RAR Scatter
Failed — Environment run executed 2026-07-14: r²=0.0001 vs registered >20% — refuted; MOND tie dissolved 2026-07-15New Prediction #2 (NP2): The scatter in the Radial Acceleration Relation depends on environment. The effect is real and statistically significant (p = 5×10−6, R²=0.14) — but on the SPARC-scale sample (N≈130–175), not the 14,585-galaxy ALFALFA-SDSS sample this page originally attributed it to (see correction below; TEST-03/TEST-05 on Tier 1: Existing Data). Correction (2026-07-04): this is not a prediction standard models avoid — MOND's External Field Effect (EFE) also predicts environment-dependent RAR scatter, so a detection here does not by itself discriminate Synchronism from MOND.
What Is RAR Scatter?
The Radial Acceleration Relation plots observed gravitational acceleration (gobs) against the acceleration predicted from baryonic mass alone (gbar). Across thousands of galaxies, this relation is remarkably tight — but not perfectly tight. The scatter around the mean relation is measured as σint (intrinsic scatter in dex).
Standard models — both CDM and basic MOND — predict that this scatter should be constant regardless of a galaxy's environment. A galaxy in a dense cluster should scatter the same amount as an isolated field galaxy.
Synchronism's Prediction
The coherence function depends on local density. Galaxies in dense environments (clusters, groups) experience a different coherence gradient than isolated galaxies. This means the RAR scatter should vary with local density. Specifically:
Cluster Galaxies
Higher ambient density → steeper coherence gradient → tighter RAR (less scatter). The external density field “stiffens” the coherence profile.
Field Galaxies
Lower ambient density → shallower coherence gradient → more scatter. Isolated galaxies have more freedom in how their coherence profiles develop.
The Test
Using the ALFALFA-SDSS cross-matched sample, σint = 0.086 dex was measured on the optimal quality cut (N = 677) — the full cross-match (N = 14,435) gives 0.118 dex; pairing the headline N with the optimal-cut statistic was a sample splice, corrected 2026-07-10 (CDM-consistent — see CDM Discrimination). The p = 5×10−6, R² = 0.14 environment-density statistics below are notfrom this sample: they trace to a SPARC-scale (N≈171) Hubble-type/morphology regression (archive Session 377), mislabeled as this test's result since 2026-04. The result:
Correction (2026-07-09): at N = 14,585, R² = 0.14 would imply p of order 10−500, not 5×10−6 — mathematically impossible together. The registered environment-density test on the 14,585-galaxy sample has never been run. Full trace on Tier 1: TEST-03/TEST-05 →
What This Means
The environment effect is real — statistically significant at better than 4.5σ — but small, and it fails the test's own pre-registered kill criterion (R² > 0.20 required; R² = 0.14 measured). Basic MOND (no EFE) does not predict environment dependence, but MOND with the External Field Effect does — EFE is a standard part of MOND phenomenology, not an ad-hoc addition, so this result does not separate Synchronism from the MOND family. CDM simulations with baryonic feedback can also potentially produce environment-dependent scatter.
Honest Caveat
86% of the RAR scatter remains unexplained by Synchronism's coherence model (R² = 0.14), below the 20% the pre-registered kill criterion required — by that standard this test has failed, not merely under-delivered. Most of the scatter likely comes from observational systematics (distance errors, inclination corrections, mass-to-light ratio assumptions) rather than any physical model. MOND plus standard M/L corrections already accounts for essentially all of the variance. See CDM Discrimination for how this same measurement bears on the CDM comparison.