Compare 5 gravitational theories against real galaxy rotation data. Which one explains flat rotation curves best?
A gas-rich dwarf irregular galaxy, excellent test case for modified gravity.
| Model | Mean Error | RMS Error | Max Deviation | Free Params | Rank |
|---|---|---|---|---|---|
LFM (Derived)BEST | 9.7% | 16.8% | 50.8% | 0 | #1 |
MOND/RAR | 13.1% | 22.0% | 63.9% | 1 | #2 |
MOND Standard | 13.2% | 22.2% | 64.4% | 1 | #3 |
NFW Dark Matter | 45.0% | 47.7% | 56.2% | 2 | #4 |
Newtonian | 46.4% | 49.3% | 59.5% | 0 | #5 |
DERIVED from GOV-01 + GOV-02 coupled wave equations (Feb 2026). At transition g = √2 × a₀ (differs from MOND φ × a₀ by ~12%). This is a TESTABLE PREDICTION, not an ansatz.
Standard gravity from visible matter only. Fails at large radii where rotation curves are flat.
Milgrom (1983). Modifies Newton below acceleration scale a₀. Uses standard interpolation μ(x) = x/√(1+x²).
McGaugh et al. (2016) empirical fit to SPARC data. Excellent fit but purely phenomenological.
Navarro-Frenk-White (1996) dark matter halo profile. Requires ~5× more dark matter than visible.
Unlike MOND (where a₀ is fitted), LFM derives the acceleration scale from cosmology. This is a prediction, not a parameter!
The interpolation function differs, but for most galaxy radii, we're either deep in Newtonian or deep MOND regime where they converge.
| Regime | g_bar/a₀ | LFM g/a₀ | MOND g/a₀ | Difference |
|---|---|---|---|---|
| Deep | 0.01 | 0.105 | 0.109 | +3.8% |
| Deep | 0.1 | 0.332 | 0.366 | +10.2% |
| Transition | 1.0 | 1.414 | 1.618 | +14.4% |
| Newtonian | 10 | 10.49 | 10.66 | +1.6% |
| Newtonian | 100 | 100.5 | 100.6 | +0.1% |
Maximum difference (~15%) occurs at the transition g_bar = a₀. In velocity space this becomes ~7% (v ~ √g).
The χ field responds to matter density. Where matter accumulates (galaxies), χ is depressed below vacuum value χ₀ = 19.
Gravity isn't a force — it's how waves propagate through χ gradients. The product structure (1/χ × dχ/dr) is key!
The (1/χ × dχ/dr) form mathematically produces a geometric mean between g_bar and (g_bar + a₀).
The acceleration scale emerges from the Hubble rate — the universe's expansion sets the transition scale!
LFM prediction matches observation within 10% — remarkable for a parameter-free derivation!
Data: SPARC (Spitzer Photometry and Accurate Rotation Curves) —Lelli, McGaugh & Schombert (2016)
References: MOND — Milgrom (1983) | RAR — McGaugh et al. (2016) | NFW — Navarro, Frenk & White (1996)