Galaxy Rotation Curves
14,760 GalaxiesGalaxy 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 is not a free parameter — it emerges from cosmology as cH₀/(2π). The coherence function provides the physical mechanism: at accelerations below a₀, the system crosses a coherence threshold and gravitational dynamics change.
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.
Missing measurement: The incremental value of adding the environmental term has not been quantified via ΔBIC (Bayesian Information Criterion) against baseline MOND on the same dataset. With N = 14,585, even a tiny effect is statistically significant; ΔBIC would determine whether the fit improvement exceeds the penalty for adding the extra parameter. Until that analysis is run, “small but detectable effect” is a qualitative description, not a measurement.