Time & Gravity · T.06 · A proposal and the two experiments that bound it · Step 7 of 9 · 13 min read
Does Gravity Collapse the Wave?
One proposal says gravity itself ends a superposition: a mass in two places pays an energy E_G for the difference between its two gravitational fields, and the superposition decays in about ħ/E_G. The same proposal predicts that charged matter should emit a faint spontaneous radiation with no external cause. Two underground detectors looked for that glow and did not see it. This page computes the model, recomputes the bound from the raw counts, and draws the line on the side the data put it.
Fixed boundaryNo theory of everything here: six evidence labels, one open question per page.
Nothing on this page is a theory of everything, and this site proposes none. Every claim carries one of six labels, each tied to a ledger row: MEASURED, DERIVED, BOUND, PROPOSED, OPEN, or SINGLE RESULT. Preprints never rise above PROPOSED. Each page ends with one open question that the next page takes up.
Plate T.06-V · A collapse-time curve falling steeply with mass beside an exclusion bar for R0, with the two bounds and the parameter-free value on the excluded side. Drawn by timegravity/make_plates.py from tools/timegravity_kernel.py.About this illustrationThis plate is a deterministic drawing, not an AI-generated image and not a photograph. The curve is the kernel's own trajectory; the shading exaggerates a clock-rate difference of about one part in 10^16 per metre so that it can be seen at all.
Instrument · The model's collapse time, and where the data draw the line
Left: the Diósi–Penrose collapse time τ = ħ/E_G for a uniform sphere of mass M and radius R displaced by d, with E_G the gravitational self-energy of the difference between the two mass distributions; sliders set log₁₀ M, log₁₀ R and d/R, and the curve shows τ against mass at the chosen R and d. Right: the exclusion line for R0, the size of the nuclear mass density the model's radiation depends on: the Gran Sasso bound (95 %), the XENONnT bound (90 %), and the parameter-free value the model would prefer, drawn on the excluded side. The knockout switches gravity off (G → 0): E_G vanishes, τ is infinite, the model predicts nothing. The planted defect draws the bound on the wrong side, as if small R0 were allowed; the verifier rejects that orientation. Keyboard: Tab and arrows. With reduced motion on, nothing animates.
Predict before you revealBefore you look at the right-hand panel: with the model's own parameter-free value R0 = 0.05 × 10⁻¹⁰ m, how many spontaneous photons should Gran Sasso have counted above background in 62 days?
E_G of the difference4.67e-33 J
Model collapse time τ0.0226 s
Photons predicted at Gran Sasso, parameter-free R01.4e+05
Parameter-free value isexcluded
The model's prediction on the left; the data's verdict on the right. Below the line the radiation would have been seen; it was not.
I · The proposal
Diósi in 1987 and Penrose in 1996 proposed that a quantum superposition of two mass distributions is unstable, with a lifetime of order ħ/E_G, where E_G is the gravitational self-energy of the difference between the two distributions; for a uniform sphere of mass M and radius R displaced far from itself, E_G = (6/5) G M²/R. This is a proposal, and the label says so. The instrument evaluates E_G in closed form and by direct numerical integration, which agree to better than one part in a thousand, so that whatever the model's fate, its arithmetic on this page is right.
For a sphere of a hundredth of a nanogram and a micrometre across, displaced by its own diameter, the model's collapse time is a few hundredths of a second. For a molecule of 25,000 atomic mass units treated as a sphere a nanometre across it is tens of thousands of years. Matter-wave interferometry, which is where superpositions are built, is nowhere near the first number yet; the test came from somewhere else.
In Plain Words · Extra-Easy Explanation
If a thing is in two places at once, its gravity is too. The proposal says nature dislikes that and resolves it, faster the heavier the thing. Nobody has caught a superposition collapsing that way. But the same proposal has a side effect: the jitter that keeps collapsing a particle's position would make charged particles radiate, always, a little. That is a prediction you can test in a quiet room with a detector and patience.
Two groups did, deep underground where cosmic rays cannot reach. They counted the photons they expected from ordinary radioactivity, and almost nothing more. The model in its simplest form would have produced thousands of times that. So that form is out, and the page says what is left.
Everyday Analogy & Controls Primer
Everyday analogy: a suspect claims to be in two cities at once. You cannot catch the moment he picks one. But a person who is constantly being yanked between two cities would leave a trail: receipts, footprints, a hum. You search the quietest room in the country for the hum. You find the usual noise and nothing else. The story that he is being yanked, in its plainest version, is no longer tenable.
How the controls work in plain words: the mass and size sliders choose the thing in two places; the model's clock on the left shows how fast it would be forced to choose. The right panel is the hum search: the line is how quiet the room was, and the model's preferred setting sits on the loud side of it. The knockout removes gravity, so the model predicts nothing at all. The planted defect paints the loud side green, which the verifier refuses.
Plate T.01-D · Visual Intuition Bridge: the everyday analogy (left) sets up one quantity with two settings (centre), and the verifier's three demands (right) are what the knockout and the sign-flip buttons in the instrument above test.
II · The bound, recomputed from the counts
dΓ/dω = (2/3) G e² N² N_a / (π^{3/2} ε₀ c³ R0³ ω) ⇒ z_s(R0) = a / R0³, a ≈ 1.8 × 10⁻²⁹ m³
In a germanium detector at Gran Sasso, 576 photons were counted in the 1,000 to 3,800 keV window over about 62 days against 506 expected from background, and the predicted spontaneous emission, which scales as 1/R0³ with R0 the size of the nuclear mass density, sets R0 > 0.54 × 10⁻¹⁰ m with probability 0.95; the parameter-free version of the model, which fixes R0 at the width of the nuclear wave function in the crystal, 0.05 × 10⁻¹⁰ m, is excluded. The verifier takes the counts and the paper's rate constant, computes a classical 95 % upper limit on the excess (about 111 photons) and inverts z_s = a/R0³: it finds R0 > 0.545 × 10⁻¹⁰ m, within 2 % of the published bound. At the parameter-free value the same formula gives about 1.4 × 10⁵ photons, three orders of magnitude above what was seen.
In 2026 the XENONnT collaboration searched its first science run, 1.16 tonne-years of liquid xenon exposure in the 1 to 140 keV electronic-recoil range, for the same spontaneous radiation and set R0 > 4.9 × 10⁻¹⁰ m at 90 % confidence (4.5 × 10⁻¹⁰ m at 95 %), about a factor of five beyond the previous world-leading limit. It is the strongest bound and, inside the ledger's replication window, a SINGLE RESULT; the row will read BOUND once it is two years old or another detector reaches it. The same paper constrains an unrelated collapse model, CSL, by two orders of magnitude; CSL is not a gravity model and is outside this page.
Matter-wave interference has been observed for molecules beyond 25,000 atomic mass units, the heaviest superpositions built so far. In the model, such a molecule treated as a nanometre-sized sphere would take tens of thousands of years to collapse, so interferometry does not yet test the proposal directly; the radiation does, and that is why the bound comes from an underground detector rather than a beam.
§ II.1 · The derivation the verifier runs, in four stages
E_G(d) = 2 U_self − U_int(d) with U_self = (3/5) G M²/R and U_int the interaction energy of two uniform spheres (G M²/d beyond contact, a quintic polynomial in d/2R when they overlap, 2 U_self when they coincide). The verifier integrates the potential of one sphere over the volume of the other on a grid and requires agreement with the closed form within 10⁻³; E_G → (6/5) G M²/R at large d and → 0 at d = 0.
Stage 2 · The predicted radiation
Donadi et al. Eq. 4: dΓ/dω = (2/3) G e² N² N_a / (π^{3/2} ε₀ c³ R0³ ω), with N the atomic number and N_a the number of atoms. Integrated over the 1,000 to 3,800 keV window and 62 days this is z_s = a/R0³ with a ≈ 1.8 × 10⁻²⁹ m³ (the paper's value, which includes the detector's efficiency). The verifier recomputes a without efficiency and gets about 1.0 × 10⁻²⁸ m³, within a factor of ten.
Stage 3 · From counts to a bound
576 counted, 506 expected: a classical 95 % upper limit on a Poisson signal over known background gives about 111 photons. Setting a/R0³ ≤ 111 gives R0 > 0.545 × 10⁻¹⁰ m, against the paper's 0.54 × 10⁻¹⁰ m (the paper uses a Bayesian treatment; the verifier accepts agreement within 20 %).
Stage 4 · The side of the line
Allowed: R0 at or above the bound. Excluded: below it, including the parameter-free 0.05 × 10⁻¹⁰ m (about 1.4 × 10⁵ predicted photons). The planted defect inverts the orientation and would call the parameter-free value allowed; the verifier fails, as it must. XENONnT's 4.9 × 10⁻¹⁰ m lies on the allowed side and tightens it.
III · What this page does not say
The bound applies to the non-dissipative, parameter-free form of the model, the form Penrose proposed. Variants with dissipation, or with R0 left as a free parameter above the bound, are not excluded by these experiments, and this page does not assess them. The page also does not say that superpositions never collapse; it says that gravity, in this one proposed way, does not do it at the rate its parameter-free form predicts.
What a superposition of two gravitational fields is, if it neither collapses at the proposed rate nor has been shown to entangle, is not a question these bounds answer; they close one road and leave the destination open. The next page takes up the strangest version of that question: an equation for the whole with no time in it at all.
IV · Where the smearing may live
Plate T.06-L · The σ ladder: three bounds from experimental data hold the smearing from below (green, allowed to the right); its authors' natural cut-off and the 2025 letter's entangling range are proposals (blue); the dashed red line is T.05's recast of the experiment's published 95 % limits onto the smeared pull, σ above 33 µm excluded (DERIVED, not a refit). The lighter dashed bar, 13.6 to 33 µm, is T.05's window where the letter's model could still entangle one published geometry, the 2024 side-by-side proposal; it is specific to that model and that geometry, not a bound on σ generally, and it moves or closes if the 2020 data are refit. The bottom row applies the model's formula to a single tubulin, the object the Orch-OR proposal refers to; the page does not assess that proposal. Each rung is a ledger row; the page draws no conclusion beyond the picture.
The model has one free length, the width σ over which each mass is smeared, and the radiation it predicts has bounded that length from below three times: analysis of LISA Pathfinder data put it above 40 fm in 2017, the Gran Sasso germanium detector above 0.54 Å in 2021, and XENONnT above 4.9 Å in 2026. The ladder draws them as the left edge of the allowed region. Everything else on it is a use of the same parameter, and the uses disagree.
Two very different uses want σ small. The authors of the hybrid form that the 2025 entanglement letter builds on called it 'the natural cutoff σ ∼ 10⁻¹² cm', a hundredth of a picometre. The one biological use of the model, Orch-OR, holds that consciousness-related collapse follows 'the specific Diósi-Penrose scheme'; on Penrose's formula the kernel finds that a single tubulin, 55 kDa, in two places a nucleon radius apart lives 6.5 × 10⁸ s at σ = 10⁻¹⁴ m and about 10³⁷ s at the laboratory rungs near 33 µm, some 5 × 10¹⁹ ages of the universe: nearly twenty-nine orders of magnitude between the two uses of one number. The page does not assess Orch-OR; it reports what the model's own formula gives at each rung. Its planted defect for this kernel drops the small-displacement series, so the direct difference returns rounding noise six orders of magnitude off and breaks the σ³ law between the top rungs, which the verifier rejects.
At the top of the ladder sits the 2025 letter's 50 to 250 µm, the range in which the model entangles two masses in a laboratory; well below it, at 33 µm, sits T.05's recast of the experiment's published 95 % limits onto the model's softened pull. On that recast the inverse-square tests leave room only below that line, and the entanglement letter needs the range above it. A 2025 preprint on the smearing profiles of these models notes that for this parameter 'upper bounds can be put by observing no deviations from Newton's law of gravitation'; it works none out and names no experiment. The 33 µm rung is this site's own recast of the published limits on T.05, not the preprint's and not a refit of the data; it superseded an earlier 44 µm edge match. Below the rung the balance loses reach quickly: at σ = 25 µm the smeared pull mimics a Yukawa of 11 µm range about seven times too weak for the published limit there, at 18 µm a 7 µm range about 140 times too weak, and at 13.6 µm the mimic falls to the shortest tabulated range, 5 µm, some five thousand times too weak; the room below 33 µm is there because no experiment reaches near-gravitational strength at ranges of 5 to 10 µm, not because of a gap in the data. T.05 adds a rung of another kind: if gravity is quantum and pure collapse exists besides, a positive witness at the 2017 geometry would put σ above 130 µm within this pure-collapse model. The ladder also carries a window of another kind, 13.6 to 33 µm: on this site's estimate the letter's model could still entangle one published geometry there, the 2024 side-by-side proposal, without contradicting the 2020 inverse-square data; it is a window for that one model and that one geometry, not a bound on σ, and it moves or closes if the 2020 data are refit. One experiment has worked at a smaller separation than the balance's 52 µm: a micro-cantilever about 25 µm from its source mass, whose published 95 % limits exclude strengths above 14,000 at a range of 10 µm. Set beside the balance's own tabulated limits on the magnitude, the balance is the stronger at ranges from 10 to 66 µm (3,100 at 10 µm) and the cantilever at 6 µm (460,000 against 730,000), where its limit is still about two thousand times the strength the smeared pull would need. Neither table reaches the room below the rung.The same torsion balances enter a second squeeze: in 2023 Oppenheim and co-workers showed that any consistent theory with classical gravity and quantum matter must trade decoherence of the matter against diffusion of the field, bounded that diffusion with Cavendish-type and rotating-attractor measurements at D₂ ≤ 10⁻⁴¹ kg² s m⁻³, and named the Diósi–Penrose kernel as a member of the class. At the laboratory rungs the model is quiet: its own decoherence falls as σ⁻³ for separations well inside the smearing, by the letter's expansion, and the radiation the three detectors bounded scales as 1/R0³, which is why their bounds run from below and sit a hundred thousand times or more under the entangling range. The handles built on the model's noise or coherence go slack as σ grows; the deficit in the mean pull grows instead, which is why the inverse-square tests are where this site's T.05 estimate is set against the model.The same torque residuals could be read into the 2023 trade-off itself. Its authors bound the field diffusion of the Diósi–Penrose-kernel class from the variance of the time-averaged force on a composite body, a sum over its nuclei of incoherent kicks, so that the ceiling grows with the number of atoms N and with the nuclear radius cubed, and they fed it Cavendish-class numbers, a 10⁻⁷ m/s² scatter over 100 s on a kilogram, for a ceiling of 10⁻⁹ kg² s m⁻¹ against an interferometry floor of 10⁻⁴⁰, a squeeze they call extremely conservative. Read with the 2020 torques instead, a residual of 0.005 fN·m on a 2 g platinum foil at an 18 mm lever arm over an averaging time of 10³ to 10⁴ s, their formula gives a ceiling between 10⁻²⁶ and 10⁻²², thirteen to sixteen orders lower, and the gap above the interferometry floor would shrink from thirty-one orders to between fourteen and eighteen. That is their estimate with better inputs, not a bound: the step from a torque residual to an acceleration is a heuristic at the level of their own Cavendish step, the averaging time is this page's assumption and enters linearly, and the number says nothing about the smeared model of T.05, whose granularity is σ rather than a nucleus and whose ceiling would sit (σ/r_N)³ higher.
No single σ serves every use on the ladder: the bounds want it above 5 Å, the biological use needs the bottom of the ladder, the entanglement letter needs the top, and the inverse-square tests, on this site's recast of their published limits, leave room only under 33 µm. The ladder shows that and the page draws no conclusion beyond it; which rung gives way is for the experiments to decide.
Grounding ledger rows cited on this page
Every row below resolves in the site's offline Crossref cache. The lint derives what each set of rows can carry; a person decided the label on each claim above. Rows pass a review date and the build fails until someone rereads the source.
Scite column: [observed: Scite ML citation classification, accessed 2026-11-09] via Scite's public tallies endpoint. The counts are a classifier's output over indexed citation statements, an evidence-synthesis habit borrowed from medicine; they never replace reading the source, and a row with more contrasting than supporting statements is flagged for a human re-read in the label checklist.
AI contribution to the cited results: none. No AI system contributed to any proposal, measurement or bound cited on this page. The page text, instrument and verifier were drafted with AI assistance and checked by the site maintainer against the primary sources listed below.
Rebuild this instrument locally and run the verifier as the acceptance gate: python skills/timegravity/t06/make_t06.py then python skills/timegravity/t06/verify_t06_collapse_bound.py (and --planted-defect, which must fail). Then python tools/check_timegravity_labels.py.
Show the SKILL.md source
---
name: timegravity-t06-collapse-bound
description: Rebuild and verify the Time & Gravity T.06 instrument - the Diosi-Penrose collapse proposal (tau = hbar / E_G for two displaced uniform spheres, closed form against numerical quadrature) and the Gran Sasso spontaneous-radiation bound on R0 recomputed from the published counts - with a planted defect that draws the bound on the wrong side.
license: MIT
compatibility: Claude Code, GitHub Copilot, Cursor, Google Antigravity, OpenAI Codex, Ollama (Qwen 3.8 / Gemma 4)
---
# Does Gravity Collapse the Wave? (T.06 · Time & Gravity)
> **Fixed Boundary (`EN`):** Nothing on this page is a theory of everything, and this site proposes none. Every claim carries one of six labels, each tied to a ledger row: MEASURED, DERIVED, BOUND, PROPOSED, OPEN, or SINGLE RESULT. Preprints never rise above PROPOSED. Each page ends with one open question that the next page takes up.
>
> **Frontera Fija (`ES-MX`):** Nada en esta página es una teoría del todo, y este sitio no propone ninguna. Cada afirmación lleva una de seis etiquetas, cada una ligada a una fila del libro de registro: MEDIDO, DERIVADO, COTA, PROPUESTO, ABIERTO o RESULTADO ÚNICO. Las prepublicaciones nunca suben de PROPUESTO. Cada página termina con una pregunta abierta que la siguiente página retoma.
## 1. Page, canonical URL and governing equations
- **Track page**: `T.06` (Time & Gravity, reading order 7 of 9, dated `2026-11-09`). Page label **BOUND**; the model itself is **PROPOSED**.
- **Canonical URL**: https://informatico.ai/timegravity/t06/ (Spanish: https://informatico.ai/es-mx/timegravity/t06/)
- **Model**: `τ = ħ / E_G`, `E_G = 2 U_self − U_int(d)`, `U_self = (3/5) G M²/R`, `U_int = G M²/d` beyond contact (quintic in d/2R when overlapping). Far apart `E_G = (6/5) G M²/R`; coincident `E_G = 0`.
- **Radiation (Donadi et al. 2021, Eq. 4)**: `dΓ/dω = (2/3) G e² N² N_a / (π^{3/2} ε₀ c³ R0³ ω)` ⇒ `z_s = a / R0³`, `a ≈ 1.8 × 10⁻²⁹ m³` in the 1,000–3,800 keV window over 62 days.
- **Central numbers**: 576 counts against 506 background ⇒ 95 % excess limit ≈ 111 ⇒ `R0 > 0.545 × 10⁻¹⁰ m` (paper: `0.54 × 10⁻¹⁰ m`); parameter-free `R0 = 0.05 × 10⁻¹⁰ m` ⇒ ≈ 1.4 × 10⁵ predicted photons, excluded. XENONnT 2026: `R0 > 4.9 × 10⁻¹⁰ m` (90 %), `4.5 × 10⁻¹⁰ m` (95 %).
- **Generator**: `python skills/timegravity/t06/make_t06.py`
- **Verifier**: `python skills/timegravity/t06/verify_t06_collapse_bound.py`
- **σ ladder** (`tools/timegravity_kernel_ladder.py`, Plate T.06-L): the smearing width on one log axis. Lower bounds: LISA Pathfinder ≥ 40.1 fm (Helou 2017), Gran Sasso > 0.54 Å, XENONnT > 4.9 Å; the authors' natural cut-off 10⁻¹⁴ m (Tilloy–Diósi 2016, footnote 3); the 2025 letter's 50–250 µm; T.05's recast of the Eöt-Wash 2020 published limits, 33.1 µm (cross-checked live against the recast kernel's σ_95; the retired 44.07 µm edge match kept reproducible). Point-mass DP rate `Γ = (G m²/ħ)[f̃(0) − f̃(Δx)]` with the small-Δx series `Δx²/(12√π σ³)(1 − 3z²/40)`: one tubulin (55 kDa) a nucleon radius apart lives 6.5 × 10⁸ s at 10⁻¹⁴ m and 2.3 × 10³⁷ s at 33 µm, the recast rung (the 25 ms count stays a verifier-internal check, not page text); σ³ law between the top rungs within 1 %. Casimir floor (Van De Kamp 2020, Eq. 14; ρ = 3.5 g/cm³, ε = 5.7, ∂B = 10⁴ T/m, W = 1 µm): gap 8.1 µm, nearest separation ≥ 17.1 µm at 10⁻¹⁵ kg (26.5 µm at 10⁻¹⁴ kg); at the recast limit σ = 33 µm the 23 µm split's window (5.7 µm) is closed, the 10, 5 and 1 µm splits stay open at 10⁻¹⁵ kg (18.3, 23.2 and 27.2 µm against the 17.1 µm floor). Same verifier; `--planted-defect` also drops the series, which breaks the σ³ law.
- **Knockout check**: `python skills/timegravity/t06/verify_t06_collapse_bound.py --planted-defect` (must exit non-zero: the bound inverted, small R0 "allowed")
- **Label lint**: `python tools/check_timegravity_labels.py` (and `--planted-defect`, `--mutants`)
## 2. Ledger rows this page may cite (timegravity/ledger.json)
| Row | Label | Source | DOI |
| --- | --- | --- | --- |
| `T06-DIOSI1987` | PROPOSED | Diósi 1987, universal master equation | https://doi.org/10.1016/0375-9601(87)90681-5 |
| `T06-PENROSE1996` | PROPOSED | Penrose 1996, gravity's role in state reduction | https://doi.org/10.1007/BF02105068 |
| `T06-DONADI2021` | BOUND | Donadi et al. 2021, Gran Sasso underground test | https://doi.org/10.1038/s41567-020-1008-4 |
| `T06-XENONNT2026` | BOUND (young: SINGLE RESULT at most) | XENONnT 2026, PRL 136, 120201 | https://doi.org/10.1103/2jm3-4976 |
| `T06-FEIN2019` | SINGLE RESULT | Fein et al. 2019, superposition beyond 25 kDa | https://doi.org/10.1038/s41567-019-0663-9 |
## 3. Tool-neutral agent packet and security boundary (`security-runtime`)
1. **Rebuild locally**: `python skills/timegravity/t06/make_t06.py`; standard library only; writes only under `src/research/timegravity/t06/files/`.
2. **Acceptance gate**: `python skills/timegravity/t06/verify_t06_collapse_bound.py` must print `"status": "PASS"` with `bound_recomputed_from_counts: PASS`; `--planted-defect` must exit non-zero. Then `python tools/check_timegravity_labels.py`.
3. **Security boundary (`security-runtime`)**: no shell outside the repository, no home-directory access, no outbound network for this task; the cache refresher is the track's only network script, run by hand by a maintainer.
## 4. Deterministic verification and falsification rules
1. `E_G` closed form against a midpoint-rule integration of one sphere's potential over the other's volume: relative difference `< 10⁻³` at `d = 0.5R, 2R, 5R`; the limits `(6/5) G M²/R` and `0` recovered.
2. The 95 % Poisson upper limit on the excess, inverted through `z_s = a/R0³`, lands within 20 % of the published `0.54 × 10⁻¹⁰ m` (achieved 2 %).
3. The rate prefactor `a` recomputed from Eq. 4 without detection efficiency lies within a decade of the paper's value.
4. The parameter-free value lies on the excluded side; XENONnT's bound lies on the allowed side above Gran Sasso's.
5. Planted defect: the orientation of the bound inverted; rule 4 fails and `--planted-defect` exits non-zero.
6. `t06_reference.json` matches `manifest.json` and regenerates byte for byte.
## 5. What the instrument shows (reader side)
- Left: the model's collapse time against mass for the chosen radius and displacement. Right: the R0 exclusion line with the Gran Sasso and XENONnT bounds and the parameter-free value on the excluded side.
- Knockout: gravity off (G → 0), the model predicts nothing. Planted defect: the bound painted on the wrong side.
- Predict before you reveal: how many photons the parameter-free model would have produced at Gran Sasso.
## 6. Exact T0–T3 truth boundary
### In the repository today (T0/T1)
- Kernel `tools/timegravity_kernel_bounds.py` (`dp_self_energy_difference`, `sphere_interaction_energy_numeric`, `poisson_upper_limit`, `gran_sasso_r0_bound`, `check_dp`), generator, verifier, ledger rows above.
### Not on this page (T2/T3)
- Dissipative variants of the model and R0 as a free parameter above the bound are not assessed. CSL is not a gravity model and is out of scope.
- No statement is made that superpositions never collapse; only that this proposal, in its parameter-free form, is excluded by the radiation it predicts.
Show the verifier verify_t06_collapse_bound.py
#!/usr/bin/env python3
"""Standalone stdlib verifier and planted-defect knockout for Time & Gravity · T.06 (Does Gravity Collapse the Wave?).
Canonical URL: https://informatico.ai/timegravity/t06/
Central number: from the Gran Sasso counts (576 measured, 506 background, 62 days) and the paper's rate constant
z_s = a/R0³, a ≈ 1.8e-29 m³, the 95 % lower bound on R0 recomputes to 0.545e-10 m, within 20 % (actually 2 %) of the
published 0.54e-10 m; the parameter-free R0 = 0.05e-10 m would have produced about 1.4e5 photons and is excluded;
E_G for two displaced uniform spheres agrees with a direct numerical integration within 1e-3. Planted defect: the
bound drawn on the wrong side (small R0 treated as allowed); `--planted-defect` must exit non-zero with FAIL on stderr.
The σ ladder (tools/timegravity_kernel_ladder.py): one tubulin a nucleon radius apart lives 6.5e8 s at σ = 1e-14 m (2.6e10 tubulins for
25 ms) and 2.3e37 s at 33 µm, T.05's recast limit; the Casimir floor of Van De Kamp et al. is 17.1 µm at 1e-15 kg; the σ³ law holds between the top rungs;
its planted defect (the small-displacement series dropped) breaks that law and `--planted-defect` must exit non-zero.
Boundary: Nothing on this page is a theory of everything, and this site proposes none.
"""
from __future__ import annotations
import hashlib
import json
import sys
from pathlib import Path
ROOT = Path(__file__).resolve().parents[3]
sys.path.insert(0, str(ROOT / "tools"))
from timegravity_kernel_bounds import DP_TOL, GS_R0_BOUND_M, check_dp # noqa: E402
from timegravity_kernel_ladder import check_ladder # noqa: E402
FILES_DIR = ROOT / "src" / "research" / "timegravity" / "t06" / "files"
def verify_reference_files() -> dict:
manifest = json.loads((FILES_DIR / "manifest.json").read_text(encoding="utf-8"))
out = {}
for entry in manifest["files"]:
raw = (FILES_DIR / entry["filename"]).read_bytes()
assert len(raw) == entry["bytes"], f"{entry['filename']}: byte count mismatch"
digest = hashlib.sha256(raw).hexdigest()
assert digest == entry["sha256"], f"{entry['filename']}: sha256 mismatch"
out[entry["filename"]] = digest[:12]
ref = json.loads((FILES_DIR / "t06_reference.json").read_text(encoding="utf-8"))
assert abs(ref["gran_sasso"]["r0_bound_recomputed_m"] - GS_R0_BOUND_M) / GS_R0_BOUND_M < 0.2, "reference bound off"
return out
def main(argv: list[str] | None = None) -> int:
args = argv if argv is not None else sys.argv[1:]
planted = "--planted-defect" in args
try:
res = check_dp(planted_defect=planted)
assert res["double_entry_ok"], f"E_G closed form vs quadrature differ by {res['max_rel_err_interaction_energy']:.2e} (> {DP_TOL})"
assert res["limits_ok"], "E_G limits (6/5 G M^2/R at large d, 0 at d = 0) not recovered"
assert res["bound_ok"], f"recomputed R0 bound {res['r0_bound_recomputed_m']:.3e} m is not within 20% of {GS_R0_BOUND_M:.2e} m"
assert res["a_within_decade"], f"rate prefactor {res['a_recomputed_no_efficiency_m3']:.2e} not within a decade of the paper's {res['a_paper_m3']:.2e}"
assert res["paramfree_excluded"], (
"the parameter-free R0 = 0.05e-10 m is treated as allowed: the bound is drawn on the wrong side "
f"(it would have produced {res['counts_at_paramfree_r0']:.2e} photons against an excess limit of {res['excess_upper_limit_counts']:.0f})"
)
assert res["xenonnt_consistent"], "the XENONnT bound does not sit on the allowed side above Gran Sasso's"
assert res["defect_rejected"], "planted bound inversion was accepted"
lad = check_ladder(planted_defect=planted)
assert lad["branch_ok"], "the point-mass gap series disagrees with the direct difference where both are accurate"
assert lad["positive_ok"] and lad["monotone_ok"], "tubulin lifetimes are not positive and increasing along the ladder"
assert lad["count_ok"], f"tubulins for 25 ms at the natural cut-off, {lad['tubulins_for_25ms_at_natural_cutoff']:.2e}, not within 1e10 … 1e11"
assert lad["span_ok"], "the lifetime span from the natural cut-off to the laboratory rung is not above 1e20"
assert lad["rung_ok"], f"the ladder's Eöt-Wash rung {lad['eotwash_matching_sigma_live_m']:.3e} m does not match the wedge kernel within 1 %"
assert lad["floor_ok"], f"the Casimir floor {lad['casimir']['floor_1e-15_m'] * 1e6:.1f} µm is not between 15 and 20 µm or the proposal's 24 µm does not clear it"
assert lad["window_ok"], "the window at the matching σ is not closed for the 23 µm split and open for 10 and 1 µm"
assert lad["scaling_ok"], f"the σ³ law between the top rungs fails: ratio {lad['sigma_cubed_ratio']:.4g} vs {lad['sigma_cubed_ratio_expected']:.4g} (the small-displacement series dropped returns rounding noise)"
assert lad["defect_rejected"], "the planted series-dropped defect was not detectable"
assert lad["diffusion_ok"], "the Oppenheim Eq. F16 table does not reproduce: their inputs must land within two orders of their printed 1e-9 and the Eöt-Wash inputs 12 to 18 orders below it, above the interferometry floor"
files = verify_reference_files()
except AssertionError as exc:
print(json.dumps({"status": "FAIL", "folio_id": "T.06", "error": str(exc)}), file=sys.stderr)
return 1
print(json.dumps({
"status": "PASS",
"folio_id": "T.06",
"canonical_url": "https://informatico.ai/timegravity/t06/",
"central_number": {"ladder_tubulins_for_25ms_at_natural_cutoff": lad["tubulins_for_25ms_at_natural_cutoff"], "ladder_tubulin_lifetime_at_recast_rung_s": lad["tubulin"]["eotwash"]["nucleon_radius"]["lifetime_s"], "ladder_casimir_floor_1e-15_m": lad["casimir"]["floor_1e-15_m"], "ladder_casimir_floor_1e-14_m": lad["casimir"]["floor_1e-14_m"], "ladder_window_23um_split_open": lad["window"]["by_mass"]["1e-15"]["splits"]["split_23um"]["open"], "ladder_window_10um_split_open": lad["window"]["by_mass"]["1e-15"]["splits"]["split_10um"]["open"], "ladder_sigma_cubed_ratio": lad["sigma_cubed_ratio"], "diffusion_ceiling_oppenheim_inputs": lad["diffusion"]["oppenheim_inputs_ceiling"], "diffusion_ceiling_eotwash": {k: v["ceiling"] for k, v in lad["diffusion"]["eotwash"].items()}, "diffusion_orders_below_printed": {k: v["orders_below_printed"] for k, v in lad["diffusion"]["eotwash"].items()}, "r0_bound_recomputed_m": res["r0_bound_recomputed_m"], "r0_bound_paper_m": res["r0_bound_paper_m"],
"excess_upper_limit_counts_95": res["excess_upper_limit_counts"], "counts_at_paramfree_r0": res["counts_at_paramfree_r0"],
"tau_1um_1e-14kg_2R_s": res["tau_1um_1e-14kg_2R_s"], "max_rel_err_E_G": res["max_rel_err_interaction_energy"]},
"geometry_checks": {"sigma_ladder_tubulin_and_casimir_floor": "PASS", "sigma_cubed_law": "PASS", "oppenheim_f16_with_eotwash_inputs": "PASS",
"E_G_closed_form_vs_quadrature": "PASS",
"bound_recomputed_from_counts": "PASS",
"paramfree_value_excluded": "PASS",
"planted_defect_knockout": "REJECTED_AS_EXPECTED",
},
"reference_files_sha256_12": files,
}, indent=2))
return 0
if __name__ == "__main__":
raise SystemExit(main())
Primary sources
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This page ends with one open question
If gravity neither collapses nor is shown to entangle, what is a superposition of slopes?
