Collapse Model Tests

Collapse models modify quantum dynamics so that localization is a physical process rather than only a rule for conditional state assignment. Their scientific value is that specified versions predict departures from ordinary quantum mechanics. The frontier is to constrain those versions with calibrated experiments and distinguish their signals from ordinary noise. Reviewed 11 October 2026; the evidence horizon comprises the cited 2020 and 2023 reviews and the 2021 underground radiation test. It is not an exhaustive latest-limit chart.

Helpful background. Collapse-model tests owns the stable model-to-observable mapping, and objective-collapse theories explains the conceptual motivation.

An exclusion belongs to a specified model

For illustration, a spatial-decoherence model can act as

$$\partial_t\rho(x,x')=-\Gamma(x-x';\theta)\rho(x,x')+\cdots,$$

where $\theta$ includes model parameters and the ellipsis includes ordinary Hamiltonian and environmental evolution. Different choices of noise spectrum, dissipation, mass coupling, and spatial correlation give different predictions. A bound on one parameterization is not a model-independent exclusion of physical collapse.

In a simple localization kernel,

$$\Gamma(\Delta x)=\Gamma_0 \left[1-e^{-\Delta x^2/(4r_C^2)}\right].$$

For $\Delta x\ll r_C$, only the combination $\Gamma_0/r_C^2$ appears at leading order; for large separation the rate saturates. This schematic formula exposes an identifiability issue. It is not the complete mass-density form factor for an extended body.

The same kernel predicts a heating diagnostic

The small-separation limit of the displayed point-particle kernel gives $\dot\rho=-\frac{D_{pp}}{\hbar^2}[x,[x,\rho]], \qquad D_{pp}=\frac{\hbar^2\Gamma_0}{4r_C^2}.$ Here the formula describes one Cartesian coordinate, Markovian white noise, and no dissipative term. Using $[x,p]=i\hbar$ in the adjoint generator yields $\frac{d}{dt}\langle p^2\rangle=2D_{pp}, \qquad \frac{d}{dt}\left\langle\frac{p^2}{2m}\right\rangle =\frac{D_{pp}}m.$ Thus a parameter pair producing localization also has a quantitative energy signature in this model. $D_{pp}$ has units of momentum squared per time; a heating rate quoted without its mass and dimensional conventions is not a directly comparable constraint.

This example does not provide an extended-body CSL heating formula. A finite mass distribution supplies geometry factors and correlated contributions; colored or dissipative noise can alter the frequency response or long-time heating. The useful research question is whether coherence and diffusion data, evaluated under the same microscopic model, select a compatible parameter region.

Research directions with distinct evidence

Interferometric tests use preserved coherence to constrain additional localization. Their interpretation requires a forward model for environmental decoherence and instrumental contrast.

Noninterferometric tests use predicted diffusion, heating, force noise, or radiation. These may be sensitive without preparing a large spatial superposition, but exclusions depend strongly on how the collapse noise couples to matter and on its frequency spectrum.

Model consistency asks whether a proposed stochastic dynamics preserves normalization, complete positivity of the ensemble evolution, acceptable energy behavior, and the intended causal structure. Phenomenological fit quality does not settle these requirements.

Donadi and colleagues’ underground experiment constrains radiation predicted by a specified regularized Diósi–Penrose model. Its result rules out the natural parameter-free version considered in that paper, while bounding a mass-density regularization scale in the broader family. It does not exclude all gravity-related collapse proposals or directly supply a CSL bound. This is an example where an ambitious verbal claim must be narrowed to the actual tested dynamics.

The reviews by Carlesso and Bassi and by Bassi, Dorato, and Ulbricht explain these complementary routes. Their figures should be read as statements about named models and assumptions. Null results narrow allowed parameters; an unexplained noise excess is not positive evidence until conventional mechanisms and parameter degeneracies have been tested.

A minimal exclusion calculation

For a single counting channel with known zero background, let the predicted mean signal be $s=\lambda A T$, where $A$ is a calibrated response coefficient and $T$ the exposure. Observing zero events gives the exact one-sided 95% Poisson upper limit $e^{-s_{95}}=0.05,\qquad \lambda_{95}=\frac{-\log0.05}{AT} \approx\frac{2.996}{AT}.$ This is a synthetic inference example, not a reported experimental collapse limit. It makes the scaling and required calibration transparent. Halving exposure doubles the bound; uncertainty in $A$ cannot be omitted because it maps counts to the physical parameter.

A spectrum with uncertain backgrounds needs a multi-bin likelihood and an explicit nuisance treatment. Since a nonnegative collapse amplitude often lies at the null boundary, a generic two-sided Gaussian error bar or an unqualified application of Wilks’ theorem can misstate coverage. Validate the chosen construction on simulated null and nonzero signals, and distinguish a confidence exclusion from a Bayesian credible region.

An entry project: a transparent exclusion calculation

Baseline. Reproduce one published exclusion at a fixed noise-spectrum convention using its forward model and public numerical inputs. First verify units and asymptotic behavior for small and large object size relative to $r_C$. Use the diffusion relation and zero-count limit above as independent checks of the dynamical and statistical code before attempting the published geometry.

Resources. A laptop, likelihood methods, Fourier transforms of simple mass distributions, and careful reading of the experimental supplement. Start with synthetic data if raw data are unavailable and label the result as a methods study.

Deliverable. Produce a parameter exclusion together with nuisance assumptions, calibration ranges, and a sensitivity analysis for one modified noise spectrum. Display the original and changed assumptions beside the curves.

Failure criterion. Stop if the published curve cannot be reproduced within stated approximations, if a geometry factor is silently absorbed into an effective rate, or if a claimed likelihood result uses only a digitized best-fit curve without uncertainty information.

Research extension. Design a combined analysis of two observables with different spectral or geometric sensitivity. Ask whether the joint dataset breaks a degeneracy that each experiment retains. A null result or demonstrated nonidentifiability is a useful outcome. Before claiming novelty, check whether the same combination has already been analyzed for the same spectral convention; a visually tighter curve obtained by changing conventions is not an improvement.

What would count as progress?

A stronger limit matters when assumptions remain comparable or are explicitly broadened. A discriminating signal would require consistent parameter estimates across independent observables, scaling tests that exclude ordinary noise alternatives, and a complete uncertainty budget. The numerical tightness of one limit alone should not dictate a student’s project: access to calibration data and a credible nuisance model often determine whether the work can reach a defensible conclusion.

Connect to massive superpositions for platform requirements and limits of semiclassical gravity for a different class of dynamical modifications.

References

• A. Bassi, M. Dorato, and H. Ulbricht, “Collapse Models: A Theoretical, Experimental and Philosophical Review,” Entropy 25, 645 (2023). Open review.

• M. Carlesso and A. Bassi, “Current tests of collapse models: How far can we push the limits of quantum mechanics?” arXiv:2001.09788 (2020). Review preprint.

• S. Donadi, K. Piscicchia, C. Curceanu, L. Diósi, M. Laubenstein, and A. Bassi, “Underground test of gravity-related wave function collapse,” Nature Physics 17, 74–78 (2021). Primary radiation test — exclusion of the specified natural DP regularization.

Entry points

Choose one model and one measurement channel before surveying exclusion plots. Extract the exact mass distribution, spectral convention, confidence procedure, and environmental assumptions into a reproducible calculation.