{"id":"e0a142ac-55dd-4dee-9466-bf582718808a","arxiv_id":"2411.17588","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Using the 2024 LISA Pathfinder noise decomposition, the CSL collapse rate is bounded below 8.3e-11 s^-1 at r_CSL=1e-7 m, and a new underground torsion balance design is projected to reach 3e-11 s^-1.","lead":"This paper updates the limits on two quantum collapse models by re-analyzing the latest LISA Pathfinder acceleration noise data. It finds a stronger bound on the CSL collapse rate and proposes a deep-underground torsion pendulum that could push the bound further.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline CSL bound treats the 1-sigma uncertainty of the LPF Brownian component as an upper limit on CSL noise, but the paper states that CSL noise would be included in that same component; without an independent subtraction of the physical Brownian background, the error bar is not a valid…","rationale":"In good faith, the paper is a parameter update using LPF's published noise decomposition plus a design study, and the arithmetic is reproducible: inserting the 2016 total-noise value into Eq. (10) reproduces the earlier Helou bound, so the numerical pipeline is not the problem. The soft spot is statistical and sits exactly at Eq. (14): the text moves from 'CSL noise will be included in the Brownian component' to 'the uncertainty of the Brownian component constrains CSL.' These are different quantities. The uncertainty of an estimated component bounds the precision of that estimate, not the magnitude of an additional source that has already been absorbed into the same component. A valid upper limit would require either using the total measured white noise as a conservative bound or subtracting an independently determined physical Brownian contribution and using the residual uncertainty. Neither is supplied. The minimum-uncertainty selection among ten runs compounds this by choosing the most favorable realization without an order-statistics correction. A single reanalysis using the actual S_Brown value, or a proper residual after independent subtraction, would settle whether 8.3e-11 s^-1 is real or an artifact of using an error bar as a signal. I also note a secondary consistency issue: Eq. (6) as printed gives α dimensions of m^-4, though Eq. (10) matches the published Helou number, suggesting a typo in α rather than in the final bound. The underground projection is explicitly a design study with hand-picked parameters, so it should be read as an estimate of potential, not as a measurement. The reader's weakest_assumption identifies the same load-bearing statistical concern, and the conditional verdict remains appropriate pending the requested reanalysis.","tokens_in":12356,"tokens_out":11940,"duration_ms":107148,"concrete_test":"Recompute Eq. (14) using the February 2017 best-fit Brownian PSD value S_Brown from Ref. [17] (Fig. 1), instead of its uncertainty ΔS_Brown, and compare the resulting λ_CSL with 8.3e-11 s^-1. If S_Brown/ΔS_Brown > 1, the headline bound is not established; then repeat the computation using the 95% upper limit on the residual white noise after subtracting the independently modeled gas-damping Brownian noise from the same run. If that residual-based upper limit is not ≤ 0.075 fm^2 s^-4/Hz, the central claim rests on an invalid use of the error bar as the signal.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section II sets Sa = ΔSa^Brown = 0.075 fm^2 s^-4/Hz in Eq. (10) to obtain λ_CSL ≤ 8.3e-11 s^-1. The load-bearing step is the claim that the 1-sigma uncertainty of the LPF Brownian component is a valid one-sided upper limit on CSL noise. The paper itself states that white CSL noise would be included in the Brownian component, so the measured S_Brown is a sum of physical Brownian noise and any CSL contribution. The uncertainty of that sum does not by itself bound the CSL part; using it as a bound is valid only if the physical Brownian level has been independently modeled and subtracted, with ΔS_Brown representing the residual uncertainty. No such subtraction, confidence level, or statistical framework is presented. Selecting the run with the minimum ΔS_Brown among ten science operations also introduces an order-statistic bias that lowers the effective limit. If the mean Brownian level rather than its error bar were used in Eq. (10), the limiting λ_CSL would be larger by roughly S_Brown/ΔS_Brown. The DP bound in Eq. (15) inherits the same issue.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":12600,"tokens_out":5275,"duration_ms":52274,"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":[{"comment":"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.","section":"Section II, Eq. (14)"},{"comment":"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.","section":"Section II, minimum-uncertainty run selection"},{"comment":"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.","section":"Section III.B, projected underground bound"}],"minor_comments":[{"comment":"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.","section":"Abstract and Introduction"},{"comment":"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.","section":"Section II, Eq. (11)"},{"comment":"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.","section":"Section II, references"},{"comment":"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.","section":"Fig. 2 and Fig. 3"},{"comment":"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.","section":"Section II, Eq. (9)"}],"recommendation":"major_revision","confidential_remarks":"The paper is a potentially useful update, but the main LPF bound is not supported by the statistical argument as written. The fix is conceptually straightforward—replace the uncertainty-as-limit step with a valid one-sided upper limit, either from a physical Brownian-noise model residual or from the total white-noise amplitude—but it will change the numerical results, possibly substantially. The underground projection also needs a more serious treatment of the seismic-rejection assumption before it can be presented as a quantitative prediction. I would encourage the authors to rework the statistical analysis and resubmit."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague —\n\nThe headline number is that LISA Pathfinder's 2024 in-depth noise analysis gives λ_CSL ≤ 8.3×10^-11 s^-1 at r_CSL = 10^-7 m, about 350 times tighter than Helou's 2017 bound. That sounds like a major step, but the statistical step behind it does not survive close reading. The paper says CSL noise would be included in LPF's fitted Brownian component, then uses the 1-sigma uncertainty of that component (0.075 fm² s^-4/Hz) as an upper limit. That is only valid if the physical Brownian background has been independently modeled and subtracted, so the uncertainty represents the residual on the CSL contribution. No such subtraction or confidence level is given. They also pick the run with the smallest uncertainty among ten, which biases the limit downward. If you used the mean Brownian level instead of its error bar, the bound would be roughly S_Brown/ΔS_Brown ≈ 15 times weaker, still an improvement over 2017 but not three orders of magnitude.\n\nWhat the paper does well: the application of Nimmrichter and Helou's formulas to the new LPF data is clean, and the authors correctly note that their DP bound (285.5 fm) is far weaker than the X-ray bound (4.94×10^5 fm) and present the kilogram-scale test as complementary rather than competitive. The deep-underground dual torsion pendulum is a reasonable design concept; the noise budget is clearly laid out. But the projection to λ_CSL < 3×10^-11 s^-1 relies on an unstated 10% common-mode rejection of seismic noise and other optimistic parameters, so it should be read as a design study, not a promise.\n\nThe paper is serious, well-cited, and the numerical update is useful to the collapse-model community. But the central bound is not rigorously established as a limit; it is an order-of-magnitude estimate that needs a proper statistical framework. I'd send it to peer review because the update is significant and the underground idea is worth discussing, but I'd require the authors to clarify the statistics and soften the claims before acceptance. I would not cite the headline bound as a hard constraint until that is fixed.","headline":"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.","tokens_in":13141,"tokens_out":4220,"would_cite":false,"duration_ms":35370,"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 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…","keywords":["continuous spontaneous localization","CSL model","Diosi-Penrose model","LISA Pathfinder","collapse-model bounds","white force noise","torsion pendulum","optomechanical force sensing"],"falsifier":"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.","tokens_in":12149,"feed_emoji":"🛰️","tokens_out":14355,"duration_ms":115642,"temperature":0.7,"pith_summary":"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 $\\lambda_{\\mathrm{CSL}}\\le 3\\times10^{-11}\\,\\mathrm{s}^{-1}$.","feed_headline":"LISA Pathfinder data cap collapse rate at 8.3e-11 per second","feed_subtitle":"New noise analysis tightens the quantum-collapse bound and points to underground torsion balances for the next test.","key_machinery":"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.","core_discovery":"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 $\\sigma_{\\mathrm{DP}}\\ge 285.5\\,\\mathrm{fm}$.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Provides the earlier gravitational-wave-detector bounds on collapse models that motivate using high-precision accelerometers for this test.","marker":"[13]"},{"why":"Supplies the original LISA Pathfinder method and the formula translating acceleration noise into a CSL lambda bound that this paper updates.","marker":"[14]"},{"why":"Gives the effective CSL force-noise spectrum and geometry factor connecting lambda_CSL to a white force noise on an optomechanical test mass.","marker":"[15]"},{"why":"Reports the first 55 days of LPF science data whose conservative bound is the baseline being improved.","marker":"[16]"},{"why":"Delivers the in-depth LPF noise decomposition, including the ten-run Brownian noise values and the February 2017 uncertainty that set the new bound.","marker":"[17]"},{"why":"Establishes the X-ray emission bound used to show that the kilogram-mass DP constraint is complementary to a stronger constraint.","marker":"[19]"},{"why":"Provides the best LPF free-fall performance curve used as a comparison bound in the CSL parameter-space plot.","marker":"[20]"}],"fun_headline_variants":["Quantum collapse capped at 8.3e-11 s^-1 by Pathfinder noise","Underground labs could slash quantum collapse bound to 3e-11","LISA Pathfinder sets sharpest limit on spontaneous collapse","Collapse model constrained tighter via kilogram-scale test masses"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Quantum collapse capped at 8.3e-11 s^-1 by Pathfinder noise","Underground labs could slash quantum collapse bound to 3e-11","LISA Pathfinder sets sharpest limit on spontaneous collapse","Collapse model constrained tighter via kilogram-scale test masses"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000726,"raw_usage":{"total_tokens":3325,"prompt_tokens":1088,"completion_tokens":2237,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":704,"completion_tokens_details":{"reasoning_tokens":2160}},"tokens_in":704,"tokens_out":2237,"duration_ms":15460,"temperature":1.0,"reasoning_tokens":2160,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:57:07.318131+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Experimental bounds on collapse models from gravi- tational wave detectors","cited_arxiv_id":null,"evidence_quote":"Provides the earlier gravitational-wave-detector bounds on collapse models that motivate using high-precision accelerometers for this test."},{"cited_title":"Lisa pathfinder appreciably constrains collapse mod- els","cited_arxiv_id":null,"evidence_quote":"Supplies the original LISA Pathfinder method and the formula translating acceleration noise into a CSL lambda bound that this paper updates."},{"cited_title":"Optomechanical sensing of spontaneous wave-function collapse","cited_arxiv_id":null,"evidence_quote":"Gives the effective CSL force-noise spectrum and geometry factor connecting lambda_CSL to a white force noise on an optomechanical test mass."},{"cited_title":"Armano, H","cited_arxiv_id":null,"evidence_quote":"Reports the first 55 days of LPF science data whose conservative bound is the baseline being improved."},{"cited_title":"In-depth analysis of lisa pathfinder performance results: Time evolution, noise projection, physical models, and implications for lisa","cited_arxiv_id":null,"evidence_quote":"Delivers the in-depth LPF noise decomposition, including the ten-run Brownian noise values and the February 2017 uncertainty that set the new bound."},{"cited_title":"Search for spontaneous radiation from wave function col- lapse in the majorana demonstrator","cited_arxiv_id":null,"evidence_quote":"Establishes the X-ray emission bound used to show that the kilogram-mass DP constraint is complementary to a stronger constraint."},{"cited_title":"Armano, H","cited_arxiv_id":null,"evidence_quote":"Provides the best LPF free-fall performance curve used as a comparison bound in the CSL parameter-space plot."}],"review_version":1}