Empirical Status of Continuous Spontaneous Localization

Comprehensive computational assessment of CSL parameter space constraints, collapse dynamics, and proposed decisive experiments

95.1% Parameter Space Excluded
0.0285 Bayes Factor (CSL/QM)
7 Experiment Classes
4.30 × 104 Adler 50% Vis. (amu)

Parameter Space Status

Theory Reference Points

Model λ (s-1) rC (m) Status
GRW (1986) 10-16 10-7 Excluded
Adler lower 10-10 10-7 Excluded
Adler upper 10-8 10-7 Excluded

Exclusion Summary

Excluded fraction 95.1%
Excluded grid points 6,088 / 6,400
Grid range (λ) 10-20 to 10-2 s-1
Grid range (rC) 10-8 to 10-4 m
Bayesian interpretation Moderate QM preference

Collapse Dynamics

Collapse Timescales

Timescale Data

Regime N τGRW (s) τAdler (s)
Micro 103 4.00 × 1014 4.00 × 106
Meso 1010 1.00 × 10-4 1.00 × 10-12
Macro 1020 1.00 × 10-24 1.00 × 10-32
Key finding: Mesoscopic collapse occurs in 0.1 ms (GRW) to 1 ps (Adler), establishing the quantum-classical boundary near 10-17 kg.

Diffusion Heating Analysis

Force Noise by Experiment

Heating Predictions

Experiment Mass (kg) SFGRW (N2/Hz) SFAdler (N2/Hz)
Cantilever (mK) 5.0 × 10-11 1.98 × 10-37 1.98 × 10-29
Nanoparticle 1.0 × 10-18 7.93 × 10-53 7.93 × 10-45
BAW resonator 5.0 × 10-4 1.98 × 10-23 1.98 × 10-15
LIGO mirror 4.0 × 101 1.27 × 10-13 1.27 × 10-5

Matter-Wave Visibility

Visibility vs. Mass

Visibility Analysis

GRW 50% threshold 3.24 × 108 amu
Adler 50% threshold 4.30 × 104 amu
Current frontier ~25,000 amu
Flight time 0.1 s
Grating period 266 nm
Key finding: The Adler model predicts visible interference loss at 4.30 × 104 amu, just beyond the current experimental frontier of ~25 kDa. Next-generation KDTL interferometers pushing to ~105 amu could provide a direct test.

Bayesian Evidence

Posterior on Collapse Rate

Bayesian Analysis Results

Bayes factor (CSL/QM) 0.0285
log10(BF) -1.55
Interpretation Moderate QM preference
Interpretation: With BF = 0.0285, the evidence moderately favors standard quantum mechanics but falls short of being decisive (which would require BF < 0.01). This aligns with the assessment by Philip Pearle that experiments remain inconclusive.

Proposed Decisive Experiments

Next-Generation Experiment Sensitivities

Experiment Type Mass (kg) Temperature (K) λmin (s-1) Reaches GRW?
MAQRO (space interferometry) Interferometry 10-17 10-3 2.81 × 10-23 Yes
Levitated nanoparticle Mechanical 10-18 10-6 1.26 × 10-12 No
Entangled massive oscillators Entanglement 10-14 10-2 1.26 × 10-14 No
Next-gen X-ray detector Radiation 100 10-2 1.00 × 10-30 Yes
Massive Stern-Gerlach Interferometry 10-20 10-3 2.81 × 10-16 No
Pathway to decisive resolution: MAQRO-type space interferometry and next-generation X-ray detectors can probe the entire theoretically motivated CSL parameter range (λ down to 10-23 and 10-30 respectively), far below the GRW reference point of 10-16.

Mass Amplification

Collapse Rate vs. Mass

Amplification Thresholds

GRW: 1-second collapse mass 1.73 × 10-19 kg
Adler: 1-second collapse mass 3.77 × 10-23 kg
Scaling law Γ ~ N2 (point-like)
Macro-objectification: The N2 amplification ensures a sharp quantum-classical boundary. Under GRW, objects heavier than ~10-19 kg undergo collapse within 1 second; under Adler, this threshold drops to ~10-23 kg (millions of amu).

CSL Empirical Validity Analysis | Open Problem PH-14985 | Data generated with NumPy/SciPy

Reference: Radenkovic et al. (2026) arXiv:2601.09769