No, classical gravity does not entangle quantized matter fields

Lajos Di\'osi

arxiv: 2511.00852 · v3 · submitted 2025-11-02 · 🪐 quant-ph · gr-qc

No, classical gravity does not entangle quantized matter fields

Lajos Di\'osi This is my paper

Pith reviewed 2026-05-18 01:50 UTC · model grok-4.3

classification 🪐 quant-ph gr-qc

keywords classical gravityquantum entanglementquantized matter fieldsHeisenberg pictureinteraction picturenon-perturbative derivationsemi-classical gravity

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The pith

Classical gravity does not entangle quantized matter fields, as shown by an exact Heisenberg picture derivation.

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

This paper refutes the claim that classical unquantized gravity can generate entanglement in quantized matter fields treated via quantum field theory. It shows that the perturbative interaction-picture calculation suggesting such entanglement is inconsistent with a simple exact non-perturbative derivation performed in the Heisenberg picture. The exact approach demonstrates that no entanglement arises from the classical gravitational interaction. A reader would care because the result sharpens the distinction between classical and quantum treatments of gravity and indicates that true gravity-induced quantum correlations require a quantized gravitational field.

Core claim

The perturbative result of Aziz and Howl in the interaction picture is inconsistent with our exact and simple non-perturbative derivation in the Heisenberg picture, that fundamentally precludes the claimed entanglement.

What carries the argument

The exact non-perturbative derivation in the Heisenberg picture of the interaction between classical gravity and quantized matter fields.

If this is right

No entanglement is generated by classical gravity acting on quantized matter fields.
Perturbative interaction-picture results for gravity-matter systems must be checked against exact Heisenberg-picture treatments.
Any observed entanglement involving gravity and matter requires quantized gravity rather than a classical gravitational field.
Semi-classical gravity models preserve the absence of gravity-induced entanglement between matter fields.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Experiments claiming to detect gravity-induced entanglement would need to isolate effects from quantized gravity rather than classical potentials.
The same Heisenberg versus interaction picture inconsistency could arise in other perturbative treatments of classical fields coupled to quantum systems.
Applying the exact Heisenberg derivation to specific gravitational potentials might reveal additional constraints on semi-classical approximations.

Load-bearing premise

The non-perturbative Heisenberg-picture treatment fully captures the interaction between classical gravity and quantized matter fields without missing contributions that the interaction-picture perturbation might overlook or approximate incorrectly.

What would settle it

A calculation or limit showing that the perturbative interaction-picture result for entanglement matches the exact Heisenberg-picture result for the same physical setup.

read the original abstract

In their recent work, Nature, {\bf 646}, 813 (2025), Aziz and Howl claim that classical (unquantized) gravity can generate entanglement of quantized matter if matter is treated within quantum field theory which is, no doubt, our ultimate theory to use. We show that the perturbative result of Aziz and Howl in interaction picture is inconsistent with our exact and simple non-perturbative derivation in Heisenberg picture, that fundamentally precludes the claimed entanglement.

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

Diósi's note argues an exact Heisenberg-picture derivation rules out entanglement from classical gravity, making the Aziz-Howl perturbative result inconsistent, but the weak-coupling limit needs explicit verification.

read the letter

Diósi's short note pushes back on Aziz and Howl by claiming that an exact non-perturbative treatment in the Heisenberg picture shows classical gravity cannot entangle quantized matter fields. This makes their interaction-picture perturbative result inconsistent with the more fundamental picture. The main new element is the targeted counter-derivation that aims to settle the question without relying on perturbation theory. It does this cleanly by contrasting the two approaches and arguing the exact result precludes the claimed effect. That focus is useful for anyone tracking these specific claims about classical gravity and quantum fields. The paper keeps the argument simple and positions the Heisenberg treatment as the reliable one for this interaction. It engages the recent Nature paper directly without overclaiming broader implications. The soft spot is the one the stress test flags: if the pictures are equivalent, the exact Heisenberg evolution should reduce to the perturbative entanglement terms at weak coupling. Any mismatch would suggest either an incomplete model of the coupling or an operator-ordering issue that the exact derivation overlooks. The abstract states the inconsistency but leaves the steps implicit, so the claim's strength depends on the full calculation holding up under that check. This is for people working on entanglement-based tests of quantum gravity or foundational questions about classical versus quantized gravity. A reader following the Aziz-Howl result would get a clear alternative view from it. I would send it to peer review. The topic matters and a focused rebuttal like this deserves referee scrutiny on the derivation details.

Referee Report

2 major / 2 minor

Summary. The manuscript argues that classical (unquantized) gravity cannot generate entanglement between quantized matter fields. It presents an exact, simple non-perturbative derivation in the Heisenberg picture that is claimed to be inconsistent with the perturbative interaction-picture result of Aziz and Howl (Nature 646, 813, 2025), thereby precluding the claimed entanglement.

Significance. If the central derivation holds, the result would be significant for the ongoing debate on whether classical gravity can produce observable quantum entanglement in matter, with direct implications for proposed table-top tests of quantum gravity. The parameter-free, exact character of the Heisenberg-picture treatment is a methodological strength that, if verified, would strengthen the case against entanglement generation.

major comments (2)

[non-perturbative derivation (Heisenberg picture)] The central claim rests on an exact non-perturbative Heisenberg-picture derivation that is asserted to preclude entanglement. However, the manuscript does not demonstrate that the perturbative expansion of this exact time-evolution operator in the weak-coupling limit recovers (or correctly modifies) the leading-order entanglement-generating terms reported by Aziz and Howl. Without this explicit limit-taking step, it remains unclear whether the two pictures are being compared on equal footing or whether operator-ordering or picture-dependent contributions have been omitted.
[comparison with Aziz and Howl result] The abstract states that the perturbative result is inconsistent with the exact derivation, but no explicit interaction Hamiltonian, stress-energy coupling, or time-evolution operator is provided to allow verification that the Heisenberg evolution fully incorporates the classical gravitational interaction without missing contributions that the interaction-picture perturbation might capture at leading order.

minor comments (2)

The title and abstract are concise, but the manuscript would benefit from a brief statement of the interaction Hamiltonian used in both pictures to facilitate direct comparison.
Notation for the quantized matter fields and the classical gravitational potential should be defined at first use to avoid ambiguity for readers familiar with the Aziz-Howl setup.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address each major comment below and indicate the revisions we will make to strengthen the presentation.

read point-by-point responses

Referee: [non-perturbative derivation (Heisenberg picture)] The central claim rests on an exact non-perturbative Heisenberg-picture derivation that is asserted to preclude entanglement. However, the manuscript does not demonstrate that the perturbative expansion of this exact time-evolution operator in the weak-coupling limit recovers (or correctly modifies) the leading-order entanglement-generating terms reported by Aziz and Howl. Without this explicit limit-taking step, it remains unclear whether the two pictures are being compared on equal footing or whether operator-ordering or picture-dependent contributions have been omitted.

Authors: We thank the referee for highlighting the importance of explicitly connecting the exact and perturbative treatments. Our Heisenberg-picture derivation is non-perturbative and exact, establishing that the unitary evolution generated by the classical gravitational interaction on quantized matter fields preserves separability and generates no entanglement. To address the concern directly, we will add a dedicated subsection in the revised manuscript that performs the weak-coupling perturbative expansion of our exact time-evolution operator. This expansion will show that the leading-order terms contain no entanglement-generating contributions, thereby demonstrating consistency with the exact result and clarifying the source of the discrepancy with the Aziz and Howl interaction-picture calculation. We maintain that the two pictures are compared on equal footing and that the exact treatment already accounts for all orders without operator-ordering ambiguities. revision: yes
Referee: [comparison with Aziz and Howl result] The abstract states that the perturbative result is inconsistent with the exact derivation, but no explicit interaction Hamiltonian, stress-energy coupling, or time-evolution operator is provided to allow verification that the Heisenberg evolution fully incorporates the classical gravitational interaction without missing contributions that the interaction-picture perturbation might capture at leading order.

Authors: We agree that greater explicitness will aid independent verification. In the revised manuscript we will include the explicit interaction Hamiltonian obtained from the coupling of the quantized matter stress-energy tensor to the classical gravitational field, together with the closed-form expression for the Heisenberg-picture time-evolution operator. These additions will make clear that our exact treatment fully incorporates the classical interaction and that the claimed inconsistency with the perturbative result is not due to omitted contributions. revision: yes

Circularity Check

0 steps flagged

No significant circularity: exact non-perturbative Heisenberg derivation stands independently

full rationale

The paper derives its central claim—that classical gravity cannot entangle quantized matter—from an exact, non-perturbative treatment in the Heisenberg picture. This derivation is presented as self-contained and does not reduce to fitted parameters from Aziz-Howl, nor does it rely on self-citations for its load-bearing steps. The claimed inconsistency with the perturbative interaction-picture result is argued directly from the difference in pictures and exactness, without the derivation itself being equivalent to its inputs by construction. This is a normal, non-circular comparison of exact versus approximate methods.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of standard quantum field theory in the Heisenberg picture applied to the interaction of classical gravity with quantized matter; no new free parameters, invented entities, or ad-hoc axioms are introduced in the abstract.

axioms (1)

standard math Standard axioms of quantum field theory and the Heisenberg picture for time evolution.
The exact non-perturbative derivation relies on these established frameworks of QFT.

pith-pipeline@v0.9.0 · 5590 in / 1085 out tokens · 34765 ms · 2026-05-18T01:50:30.031149+00:00 · methodology

discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

exact time-dependent solution ... covariant Klein–Gordon equation in the classical spacetime determined by the semiclassical Einstein equation ... reduces to the non-linear Schrödinger–Newton equation

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Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages

[1]

Classical theories of grav- ity produce entanglement,

Joseph Aziz and Richard Howl, “Classical theories of grav- ity produce entanglement,” Nature646, 813–817 (2025)

work page 2025
[2]

Is there a ‘smoking gun’ test for quantum gravity?

Zachary Weller-Davies, “Is there a ‘smoking gun’ test for quantum gravity?” Nature646, 809–810 (2025)

work page 2025
[3]

Les theories relativistes de la gravita- tion,

Christian Møller, “Les theories relativistes de la gravita- tion,” Colloques Internationaux CNRS91, 353 (1962)

work page 1962
[4]

On quantization of fields,

Leon Rosenfeld, “On quantization of fields,” Nuclear Physics40, 1 (1963)

work page 1963
[5]

Gravitation and quantum-mechanical localiza- tion of macro-objects,

L. Di´ osi, “Gravitation and quantum-mechanical localiza- tion of macro-objects,” Physics Letters A105, 199–202 (1984)

work page 1984
[6]

On gravity’s role in quantum state re- duction,

Roger Penrose, “On gravity’s role in quantum state re- duction,” General Relativity and Gravitation28, 581–600 (1996)

work page 1996

[1] [1]

Classical theories of grav- ity produce entanglement,

Joseph Aziz and Richard Howl, “Classical theories of grav- ity produce entanglement,” Nature646, 813–817 (2025)

work page 2025

[2] [2]

Is there a ‘smoking gun’ test for quantum gravity?

Zachary Weller-Davies, “Is there a ‘smoking gun’ test for quantum gravity?” Nature646, 809–810 (2025)

work page 2025

[3] [3]

Les theories relativistes de la gravita- tion,

Christian Møller, “Les theories relativistes de la gravita- tion,” Colloques Internationaux CNRS91, 353 (1962)

work page 1962

[4] [4]

On quantization of fields,

Leon Rosenfeld, “On quantization of fields,” Nuclear Physics40, 1 (1963)

work page 1963

[5] [5]

Gravitation and quantum-mechanical localiza- tion of macro-objects,

L. Di´ osi, “Gravitation and quantum-mechanical localiza- tion of macro-objects,” Physics Letters A105, 199–202 (1984)

work page 1984

[6] [6]

On gravity’s role in quantum state re- duction,

Roger Penrose, “On gravity’s role in quantum state re- duction,” General Relativity and Gravitation28, 581–600 (1996)

work page 1996