MOND-Synchronism Comparator
The Acceleration Scale a₀
MOND (Milgrom 1983)
a₀ ≈ 1.2 × 10⁻¹⁰ m/s²
Status: Empirical constant, fitted to data. Milgrom noted in 1983 that a₀ is close to cH₀ (the prefactor varies by author).
Synchronism
a₀ = cH₀/(2π) ≈ 1.04 × 10⁻¹⁰ m/s²
Status: Reparametrization. This is the same numerical coincidence Milgrom noted (1/2π = 0.159 vs 1/6 = 0.167), not a derivation. The Hubble-sphere calculation the archive describes gives cH₀/2, not cH₀/2π. It is 13% below the observed 1.2. See Relation to MOND.
Head-to-Head Comparison
| Feature | MOND | Synchronism (current status) |
|---|---|---|
| a₀ origin | Empirical fit | Same coincidence restated (Reparametrization) |
| Galaxy rotation curves (RAR) | Good fit | Free γ lands on 0.489 ≈ ½, i.e. MOND's simple μ (Reparametrization). The framework's own γ = 2 loses by ΔBIC +184 (Υ frozen; +46 with Υ free per law) (Failed) |
| Stated variable | Acceleration | Local density ρ, but every quantitative galaxy fit used acceleration. Keyed on density, the best fit keeps only a weak response (γ → 0.046, boost ∝ ρ^−0.10, knee below every disc; that response is g_bar’s: at fixed g_bar, density adds nothing, partial slope +0.003, 95% CI −0.022 to +0.027) and loses by ΔBIC +2843 |
| Boost at low acceleration | Unbounded | Capped at 1/Ω_m = 3.17 in one reading. Excluded by the SPARC BTFR slope for caps ≲ 5.3 (Failed; the headline kill depends on the cap convention) |
| RAR environment dependence | Via the external field effect | Predicted density dependence not seen: r² = 0.0001 vs a kill bar of 0.09 (Failed) |
| Solar System (Cassini) | Simple μ and McGaugh's RAR function are both excluded. Sharper transitions (δ ≥ 4) passed only with a₀ held fixed; with a₀ refit to SPARC no δ up to 6 passes (δ = 4: +9.2σ). Dropping bulge-dominated galaxies brings δ = 6 to +3.0σ, and Desmond, Hees & Famaey find 1.9σ with extra M/L freedom | At the SPARC-preferred γ it is simple μ, so it is excluded too, +17.7 to +18.0σ. With a₀ refit, every γ from 0.3 to 3 fails (14.5–19σ; 13–18σ without bulges): the compander has no sharp-transition member (Failed, inherited from MOND) |
| Wide binaries | Disputed in the literature | Density-keyed ratio identically null (γ_g ≡ 1) and that branch already fails lunar ranging; the acceleration-keyed reading inherits MOND's outcome (Self-Eliminating-or-Tie) |
| Cosmology | Needs extra ingredients for the CMB | The dark-energy sector is ΛCDM at its best fit, and it needs cold dark matter put in by hand (checked 2026-09-22) |
| Relativistic extension | TeVeS, AeST | Static gravity reproduces GR. The radiative sector predicts scalar gravitational waves, which is refuted (Failed) |
| Chemistry / quantum | Not addressed | The chemistry γ ≈ 1 boundary mostly restates the Debye model; the Intent field equals |ψ|² wherever tested (Reparametrization) |
| Freeman's Law | Σ₀ = a₀/(2πG) | The same relation, relabelled through ρ_crit (Reparametrization) |
Is There Still a Discriminator?
This page used to call wide-binary density dependence (TEST-02) “the decisive discriminator”. It isn't. The density-keyed signal is too small for Gaia DR3, and the acceleration-keyed reading is MOND. The framework's two genuinely non-MOND features were the density keying and the bounded boost. The density keying fails on data (the environment test, and the locality argument on Key Claims). The bounded boost fails the BTFR slope for caps up to about 5.4. Open question: is there a version of C that differs from MOND anywhere data can reach and hasn't lost? If you can construct one, that is the most useful thing a reader could bring to this project. The scorecard is on Honest Assessment.