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REVIEW 4 major objections 5 minor 31 references

Improved bounds on collapse models from rotational noise of LISA Pathfinder

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read LISA Pathfinder's rotational noise yields the tightest bound yet on CSL collapse parameters in the micrometer-to-millimeter window.

desk verdict A sound conservative CSL bound from LISA Pathfinder's rotational noise, with a useful rotational-vs-translational design criterion—but the factor-of-2 gain rests on one digitized, error-bar-free noise value. read the letter →

arxiv 2501.08971 v2 pith:Q4N22MQG submitted 2025-01-15 quant-ph

Davide Giordano Ario Altamura , Andrea Vinante , Matteo Carlesso This is my paper · ORCID
classification quant-ph
keywords spontaneouswavefunctioncollapseCSLmodelrateboundsLISAPathfinderrotationalnoisetorquespectrumnon-interferometrictestsratiocriterion
topics The Measurement Problem
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

Spontaneous collapse models modify quantum mechanics with stochastic, mass-proportional terms, and their two phenomenological constants must be pinned down by experiment. This paper shows that the rotational, torque-like noise of LISA Pathfinder's test masses constrains the CSL collapse rate $\lambda$ more tightly than the previously used translational noise, by roughly a factor of two for $r_C$ between about $10^{-5.5}$ m and $10^{-3.5}$ m. It also identifies the general condition under which rotational readout beats translational readout: the collapse-induced torque-to-force noise ratio must exceed the corresponding ratio of the dominant physical noise. This matters because it tightens the most stringent non-interferometric test in a key parameter window and gives a concrete design rule for future torque-noise experiments.

What carries the argument

The central object is the dimensionless ratio $\alpha = S^\tau/S^F$ between torque and force density noise spectra, evaluated for both the CSL signal and the dominant experimental noise. For the cube geometry the CSL ratio follows from the diffusion coefficients $\eta_R^{(\mathrm{cube})}$ and $\eta_V^{(\mathrm{cube})}$ given in Appendix A, reducing to $\alpha_{\mathrm{CSL}} \simeq L^2/6$ for $\beta = L/r_C \gg 1$; comparing it with the confined-gas value $\alpha_{\mathrm{conf}} \simeq 0.04 L^2$ and the infinite-gas value $\alpha_\infty = 0.226 L^2$ decides which readout wins. The experimental bound itself is obtained by identifying the minimum of the LISA Pathfinder angular acceleration spectrum in Fig. 11 of Ref. [15] and converting it to torque noise with $S^\tau_{\mathrm{exp}} = I^2 S_{\Delta\gamma}/4$.

What would settle it

Re-extract the minimum torque noise from the original LISA Pathfinder angular acceleration data with a calibrated noise model: if the minimum torque density at $3 \times 10^{-3}$ Hz comes out above about $1.1 \times 10^{-33}\,\mathrm{N^2\,m^2/Hz}$ (twice the quoted value), the claimed factor-of-two improvement over the translational bound disappears; if it comes out lower, the bound tightens.

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Extended reading notes

Core claim

The paper derives the first experimental bound on the CSL parameters from LISA Pathfinder's rotational noise, attributing all measured torque noise $S^\tau_{\mathrm{exp}} = 5.7 \times 10^{-34}\,\mathrm{N^2\,m^2/Hz}$ (read from the angular acceleration spectrum at $3 \times 10^{-3}$ Hz and converted through $S^\tau = I^2 S_{\Delta\gamma}/4$) to the CSL stochastic torque. Imposing $S^\tau_{\mathrm{CSL}} \le S^\tau_{\mathrm{exp}}$ yields an upper bound on $\lambda(r_C)$ that is about a factor of two stronger than the previous translational bound in the window $r_C \sim 10^{-5.5}$ m to $10^{-3.5}$ m, making it the most stringent CSL constraint there. The physical origin is the ratio $\alpha = S^\tau/S^F$: for a cubic test mass with $r_C \ll L$, $\alpha_{\mathrm{CSL}} \simeq L^2/6$, while the confined gas in the electrode enclosure gives $\alpha_{\mathrm{conf}} \simeq 0.04 L^2$, so the collapse torque noise is comparatively larger; in an infinite gas reservoir $\alpha_\infty = 0.226 L^2 > \alpha_{\mathrm{CSL}}$, so translational readout remains better there. The paper states this as a general criterion for choosing rotational versus translational degrees of freedom in collapse-model searches.

Load-bearing premise

The conclusion rests on a single digitized minimum torque noise value $S^\tau_{\mathrm{exp}} = 5.7 \times 10^{-34}\,\mathrm{N^2\,m^2/Hz}$ taken from a plot in Ref. [15] with no quoted uncertainty; if the true noise floor is higher, the bound weakens and the factor-of-two improvement can shrink or vanish.

Editorial extensions

If this is right

  • For $r_C$ roughly between $10^{-5.5}$ m and $10^{-3.5}$ m, the rotational LISA Pathfinder bound becomes the most stringent CSL constraint currently available.
  • A dedicated torque-noise experiment with a tightly enclosed test mass could exclude parameter regions inaccessible to translational measurements.
  • In open gas reservoirs, translational readout remains the better choice, so the experimental geometry determines which degree of freedom to monitor.
  • Repeating the same conservative analysis on the translational LISA Pathfinder dataset recovers the earlier translational bound, confirming the consistency of the method.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the full LISA Pathfinder angular dataset is re-analyzed with a calibrated noise model, the minimum torque noise could shift; a lower floor would push the CSL bound further down, while a higher floor would weaken or erase the claimed factor-of-two improvement.
  • The $\alpha$-ratio criterion is a transferable design rule: any noise source whose torque-to-force ratio is smaller than the CSL ratio favors rotational readout, which may help optimize future optomechanical and levitated-particle experiments.
  • For non-cubic test masses, the shape dependence of $\alpha_{\mathrm{CSL}}$ could be engineered to raise the collapse torque noise relative to physical noise, potentially extending the excluded region beyond the cubic case treated here.
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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

4 major / 5 minor

Summary. The manuscript derives an upper bound on the CSL collapse rate λ as a function of the correlation length r_C from the rotational (angular) noise of the two LISA Pathfinder test masses. The CSL-induced torque noise spectrum for cubic test masses is computed analytically, compared with the minimum measured angular acceleration noise digitized from Ref. [15], and converted to an exclusion curve that the authors claim improves the previous translational bound by about a factor of two for r_C between roughly 10^-5.5 m and 10^-3.5 m. The paper also proposes a criterion based on the ratio α = S^τ/S^F to identify when rotational degrees of freedom provide stronger CSL constraints than translational ones.

Significance. If the experimental input is reliable, this is a genuinely new non-interferometric CSL constraint in a parameter window previously probed mainly by LISA Pathfinder translational data and related analyses. The paper's strengths are the clean analytical derivation of the CSL torque noise spectral density for a cube (Appendix A), the conservative comparison S^τ_CSL ≤ S^τ_exp, and a transparent geometric criterion for choosing rotational over translational observables. The bound is not obtained by fitting any CSL parameter, and the authors are explicit about the scope and assumptions of their conservative procedure, including their criticism of the stronger bound in Ref. [26]. However, the central quantitative claim rests on a single digitized experimental value with no quoted uncertainty, which is a load-bearing issue that needs to be addressed.

major comments (4)
  1. [Sec. III, Eq. (10)] The central numerical result rests on a single digitized point: S^τ_exp = 5.7×10^-34 N² m²/Hz, read from Fig. 11 of Ref. [15] with no stated statistical or systematic uncertainty. Since the exclusion bound scales linearly with S^τ_exp and the claimed improvement over the translational bound is only about a factor of two, a ±30% error in the noise floor (or an equivalent error in the conversion) can make the claimed improvement disappear or grow substantially. The authors should quote the uncertainty from the original dataset, or conservatively use an upper envelope of the measured spectrum, and propagate this uncertainty into the λ exclusion curve shown in Fig. 2.
  2. [Sec. III, Eq. (10)] The conversion S^τ_exp = (1/4) I² S_Δγ needs to be justified against the definitions of S_Δγ in Ref. [15] and against the relative-coordinate definitions in Sec. II. For two identical cubes with relative angular acceleration Δγ = γ1 - γ2 and relative torque τ_rel = τ1 - τ2, the standard relation would be S_τ = I² S_Δγ if τ_rel is defined as in the text, or possibly I²/4 if τ_rel is defined as (τ1-τ2)/2, which is not what is written in Sec. II. The factor of 1/4 directly multiplies the reported bound, so this point must be reconciled with Eq. (7) and with the experimental definition before the factor-of-two improvement can be considered established.
  3. [Sec. IV] The explanation of why rotational noise is favorable relies on the ratio α_conf ≃ 0.04 L², inferred from Fig. 5 of Ref. [24] with no stated uncertainty, and on the representative translational force noise S^F_conv = 3.15×10^-30 N²/Hz from Ref. [14]. These values are used to quantify the improvement and to compare with α_CSL. The sensitivity of the claimed factor-of-two improvement to these inputs is not shown; the comparison as written is a single-point, no-error-bar argument. At minimum, the authors should state the accuracy to which α_conf is known or demonstrate that the qualitative conclusion is robust across the plausible range of α_conf.
  4. [Sec. V and Fig. 2] The conclusion states that the derived bound is 'the most stringent constraint on the CSL model for the values of r_C between the micro and millimeter scale.' This claim should be checked against all curves shown in Fig. 2 in that interval: the figure includes a cantilever bound (green), a rotational optomechanical region (cyan), and an X-ray bound (orange), any of which may be comparable or stronger in parts of that window. The authors should explicitly state which other limits they compare against and confirm that their red curve lies below them across the entire claimed interval.
minor comments (5)
  1. [Fig. 2] The label 'GRW' appears in the exclusion plot without being defined or explained in the caption or text; presumably it refers to the GRW parameter values, but the reader should not have to infer this.
  2. [Abstract and Sec. V] The phrase 'micro and millimeter scale' is unclear; it should read 'micrometer and millimeter scale' to specify the r_C range.
  3. [Throughout] There are several LaTeX artifacts and spacing errors, for example 'Schr¨ odinger' and 'detectors[13, 14, 19]'; these should be corrected in the production version.
  4. [Eq. (11) and Appendix A] The derivation of Eq. (11) is compact; a short consistency check showing that the β≫1 limit reproduces α_CSL ≃ L²/6 would help the reader verify the algebra.
  5. [Sec. IV] The inference of α_conf from Fig. 5 of Ref. [24] is not reproducible from the text; a direct citation of the value or an explicit formula with its error would strengthen the discussion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the bound follows from an inequality between an unfitted CSL torque spectrum and an independently measured rotational-noise floor.

full rationale

The derivation is self-contained. The theoretical torque spectrum S_tau_CSL = hbar^2 eta_R is obtained from the CSL master equation and the cube geometry in Appendix A, with no free parameter adjusted to the LISA Pathfinder data. The experimental input, S_tau_exp = 5.7e-34 N^2 m^2/Hz at 3e-3 Hz, is taken from Fig. 11 of Ref. [15], an external LISA Pathfinder publication, and converted with the relation S_tau_exp = (1/4) I^2 S_DeltaGamma. The bound is set by the conservative inequality S_tau_CSL <= S_tau_exp, which is a comparison rather than a fit. The alpha ratios used to compare rotational and translational sensitivity come from earlier gas-damping literature (Refs. [23,24]) and from closed-form CSL diffusion coefficients, not from parameters fitted in this paper. Citations to the authors' prior work (Refs. [13,14,17]) supply the model formula and the prior translational bound for comparison; none injects the target result as an assumption. The discussion of the competing analysis in Ref. [26] explicitly separates the paper's conservative bound from an error-bar-based subtraction procedure and does not rest on a self-citation. No step in the chain defines a quantity in terms of the quantity it is supposed to predict, and no fitted input is renamed as a prediction. Therefore there is no circularity.

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

The paper's central bound uses no free parameters: it compares the model's white-noise spectrum to a single measured value. The supporting ratio analysis relies on two literature values for gas damping, which are inputs rather than fits. No new entities are postulated.

assumptions (5)
  • domain assumption The CSL master equation (Eq. 1) and the stochastic potential (Eq. 3) correctly describe spontaneous collapse.
    The paper adopts the standard CSL model, including the mass-proportional noise with reference mass m0. The bound is only meaningful within this model.
  • domain assumption The CSL-induced torque and force noises are white, with correlations E[τ_rel(t)τ_rel(s)] = ℏ^2 η_R δ(t-s).
    This follows from the unravelling of the master equation; the paper assumes this throughout the derivation of the bound.
  • domain assumption The total measured torque noise of LISA Pathfinder can be used as an upper bound on any CSL contribution.
    Standard conservative approach: no known noise sources are subtracted; the measured noise floor is attributed entirely to non-CSL effects, so S_CSL ≤ S_exp.
  • domain assumption The value α_conf ≈ 0.04 L^2 inferred from Fig. 5 of Ref. [24] correctly describes the gas noise ratio in the LISA Pathfinder geometry.
    Used in the discussion to explain why rotational noise gives a stronger bound; not used to compute the bound itself.
  • domain assumption The value α_∞ = 0.226 L^2 from Ref. [23] correctly describes gas noise in an infinite volume.
    Used as the comparison case in the conditions analysis.

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Cite this review

Pith. "Pith review of Improved bounds on collapse models from rotational noise of LISA Pathfinder." pith.science (2026). https://pith.science/paper/Q4N22MQG

@misc{pith2026250108971,
  author       = {Pith},
  title        = {Pith review of: Improved bounds on collapse models from rotational noise of LISA Pathfinder},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q4N22MQG}},
  note         = {Machine review of arXiv:2501.08971}
}
read the original abstract

Spontaneous wavefunction collapse models offer a solution to the quantum measurement problem, by modifying the Schr\"odinger equation with nonlinear and stochastic terms. The Continuous Spontaneous Localisation (CSL) model is the most studied among these models, with phenomenological parameters that are constrained by experiments. Here, we exploit the recent analysis of LISA Pathfinder's angular motion data to derive a tighter constraint than previously achieved with translational motion. Moreover, we identify the general conditions for preferring rotational measurement over translational ones for constraining the CSL model.

Figures

Figures reproduced from arXiv: 2501.08971 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic of the experimental setup. Bottom right: disposition of the two test masses (TM) separated by a distance [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. represents a direct comparison of the ratio α/L2 as a function of β for the noise sources considered above. From a comparison of the coefficient for the CSL case (αCSL, blue line) and that of the confined gas (αconf, red line), we can see that for large enough values of β the rotational noise becomes favorable for a system enclosed in a box. Conversely, the coefficient for the case of an infinite volume of gas (α∞, … view at source ↗
Figure 2
Figure 2. FIG. 2. Exclusion plot for the CSL parameters [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Ratio [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Reference graph

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