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Updating the constraint on the quantum collapse models via kilogram masses

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Pith's one-line read LISA Pathfinder's latest noise decomposition bounds the CSL collapse rate to $\lambda_{\mathrm{CSL}}\le 8.3\times10^{-11}\,\mathrm{s}^{-1}$ at $r_{\mathrm{CSL}}=10^{-7}\,\mathrm{m}$, and a deep-underground torsion-balance version could…

desk verdict Useful CSL/DP update from new LPF data, but the headline bound relies on a questionable use of the Brownian error bar as a limit. read the letter →

arxiv 2411.17588 v1 pith:KGVFP5QF submitted 2024-11-26 quant-ph

Qi Dai , Haixing Miao , Yiqiu Ma This is my paper · ORCID
classification quant-ph
keywords continuousspontaneouslocalizationCSLmodelDiosi-PenroseLISAPathfindercollapse-modelboundswhiteforcenoisetorsionpendulumoptomechanicalsensing
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

This paper claims that the newest LISA Pathfinder noise analysis tightens the limits on collapse models, hypothetical modifications of quantum mechanics meant to explain why macroscopic objects behave classically. Because the CSL collapse force is white, any such signal would sit inside the Brownian, white-noise component of the spacecraft's measured acceleration noise. The paper takes the smallest statistical uncertainty of that Brownian component over ten science runs, $0.075\,\mathrm{fm^2\,s^{-4}/Hz}$, as a one-sided upper limit on any hidden white force noise, obtaining $\lambda_{\mathrm{CSL}}\le 8.3\times10^{-11}\,\mathrm{s}^{-1}$ at $r_{\mathrm{CSL}}=10^{-7}\,\mathrm{m}$. That is more than two orders of magnitude tighter than the earlier LPF-based bound, while the same data imply a Diosi-Penrose cutoff $\sigma_{\mathrm{DP}}\ge 285.5\,\mathrm{fm}$. The paper further estimates that a deep-underground dual torsion-balance device could reach $\lambda_{\mathrm{CSL}}\le 3\times10^{-11}\,\mathrm{s}^{-1}$.

What carries the argument

The load-bearing mechanism is the white force noise that a collapse model would imprint on a free kilogram-scale test mass, expressed by the effective force-noise spectrum $D_{\mathrm{CSL}}=\lambda_{\mathrm{CSL}}(\hbar/r_{\mathrm{CSL}})^2\alpha$, where $\alpha$ is a shape- and density-dependent geometry factor. The second ingredient is the LISA Pathfinder noise decomposition $S_a=S_a^{\mathrm{Brown}}+S_a^{\mathrm{color}}$, which isolates the white Brownian component so that its statistical uncertainty can be used as a one-sided bound on an unseen white noise source. The derivation also relies on the conversion $S_a=4S_F/M^2$ between force noise and the relative acceleration noise of two test masses.

What would settle it

Re-analyze the LISA Pathfinder acceleration residuals after subtracting the modelled outgassing and Brownian contributions: if an unmodelled white force noise at or above $0.075\,\mathrm{fm^2\,s^{-4}/Hz}$ remains, the claimed $\lambda_{\mathrm{CSL}}\le 8.3\times10^{-11}\,\mathrm{s}^{-1}$ would not follow, and if the Brownian uncertainty varies materially across the ten science runs the choice of the February 2017 run would need separate justification.

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Extended reading notes

Core claim

The central claim is that the CSL collapse rate at the canonical nucleon length scale $r_{\mathrm{CSL}}=10^{-7}\,\mathrm{m}$ is at most $\lambda_{\mathrm{CSL}}=8.3\times10^{-11}\,\mathrm{s}^{-1}$, and that this follows from the February 2017 LISA Pathfinder science run once the data are decomposed into a white Brownian part and a colored 'noise over Brownian' part. The derivation uses the effective force-noise spectrum $D_{\mathrm{CSL}}=\lambda_{\mathrm{CSL}}(\hbar/r_{\mathrm{CSL}})^2\alpha$ with geometry factor $\alpha$, converted to relative acceleration via $S_a=4S_F/M^2$. Since CSL noise is white and pressure- and temperature-independent, it must be contained in the Brownian component, whose run uncertainty $\sigma_{\mathrm{Brown}}=0.075\,\mathrm{fm^2\,s^{-4}/Hz}$ then acts as the cap. The same step applied to the Diosi-Penrose correlator yields $\sigma_{\mathrm{DP}}\ge 285.5\,\mathrm{fm}$.

Load-bearing premise

The argument assumes that any CSL-induced white force noise would show up inside the Brownian component of LISA Pathfinder's acceleration noise, and that the 1-$\sigma$ uncertainty of that component from the February 2017 run, $0.075\,\mathrm{fm^2\,s^{-4}/Hz}$, is a valid one-sided upper limit on such unseen noise.

Editorial extensions

If this is right

  • At $r_{\mathrm{CSL}}=10^{-7}\,\mathrm{m}$, the CSL rate is bounded by $8.3\times10^{-11}\,\mathrm{s}^{-1}$, more than two orders of magnitude tighter than the $2.96\times10^{-8}\,\mathrm{s}^{-1}$ bound from the first 55 days of LPF data.
  • The same LPF data set the Diosi-Penrose regularisation scale to $\sigma_{\mathrm{DP}}\ge 285.5\,\mathrm{fm}$, a platform-based probe complementary to stronger X-ray emission constraints.
  • A deep-underground dual torsion-balance device with calibrated thermal and gas-damping noise and correlated seismic subtraction is projected to reach $\lambda_{\mathrm{CSL}}\le 3\times10^{-11}\,\mathrm{s}^{-1}$ and $\sigma_{\mathrm{DP}}\ge 945.2\,\mathrm{fm}$.
  • Low-frequency, kilogram-scale test masses become a practical experimental platform for collapse tests, since the CSL white force noise is relatively enhanced at millihertz frequencies where the standard quantum limit is less restrictive.

Reading between the lines

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

  • The paper's numerical bound treats the 1-$\sigma$ uncertainty of one Brownian-noise estimate as an upper limit on an unseen source; a more conventional upper limit using the Brownian mean plus its uncertainty would be weaker, so the quoted $8.3\times10^{-11}\,\mathrm{s}^{-1}$ is the optimistic reading of the decomposition.
  • If the same procedure is applied to a quieter future test mass or a mission with less outgassing, the CSL bound should scale roughly linearly with the Brownian uncertainty, making the white-noise floor the quantity to chase.
  • A direct experimental check of the paper's logic would be to subtract the modelled outgassing contribution from the LPF residuals and search for any remaining white floor; a residual at or above $0.075\,\mathrm{fm^2\,s^{-4}/Hz}$ would mean the bound does not follow as stated.
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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

3 major / 5 minor

Summary. The paper claims to update bounds on the CSL and Diósi-Penrose collapse models using the 2024 LISA Pathfinder in-depth noise decomposition. The central step is to take the quoted uncertainty of the Brownian (white) acceleration-noise component, ΔS_Brown = 0.075 fm^2 s^-4/Hz from the February 2017 run, and insert it into Eq. (10) as if it were an upper limit on any white-force-noise contribution from CSL, obtaining λ_CSL < 8.3 × 10^-11 s^-1 at r_CSL = 10^-7 m and σ_DP > 285.5 fm. The paper also proposes a dual torsion-balance optomechanical device in a deep underground laboratory and projects a further bound λ_CSL < 3 × 10^-11 s^-1. The manuscript is clearly written and builds on published LPF data, but the main statistical inference is not valid as stated.

Significance. If the LPF-derived bound were valid, it would substantially improve the earlier Helou et al. constraint by exploiting the noise decomposition rather than the total noise level, and the underground proposal would be a useful forward-looking suggestion. The paper's strengths are its transparent mapping from force-noise power spectral density to collapse parameters, its use of up-to-date LPF results, and its explicit experimental parameters for a proposed future device. However, the central numerical bounds rest on treating a 1σ statistical uncertainty of a component that would contain any CSL signal as a one-sided upper limit on that signal. This is not statistically justified, so the main quantitative claims are not established by the present analysis.

major comments (3)
  1. [Section II, Eq. (14)] The inference from the LPF Brownian-component uncertainty to a CSL upper limit is invalid. The paper states that 'Since the CSL force noise is white, it will also be included in the Brownian component S^Brown_aa' and then concludes that the uncertainty of that component can constrain CSL. But if CSL noise is inside the same measured component, then the measured S_Brown is the sum of the physical Brownian noise and any CSL contribution, and the 1σ uncertainty of that sum does not bound the CSL part. A valid one-sided upper limit would require either an independent physical prediction of the Brownian contribution (with its own uncertainty) so that the residual S_meas - S_pred constrains CSL, or treating the total measured white-noise amplitude as the CSL upper limit. Using only ΔS_Brown in Eq. (10) underestimates λ_CSL by roughly S_Brown/ΔS_Brown relative to using the measured total white level. The DP bound in Eq. (15) inherits the same problem because it uses the same S_a input.
  2. [Section II, minimum-uncertainty run selection] The choice of 'the minimum uncertainty of the Brownian noise among all 10 science operations' is an order statistic, and no confidence level or statistical justification is given for using it as a hard upper bound. Without a stated coverage (e.g., 95% upper limit), and without accounting for the fact that selecting the smallest of ten error bars biases the limit optimistically, the quoted λ_CSL is not a reproducible statistical statement. The authors should either use a conservative maximum over runs, combine runs with a proper model, or provide a valid one-sided confidence bound.
  3. [Section III.B, projected underground bound] The projected bound λ_CSL < 3 × 10^-11 s^-1 depends on the assumption that common-mode rejection reduces rotational seismic noise to '10 percent of the seismic noise for a single torsion balance' and on a residual force-noise floor of 1 × 10^-17 N/√Hz. The 10% factor is introduced without a calculation, reference, or sensitivity analysis, and the noise budget in Fig. 3 is not derived in sufficient detail to reproduce it. As a result, the underground projection is an optimistic estimate rather than a derived bound; the manuscript should either justify the rejection factor with a model of the two-balance correlation or present a range of projected bounds under different assumptions.
minor comments (5)
  1. [Abstract and Introduction] There are several typos and infelicities: 'mili-Hertz' should be 'milli-Hertz', 'constraint to be' should be 'constrained to be', and 'the mass of the mass of a nucleon' repeats 'mass'. These should be corrected in a revision.
  2. [Section II, Eq. (11)] The notation around Eq. (11) is inconsistent: the symbols M and m are both used for the test mass in Eqs. (8)-(11), and the reader must infer that 'm' in Eq. (11) is the same as M. Please use a single symbol for the test-mass mass.
  3. [Section II, references] In the text 'In 2016, Helou et al.[13, 14] use LPF's data', the citations do not match: reference [13] is Carlesso et al. and reference [14] is Helou et al. The sentence should cite only [14], or the references should be reordered.
  4. [Fig. 2 and Fig. 3] The figure captions are not fully self-contained: Fig. 2 mentions the 'LPF's best data [20]' line but the text does not explain which data set this refers to, and Fig. 3's right panel is described only qualitatively. A sentence defining the line styles and the noise-budget components would improve readability.
  5. [Section II, Eq. (9)] The factor of 4 in Eq. (9) is stated without derivation; while it follows from the relative-acceleration geometry used in the cited prior work, a brief explanation or reference to the derivation would make the paper more self-contained.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the CSL bound is an external-data substitution into standard collapse-model formulas.

full rationale

The derivation chain for Eq. (14) is not circular. The input, sigma_Brown = 0.075 fm^2 s^-4/Hz, is taken from the published LISA Pathfinder noise decomposition of Ref. [17], not from any fit of lambda_CSL performed by this paper. Equation (10) is an external relation from Refs. [12, 13] that maps an assumed white acceleration-noise level into a CSL collapse rate; the paper substitutes the published uncertainty for S_a and computes the resulting lambda value. No collapse-model parameter is used to fix the input, no uniqueness theorem is imported from the authors, and no known result is renamed as a new prediction. Section III is likewise a sensitivity projection based on an assumed noise floor, not a parameter recovered from the output. The only caveat is statistical: treating the 1-sigma uncertainty of a fitted Brownian component as a one-sided upper limit on a white signal that would be absorbed into the same fitted component is a validity and confidence-level concern, but that is a correctness risk, not a circular reduction of the claim to its own input. Therefore no circular step meets the quoted-evidence standard.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The LPF bound uses one external data number (Brownian noise uncertainty) plus standard formulas; the underground projection introduces two hand-chosen parameters and several design-dependent assumptions.

free parameters (2)
  • Seismic noise common-mode reduction factor = 10%
    Hand-chosen reduction of rotational seismic noise when combining two torsion balances; no measurement or detailed model shown.
  • Residual force noise floor = 1e-17 N/Hz
    Target noise floor after calibration and optimal combination; it is an assumed sensitivity, not a result of a full derivation.
assumptions (5)
  • domain assumption CSL force noise is white and additive to the LPF Brownian noise component.
    Required for the bound in Section II; if the LPF white noise contains unmodeled non-CSL sources, the bound would be weaker.
  • domain assumption The Nimmrichter force-noise formula (Eqs. 4-6) applies to the LPF test masses.
    Used to convert measured acceleration noise into a lambda_CSL bound; taken from prior literature.
  • domain assumption The relative acceleration noise is 4 S_F / M^2 (Eq. 9).
    This factor of 4 is inherited from Helou et al.; the paper does not re-derive it, and a factor of 2 would change the bound.
  • domain assumption The DP model formula (Eq. 8) and lattice constant a for LPF apply.
    Used to derive sigma_DP > 285.5 fm; the DP bound is noted to be weaker than the X-ray bound.
  • domain assumption The LPF Brownian noise uncertainty from Ref. [17] is statistically representative for bounding new white noise.
    The paper selects the minimum uncertainty among ten runs, implicitly assuming that run's uncertainty is the appropriate limit.

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Cite this review

Pith. "Pith review of Updating the constraint on the quantum collapse models via kilogram masses." pith.science (2026). https://pith.science/paper/KGVFP5QF

@misc{pith2026241117588,
  author       = {Pith},
  title        = {Pith review of: Updating the constraint on the quantum collapse models via kilogram masses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KGVFP5QF}},
  note         = {Machine review of arXiv:2411.17588}
}
abstract

Quantum mechanics, which governs all microscopic phenomena, encounters challenges when applied to macroscopic objects that exhibit classical behavior. To address this micro-macro disparity, collapse models such as the Continuous Spontaneous Localization (CSL) and Diosi-Penrose (DP) models have been proposed. These models phenomenologically modify quantum theory to reconcile its predictions with the observed classical behavior of macroscopic systems. Based on previous works\,([Phys.\,Rev\,D,\,95(8):084054\,(2017)] and [Phys.\,Rev.\,D,\,94:124036,\,(2016)]), an improved bound on the collapse model parameters is given using the updated acceleration noise data released from LISA Pathfinder\,([Phys.\,Rev.\,D, 110(4):042004,\,(2024)]). The CSL collapse rate is bounded to be at most $\lambda_{\rm CSL} \leq 8.3\times 10^{-11}$\,$s^{-1}$ at the mili-Hertz band when $r_{\rm CSL}=10^{-7}\,{\rm m}$, and the DP model's regularization cut-off scale is constraint to be $\sigma_{\rm DP}\sim 285.5$\,fm. Furthermore, we discuss the potential advantages of using deep-underground laboratories to test these quantum collapse models. Our results show the quiet seismic condition of the current deep-underground laboratory has the potential to further constrain the CSL collapse model to $\lambda_{\rm CSL}\leq3\times 10^{-11}\,{\rm s}^{-1}$ when $r_{\rm CSL}=10^{-7}\,{\rm m}$.

Figures

Figures reproduced from arXiv: 2411.17588 by the authors.

Figure 1
Figure 1. FIG. 1. Brownian noise level of the LPF reproduced from Ref. [ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Bound on the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Left panel: Schematic diagram of the optomechanical device in the deep underground laboratory to test collapse model. The two [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Improved bounds on collapse models from rotational noise of LISA Pathfinder

    quant-ph 2025-01 conditional novelty 6.0 of 10

    Using LISA Pathfinder's measured rotational noise, the authors constrain the CSL collapse rate to values roughly a factor of 2 tighter than the existing translational bound for correlation lengths between tens of micr...

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