arxiv: 2605.13490 · v1 · submitted 2026-05-13 · ✦ hep-th · gr-qc

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What does it mean to have a quantum gravitational theory of de Sitter Space?

Tom Banks

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Pith reviewed 2026-05-14 18:26 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords de Sitter spacequantum gravityfinite dimensional quantum systemsquantum measurement theorysuperstring theoryambiguity in models

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The pith

If de Sitter space is a finite quantum system then all models of it are ambiguous

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

The paper claims that representing de Sitter space by a finite dimensional quantum system makes every possible model of it ambiguous when combined with semi-classical gravity and the rules of quantum measurements. This would matter for our universe if it approaches a de Sitter state in the far future. Even in that case a precise model might exist by embedding it into a sequence of models that approach a unique superstring theory in flat space. Local experiments inside the universe can access only a tiny fraction of the total quantum information.

Core claim

If de Sitter space is indeed represented by a finite dimensional quantum system, then semi-classical considerations, combined with the fundamental principles of quantum measurement theory, imply that any theoretical model of it is ambiguous. If our own universe asymptotes to such a de Sitter state, and if a model of it as a finite system can be embedded in a sequence of models that converges to a non-perturbative completion of a unique superstring model in asymptotically flat space, then one might be able to find a very precise mathematical model of our universe. However, even the most comprehensive experiments possible to local detectors in the universe cannot measure more than a tiny of q

What carries the argument

Finite dimensional quantum system representation of de Sitter space, which introduces ambiguity through quantum measurement principles

Load-bearing premise

De Sitter space is represented by a finite dimensional quantum system and our universe asymptotes to such a de Sitter state

What would settle it

Evidence that de Sitter space requires an infinite dimensional Hilbert space or that local measurements can access a substantial portion of the total quantum information would falsify the claim

read the original abstract

We argue that if de Sitter space is indeed represented by a finite dimensional quantum system, then semi-classical considerations, combined with the fundamental principles of quantum measurement theory, imply that any theoretical model of it is ambiguous. If our own universe asymptotes to such a de Sitter state, and if a model of it as a finite system can be embedded in a sequence of models that converges to a non-perturbative completion of a unique superstring model in asymptotically flat space, then one might be able to find a very precise mathematical model of our universe. However, even the most comprehensive experiments possible to local detectors in the universe cannot measure more than a tiny fraction of the total number of q-bits in the system.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Banks claims any finite-dimensional model of de Sitter must be ambiguous because local observers access only a tiny fraction of the qubits, but the step from limited measurability to actual model under-determination is not derived.

read the letter

Banks argues that if de Sitter space is a finite quantum system, semi-classical considerations plus quantum measurement theory force any model of it to be ambiguous. Local detectors can probe only a small slice of the total Hilbert space, so the global description stays under-determined even in principle. If our universe approaches such a state, this would block a unique non-perturbative model embeddable in string theory. The paper does a clean job restating the finite-entropy premise for de Sitter and linking it to everyday limits on what can be measured. That connection is worth making explicit for cosmology. The soft spot is exactly where the stress-test note flags it: limited access does not by itself prove multiple distinct models fit all possible local data. A concrete finite Hilbert space with a fixed Hamiltonian can be mathematically unique even when most qubits remain unobservable. The abstract gives no explicit under-determination result or pair of models that agree locally but differ globally, so the central claim rests on an intuitive leap rather than a shown implication. This is aimed at people already working on quantum gravity foundations and de Sitter holography. A reader who knows the finite-dimensional literature will see the point quickly and may want to sharpen or refute it. It is not a calculation or theorem, but the question is live enough that it deserves referee time. I would send it to review rather than desk-reject; the discussion could clarify whether the ambiguity follows or needs more structure.

Referee Report

2 major / 0 minor

Summary. The paper argues that if de Sitter space is represented by a finite-dimensional quantum system, then semi-classical considerations combined with quantum measurement theory imply that any theoretical model of it is ambiguous, since local observers can access only a tiny fraction of the total qubits. It further posits that if our universe asymptotes to such a state and a finite model can be embedded in a sequence converging to a non-perturbative superstring completion in asymptotically flat space, a precise mathematical model of our universe might still be attainable despite the observational limits.

Significance. If the central implication holds, the result would indicate a fundamental under-determination in quantum gravitational models of de Sitter space, with potential consequences for cosmological applications of quantum mechanics and string theory embeddings. The conceptual link between limited local access and model ambiguity could inform debates on the consistency of finite-dimensional Hilbert space descriptions with semi-classical gravity, though its impact hinges on whether the logical steps from finite dimensionality to ambiguity are made rigorous.

major comments (2)

[Abstract / central argument] The manuscript states that finite dimensionality plus limited local observability forces any model to be ambiguous, but provides no explicit derivation showing under-determination: i.e., no demonstration that distinct global Hamiltonians or states on the full Hilbert space can produce identical statistics for all measurements accessible to local detectors. Without this step, the inference from 'tiny fraction of qubits observable' to 'multiple consistent models' does not follow.
[Abstract] The mapping from the semi-classical de Sitter geometry to a concrete finite-dimensional quantum system (specific dimension, Hamiltonian, and state) is not detailed, leaving unclear how the semi-classical considerations are supposed to constrain or fail to constrain the quantum model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and have revised the text to improve clarity and rigor where possible.

read point-by-point responses

Referee: [Abstract / central argument] The manuscript states that finite dimensionality plus limited local observability forces any model to be ambiguous, but provides no explicit derivation showing under-determination: i.e., no demonstration that distinct global Hamiltonians or states on the full Hilbert space can produce identical statistics for all measurements accessible to local detectors. Without this step, the inference from 'tiny fraction of qubits observable' to 'multiple consistent models' does not follow.

Authors: We agree that an explicit illustration strengthens the presentation. The central claim rests on the standard quantum-mechanical fact that the reduced density matrix on a small subsystem does not uniquely determine either the global state or the Hamiltonian. In the revised manuscript we have added a short subsection (new Section 2.1) that recalls this result with a simple two-qubit example: two distinct global pure states yield identical local measurement statistics on one qubit, and likewise for local Hamiltonians acting only on the accessible subsystem. We then note that the same logic applies when the accessible fraction is exponentially small, as in de Sitter space. This makes the under-determination explicit without requiring a full non-perturbative construction. revision: yes
Referee: [Abstract] The mapping from the semi-classical de Sitter geometry to a concrete finite-dimensional quantum system (specific dimension, Hamiltonian, and state) is not detailed, leaving unclear how the semi-classical considerations are supposed to constrain or fail to constrain the quantum model.

Authors: The manuscript is deliberately conceptual and does not attempt to construct a specific finite-dimensional model. Semi-classical geometry fixes the dimension of the Hilbert space via the de Sitter entropy but leaves the detailed Hamiltonian and state under-determined; our argument concerns the additional ambiguity that arises once local observability is taken into account. We have added a clarifying paragraph in the introduction of the revised version that separates these two layers of under-determination and states explicitly that the paper does not claim to derive a unique model from semi-classics alone. revision: partial

Circularity Check

0 steps flagged

No circularity: ambiguity follows from finite-dimensional assumption plus standard measurement limits

full rationale

The paper's derivation begins with the explicit conditional premise that de Sitter space is a finite-dimensional quantum system and then invokes standard semi-classical horizon geometry together with the principle that local observers access only a subregion whose entropy is a tiny fraction of the total. From this it concludes that any concrete model remains under-determined by all possible local measurements. No equation or claim reduces a derived quantity to a fitted parameter by construction, no uniqueness theorem is imported from the author's prior work to force the conclusion, and the limited observability statement is not redefined in terms of the ambiguity result itself. The argument is therefore self-contained against external benchmarks of quantum measurement theory and does not rely on a self-citation chain for its load-bearing step.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the premise that de Sitter space admits a finite-dimensional quantum description, which is treated as an input rather than derived within the paper.

axioms (1)

domain assumption De Sitter space is represented by a finite dimensional quantum system
Invoked at the opening of the abstract as the conditional starting point for the ambiguity conclusion.

pith-pipeline@v0.9.0 · 5409 in / 1167 out tokens · 37434 ms · 2026-05-14T18:26:02.106550+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages · 5 internal anchors

[2]

Cosmological Breaking of Supersymmetry?

T. Banks, “Cosmological breaking of supersymmetry?,” Int. J. Mod. Phys. A16, 910- 921 (2001) doi:10.1142/S0217751X01003998 [arXiv:hep-th/0007146 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0217751x01003998 2001
[3]

Towards a quantum theory of de Sitter space

T. Banks, B. Fiol and A. Morisse, “Towards a quantum theory of de Sitter space,” JHEP 12, 004 (2006) doi:10.1088/1126-6708/2006/12/004 [arXiv:hep-th/0609062 [hep-th]]

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Effective Field Theory, Black Holes, and the Cosmological Constant

A. G. Cohen, D. B. Kaplan and A. E. Nelson, “Effective field theory, black holes, and the cosmological constant,” Phys. Rev. Lett.82, 4971-4974 (1999) doi:10.1103/PhysRevLett.82.4971 [arXiv:hep-th/9803132 [hep-th]]. T. Banks and P. Draper, “Remarks on the Cohen-Kaplan-Nelson bound,” Phys. Rev. D101, no.12, 126010 (2020) doi:10.1103/PhysRevD.101.126010 [ar...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.82.4971 1999
[5]

Recurrent nightmares? Measurement theory in de Sitter space,

T. Banks, W. Fischler and S. Paban, “Recurrent nightmares? Measurement theory in de Sitter space,” JHEP12, 062 (2002) doi:10.1088/1126-6708/2002/12/062 [arXiv:hep- th/0210160 [hep-th]]

work page doi:10.1088/1126-6708/2002/12/062 2002
[6]

JT de Sitter gravity as a model of Coleman-de Luccia tunneling,

T. Banks and S. A, “JT de Sitter gravity as a model of Coleman-de Luccia tunneling,” JHEP12, 085 (2025) doi:10.1007/JHEP12(2025)085 [arXiv:2506.09283 [hep-th]]

work page doi:10.1007/jhep12(2025)085 2025
[7]

Quantum theory of three-dimensional de Sitter space,

S. A, T. Banks and W. Fischler, “Quantum theory of three-dimensional de Sitter space,” Phys. Rev. D109, no.2, 025011 (2024) doi:10.1103/PhysRevD.109.025011 [arXiv:2306.05264 [hep-th]]

work page doi:10.1103/physrevd.109.025011 2024
[8]

Double-scaled SYK and de Sitter holography,

V. Narovlansky and H. Verlinde, “Double-scaled SYK and de Sitter holography,” JHEP05, 032 (2025) doi:10.1007/JHEP05(2025)032 [arXiv:2310.16994 [hep-th]]; H. Verlinde,“Double-scaled SYK, chords and de Sitter gravity,” JHEP03, 076 (2025) doi:10.1007/JHEP03(2025)076 [arXiv:2402.00635 [hep-th]]; D. Tietto and H. Verlinde, “A microscopic model of de Sitter spa...

work page doi:10.1007/jhep05(2025)032 2025
[9]

Scrambling in Double-Scaled SYK and De Sitter Space,

L. Susskind, “Scrambling in Double-Scaled SYK and De Sitter Space,” [arXiv:2205.00315 [hep-th]]; H. Lin and L. Susskind, “Infinite Temperature’s Not So Hot,” [arXiv:2206.01083 [hep-th]]; L. Susskind, JHAP5, no.1, 1-30 (2025) doi:10.22128/jhap.2024.920.1103 [arXiv:2209.09999 [hep-th]]; L. Susskind, “Scrambling in Double-Scaled SYK and De Sitter Space,” [ar...

work page doi:10.22128/jhap.2024.920.1103 2025
[10]

M Theory As A Matrix Model: A Conjecture

T. Banks, W. Fischler, S. H. Shenker and L. Susskind, “M theory as a matrix model: A conjecture,” Phys. Rev. D55, 5112-5128 (1997) doi:10.1201/9781482268737- 37 [arXiv:hep-th/9610043 [hep-th]]

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[11]

Old Ideas for New Physicists 2,

T. Banks, “Old Ideas for New Physicists 2,” [arXiv:2307.15812 [hep-ph]]

work page arXiv
[12]

CP Violation and Baryogenesis in the Presence of Black Holes

T. Banks and W. Fischler, “CP Violation and Baryogenesis in the Presence of Black Holes,” [arXiv:1505.00472 [hep-th]]. 6

work page internal anchor Pith review Pith/arXiv arXiv