Galaxy Curve Plotter
The dark matter puzzle in one picture: Physics predicts that galaxies should rotate more slowly at their outer edges (like planets in the solar system — the further out, the slower). They don't. The outer stars rotate just as fast as the inner ones. Something invisible is adding gravity. Most physicists call it dark matter — a proposed invisible substance that has never been directly detected; we infer it only from its gravitational pull (whether it's real stuff or a placeholder for missing physics is exactly what's being debated). MOND (Modified Newtonian Dynamics) explains the same curves by changing the gravity law. Synchronism offers a third interpretation: the coherence function C(ρ) mimics the extra gravity via density-dependent coupling. All three fit the observations; none is confirmed over the others by rotation curve data alone — though the fits are not on equal footing: MOND uses one global constant (a₀) for every galaxy, while the violet Synchronism curve refits ρcrit per galaxy.
Select a SPARC galaxy. The plot shows four things: what visible matter predicts (dashed), what we observe (dots), what Synchronism gives (violet), and what MOND gives (green). Notice that Synchronism and MOND nearly overlap — the framework's own Honest Assessment labels this a reparametrization — plain words: the same curve wearing a different costume; fitting a known curve isn't discovering anything new. Plain verdict for casual readers: these curves look great but don't prove the idea — all three models (Synchronism, MOND, and NFW dark-matter halo) fit galaxy rotation curves about equally well. What matters is whether any makes a different, testable prediction, and the ensemble test (SPARC RAR, ΔBIC=+184) shows Synchronism collapses to MOND when γ is freed. See what the tests actually say →
- Dashed gray — Newtonian prediction using visible matter only. Drops off at the edges; this is the puzzle.
- Dots — observed rotation velocities. Flat at large radius; doesn't drop like Newtonian says it should.
- Violet — Synchronism at γ=2 (consistency check, per-galaxy ρcrit refit). Not a parameter-free prediction, and γ=2 is rejected at ΔBIC=+184 on the ensemble RAR.
- Green dashed — MOND. Also fitted to Vflat. Synchronism and MOND nearly overlap — this is what a reparametrization looks like.
What You're Seeing
The dashed line is what rotation curves should look like with only visible matter (stars + gas). The blue dots are what we actually observe. The gap is the “dark matter problem.”
Synchronism's violet curve fills the gap using C(ρ) with γ = 2 (uncorrelated stars) — no dark matter particles needed. The coherence function adds an effective mass component from the density field itself.
The green dashed curve is MOND (Modified Newtonian Dynamics), which modifies gravity below the acceleration scale a₀ ≈ 1.2×10⁻¹⁰ m/s². Notice that Synchronism and MOND nearly overlap — both use the same interpolating function (McGaugh et al. 2016 RAR), and the site labels this a reparametrization.
Note: Curves shown are simplified models for illustration. Actual SPARC fits use full surface brightness profiles and mass-to-light ratios. See the research data for precise fits.