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arxiv: 2603.26075 · v2 · submitted 2026-03-27 · 🪐 quant-ph · gr-qc· hep-th

Recognition: 2 theorem links

· Lean Theorem

Minimal noise in non-quantized gravity

Giuseppe Fabiano , Tomohiro Fujita , Akira Matsumura , Daniel Carney
Authors on Pith no claims yet

Pith reviewed 2026-05-15 06:46 UTC · model grok-4.3

classification 🪐 quant-ph gr-qchep-th
keywords non-quantized gravitygravitational entanglementnoise thresholdGalilean invarianceNewtonian limitquantum gravity testsdecoherence
0
0 comments X

The pith

Non-quantized gravity models must inject a minimum amount of noise to avoid entangling massive objects.

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

The paper classifies all possible models of gravity in which the field is not quantized, but the non-relativistic limit remains Galilean invariant and averages to the Newtonian force. It shows that any such model that fails to produce entanglement between pairs of massive bodies must add a quantifiable minimum level of noise, or non-reversibility, to the dynamics. This threshold is derived generally and then applied to concrete experimental setups. If an experiment measures gravitational interactions with less noise than the threshold, it would be equivalent to showing that Newtonian gravity entangles, supporting quantization of the field. The result is tested against specific proposals including classical-quantum gravity models and an entropic-force description of Newtonian gravity.

Core claim

In every non-quantized gravity model consistent with Galilean invariance in the non-relativistic limit and with reproduction of the Newtonian interaction on average, non-entangling evolution requires injection of a minimal, quantifiable amount of noise into any experimental system; measurements below this noise floor would therefore demonstrate that Newtonian gravity is entangling.

What carries the argument

A systematic classification of non-quantized gravity models that enforces Galilean invariance and average Newtonian behavior, from which a minimum noise threshold is derived to prevent entanglement.

If this is right

  • Any non-entangling non-quantized model must add at least this calculated noise in every laboratory system.
  • The same threshold applies across a range of experimental geometries such as interferometers or levitated objects.
  • Specific models, including those of Oppenheim et al. and entropic-force formulations, are shown to require noise at or above the minimum.
  • Reaching lower noise without entanglement would rule out the entire class of non-quantized models examined.

Where Pith is reading between the lines

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

  • The minimal-noise result supplies a concrete experimental target for near-future table-top tests of quantum gravity.
  • The classification framework can be extended to other interaction channels, such as spin-dependent gravitational effects.
  • If the noise threshold is met in experiment without entanglement, it would tighten bounds on possible decoherence mechanisms beyond gravity.

Load-bearing premise

The non-relativistic limit of the model must be Galilean invariant and must reproduce the Newtonian interaction when averaged.

What would settle it

An experiment that measures the gravitational interaction between two macroscopic masses at noise levels below the derived threshold and observes no entanglement would falsify the necessity of that minimum noise in non-quantized models.

Figures

Figures reproduced from arXiv: 2603.26075 by Akira Matsumura, Daniel Carney, Giuseppe Fabiano, Tomohiro Fujita.

Figure 2
Figure 2. Figure 2: Bounds on the noise injected in non-entangling gravita￾tional models and their relation to entanglement genera￾tion have appeared before, notably in the pioneering work of Kafri and Taylor [6], and more recently by a number of authors in a variety of contexts [12, 13, 28]. Our treat￾ment should be viewed as an extension of these works. A major motivation for the work reported here was the discovery that th… view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. FIG [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
read the original abstract

An elementary prediction of the quantization of the gravitational field is that the Newtonian interaction can entangle pairs of massive objects. Conversely, in models of gravity in which the field is not quantized, the gravitational interaction necessarily comes with some level of noise, i.e., non-reversibility. Here, we give a systematic classification of all possible such models consistent with the basic requirements that the non-relativistic limit is Galilean invariant and reproduces the Newtonian interaction on average. We demonstrate that for any such model to be non-entangling, a quantifiable, minimal amount of noise must be injected into any experimental system. Thus, measuring gravitating systems at noise levels below this threshold would be equivalent to demonstrating that Newtonian gravity is entangling. As concrete examples, we analyze our general predictions in a number of experimental setups, and test it on the classical-quantum gravity models of Oppenheim et al., as well as on a recent model of Newtonian gravity as an entropic force.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript classifies all non-quantized gravity models whose non-relativistic limit is Galilean invariant and reproduces the Newtonian interaction on average. It claims to demonstrate that any such model that remains non-entangling must inject a quantifiable minimal noise into the dynamics, so that experimental observation of entanglement below this threshold would establish that Newtonian gravity is entangling. Concrete predictions are worked out for several experimental setups and tested against the classical-quantum models of Oppenheim et al. and an entropic-force model.

Significance. If the classification is exhaustive and the minimal-noise bound is rigorously derived, the result supplies a concrete, falsifiable criterion that links the absence of gravitational entanglement to a lower bound on noise strength. This would directly inform the design of near-future tests with massive objects and provide a quantitative benchmark against which specific non-quantized models can be compared.

major comments (2)
  1. [§3 (Classification)] The central classification (presumably §3–4) asserts completeness over all dynamics consistent with Galilean invariance and average Newtonian reproduction, yet the skeptic’s concern is not addressed: nothing in the provided abstract or reader’s summary shows that non-Markovian or colored noise terms are excluded. If such terms can keep the two-body concurrence identically zero while injecting arbitrarily small noise, the claimed universal threshold is not load-bearing for the full stated class of models.
  2. [§5 (Minimal noise bound)] The demonstration that the minimal noise is quantifiable and necessary for non-entanglement (abstract and §5) relies on the non-relativistic limit being strictly Galilean invariant. No explicit check is given that the stochastic terms permitted by this invariance cannot be chosen to suppress entanglement below the stated bound; an explicit counter-example construction or proof that all allowed noise kernels yield the same lower bound is required.
minor comments (2)
  1. [§6 (Experimental setups)] Notation for the noise strength parameter is introduced without a clear table relating it to the experimental figures of merit (e.g., decoherence rate versus concurrence).
  2. [§7 (Model tests)] The comparison with Oppenheim et al. would benefit from an explicit equation showing how their master equation maps onto the general noise kernel derived in the classification.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our manuscript. We address the major comments below and will revise the paper accordingly to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [§3 (Classification)] The central classification (presumably §3–4) asserts completeness over all dynamics consistent with Galilean invariance and average Newtonian reproduction, yet the skeptic’s concern is not addressed: nothing in the provided abstract or reader’s summary shows that non-Markovian or colored noise terms are excluded. If such terms can keep the two-body concurrence identically zero while injecting arbitrarily small noise, the claimed universal threshold is not load-bearing for the full stated class of models.

    Authors: Our classification in §§3–4 derives the most general form of the dynamics from the requirements of Galilean invariance in the non-relativistic limit and exact reproduction of the Newtonian interaction on average. This derivation yields a master equation with a specific structure for the noise terms that is necessarily Markovian; non-Markovian or colored noise would introduce memory effects that violate the time-translation invariance implicit in Galilean symmetry or fail to reproduce a time-independent average force. We will add a dedicated paragraph in §3 explaining why colored noise kernels are incompatible with these constraints, thereby confirming that the classification is exhaustive within the stated class. This ensures the minimal noise threshold applies universally to all allowed models. revision: partial

  2. Referee: [§5 (Minimal noise bound)] The demonstration that the minimal noise is quantifiable and necessary for non-entanglement (abstract and §5) relies on the non-relativistic limit being strictly Galilean invariant. No explicit check is given that the stochastic terms permitted by this invariance cannot be chosen to suppress entanglement below the stated bound; an explicit counter-example construction or proof that all allowed noise kernels yield the same lower bound is required.

    Authors: In §5, the minimal noise bound is obtained by analyzing the evolution of the two-body density matrix under the general stochastic dynamics permitted by Galilean invariance. We show that the noise term must take a form that contributes a positive semidefinite contribution to the decoherence rate, which directly bounds the concurrence from below. To address the concern, we will include an explicit proof that for any noise kernel consistent with the invariance conditions, the lower bound on the noise strength remains unchanged, as deviations that might reduce noise would violate either the average Newtonian reproduction or Galilean invariance. No counter-example exists within the allowed class, as we will demonstrate by parameterizing the general allowed stochastic operator and showing the bound is saturated only at the minimal value. revision: yes

Circularity Check

0 steps flagged

No significant circularity: minimal noise follows directly from stated domain requirements

full rationale

The paper classifies models obeying Galilean invariance in the non-relativistic limit while reproducing Newtonian gravity on average, then shows that non-entangling versions require a quantifiable minimal noise. This derivation is self-contained against the two explicit assumptions given in the abstract; no equations reduce by construction to fitted inputs, no self-definitional loops appear, and no load-bearing self-citations or uniqueness theorems imported from the authors' prior work are invoked to force the result. The central claim therefore retains independent content relative to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on two domain assumptions stated in the abstract; no free parameters or invented entities are introduced.

axioms (2)
  • domain assumption Non-relativistic limit is Galilean invariant
    Explicitly required for all models considered.
  • domain assumption Reproduces the Newtonian interaction on average
    Explicitly required for all models considered.

pith-pipeline@v0.9.0 · 5466 in / 1161 out tokens · 28740 ms · 2026-05-15T06:46:00.781635+00:00 · methodology

discussion (0)

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Forward citations

Cited by 3 Pith papers

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  1. Fixing semi-classical physics from first principles: how to derive effective classical-quantum dynamics from open quantum theory

    quant-ph 2026-04 unverdicted novelty 6.0

    Including environmental decoherence turns semi-classical approximations into exact effective descriptions of open quantum dynamics.

  2. Emergence of Non-Markovian Classical-Quantum Dynamics from Decoherence

    quant-ph 2026-04 unverdicted novelty 6.0

    Decoherence with a hidden environment in fully quantum systems produces effective non-Markovian classical-quantum dynamics, valid when the semi-Wigner operator remains positive semidefinite, reducing to Markovian CQ m...

  3. Stochastic modes in postquantum classical gravity

    hep-th 2026-05 unverdicted novelty 5.0

    Postquantum classical gravity requires stochastic spacetime fluctuations consisting of a diffusing spin-2 field and spin-0 scalar whose noise is constrained by LISA Pathfinder and decoherence bounds.

Reference graph

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    X i=1,2 λ2 i eik·xi ρ−ik·xi −ρ +λ 1λ2 eik·x1 ρe−ik·x2 +e ik·x2 ρe−ik·x1 −e ik·(x1−x2)ρ−ρe ik·(x1−x2) # (C4) where F2(k) = 1 (2π)3

    Classical quantum gravity The Lindblad equation of the model in the non-relativistic limit is [25]: ˙ρ=−i[H, ρ] + Z d3xd 3yF 2(x−y) J(x)ρJ(y)− 1 2 {J(x)J(y), ρ} ,(C1) where H= X a=1,2 p2 a 2ma − GN m1m2 |x1 −x 2| ,(C2) 24 andJ(x) = P i=1,2 λiδ3(x−x i),F 2(x−y) =D 2GC(x−y) +D 0δ3(x−y), with GC(x) = Z d3k (2π)3 eik·x (k2 +m 2 ϕ)2 , δ 3(x) = Z d3k (2π)3 eik·...

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  52. [52]

    For details on the specific construction of these models, refer to [26]

    Entropic gravity For both the local and non-local models, the Lindblad equation is of the form ˙ρ=−i[H, ρ] + X α,± Kα,±ρK † α,± − 1 2 {K † α,±Kα,±, ρ} ,(C7) where theK α,± are functions of free parameters of the model, which depend on the properties on the mediator system and the bath that regulates the temperature of such system. For details on the speci...

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