The empirical acceleration scale at which galaxy rotation curves deviate from Newtonian gravity, derived from first principles.
Since Milgrom's 1983 observation, it has been known that galaxy rotation curves deviate from Newtonian predictions below a characteristic acceleration scale a0 ≈ 1.2×10−10 m/s². This “MOND acceleration” appears across thousands of galaxies of different sizes, types, and masses.
The SPARC catalog (Lelli, McGaugh & Schombert 2016) confirmed this with 175 galaxies. The Radial Acceleration Relation shows a tight empirical correlation across diverse galaxy types. But no theory has explained why this particular value.
The STF activation threshold is set by the cosmological background curvature rate. When local gravitational acceleration drops below the threshold set by the Hubble flow, the scalar field activates. This threshold is:
This uses only two measured quantities: the speed of light and the Hubble constant. The factor of 2π arises naturally from the field's oscillation mode in the cosmological background.
| Source | Value (m/s²) | Method |
|---|---|---|
| STF derived | 1.16×10−10 | a0 = cH0/(2π) with H0 = 75 km/s/Mpc |
| SPARC observed | (1.2 ± 0.2)×10−10 | Empirical fit to 175 galaxies |
| Milgrom 1983 | ~1.2×10−10 | Original empirical estimate |
For 40 years, a0 has been an unexplained empirical constant. MOND uses it but doesn't derive it. ΛCDM doesn't predict it at all. The STF derives it from the Hubble constant alone — explaining why it takes the value it does and predicting that it should vary with redshift as H(z) evolves.
This prediction is falsified if a0 is shown to be independent of H0, or if high-redshift galaxy kinematics reveal an a0 that doesn't scale with H(z).