van Raamsdonk, and van Raamsdonk (2010) are accurate and the application of Crowther’s criteria is transparent, giving the paper lasting value as a cautionary map of the literature.

minor comments (4)
  1. §3: A short explicit statement that the paper evaluates the claims under Crowther’s criteria without claiming those criteria are the only possible reading of physicists’ usage would further forestall the “wrong yardstick” worry already flagged in the text.
  2. §5: The discussion of whether a 4-d bulk metric is “qualitatively different” from a 3-d induced metric could be tightened by one sentence noting that the same question arises for target-space vs. phenomenal metrics in string theory (already cited).
  3. §7: The argument that path-connectedness may fail novelty because component path-relations already exist on the CFT side is suggestive; a brief remark on whether a totally path-disconnected CFT dual is known (or known to be impossible) would clarify the residual uncertainty.
  4. Typographical: “reletivity” (p. 11), “fomula” (p. 12), and occasional missing spaces around citations should be corrected in production.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: conceptual analysis of independent physics results under external philosophical criteria

full rationale

This is a philosophy-of-physics paper that disambiguates three distinct emergence claims (bulk metric, gravitational dynamics, topological connectivity) behind the slogan “spacetime from entanglement.” Its load-bearing steps are reconstructions of published technical results (HRT formula; Bao et al. 2019/2021 Jacobi reconstruction of the bulk metric from extremal-area data plus boundary metric/extrinsic curvature; Faulkner et al./Lashkari et al./Swingle–Van Raamsdonk first-law-of-entanglement derivations of linearized Einstein equations; van Raamsdonk 2010 thermofield-double connectivity argument) followed by an assessment against Crowther’s external determination-plus-novelty conditions. No equation is derived by fitting a free parameter to data and then “predicting” a related quantity; no uniqueness theorem is imported from the author’s own prior work to force the conclusion; no ansatz is smuggled in via self-citation. The author’s earlier papers (Jaksland 2018, 2021; Jaksland & Linnemann 2020, 2024; Jaksland & Salimkhani 2023) are cited only for background or related discussion and are not load-bearing for the central negative verdicts. The derivation chain is therefore self-contained against external benchmarks and exhibits no circular reduction of the form “X derives Y by construction from X.” Score 0 is the honest finding.

Assumptions & free parameters 0 free parameters · 5 assumptions · 1 invented entities

The paper is conceptual; it inherits the AdS/CFT dictionary, the HRT formula, and Crowther’s emergence conditions as background. No free parameters are fitted. The only non-standard framing is the label ‘contrasting emergence claim,’ which is introduced for clarity rather than as a new physical entity.

assumptions (5)
  • domain assumption Crowther’s conditions: emergence requires (at least) determination/supervenience and qualitative novelty of the emergent relative to the basis (§3).
    Adopted as the standard for assessing physicists’ emergence talk; if a different notion is intended the negative verdicts change.
  • domain assumption HRT formula equates boundary entanglement entropy to area of bulk extremal surfaces (in the classical large-N limit) (§2).
    Taken from the physics literature as the starting dictionary entry; quantum corrections are set aside by the papers under discussion.
  • domain assumption Boundary data needed for bulk-metric reconstruction include the induced boundary metric, extrinsic curvature, and region embeddings in addition to entanglement entropies (Bao et al. 2019/2021, §4–5).
    Directly from the cited reconstruction papers; used to show determination fails for entanglement alone.
  • domain assumption Linearized Einstein equations about AdS are dual to the first law of entanglement entropy once a background metric is fixed (§6).
    Taken from Faulkner et al. / Lashkari et al. / Swingle–van Raamsdonk; used to isolate the dynamics claim.
  • domain assumption Thermofield-double entanglement is necessary but not sufficient for bulk path-connectedness (van Raamsdonk 2010; finite-β thermal AdS counter-example) (§7).
    Used to show determination fails for connectivity.
invented entities (1)
  • contrasting emergence claim
    purpose: Label for slogans that leave part of the emergence basis implicit while still satisfying determination once the implicit elements are restored.
    Terminological device introduced in §5; not a physical postulate and has no independent empirical content.

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Pith. "Pith review of Spacetime from Entanglement: The Emergence of Metric, Gravity, or Topology." pith.science (2026). https://pith.science/paper/6375AMX2

@misc{pith2026260709823,
  author       = {Pith},
  title        = {Pith review of: Spacetime from Entanglement: The Emergence of Metric, Gravity, or Topology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6375AMX2}},
  note         = {Machine review of arXiv:2607.09823}
}
read the original abstract

In AdS/CFT, one often finds claims along the lines that ``spacetime emerges from entanglement." This paper argues that behind these general statements hide three distinct emergence claims about, respectively, metric, gravitational dynamics, and topological connectivity. Thus, despite being advertised with the same terminology, these results are not about the same spatiotemporal aspects. They can therefore not just be grouped as evidence for one unanimous conclusion, though they do point in similar directions. The paper also investigates whether the three emergence claims satisfy two of the necessary conditions for emergence: Determination and novelty. The paper argues that none of the emergence claims satisfies the determination condition: More than entanglement is needed to furnish the emergence basis. Besides entanglement, the emergence basis for the bulk metric must include the induced metric on the boundary. Thus, this claim might not satisfy the novelty condition for emergence that the emergent should be novel as compared to the emergence basis. Likewise, the emergence basis for topological connectivity seems to include connectivity whereby this emergence claim is also questionable. The paper concludes that only gravitational dynamics is novel compared to the fully furnished emergence basis.

Figures

Figures reproduced from arXiv: 2607.09823 by the authors.

Figure 1
Figure 1. Illustration of the AdS/CFT correspondence. With an AdS metric in the interior, this [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Penrose diagram of the eternal black hole. The regions I and II lie outside ( [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗

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