Spontaneous Collapse Models

Matteo Carlesso; Sandro Donadi

Spontaneous Collapse Models

T0 review · 0 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Spontaneous collapse gives quantum measurement a testable solution

desk verdict A competent, clearly written review of collapse models with no new results; useful as a map of current experimental bounds, but watch the Eq. (31) master-equation factor and treat the bounds as model-specific. read the letter →

arxiv 2508.18822 v1 pith:HKJDXBU5 submitted 2025-08-26 quant-ph

Matteo Carlesso , Sandro Donadi This is my paper · ORCID

classification quant-ph

keywords quantummeasurementproblemmodificationsofmechanicsspontaneouscollapsemodelsGRWmodelCSLDiósi-Penroseexperimentaltestsamplificationmechanism

topics The Measurement Problem

open problems 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

The paper argues that spontaneous collapse models resolve the quantum measurement problem by replacing the two dynamical postulates of quantum mechanics with a single non-linear, stochastic modification of the Schrödinger equation. These modifications localize wavefunctions in space, with negligible effects on microscopic systems but dominant effects on macroscopic ones, thereby explaining why superpositions are never seen at everyday scales. Because the collapse dynamics changes the predictions of the theory, it is experimentally testable. The review presents the three central models, derives their predictions, and compiles the bounds current experiments place on the collapse rate and localization width.

What carries the argument

The central objects are the GRW model (discrete spontaneous localizations with rate λ and width r_C), the CSL model (a continuous stochastic differential equation with mass-density collapse operator M(x) = Σ m_i g(x − q_i)), and the Diósi-Penrose model (collapse driven by gravitational noise with 1/|r−r'| correlations). The identity that carries the argument is the linearity of the density-matrix evolution map: avoiding superluminal signalling forces the state-vector dynamics to be both non-linear and stochastic. The amplification mechanism, by which the collapse rate scales with particle number (linearly for GRW, up to quadratically for CSL), is what connects microscopic and macroscopic beh

What would settle it

A cryogenic kilogram-scale crystal isolated from all known heating sources, with heat capacity and thermometry sensitive to shifts of a few tens of pW/kg, should reveal the CSL heating rate predicted at the proposed parameter values; observing none would falsify the mass-proportional CSL model in that region of λ and r_C.

Watch

Extended reading notes

Core claim

The paper claims that collapse models offer a simple way out of the measurement problem: a unified dynamics that includes both the unitary evolution and the collapse as a single process, so no separate measurement postulate is required. The modification must be both non-linear and stochastic; deterministic non-linearities would permit faster-than-light signalling, as shown by an argument based on the evolution of ensembles. Because the collapse operators couple to mass, the collapse rate amplifies with particle number, leaving microscopic systems essentially unaffected while rapidly suppressing macroscopic superpositions. The models' distinctive predictions—degraded interference, energy heat

Load-bearing premise

All quoted bounds and amplification laws assume the collapse operators couple to the mass density; if the true collapse mechanism coupled to a different observable, these numbers would not apply.

Editorial extensions

If this is right

The measurement problem can be addressed without abandoning quantum mechanics; a single dynamical law covers both microscopic and macroscopic systems.
The amplification mechanism explains why macroscopic superpositions are never observed while microscopic ones persist, without an ad hoc measurement postulate.
Current experiments already exclude the originally proposed GRW parameters and much of the Adler range; remaining allowed values concentrate at large r_C or very low λ.
Non-interferometric tests—bulk heating, cold-atom diffusion, optomechanical noise, and spontaneous radiation—are more powerful than interferometry for many parameter regions.
Colored and dissipative generalizations show that the testable core of collapse models survives relaxing the white-noise and energy-conservation idealizations.

Reading between the lines

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

Because the bounds depend on the mass-proportional coupling, a future model coupling collapse to a different observable would evade these bounds; the exclusion plots are conditional on that physical assumption.
As optomechanical and interferometric sensitivities improve, the remaining parameter window for simple white-noise mass-proportional models may close, shifting interest to the colored and dissipative parameter space.
The same experimental techniques used to constrain collapse models double as generic sensors for any stochastic modification of quantum mechanics; a null result constrains a broader class of quantum-noise theories.
If any of these models is confirmed, quantum mechanics would be an effective theory and the superposition principle would have a fundamental range limit.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

This is a review, not a research preprint. That should shape how you read it. It gives a coherent tour of GRW, CSL, the Diósi-Penrose model, and their colored and dissipative variants, and it collects the current experimental constraints from independent groups (Majorana, LISA Pathfinder, cold atoms, optomechanics). As a map of the available bounds, it is solid and useful. As a contribution, it contains no new math or data. That is fine for its genre, and the authors do not claim otherwise.

The mathematics is mostly right. The one thing I noticed: Eq. (31) writes the CSL master-equation coefficient as -γ, while the Itô derivation in Eq. (33) and the model-specific equations that follow, e.g. Eq. (43), carry -γ/2. This is almost certainly a typo, and nothing later depends on the factor in Eq. (31), so it is not load-bearing. Still, it should be corrected.

The high self-citation count is less suspicious than it looks: Carlesso and Donadi are central contributors to these bounds, and the key experimental constraints are external. The paper also acknowledges that the mass-proportional collapse operator is a modeling choice and that other choices change predictions (Secs. 4.2.5, 5.2). So the strongest skeptical concern—that all bounds depend on one coupling assumption—is not buried; it is in the text. The claims are framed as constraints on specific models, not on all possible collapse mechanisms. That is honest.

Soft spots: Sec. 3.4 literally calls the collapse proof 'a scratch of the proof,' and the colored-noise master equation is quoted rather than derived. For a pedagogical review that is acceptable, though it is not a reference-grade derivation. The paper would be stronger if it said explicitly which bounds change under alternative couplings, but it already flags the issue.

Who should read it: graduate students entering the field and researchers who want a compact citation source for current bounds. Would I send it to referees? Yes, as a review it deserves one; I would ask the referee specifically to check the Eq. (31) factor and the quoted bounds. I would cite it as a review, not as a source of new results.

Recommendation: engage with it. It is a competent, honest survey.

Referee Report

0 major / 6 minor

Summary. This paper is a review of spontaneous collapse models as phenomenological resolutions of the quantum measurement problem. It introduces the GRW, CSL, and Diósi-Penrose models, derives or sketches their master equations, and collects experimental constraints from interferometric and non-interferometric tests, including cold atoms, optomechanical systems, bulk heating, and spontaneous photon emission. It also discusses colored and dissipative generalizations and their experimental status. The central claim is that collapse models modify quantum mechanics with non-linear stochastic terms, avoid superluminal signalling, and yield testable predictions that can be used to bound the model parameters.

Significance. If taken as an introductory review, the paper is a competent and useful reference. The standard equations of GRW, CSL, and Diósi-Penrose are presented correctly, and the quoted experimental bounds are traceable to published experiments, including independent work from the Majorana Collaboration, LISA Pathfinder, and molecular interferometry. The paper explicitly acknowledges the model-dependence of the bounds and the roles of free parameters such as r_C, R_0, Omega_C, chi, and beta. A particular strength is the clear distinction between interferometric and non-interferometric tests and the explicit presentation of falsifiable predictions. The paper does not claim new derivations; its value lies in synthesis and critical presentation.

minor comments (6)

[Sec. 3.4, Eq. (31)] The master equation coefficient is written as -gamma sum_i [A_i,[A_i,rho]], whereas the Itô derivation in Eq. (33) gives -gamma/2 sum_i [A_i,[A_i,rho]], and the later CSL master equation, Eq. (43), contains the correct 1/2 factor. Since no subsequent bound uses Eq. (31) directly, this does not affect the conclusions, but the inconsistency should be corrected.
[Sec. 3.4, Eq. (32)] The 'scratch of the proof' leaves the derivation of Eq. (32) implicit. For a review this is acceptable, but a brief indication of how the Itô rule is used to obtain the variance evolution would improve readability.
[Sec. 4.1] The 'reasonable' theoretical lower bound is defined by the assumption that a 10 micrometer object collapses within 0.01 s. This is a heuristic anthropic-style criterion; the text should perhaps label it more explicitly as an illustrative benchmark rather than a rigorous model constraint.
[Fig. 3 caption] The sentence stating 'The theoretical values proposed by GRW and the ranges proposed by Adler are shown respectively as a black dot and black dots with bars...' appears twice. This duplication should be removed.
[Sec. 2.1, Ref. [1]] The sentence 'It has been advocated that decoherence resolves the measurement problem [1]' cites Ref. [1], which seems unrelated to the decoherence literature. A standard reference on decoherence and the measurement problem would be more appropriate.
[Sec. 5.2] The phrase 'one derives – thorough a non-trivial unravelling technique' contains a typo: 'thorough' should be 'through'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: review-level exposition; central constraints come from independent experiments, and model-dependence is explicit.

full rationale

This is a review article, not an original derivation claiming to predict collapse from first principles. The central assertion—that collapse models resolve the measurement-problem ambiguity by prescribing a unified stochastic non-linear dynamics and that their free parameters (λ, r_C, R0) can be bounded experimentally—does not reduce to its inputs. The mass-proportional form of the CSL operator M(x)=Σ_i m_i g(x−q_i) is explicitly presented as the definition of the model (Sec. 3.4, Eq. (40)), not as a derived prediction; the paper also notes in Secs. 4.2.5 and 5.2 that different collapse-operator choices change the bounds, so the quoted bounds are correctly scoped to the CSL/DP parameterizations. The experimental bounds come mostly from independent groups (cold-atom interferometry [14], molecular interferometry [13], Majorana radiation search [12], LISA Pathfinder [23], optomechanics [19–22]). The authors' self-citations (e.g., [2,17,18,24,27,29]) supply theoretical formulas or summary plots, but those formulas are parameter-free model calculations whose assumptions do not include the bounds themselves, and the decisive constraints are externally reproduced. No fitted parameter is renamed as a prediction. The only internal discrepancy found is the 1/2 factor in the master equation: Eq. (31) writes −γΣ[A_i,[A_i,ρ]], while the Itô derivation in Eq. (33) yields −γ/2Σ[A_i,[A_i,ρ]]; later model-specific equations, such as Eq. (43), carry the correct 1/2, and no bound depends on Eq. (31) as written. This is a consistency/typo issue, not circularity. Accordingly, no circular step is identified.

Assumptions & free parameters 6 free parameters · 6 assumptions · 2 invented entities

The review builds on models whose free parameters (lambda, r_C, R0, Omega_C, chi, beta) are introduced ad hoc and then constrained by experiments. The central predictions depend on the choice of mass-proportional coupling and on several domain assumptions about the nature of the collapse noise.

free parameters (6)

lambda (CSL collapse rate) = No unique fitted value; bounded, e.g. lambda < 4.9e-15 s^-1 at r_C = 1e-7 m from photon emission
Core free parameter of GRW/CSL; sets the collapse frequency per particle.
r_C (CSL localization length) = Bounded over roughly 1e-10 to 1e-5 m; no unique fitted value
Determines the spatial resolution of the collapse; constrained by interferometric and non-interferometric tests.
R0 (DP cutoff / coarse-graining length) = R0 >= 4.94e-10 m (Majorana bound)
Regularization scale in the Diósi-Penrose model; Sec. 3.5 explicitly calls it a free parameter.
Omega_C (colored noise cutoff frequency) = Suggested ~1e12 Hz if the noise has cosmological origin
Introduced in Sec. 5.1 to describe colored noise; a new phenomenological parameter.
chi (dissipative CSL parameter) = Related to T_CSL via Eq. (71); for T_CSL = 1 K, chi is small
Controls the dissipative term and the effective noise temperature in dissipative CSL.
beta (dissipative strength in alternative operator) = Not specified in this paper
New phenomenological parameter in Eq. (79) for the dissipative operator of [31].

assumptions (6)

standard math Itô stochastic calculus and Wiener processes provide the mathematical framework for the continuous collapse equations (Eqs. 30, 37).
The paper uses Itô rules and the Stratonovich equivalence to derive master equations and experimental predictions.
domain assumption Any acceptable modification of quantum mechanics must be non-linear and stochastic, because non-linear deterministic modifications allow superluminal signalling (Gisin argument, Sec. 3.2).
This justifies the structure of all collapse models considered; it relies on the no-superluminal-signalling principle.
ad hoc to paper The collapse mechanism couples to mass density through operators of the form M(x) = sum_i m_i g(x - q_i) (Sec. 3.4, Eq. 40).
The mass-proportional coupling is postulated, not derived; all experimental bounds on lambda and r_C depend on this specific choice.
ad hoc to paper The Diósi-Penrose model requires a finite UV cutoff R0 to regularize divergent integrals (Sec. 3.5); the model does not predict R0.
The paper notes that R0 = 1e-15 m is excluded by data, so R0 is treated as a free parameter.
domain assumption The colored-noise master equation is a first-order perturbative expansion in the coupling gamma (Sec. 5.1, Eq. 60).
The review adopts this perturbative treatment without proving its validity for the parameter regimes considered.
ad hoc to paper The 'reasonable' theoretical lower bound on collapse parameters assumes a 10 µm object must collapse within 0.01 s (Sec. 4.1).
These anthropocentric thresholds are chosen to keep the collapse mechanism hidden from normal human perception.

invented entities (2)

Universal collapse noise field w_t(x) / W_t(x)
purpose: Stochastic field that couples to mass density and induces wavefunction collapse in GRW/CSL/DP models.
The noise field is postulated; there is no direct detection, only indirect bounds on its effects (heating, decoherence, photon emission).
GRW spontaneous localizations (sudden jumps)
purpose: Discrete, random position localizations with Poisson rate lambda in the GRW model.
No independent evidence for the jumps; their rate lambda is the free parameter bounded by experiments.

how reviews work

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Cite this review

Pith. "Pith review of Spontaneous Collapse Models." pith.science (2026). https://pith.science/paper/HKJDXBU5

@misc{pith2026250818822,
  author       = {Pith},
  title        = {Pith review of: Spontaneous Collapse Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HKJDXBU5}},
  note         = {Machine review of arXiv:2508.18822}
}

read the original abstract

Collapse models are phenomenological models introduced to solve the measurement problem in quantum mechanics. They modify the Schr\"odinger equation by adding non-linear and stochastic terms, which induce the wavefunction collapse in space. The collapse effects are negligible for microscopic systems but become dominant in the macroscopic regime, thus also describing coherently the quantum-to-classical transition. Collapse models make different predictions compared to those of quantum mechanics; hence they can be tested. Here we introduce the most relevant collapse models present in the literature, and describe their main features. We also discuss how one can test them in different experiments, underlying the differences with predictions of quantum mechanics, and show how these experiments can set bounds on the collapse parameters. We conclude with a brief summary of the colored and dissipative generalization of such models and their experimental tests.

Figures

Figures reproduced from arXiv: 2508.18822 by the authors.

**Figure 2.** Experimental upper bounds on CSL parameters [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗

**Figure 3.** Exclusion plot for the CSL parameters λ and rC from noninterferometric tests. The colored areas correspond to experimentally excluded regions. The yellow and brown areas are from phonon excitation in the CUORE experiment [16] and in Neptune [17] respectively. The red area is from cold-atom experiment [18]. The purple, green and blue areas are from different optomechanical experiments [19, 20, 21, 22, 23]. The oran… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Exclusion plot for the DP parameter R0 from non-interferometric tests. The colored areas correspond to experimentally excluded values of R0. The brown area is from the heating rate of Neptune [17], the blue bound is from LISA Pathfinder [23], the orange one is from rad…

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

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Sandro Donadi and Angelo Bassi. Seven nonstandard models coupling quantum matter and gravity. A VS Quantum Science, 4(2):025601, 2022

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