Galaxy Rotation Curves
TEST-03 Kill Criterion TriggeredGalaxy rotation curves are the most important empirical test for any theory of gravity at galactic scales. Stars and gas in the outer regions of disk galaxies orbit faster than Newtonian gravity predicts from visible mass alone. The Radial Acceleration Relation (RAR) captures this: observed acceleration correlates tightly with the acceleration predicted from baryonic mass, but systematically exceeds it below a critical scale.
Synchronism's coherence function predicts how and where rotation curves should flatten. We tested this against two major datasets.
Dataset Results
SPARC Dataset
175 galaxies with high-quality photometry and resolved rotation curves (Lelli, McGaugh & Schombert 2016). The gold standard for RAR studies. [Public data]
- Tight RAR confirmed (σint ≈ 0.057 dex) — McGaugh et al. 2016 measured value, restated
- Coherence function fits within observational scatter
- Environment-dependent effects visible but sample too small for strong statistics
ALFALFA-SDSS Dataset
14,585 galaxies from the ALFALFA HI survey cross-matched with SDSS photometry. Unresolved rotation curves but massive statistical power. [ALFALFA data] [SDSS DR17]
- Environment-dependent RAR scatter detected at p = 5 × 10−6
- σint = 0.086 ± 0.003 dex (below CDM prediction)
- Cluster vs. field galaxies show different scatter — as predicted
The Interpolating Function
Attribution: The equation below is the standard RAR interpolating function from McGaugh, Lelli & Schombert (2016) — already in the literature for a decade and widely used to fit SPARC. Synchronism's specific contribution is not the function itself, but the environmental scatter ansatz on top of it (the claim that σint depends on local density). All fit-quality claims refer to that ansatz and to the McGaugh-2016 baseline together.
In Synchronism, the acceleration scale a₀ ≈ cH₀/(2π) is a 40-year-old dimensional coincidence (Milgrom 1983), discussed by Famaey & McGaugh (2012), McCulloch, Verlinde, and Smolin under different theoretical umbrellas. The 2π prefactor is chosen to match the observed value; cH₀/(2π) ≈ 1.08×10⁻¹⁰ m/s² undershoots the observed 1.2×10⁻¹⁰ by ∼10%. Synchronism's contribution is the coherence-function mechanism that provides areason for this scale — not the identification itself. See Honest Assessment and Parameter Derivations for prior-art acknowledgment and the canonical reparametrization framing.
Key Results Summary
Structural Failure: Dark Matter Mechanism (March 2026)
Synchronism's CFD viscosity interpretation mapped low coherence (dark matter) to high viscosity — predicting dark matter should be stickier than baryons. The Bullet Cluster (1E 0657-558) shows the opposite: dark matter halos pass through each other with negligible self-interaction (σ/m < 0.47 cm²/g, Harvey et al. 2015). The prediction has the wrong sign. This is a structural failure, not a parameter problem — no adjustment to A, γ, or ρcrit can fix a sign error in the mechanism.
The galaxy rotation fit results on this page are independent of the CFD interpretation and stand as-is (reparametrization of MOND with an environmental scatter term). But the claim that “dark matter effects arise from incomplete decoherence” is under structural revision. Full failure analysis →
Honest Caveat
The environment-dependent scatter is real and statistically significant (p = 5×10−6with N = 14,585), but it explains only 14% of the total RAR scatter (R² = 0.14). The remaining 86% is unexplained by the coherence model. Furthermore, standard MOND plus mass-to-light ratio corrections already explains essentially all of the RAR variance. Synchronism adds a small, detectable effect on top of what MOND already provides — it does not replace MOND's success.
TEST-03 connection: The R² = 0.14 result above is what TEST-03 measures. The pre-registered kill criterion for TEST-03 is R² < 0.20 — meaning the environmental coherence term must explain at least 20% of intrinsic RAR scatter to survive. At R² = 0.14, TEST-03 has already tripped its own kill criterion. The σint = 0.086 dex and R² = 0.14 figures on this page are the same finding viewed from two angles; both point to the same conclusion.
ΔBIC note: The incremental value of the environmental scatter term above baseline MOND has not been quantified via ΔBIC on the ALFALFA-SDSS dataset. A separate ΔBIC analysis was run for the RAR transition-shape question (see below) — which is the more fundamental discriminating question.
RAR Transition Shape: The Decisive Test — CLOSED (2026-05-21)
The environment-dependent scatter tests (TEST-01, TEST-05) probe the size of deviations from MOND's RAR. A more fundamental question is whether the compander's functional form (μSyn = tanh(γ ln(1+x)), γ=2) differs from McGaugh's interpolating function ν(x) = 1/(1−e−√x) in the shape of the transition — the only test that could discriminate the two frameworks without assuming any environmental coupling.
This test was run on 2807 real SPARC points (Lelli-McGaugh-Schombert 2016, 10% velocity-error cut) with a₀ free and standard M/L priors. Result:
| Model | RMS (dex) | ΔBIC vs McGaugh |
|---|---|---|
| McGaugh ν (standard MOND) | 0.1437 | — (reference) |
| Compander μ, γ=2 pinned | 0.1485 | +184 |
| Compander μ, γ free (best fit: γ=0.49) | 0.1437 | +7.1 |
Kill criterion triggered. ΔBIC = +184 ≫ 10 refutes the γ=2 compander as the galaxy mechanism. Conservative correction for intra-galaxy point correlation (effective N≈500–1000): ΔBIC ≈ 33 — still decisive. The residual is a coherent S-shaped ≈0.05–0.10 dex signature at the transition, significant at ~8σ per bin.
Note on γ=2: γ=2 follows from Ncorr=1 (individual stars taken as uncorrelated), but Ncorr is asserted, not independently counted. The SPARC-preferred γ≈0.49 back-implies Ncorr≈17, contradicting the independent-stars premise. γ=2 is the most charitablepin for galaxies given the framework's own logic — not a prediction derived from independent evidence.
The fork that closes the question: free-γ converges to γ≈0.49 with RMS identical to McGaugh to four digits. ΔBIC=+7 is entirely the BIC penalty for the extra parameter — the fit improvement is zero. There is no γ for which the compander is both (a) distinct from MOND and (b) consistent with SPARC. Pin γ=2 → refuted. Fit γ → MOND.
Net discriminating galaxy tests vs MOND: 0, by execution. Script + full analysis: explorer/scripts/rar_transition_shape_real_sparc.py, finding: explorer/findings/rar-transition-shape-real-sparc-result.md.
Wide Binaries
The RAR environmental scatter (TEST-03) tripped its kill criterion, and the RAR transition-shape test (above) has now closed the main galaxy-scale question. The wide binary test (TEST-02) was previously identified as a discriminator, but with the compander collapsing to MOND at its best-fit γ, the wide-binary question is now whether MOND+EFE and the compander (at fitted γ≈0.49) diverge in a density-stratified wide-binary sample. Wide stellar binaries (separations > 0.1 pc) probe the sub-a₀ acceleration regime in a fundamentally different mass and density environment from galaxy rotation curves — no dark matter halos, no baryonic feedback, just two stars in a nearly Keplerian orbit.
The key papers are Pittordis & Sutherland (2023) and Hernandez et al. (2024), using Gaia DR3. They disagree on the strength of the MOND signal. Synchronism predicts a density-dependent wide binary anomaly (stronger anomaly in denser stellar fields). Gaia DR3 is public; stratifying the sample by local stellar density is a tractable one-week analysis. See TEST-02 for the kill criterion.
GW170817 and the Speed of Gravity
The binary neutron star merger GW170817 constrained |cGW − c|/c < 10−15, killing TeVeS, Bekenstein-Sanders, and large swaths of Horndeski parameter space (Sakstein & Jain 2017, Ezquiaga & Zumalacárregui 2017). Synchronism is marketed in part as a modified-gravity alternative, so this constraint is relevant.
Synchronism's posture: The coherence function C(ρ) is not a tensor-vector-scalar theory and does not introduce new propagating tensor degrees of freedom. It does not modify the graviton kinetic term or introduce derivative couplings of a scalar to the metric that would change gravitational wave speed. Therefore the framework's prediction is cGW = c by construction, and GW170817 does not apply.