{"id":"02c84bd8-ea7f-4ae7-a81b-d7580e447fd9","arxiv_id":"2501.08971","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"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 micrometers and millimeters.","lead":"By reusing the angular motion measurements of the LISA Pathfinder spacecraft, this paper places a new limit on the strength of spontaneous wavefunction collapse. The new limit is about twice as strong as the best previous limit in a narrow range of the collapse model's parameters.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The factor-of-2 improvement over the translational bound rests on a single digitized torque-noise value (5.7e-34 N^2m^2/Hz) with no quoted uncertainty; if that value or the conversion in Eq. (10) is off by ~30%, the claimed improvement can vanish.","rationale":"The most load-bearing assumption is the numerical value of the experimental torque noise floor. The theoretical framework (CSL diffusion coefficients, geometry factors) is standard and the derivation of the condition S^τ_CSL ≤ S^τ_exp is correct. The paper's novelty is specifically the claimed factor-of-2 improvement; that factor is the ratio α_exp/α_CSL, and α_exp is fixed by the single digitized number. Without a quoted uncertainty, the improvement margin is unquantified. The paper acknowledges a factor-of-2 discrepancy with the gas-noise model, so the measured number is not yet independently confirmed. A secondary concern is the normalization of the relative-coordinate CSL noise: the equations of motion use the relative coordinate with reduced parameters, and it should be verified that the single-cube η_R in Appendix A is correctly converted to the relative torque spectrum (a possible factor of 1/2). This factor cancels in the ratio α_CSL, so it does not affect the improvement claim, but it would shift the absolute bound; checking it is worthwhile. These are addressable with archival data, so the paper warrants CONDITIONAL rather than REJECT. The reader identified the same central issue, hence agreement.","tokens_in":8408,"tokens_out":20489,"duration_ms":190850,"concrete_test":"Download the full angular acceleration noise amplitude spectral density from Ref. [15] (or the LISA Pathfinder data archive), locate the global minimum and its 1σ statistical uncertainty with the same binning as the published figure, and recompute S^τ_exp via Eq. (10). Then propagate the uncertainty into the CSL λ bound and compare with the translational bound recomputed from the same archival force-noise data. If the best-estimate S^τ_exp shifts by more than ~30% or the 1σ range spans a factor of ~2, the claimed improvement is not robust. Additionally, verify the conversion factor by deriving S_Δγ from the published torque noise using the mechanical transfer function (including stiffness and damping) in Ref. [15]; if the transfer function is not flat at 3×10^-3 Hz, Eq. (10) needs a frequency-dependent correction.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central quantitative claim — a factor-of-2 improvement over the translational bound and the most stringent CSL constraint for r_C between 10^-5.5 and 10^-3.5 m — is set by the value S^τ_exp = 5.7×10^-34 N^2 m^2/Hz. This is obtained in Sec. III by digitizing the minimum of the angular acceleration spectrum S^{1/2}_Δγ from Fig. 11 of Ref. [15] and applying S^τ_exp = (1/4) I^2 S_Δγ, with I = mL^2/6. The paper quotes no statistical or systematic uncertainty on this minimum, and no error bar is propagated into λ_bound. Because the bound scales linearly with S^τ_exp, a 30% error in the noise floor translates directly into a 30% shift in the excluded λ, while the claimed improvement margin over the prior translational bound is only a factor of 2. The digitization is vulnerable to plot-resolution and baseline-subtraction artifacts, and the conversion assumes the measured S_Δγ is the relative angular acceleration of two identical free masses, which should be checked against the experimental definition in Ref. [15]. The paper itself notes a factor-of-2 inconsistency between the measured torque noise and the gas-noise prediction (Sec. IV), so the systematics of the reported number matter. The comparison to the previous bound from Ref. [13] also relies on a single representative force-noise value, 3.15×10^-30 N^2/Hz, and the ratio α_exp/α_CSL is what sets the improvement factor.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":8724,"tokens_out":4975,"duration_ms":51975,"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":[{"comment":"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.","section":"Sec. III, Eq. (10)"},{"comment":"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.","section":"Sec. III, Eq. (10)"},{"comment":"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.","section":"Sec. IV"},{"comment":"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.","section":"Sec. V and Fig. 2"}],"minor_comments":[{"comment":"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.","section":"Fig. 2"},{"comment":"The phrase 'micro and millimeter scale' is unclear; it should read 'micrometer and millimeter scale' to specify the r_C range.","section":"Abstract and Sec. V"},{"comment":"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.","section":"Throughout"},{"comment":"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.","section":"Eq. (11) and Appendix A"},{"comment":"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.","section":"Sec. IV"}],"recommendation":"major_revision","confidential_remarks":"The paper's central derivation is sound and the topic is suitable for the journal, but the factor-of-two improvement is currently anchored to a single digitized experimental value with no uncertainty estimate. This is fixable: the authors should obtain or justify an error bar for S^τ_exp from the LISA Pathfinder collaboration paper, or recast the bound using a conservative upper envelope. The editor may also wish to check that the 'first experimental bound from rotational noise' claim is not contested by the related work in Ref. [26], which the authors themselves discuss."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nQuick take: this paper derives a new conservative upper bound on the CSL collapse rate from the rotational (angular acceleration) noise of LISA Pathfinder, about a factor of 2 tighter than the earlier translational bound in a narrow r_C window. It also gives a general criterion—comparing the torque-to-force noise ratio α for CSL against the experimental noise—for when rotational sensing beats translational. That criterion is the most useful part for future experiment design.\n\nWhat's genuinely new: the torque formulas for a cube already existed in Refs. [13,14]; what's new is applying them to the actual measured rotational spectrum rather than a converted translational estimate, plus the α-ratio analysis. The paper is honest: it states the conservative approach, flags a factor-of-2 inconsistency between the measured torque noise and the gas-noise prediction, and openly discusses the concurrent work [26] that gets a much stronger bound by modeling the noise away.\n\nSoft spots: the central number, S_τ^exp = 5.7 × 10^-34 N² m²/Hz, is digitized from a figure in Ref. [15] with no uncertainty, and the conversion assumes the plotted S_Δγ is the relative angular acceleration of two identical free masses. The factor-of-2 improvement over the previous bound is exactly the kind of claim that a 30% systematic error would destroy; the stress-test note on this is right. The comparison also leans on one representative force-noise value from Ref. [13] and an α_conf read from a plot in Ref. [24]. None of this invalidates the logic—a conservative bound from an independently measured noise floor is sound—but it means the quantitative gain should be framed with a robustness check rather than as a firm factor of 2.\n\nOn the \"first experimental bound\" claim: it's defensible only in the narrow sense of rotational noise with a conservative analysis; the earlier concurrent paper [26] appears to have set a stronger bound using modeling. The authors acknowledge this, so it's a matter of emphasis, not concealment.\n\nBottom line: solid, modest contribution. The α-ratio criterion is a real tool, and the paper is well worth referee time. I'd send it to review, asking for error propagation on the digitized value and a sensitivity analysis on the improvement factor.\n\nBest","headline":"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.","tokens_in":9261,"tokens_out":2456,"would_cite":true,"duration_ms":23964,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"LISA Pathfinder's rotational noise yields the tightest bound yet on CSL collapse parameters in the micrometer-to-millimeter window.","keywords":["spontaneous wavefunction collapse","CSL model","collapse rate bounds","LISA Pathfinder","rotational noise","torque noise spectrum","non-interferometric tests","noise ratio criterion"],"falsifier":"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.","tokens_in":8203,"feed_emoji":"🛰️","tokens_out":5286,"duration_ms":53224,"temperature":0.7,"pith_summary":"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.","feed_headline":"LISA Pathfinder's rotational noise tightens the CSL collapse bound","feed_subtitle":"Torque noise from angular data beats the previous translational bound by roughly a factor of two.","key_machinery":"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 $S^\\tau_{\\mathrm{exp}} = I^2 S_{\\Delta\\gamma}/4$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the measured angular acceleration spectrum of LISA Pathfinder from which $S^\\tau_{\\mathrm{exp}} = 5.7 \\times 10^{-34}\\,\\mathrm{N^2\\,m^2/Hz}$ is read.","marker":"[15]"},{"why":"Provides the previous translational bound from gravitational-wave detectors that the new rotational bound improves, and the conversion relation used for the torque noise.","marker":"[13]"},{"why":"Gives the confined-gas Brownian noise ratio $\\alpha_{\\mathrm{conf}} \\simeq 0.04 L^2$, which is the key comparison making rotational noise favorable in the enclosed geometry.","marker":"[24]"},{"why":"Gives the infinite-gas ratio $\\alpha_\\infty = 0.226 L^2$, defining the regime where translational readout wins.","marker":"[23]"},{"why":"Provides the earlier force-to-torque conversion for LISA Pathfinder and the translational bound that the paper compares against.","marker":"[14]"},{"why":"The related work that sets a stronger but model-dependent bound by fully modeling the noise, which the paper contrasts with its conservative approach.","marker":"[26]"}],"fun_headline_variants":["Rotational noise from LISA Pathfinder halves CSL bound","LISA Pathfinder's rotation sharpens collapse-model limits","CSL collapse bound improved by LISA Pathfinder's angular noise","Why rotational motion beats translational for collapse searches","Torque noise of LISA Pathfinder sets tightest CSL constraint yet"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Rotational noise from LISA Pathfinder halves CSL bound","LISA Pathfinder's rotation sharpens collapse-model limits","CSL collapse bound improved by LISA Pathfinder's angular noise","Why rotational motion beats translational for collapse searches","Torque noise of LISA Pathfinder sets tightest CSL constraint yet"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000262,"raw_usage":{"total_tokens":1591,"prompt_tokens":937,"completion_tokens":654,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":553,"completion_tokens_details":{"reasoning_tokens":569}},"tokens_in":553,"tokens_out":654,"duration_ms":6188,"temperature":1.0,"reasoning_tokens":569,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:13:40.827422+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Carlesso, A","cited_arxiv_id":null,"evidence_quote":"Supplies the measured angular acceleration spectrum of LISA Pathfinder from which $S^\\tau_{\\mathrm{exp}} = 5.7 \\times 10^{-34}\\,\\mathrm{N^2\\,m^2/Hz}$ is read."},{"cited_title":"Di´ osi, Testing spontaneous wave-function collapse models on classical mechanical oscillators, Physical review letters 114, 050403 (2015)","cited_arxiv_id":null,"evidence_quote":"Provides the previous translational bound from gravitational-wave detectors that the new rotational bound improves, and the conversion relation used for the torque noise."},{"cited_title":"Toroˇ s, G","cited_arxiv_id":null,"evidence_quote":"Gives the confined-gas Brownian noise ratio $\\alpha_{\\mathrm{conf}} \\simeq 0.04 L^2$, which is the key comparison making rotational noise favorable in the enclosed geometry."},{"cited_title":"2 3 − e − L2 4r2 C L rC 2 + 32 1 − e − L2 4r2 C − √π","cited_arxiv_id":null,"evidence_quote":"Gives the infinite-gas ratio $\\alpha_\\infty = 0.226 L^2$, defining the regime where translational readout wins."},{"cited_title":"Carlesso, M","cited_arxiv_id":null,"evidence_quote":"Provides the earlier force-to-torque conversion for LISA Pathfinder and the translational bound that the paper compares against."},{"cited_title":"Cavalleri, G","cited_arxiv_id":null,"evidence_quote":"The related work that sets a stronger but model-dependent bound by fully modeling the noise, which the paper contrasts with its conservative approach."}],"review_version":1}