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gravitational-collapse

#+BEGIN_SRC text BLOCK A — Deep dive: Are “gravitational-collapse” models actively probed in non-biological systems?

Short answer Yes. Objective-collapse models tied to gravity — chiefly Diósi–Penrose (DP) and mass-proportional CSL used as its testable stand-in — are being hammered by tabletop mechanics, low-background radiation searches, precision interferometry, and space missions. Large swathes of parameter space are already excluded; the parameter-free DP option is ruled out. Rev. Mod. Phys. 2013, Nature Physics review 2022, Nature Physics 2021, EPJ C 2021.

What “gravitational-collapse” means in practice • DP posits reduction when the gravitational self-energy of a mass-density superposition exceeds ℏ/τ; regularization requires a spatial cutoff R₀ for nuclear mass densities.
• CSL provides a two-parameter testbed: collapse rate λ and correlation length r_C (often quoted at r_C=10⁻⁷ m). GRW’s “minimal” λ≈10⁻¹⁶ s⁻¹; Adler argued λ≈10⁻⁸±¹ s⁻¹. Rev. Mod. Phys. 2013, EPJ C 2021.

Non-interferometric radiation tests (strongest sub-micron constraints) • Spontaneous X-ray emission from solids: a dedicated underground Ge detector found no excess, giving λ < 5.2×10⁻¹³ s⁻¹ at r_C=10⁻⁷ m (95% C.L.) and the tightest map below r_C≲10⁻⁶ m. EPJ C 2021.
• Gravity-related DP diffusion also implies radiation; the Gran Sasso “underground test” set a lower bound on the DP mass-density cutoff R₀ that is ~10³ larger than previous, ruling out the parameter-free DP model. Nature Physics 2021.

Precision inertial sensors and space missions • LISA Pathfinder (translation): CSL λ constrained to ≲3×10⁻⁸ s⁻¹ near r_C=10⁻⁷ m; also sets R₀≳40 fm for DP, i.e., beyond nuclear size. PRD 2017.
• LISA Pathfinder (rotation): new re-analysis turns rotational noise into the most stringent CSL bounds between micrometer and millimeter scales, improving on translation-only constraints. PRA 2025.
• Cryogenic nanocantilevers and multilayer test masses suppress thermal noise while amplifying CSL backaction; no excess seen, excluding parts of the Adler band. PRL 2020, Nature Physics review 2022.

Bulk heating and astrophysical probes • White-noise CSL would inject heat in macroscopic bodies. Updated geophysical budgets give λ≲3.0×10⁻¹¹ s⁻¹ (Earth) and λ≲9.5×10⁻¹² s⁻¹ (Moon) at r_C=10⁻⁷ m — competitive and model-wide. arXiv 2024.
• Neutron-star heating provides complementary reach in principle; current analyses show strong pressure on large-λ regions. Nature Physics review 2022.

Interferometric superpositions (direct macroscopicity stress-tests) • Matter-wave interference of >25 kDa molecules preserves coherence where objective-collapse would predict loss, cutting into CSL parameter space; this is the cleanest “non-biological” superposition test to date. Nature Physics 2019, Nature Physics review 2022.
• Cold-atom/BEC and levitated optomechanics roadmaps target larger masses and longer times to decisively carve the remaining λ–r_C wedges. Nature Physics review 2022.

High-energy baselines: neutrinos as natural interferometers • Penrose-style collapse mapped onto neutrino oscillations: momentum-diffusion versions are excluded by IceCube data given realistic source wave-packet widths. PRD 2024.
• Independent check: IceCube’s Nature Physics analysis finds no atmospheric-neutrino decoherence from putative quantum-gravity noise, setting world-leading Lindblad-type limits that squeeze collapse-like channels. Nature Physics 2024.

Where the numbers sit (reference r_C = 10⁻⁷ m unless noted)

| Probe / platform | Bound / result | Implication | |-----------------------------------------------+--------------------------------------------------+---------------------------------------------------| | X-ray spontaneous emission (Ge, underground) | λ < 5.2×10⁻¹³ s⁻¹ (95% C.L.) | Strongest CSL bounds for r_C≲10⁻⁶ m | | LISA Pathfinder (translation) | λ ≲ 3×10⁻⁸ s⁻¹; DP cutoff R₀ ≳ 40 fm | Cuts into Adler band; excludes DP with nuclear-size cutoff | | LISA Pathfinder (rotation, re-analysis) | Tightest mid-scale CSL bounds (μm–mm) | Outperforms translation-only constraints | | Earth/Moon heat-flux (geophysical) | λ ≲ 3.0×10⁻¹¹ / 9.5×10⁻¹² s⁻¹ | Global white-noise CSL severely limited | | Macromolecule interferometry (>25 kDa) | Coherence intact | Excludes parts of CSL map; pushes mass–time frontier | | DP radiation (Gran Sasso “underground test”) | R₀ lower bound ↑ by ~10³ vs prior | Parameter-free DP ruled out | | Neutrino oscillations (IceCube, models) | Momentum-diffusion DP disfavored; no decoherence | Constrains collapse-like Lindblad noise channels |

EPJ C 2021, PRD 2017, PRA 2025, arXiv 2024, Nature Physics 2019, Nature Physics 2021, Nature Physics 2024.

Big-picture takeaways for Orch OR’s “gravitational-collapse” pillar

  1. A collapse mechanism strong enough to matter in mesoscopic systems is increasingly incompatible with null-noise data, unless it is highly colored, cutoff-regularized, or otherwise fine-tuned. Nature Physics review 2022, EPJ C 2021, PRD 2017.
  2. The cleanest laboratory falsifiers are non-biological: radiation searches, space inertial sensors, and molecule interferometers. They already exclude parameter-free DP and heavily squeeze CSL near canonical r_C. Nature Physics 2021, EPJ C 2021, Nature Physics 2019.
  3. High-energy baselines add orthogonal pressure: neutrino decoherence and Penrose-mapped diffusion channels are strongly bounded. PRD 2024, Nature Physics 2024.

What to watch next (practical, near-term moves) • Rotational metrology + shape-optimized test masses to amplify collapse backaction (ongoing). PRA 2025, Nature Physics review 2022.
• Heavier, slower interferometers (space-based and on-chip) to extend macroscopicity while killing technical decoherence. Nature Physics review 2022.
• Multi-platform consistency checks (radiation + mechanics + interferometry) to corner colored-noise or dissipative variants. Nature Physics review 2022.

Bottom line Yes — “gravitational-collapse” is an active, empirical research program in non-biological systems, and its most natural, parameter-free incarnations are already ruled out; the viable space for DP/CSL-like dynamics is now narrow and contrived. Nature Physics 2021, EPJ C 2021, PRD 2017, PRA 2025, Nature Physics 2019, Nature Physics review 2022, PRD 2024, Nature Physics 2024. #+END_SRC