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arxiv: 2510.20991 · v2 · submitted 2025-10-23 · 🪐 quant-ph · gr-qc

Absence of gravitationally induced entanglement in certain semi-classical theories of gravity

Ward Struyve This is my paper

Pith reviewed 2026-05-18 04:02 UTC · model grok-4.3

classification 🪐 quant-ph gr-qc
keywords semi-classical gravitygravitationally induced entanglementNewton-Schrödinger modelBohmian gravityquantum gravity testsDöner-Grossardt model
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The pith

Certain semi-classical gravity models generate no entanglement between massive particles.

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

The paper analyzes a class of semi-classical theories in which gravity acts as a classical potential inside the Schrödinger equation. It shows that the Newton-Schrödinger model, the Bohmian analogue, and the Döner-Grossardt interpolator all fail to produce entanglement in the two-particle setup proposed by Bose et al. and Marletto and Vedral. This stands in contrast to the ordinary Newtonian potential, which does create entanglement when treated as a quantum interaction. A sympathetic reader cares because the result indicates that the absence of entanglement in the experiment would not rule out every classical treatment of gravity.

Core claim

In the examined semi-classical models gravity enters the multi-particle Schrödinger equation as a classical potential sourced either by the expectation value of the mass density or by the actual particle positions, and under this dynamics no gravitationally induced entanglement appears between the two massive systems.

What carries the argument

Insertion of a classical gravitational potential into the Schrödinger equation, sourced either by the wave-function expectation value or by actual particle positions without quantum fluctuations in the field.

If this is right

  • The proposed experiment would detect no entanglement if gravity is described by any of the examined semi-classical models.
  • These models remain consistent with a null result in the entanglement test.
  • The capacity of gravity to induce entanglement depends on whether its source is the expectation value, actual positions, or a fully quantum field.

Where Pith is reading between the lines

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

  • A null result in the experiment could be explained by semi-classical gravity rather than by the absence of quantum effects.
  • Tests that probe back-reaction or gravitational fluctuations would be needed to distinguish these models from full quantum gravity.
  • The same sourcing distinction may apply to other hybrid quantum-classical theories beyond gravity.

Load-bearing premise

Gravity is modeled as a strictly classical potential inserted into the Schrödinger equation with the source taken either as the wave-function expectation value or as actual particle positions and without quantum fluctuations or back-reaction in the gravitational field itself.

What would settle it

Observation of entanglement between the two particles in the proposed Bose-Marletto-Vedral experiment would show that the semi-classical models do generate gravitationally induced entanglement.

Figures

Figures reproduced from arXiv: 2510.20991 by Ward Struyve.

Figure 1
Figure 1. Figure 1: Entanglement witness W evaluated for the different potentials VN, VeNS and VeNSB, plotted as a function of time. Negativity of the witness indicates entanglement. with σx, σy, σz the Pauli matrices. If W = ⟨ψ|Wc|ψ⟩ < 0, then |ψ⟩ is entangled. For the state (22), the witness is W = 1 − 1 2 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
read the original abstract

Bose et al. and Marletto and Vedral proposed an experiment to test whether gravity can induce entanglement between massive systems, arguing that the capacity to do so would imply the quantum nature of gravity. In this work, a class of semi-classical models is examined that treat gravity classically, through some potential in the Schr\"odinger equation, and it is shown that these models do not generate entanglement. This class includes the Newton-Schr\"odinger model, where gravity is sourced by the wave function, the Bohmian analogue, where gravity is sourced by actual point-particles, and an interpolating model proposed by D\"oner and Grossardt. These models are analyzed in the context of the proposed experiment and contrasted with the standard Newtonian potential, which does generate 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.

Referee Report

0 major / 2 minor

Summary. The manuscript analyzes a class of semi-classical models of gravity (Newton-Schrödinger, Bohmian analogue, and Döner-Grossardt interpolator) in which the gravitational interaction enters the many-body Schrödinger equation as a classical c-number potential. It shows that, when the potential is sourced either by the expectation value of the mass density or by the actual particle positions, an initially factorized two-particle state remains factorized under time evolution. This is contrasted with the standard operator-valued Newtonian gravitational potential, which does generate entanglement. The analysis is carried out in the setting of the proposed Bose et al. / Marletto-Vedral experiment to detect gravitationally induced entanglement.

Significance. If the central derivations are correct, the result supplies a precise demarcation: the proposed entanglement test would rule out this well-defined family of semi-classical models while remaining compatible with a purely classical gravitational field. The paper thereby sharpens the interpretational stakes of the experiment by exhibiting an explicit dynamical mechanism (the c-number character of the potential) that prevents entanglement generation. The absence of free parameters or ad-hoc fitting in the no-entanglement conclusion is a notable strength.

minor comments (2)
  1. [§2.2] §2.2: the explicit form of the Döner-Grossardt interpolating potential is stated only in words; an equation defining the weighting between expectation-value and point-particle sourcing would improve reproducibility.
  2. [Figure 1] Figure 1 caption: the time axis is labeled in units of ħ/Gm² but the numerical values used in the accompanying text are not cross-referenced, making it difficult to verify the plotted curves against the analytic expressions.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their positive assessment and recommendation for minor revision. The report provides an accurate summary of our analysis showing that certain semi-classical gravity models do not generate entanglement, in contrast to the standard quantum treatment. We address the points from the summary and significance sections below.

read point-by-point responses

  1. Referee: The manuscript analyzes a class of semi-classical models of gravity (Newton-Schrödinger, Bohmian analogue, and Döner-Grossardt interpolator) in which the gravitational interaction enters the many-body Schrödinger equation as a classical c-number potential. It shows that, when the potential is sourced either by the expectation value of the mass density or by the actual particle positions, an initially factorized two-particle state remains factorized under time evolution. This is contrasted with the standard operator-valued Newtonian gravitational potential, which does generate entanglement. The analysis is carried out in the setting of the proposed Bose et al. / Marletto-Vedral experiment to detect gravitationally induced entanglement.

    Authors: This is a precise summary of the manuscript. Our derivations explicitly demonstrate that the c-number character of the gravitational potential in these models preserves factorization of an initially separable state, unlike the operator-valued potential in the standard Newtonian case. The analysis is indeed framed in the context of the proposed entanglement experiment. revision: no

  2. Referee: If the central derivations are correct, the result supplies a precise demarcation: the proposed entanglement test would rule out this well-defined family of semi-classical models while remaining compatible with a purely classical gravitational field. The paper thereby sharpens the interpretational stakes of the experiment by exhibiting an explicit dynamical mechanism (the c-number character of the potential) that prevents entanglement generation. The absence of free parameters or ad-hoc fitting in the no-entanglement conclusion is a notable strength.

    Authors: We agree with this interpretation of the results. The derivations in the paper establish the no-entanglement outcome directly from the structure of the models without introducing free parameters, providing a clear dynamical reason why entanglement is absent. We believe the central derivations are correct as detailed in the full text. revision: no

  3. Referee: REFEREE RECOMMENDATION: minor_revision

    Authors: We will carry out a minor revision to improve clarity in a few derivations and add a brief remark on the implications for the experiment, but no changes to the main conclusions or technical results are required. revision: partial

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central result follows directly from inserting a classical c-number gravitational potential (sourced by expectation values or actual positions) into the Schrödinger equation and observing that an initially factorized state remains factorized under the resulting separable dynamics. This is a straightforward consequence of the modeling assumptions stated in the abstract and contrasted with the operator-valued Newtonian case; no algebraic reduction to a fitted input, self-definition, or load-bearing self-citation is present in the provided derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that gravity remains strictly classical and enters the dynamics solely through a potential term whose source is either the expectation value or the actual particle positions. No free parameters or new entities are introduced beyond the definitions of the three models.

axioms (1)
  • domain assumption Gravity is treated as a classical potential in the Schrödinger equation, sourced either by the expectation value of the mass density or by actual particle positions.
    This assumption defines the semi-classical models and is invoked throughout the analysis of entanglement generation.

pith-pipeline@v0.9.0 · 5652 in / 1297 out tokens · 53397 ms · 2026-05-18T04:02:41.693826+00:00 · methodology

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Reference graph

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