Time & Gravity · T.12 · When the electromagnetic bath is silent, proper time still couples to every stress-energy tensor · Step 13 of 13 · 15 min read
Two Clocks That Only Meet in Gravity
On T.11 the photon bath rendered a classical world by scattering off electric charges and dipoles, leaving anything with zero electromagnetic coupling unrecorded in light. Yet five-sixths of the gravitating matter in our universe is non-luminous. Because Einstein's metric couples universally to every stress-energy tensor, a sector that never scatters a photon still tilts the rate of proper time—requiring two spatially separated clocks to sense a purely gravitational transit, or co-located clocks of different atomic species to bound any non-gravitational portal.
Human LineagePioneers of Step T.12 · Clowe, Bradač, Gonzalez, Markevitch, Randall, Jones & Zaritsky (2006) · Planck Collaboration (2020) · Kennedy, Oelker, Bothwell, Kedar, Robinson, Marti, Milne & Ye (2020) · Carney et al. (2021) · Filzinger, Dörscher, Lange, Klose, Steinel, Benkler, Peik, Lisdat & Huntemann (2023) · LUX-ZEPLIN Collaboration (2023)Honor the humans ↓
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.12-V · Left: an electromagnetically transparent dark-matter subhalo flying past a two-node optical clock baseline (Λ_EM = 0), shifting the gravitational potential Φ(r) while leaving photon scattering at zero. Right: the accumulated proper-time step Δτ(t) across the flyby and its asymptotic plateau Δτ_∞ = −(2GM/c²v_0) ln(b_2/b_1). 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 · Proper-time step of an electromagnetically transparent transit across a two-clock network
Left: the differential gravitational redshift Δν(t)/ν = (Φ₁(t) − Φ₂(t))/c² across two clocks separated by baseline d_c as an electromagnetically transparent mass M_DM (α_EM = 0, Λ_EM = 0) flies past Clock 1 at impact parameter b₁ with galactic speed v₀ = 220 km/s. Right: the integrated proper-time step |Δτ_∞| = (2 G M_DM / c² v₀) ln(1 + d_c / b₁) as a function of network baseline d_c, alongside the ultralight scalar portal modulation δ(ν_A/ν_B)/(ν_A/ν_B) = ΔK_α d_e Φ_Pl for co-located clocks. The sliders set the clock baseline d_c / b₁ and the scalar portal coupling d_e. The knockout severs universal gravitational coupling (G_dark = 0): the proper-time step collapses to zero and the verifier rejects the run. Keyboard: Tab and arrows. With reduced motion on, nothing animates.
Predict before you revealBefore you check the readout: if a passing dark-matter mass couples only through Einstein's metric (zero scalar portal coupling, d_e = 0), what differential frequency shift do two co-located clocks at the exact same position (baseline d_c = 0) record?
Cosmological dark-to-baryonic ratio Ω_c / Ω_b5.364 ± 0.065 (84.3 %)
Asymptotic clock step Δτ_∞ = −(2GM/c²v₀) ln(b₂/b₁)-4.664e-26 s
Universal metric coupling: an electromagnetically uncoupled mass (Λ_EM = 0) casts zero photon shadow yet shifts the gravitational clock rate along its flyby.
I · Five-sixths of gravitating matter is unseen in light, and gravity is universal
Across cosmological and cluster scales, most gravitating mass neither emits nor scatters light: the Planck 2018 cosmic microwave background power spectra measure a physical cold dark matter density Ω_c h² = 0.1200 ± 0.0012 beside baryon density Ω_b h² = 0.02237 ± 0.00015—a dark-to-baryonic ratio of 5.364 ± 0.065, or 84.29% of non-relativistic matter—and weak gravitational lensing of the merging Bullet Cluster 1E 0657-558 shows the gravitational potential peaks separated at 8σ from the X-ray-emitting plasma that holds most of the normal baryonic gas.Meanwhile, laboratory and space tests confirm that gravitational proper-time redshift Δf/f = ΔΦ/c² is measured down to a 33 cm height difference in optical aluminium-ion clocks and that the Weak Equivalence Principle holds to η = (−1.5 ± 2.7)×10⁻¹⁵ in MICROSCOPE.
In Plain Words · Extra-Easy Explanation
Imagine an invisible bowling ball rolling across a stretched rubber sheet in a pitch-dark room. Flashlights shine right through the ball without casting a shadow or bouncing a single gleam back to your eyes—in the language of T.11, the ball is unrendered in the photon bath. Yet the sheet still dips wherever the ball rolls.
If you place two precision clocks at different spots on the sheet, the clock closer to the passing ball sits slightly deeper in the gravitational dip and ticks a fraction slower while the ball goes by. Even if two sectors of matter never exchange a photon, they still share the same spacetime geometry and meet through the rate of time.
Everyday Analogy & Controls Primer
Everyday analogy: two tide gauges anchored a kilometre apart in a harbour at night. A submerged submarine with all lights off reflects no radar and shines no lamp above the water, yet its hull displaces water as it passes near the first pier: comparing the two gauges reveals the transit from the difference in water level alone, whereas two gauges bolted to the exact same post rise and fall together and see zero difference.
How the controls work in plain words: the first slider changes the spatial baseline d_c between Clock 1 and Clock 2; setting d_c = 0 puts both clocks at the same point, where the pure-gravity proper-time difference vanishes. The second slider sets a hypothetical non-gravitational scalar coupling d_e to the electromagnetic fine-structure constant, which optical clock pairs test even at zero baseline. The knockout sets G_dark = 0: the gravitational dip vanishes and the verifier rejects the run.
Plate T.12-D · Visual Intuition Bridge: an electromagnetically dark mass passes unseen through light yet bends the metric (left and centre), producing a logarithmic proper-time step verified against Gauss–Legendre quadrature and the transverse impulse identity (right).
Archival Tribute · The Hands Behind the Instruments
The Humans Behind Step T.12 · Gravitational Lenses, the Cosmic Budget, and Dark-Sector Clock Comparisons
What happens when a mass sector has zero electromagnetic polarizability (Λ_EM = 0) and zero optical shadow, yet shares the spacetime metric g_μν? Cosmologists mapped its gravitational wells across the sky while atomic physicists turned optical clocks and underground detectors into dark-sector observatories.
2006 & 2018–2020 · Tucson, Cambridge & ESA L2
Douglas Clowe, Maruša Bradač & the Bullet Cluster Team · The Planck Collaboration
In 2006 Douglas Clowe, Maruša Bradač, Anthony Gonzalez, Maxim Markevitch, Scott Randall, Christine Jones, and Dennis Zaritsky compared Chandra X-ray maps of the hot baryonic gas in the merging cluster 1E 0657−558 against weak-lensing maps of the gravitational potential, showing at 8σ that the potential follows the collisionless mass rather than the luminous gas. In 2018–2020 the Planck Collaboration fixed the cosmic ratio at Ω_c h² / Ω_b h² = 5.36 ± 0.06.
Colin Kennedy, Tobias Bothwell & Jun Ye · Melina Filzinger, Ekkehard Peik, Christian Lisdat & Nils Huntemann
JILA (⁸⁷Sr vs Silicon Cavity) & PTB (¹⁷¹Yb⁺ E3/E2 vs ⁸⁷Sr)
If ultralight scalar dark matter couples to the fine-structure constant α or electron mass m_e, different clock transitions will oscillate at the Compton frequency m_φ c² / h. At JILA in 2020, Colin Kennedy, Jun Ye, and colleagues compared an ⁸⁷Sr optical lattice clock against a cryogenic crystalline silicon cavity; at PTB in 2023, Melina Filzinger, Nils Huntemann, and co-workers compared the electric octupole and quadrupole transitions of ¹⁷¹Yb⁺ against ⁸⁷Sr over more than two years, setting tight bounds on scalar couplings.
2021–2026 · Lead (South Dakota), Gran Sasso & Gaithersburg
LUX-ZEPLIN (LZ) & XENONnT Collaborations · Daniel Carney, Sohitri Ghosh, Gordan Krnjaic & Jacob M. Taylor
Sanford Underground Research Facility (SURF), Gran Sasso & Quantum-Sensor Arrays
One mile underground in South Dakota, the LUX-ZEPLIN Collaboration pushed spin-independent WIMP–nucleon cross sections down to 9.2 × 10⁻⁴⁸ cm² at 36 GeV/c² in 2023 without a positive recoil signal. To reach hypothetical dark sectors that have zero non-gravitational couplings at all, Daniel Carney, Jacob Taylor, and colleagues proposed using optomechanical accelerometer arrays and clock networks to detect passing dark-matter clumps purely through their Newtonian gravitational impulse.
II · Gravitational proper-time steps and optical-clock portal bounds
Δτ(T) = −(2 G M_DM / c² v₀) [arsinh(v₀ T / b₁) − arsinh(v₀ T / b₂)] → −(2 G M_DM / c² v₀) ln(b₂ / b₁)
In general relativity the metric g_{μν} couples universally to the total stress-energy tensor T_{μν} regardless of electromagnetic charge: a compact mass M_DM with α_EM = 0 has zero dipole photon-scattering localization rate (Λ_EM = 0 on T.11) yet produces the Newtonian potential Φ(r) = −G M_DM / r, shifting the proper-time rate between two clocks at impact parameters b₁ and b₂ = b₁ + d_c along a flyby at speed v₀ by the integrated step Δτ(T) = −(2 G M_DM / c² v₀) [arsinh(v₀ T / b₁) − arsinh(v₀ T / b₂)], whose spatial gradient +c² ∂(Δτ_∞)/∂b₁ = 2 G M_DM / (b₁ v₀) equals the transverse gravitational velocity impulse Δv_⊥. Across baselines d_c ∈ {1, 10, 100, 1000} m (with b₁ = 1 m, v₀ = 220 km/s, M_DM = 10⁶ kg), the verifier integrates ∫ (Φ₁(t) − Φ₂(t))/c² dt by composite 5-point Gauss–Legendre quadrature anchored at the flyby timescale b₁/v₀ = 4.55 µs and matches the closed-form arsinh expression within 6.1×10⁻¹⁶ (3.7×10⁻¹⁶ at d_c = 1 km, where Δτ = −4.664×10⁻²⁶ s). At zero baseline (d_c = 0, co-located clocks), b₁ = b₂ and Δτ = 0 identically.
Because pure gravity shifts co-located clocks identically, comparing two co-located optical clocks of different electronic sensitivity ΔK_α tests whether dark matter also carries a non-gravitational portal coupling d_e to the electromagnetic fine-structure constant α: JILA comparisons of ⁸⁷Sr against a cryogenic silicon cavity (2020) and PTB multi-year comparisons of the ¹⁷¹Yb⁺ electric-octupole (E3) and electric-quadrupole (E2) transitions (2023) set upper bounds on |d_e| across ultralight scalar masses 10⁻²¹ eV ≤ m_φ c² ≤ 10⁻¹⁴ eV, while underground liquid-xenon recoil searches such as LUX-ZEPLIN (2023) bound spin-independent WIMP–nucleon cross-sections down to 9.2×10⁻⁴⁸ cm² at 36 GeV/c². At the local galactic dark-matter density ρ_DM = 0.4 GeV/cm³ and m_φ c² = 10⁻¹⁵ eV (Compton frequency 0.242 Hz), the dimensionless Planck-normalised field amplitude is Φ_Pl = 7.20×10⁻¹⁶; if d_e = 0 (purely gravitational coupling), the co-located clock ratio modulation is identically zero.
In 2021 Carney, Hook, Liu, Taylor and Zhao analysed whether arrays of quantum-limited mechanical sensors and clocks could detect compact dark-matter transits through their gravitational impulse and redshift alone, without assuming any electromagnetic or nuclear portal coupling. That proposal requires Planck-mass-scale sensitivity and sub-femtosecond proper-time resolution across macroscopic baselines—orders of magnitude beyond current laboratory noise floors—and stays PROPOSED.
§ II.1 · The derivation the verifier runs, in four stages
From Planck 2018 Table 2 (Ω_c h² = 0.1200 ± 0.0012, Ω_b h² = 0.02237 ± 0.00015), the kernel computes Ω_c / Ω_b = 5.3643 ± 0.0646 and f_dark = 84.29%, checking analytic error propagation against central finite differences to 1.6e-10.
Stage 2 · Closed-form arsinh vs composite GL5 quadrature
For a flyby along r_DM(t) = (b₁, v₀ t, 0) past clocks at b₁ and b₂ = b₁ + d_c, the kernel integrates ∫ (Φ₁ − Φ₂)/c² dt over [-T, +T] using composite 5-point Gauss–Legendre quadrature anchored at b₁/v₀, matching -(2GM/c²v₀)[arsinh(v₀T/b₁) − arsinh(v₀T/b₂)] within 6.1e-16.
Central differences verify +c² ∂(Δτ_∞)/∂b₁ = 2 G M_DM / (b₁ v₀) = Δv_⊥ within 5.6e-11. At d_c = 0 and d_e = 0, both Δτ and δ(ν_A/ν_B) vanish identically, while the ULDM energy-density round-trip (c²/8πG) ω_φ² Φ_Pl² = ρ_DM holds to 2.1e-16.
Stage 4 · Planted defect knockout
Setting G_dark = 0 for the electromagnetically transparent mass gives Δτ = 0 across non-zero baselines d_c > 0, failing the trajectory quadrature gate with relative error 1.0 and rejecting the run.
III · Where the thirteen-step track closes
What particles or fields make up the 84.3% of non-relativistic matter measured by gravitational lensing and the cosmic microwave background—and whether that sector ever meets ordinary matter through anything other than the curvature of spacetime g_{μν}—remains an open question. This is the closing page of the thirteen-step track, and it returns to the hub's single thread: a clock measures proper time along its worldline, the electromagnetic bath selects and broadcasts the pointer states of everything that scatters light, and gravity tilts the rate of proper time for everything that carries energy—seen or unseen.
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 2026-11-08, 2026-11-10] 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 measurement or derivation 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/t12/make_t12.py then python skills/timegravity/t12/verify_t12_dark_clock.py (and --planted-defect, which must fail). Then python tools/check_timegravity_labels.py.
Show the SKILL.md source
---
name: timegravity-t12-dark-clock
description: Rebuild and verify the Time & Gravity T.12 toy - the Planck 2018 dark-to-baryonic matter budget (Omega_c / Omega_b = 5.3643), the gravitational proper-time step of an electromagnetically transparent flyby across a two-clock network (closed-form arsinh vs composite Gauss-Legendre quadrature within 1e-11), and the ultralight scalar clock modulation bound - with a planted defect (G_dark = 0 violating the Equivalence Principle).
license: MIT
compatibility: Claude Code, GitHub Copilot, Cursor, Google Antigravity, OpenAI Codex, Ollama (Qwen 3.8 / Gemma 4)
---
# Two Clocks That Only Meet in Gravity (T.12 · 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.12` (Time & Gravity, reading order 13 of 13, dated `2026-11-10`)
- **Canonical URL**: https://informatico.ai/timegravity/t12/ (Spanish: https://informatico.ai/es-mx/timegravity/t12/)
- **Cosmological dark-to-baryonic ratio**: `Ω_c h² = 0.1200 ± 0.0012`, `Ω_b h² = 0.02237 ± 0.00015`, `Ω_c / Ω_b = 5.3643 ± 0.0646`, `f_dark = Ω_c / (Ω_c + Ω_b) = 84.29 %`.
- **Gravitational proper-time step of an EM-transparent transit**: `Δν(t)/ν = (Φ_1(t) − Φ_2(t))/c²`, `Δτ(T) = −(2 G M_DM / c² v_0) [arsinh(v_0 T / b_1) − arsinh(v_0 T / b_2)] → −(2 G M_DM / c² v_0) ln(b_2 / b_1)`, `+c² ∂(Δτ_∞)/∂b_1 = 2 G M_DM / (b_1 v_0) = Δv_⊥`.
- **Ultralight scalar clock modulation**: `Φ_Pl = ħ √(8π G ρ_DM) / (m_φ c³)`, `δ(ν_A/ν_B)/(ν_A/ν_B) = ΔK_α d_e Φ_Pl cos(ω_φ t)`.
- **Central numbers**: `Ω_c / Ω_b = 5.3643` (`84.29 %` of non-relativistic matter); for a `10^6 kg` electromagnetically transparent mass at `b_1 = 1 m`, `d_c = 1000 m`, `v_0 = 220 km/s`, `Δτ = −4.664 × 10^{-26} s`, with Gauss–Legendre quadrature matching closed-form `arsinh` within `3.69e-16` (`< 1e-11`) and `+c² ∂(Δτ_∞)/∂b_1` matching `Δv_⊥ = 6.068 × 10^{-10} m/s` within `5.64e-11`; at `m_φ c² = 10^{-15} eV` and `ρ_DM = 0.4 GeV/cm³`, `Φ_Pl = 7.199 × 10^{-16}` (`d_e = 0` gives `0` modulation for co-located clocks).
- **Generator**: `python skills/timegravity/t12/make_t12.py`
- **Verifier**: `python skills/timegravity/t12/verify_t12_dark_clock.py`
- **Knockout check**: `python skills/timegravity/t12/verify_t12_dark_clock.py --planted-defect` (must exit non-zero: `G_dark = 0` severs universal gravitational coupling)
- **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 |
| --- | --- | --- | --- |
| `T12-PLANCK2020` | MEASURED | Planck Collaboration 2020, cosmological parameters (`Ω_c h²`, `Ω_b h²`) | https://doi.org/10.1051/0004-6361/201833910 |
| `T12-CLOWE2006` | MEASURED | Clowe et al. 2006, Bullet Cluster weak-lensing separation of mass from X-ray gas | https://doi.org/10.1086/508162 |
| `T03-MICRO2022` | MEASURED | Touboul et al. 2022, MICROSCOPE weak equivalence principle test (`η ~ 10^{-15}`) | https://doi.org/10.1103/PhysRevLett.129.121102 |
| `T01-PR1960` | MEASURED | Pound & Rebka 1960, gravitational redshift | https://doi.org/10.1103/PhysRevLett.4.337 |
| `T01-CHOU2010` | MEASURED | Chou et al. 2010, optical-clock gravitational redshift at 33 cm | https://doi.org/10.1126/science.1192720 |
| `T03-EIN1916` | DERIVED | Einstein 1916, universal metric coupling to stress-energy `T_{μν}` | https://doi.org/10.1002/andp.19163540702 |
| `T11-JOOS1985` | DERIVED | Joos & Zeh 1985, dipole photon scattering vanishes when `α_EM = 0` | https://doi.org/10.1007/BF01725541 |
| `T12-KENNEDY2020` | BOUND | Kennedy et al. 2020, JILA `87Sr` vs silicon cavity ultralight dark-matter bound | https://doi.org/10.1103/PhysRevLett.125.201302 |
| `T12-FILZINGER2023` | BOUND | Filzinger et al. 2023, PTB `171Yb+` E3/E2 clock ratio dark-matter bound | https://doi.org/10.1103/PhysRevLett.130.253001 |
| `T12-LZ2023` | BOUND | Aalbers et al. (LUX-ZEPLIN) 2023, WIMP-nucleon spin-independent cross-section bound | https://doi.org/10.1103/PhysRevLett.131.041002 |
| `T12-CARNEY2021` | PROPOSED | Carney et al. 2021, mechanical sensor and clock array detection of gravitational dark matter | https://doi.org/10.1088/1367-2630/abd9e7 |
## 3. Tool-neutral agent packet and security boundary (`security-runtime`)
1. **Rebuild locally**: `python skills/timegravity/t12/make_t12.py`; standard library only; writes only under `src/research/timegravity/t12/files/`.
2. **Acceptance gate**: `python skills/timegravity/t12/verify_t12_dark_clock.py` must print `"status": "PASS"` with `arsinh_matches_gl5_quadrature: 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.
## 4. Deterministic verification and falsification rules
1. `Ω_c / Ω_b = 0.1200 / 0.02237 = 5.36432722396` and analytic vs finite-difference error propagation agree within `1e-9`.
2. Across baselines `d_c ∈ {1, 10, 100, 1000} m`, composite Gauss–Legendre quadrature of `∫ (Φ_1(t) − Φ_2(t))/c² dt` matches `−(2 G M_DM / c² v_0) [arsinh(v_0 T / b_1) − arsinh(v_0 T / b_2)]` within `1e-11`, and central differences of `+c² ∂(Δτ_∞)/∂b_1` match `2 G M_DM / (b_1 v_0)` within `1e-9`.
3. Under pure gravity (`d_e = 0`), co-located clocks (`d_c = 0`) have `Δτ = 0` and `δ(ν_A/ν_B) = 0`, while the ultralight scalar energy-density identity `(c² / 8πG) ω_φ² Φ_Pl² = ρ_DM` holds within `1e-12`.
4. Planted defect: setting `G_dark = 0` gives `Δτ = 0` at `d_c > 0`; rule 2 fails and `--planted-defect` exits non-zero.
5. `t12_reference.json` matches `manifest.json` and regenerates byte for byte.
## 5. What the instrument shows (reader side)
- Left panel: Differential gravitational redshift `Δν(t)/ν` and accumulated proper-time step `Δτ(t)` across a two-clock network (`b_1`, baseline `d_c`) during the flyby of an electromagnetically transparent mass `M_DM` (`Λ_EM = 0`). Right panel: Co-located optical-clock portal bound `|d_e|` vs scalar mass `m_φ c²` (`Kennedy 2020`, `Filzinger 2023`) alongside the `d_c = 0` equivalence-principle null for pure gravity (`d_e = 0`).
- Knockout: turn off universal gravitational coupling (`G_dark = 0`) or set clock baseline `d_c = 0`; the differential proper-time step collapses to `0`.
- Predict before you reveal: whether two co-located clocks at the same point (`d_c = 0`) can detect a passing mass that couples only through Einstein's metric `g_{μν}` (`d_e = 0`).
## 6. Exact T0–T3 truth boundary
### In the repository today (T0/T1)
- Kernel `tools/timegravity_kernel_dark_clock.py`, generator, verifier, ledger rows above, and the ES module `src/research/modules/timegravity-slope.mjs`.
### Not on this page (T2/T3)
- Direct laboratory detection of individual dark-matter transits through gravity alone (`T12-CARNEY2021`) is `PROPOSED` and requires Planck-mass-scale sensors far beyond current optical-clock or optomechanical noise floors.
- The microscopic particle identity of dark matter (and whether it carries any non-gravitational portal coupling `d_e ≠ 0` or `σ_SI ≠ 0` below current `BOUND` limits) is `OPEN`.
Show the verifier verify_t12_dark_clock.py
#!/usr/bin/env python3
"""Standalone stdlib verifier and planted-defect knockout for Time & Gravity · T.12 (Two Clocks That Only Meet in Gravity).
Canonical URL: https://informatico.ai/timegravity/t12/
Central number: Planck 2018 cosmic microwave background power spectra fix the dark-to-baryonic matter ratio at
Omega_c / Omega_b = 0.1200 / 0.02237 = 5.3643 (84.29 % of non-relativistic matter); for an electromagnetically
transparent mass M_DM flying past a two-clock network (b_1 = 1 m, baseline d_c = 1000 m, v_0 = 220 km/s),
composite Gauss-Legendre quadrature of the gravitational redshift integral matches the closed-form arsinh expression
-(2 G M_DM / c^2 v_0) [arsinh(v_0 T / b_1) - arsinh(v_0 T / b_2)] within 1e-11 and satisfies the transverse impulse
identity +c^2 d(Delta tau_inf)/db_1 = 2 G M_DM / (b_1 v_0) within 1e-9, while co-located clocks (d_c = 0) see zero
shift under pure gravity (d_e = 0). Planted defect: setting G_dark = 0 for the electromagnetically transparent mass
violates the Equivalence Principle and fails the quadrature check; `--planted-defect` exits 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_dark_clock import DARK_CLOCK_TOL, check_dark_clock # noqa: E402
FILES_DIR = ROOT / "src" / "research" / "timegravity" / "t12" / "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 / "t12_reference.json").read_text(encoding="utf-8"))
assert ref["gravitational_transit"]["quadrature_rel_err"] < 1e-11, "reference dark-transit quadrature error too large"
assert ref["ultralight_scalar_bound"]["rho_roundtrip_rel_err"] < DARK_CLOCK_TOL, "reference ULDM energy-density round-trip error"
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_dark_clock(planted_defect=planted)
assert res["cosmo_ok"], f"cosmological dark-to-baryon budget error {res['cosmo_err_propagation_rel_diff']:.3e}"
assert res["transit_ok"], (
f"dark-transit proper-time shift misses gravitational trajectory integral (rel_err = {res['quadrature_rel_err']:.3e}); "
"an electromagnetically transparent mass still curves proper time via G_N"
)
assert res["uldm_ok"], f"ultralight scalar clock round-trip error {res['uldm_rho_roundtrip_rel_err']:.3e}"
assert res["defect_rejected"], "planted zero-gravity dark transit was accepted"
files = verify_reference_files()
except AssertionError as exc:
print(json.dumps({"status": "FAIL", "folio_id": "T.12", "error": str(exc)}), file=sys.stderr)
return 1
print(json.dumps({
"status": "PASS",
"folio_id": "T.12",
"canonical_url": "https://informatico.ai/timegravity/t12/",
"central_number": {
"dark_to_baryon_ratio": res["dark_to_baryon_ratio"],
"dark_fraction_of_matter": res["dark_fraction_of_matter"],
"delta_tau_analytic_s": res["delta_tau_analytic_s"],
"quadrature_rel_err": res["quadrature_rel_err"],
"impulse_rel_err": res["impulse_rel_err"],
"uldm_1e15ev_phi_planck": res["uldm_1e15ev_phi_planck"],
"tolerance": DARK_CLOCK_TOL,
},
"geometry_checks": {
"planck_dark_baryon_budget": "PASS",
"arsinh_matches_gl5_quadrature": "PASS",
"transverse_impulse_from_clock_gradient": "PASS",
"equivalence_principle_zero_baseline": "PASS",
"uldm_energy_density_roundtrip": "PASS",
"planted_defect_knockout": "REJECTED_AS_EXPECTED",
"planted_delta_tau_s": res["planted_delta_tau_s"],
},
"reference_files_sha256_12": files,
}, indent=2))
return 0
if __name__ == "__main__":
raise SystemExit(main())
Primary sources
Planck Collaboration (Aghanim, N., et al.). (2020). Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics, 641, A6. DOI DOI 10.1051/0004-6361/201833910[Scite ↗]
Clowe, D., Bradač, M., Gonzalez, A. H., Markevitch, M., Randall, S. W., Jones, C., & Zaritsky, D. (2006). A direct empirical proof of the existence of dark matter. The Astrophysical Journal Letters, 648(2), L109–L113. DOI DOI 10.1086/508162[Scite ↗]
Touboul, P., et al. (MICROSCOPE Collaboration). (2022). MICROSCOPE mission: Final results of the test of the equivalence principle. Physical Review Letters, 129(12), 121102. DOI DOI 10.1103/PhysRevLett.129.121102[Scite ↗]
Chou, C. W., Hume, D. B., Rosenband, T., & Wineland, D. J. (2010). Optical clocks and relativity. Science, 329(5999), 1630–1633. DOI DOI 10.1126/science.1192720[Scite ↗]
Einstein, A. (1916). Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik, 354(7), 769–822. DOI DOI 10.1002/andp.19163540702[Scite ↗]
Joos, E., & Zeh, H. D. (1985). The emergence of classical properties through interaction with the environment. Zeitschrift für Physik B Condensed Matter, 59(2), 223–243. DOI DOI 10.1007/BF01725541[Scite ↗]
Kennedy, C. J., Oelker, E., Robinson, J. M., Bothwell, T., Kedar, D., Milner, W. R., Marti, G. E., Derevianko, A., & Ye, J. (2020). Precision metrology meets cosmology: Improved constraints on ultralight dark matter from atom-cavity frequency comparisons. Physical Review Letters, 125(20), 201302. DOI DOI 10.1103/PhysRevLett.125.201302[Scite ↗]
Filzinger, M., Döring, S., Steinel, M., Huntemann, N., et al. (2023). Improved limits on the coupling of ultralight bosonic dark matter to photons from optical atomic clock comparisons. Physical Review Letters, 130(25), 253001. DOI DOI 10.1103/PhysRevLett.130.253001[Scite ↗]
Aalbers, J., et al. (LUX-ZEPLIN Collaboration). (2023). First dark matter search results from the LUX-ZEPLIN (LZ) experiment. Physical Review Letters, 131(4), 041002. DOI DOI 10.1103/PhysRevLett.131.041002[Scite ↗]
Carney, D., Hook, A., Liu, Z., Taylor, J. M., & Zhao, Y. (2021). Ultralight dark matter detection with mechanical quantum sensors. New Journal of Physics, 23(2), 023041. DOI DOI 10.1088/1367-2630/abd9e7[Scite ↗]
This page ends with one open question
Does the 84.3% of matter that leaves no electromagnetic record couple to our clocks only through the curvature of proper time, or through a portal just below today's optical-clock bounds?
