MOND Unification
10% ErrorThis is one of Synchronism's strongest results. The MOND acceleration scale a₀ — a number that Milgrom introduced in 1983 as a fundamental constant of nature —emerges from basic cosmological parameters. It is not fundamental. It is derived.
The Significance
In Modified Newtonian Dynamics (MOND), a₀ is the acceleration below which gravity deviates from Newton's law. Milgrom observed it empirically:
For 40 years, the coincidence that a₀ ≈ cH₀ has been noted by many researchers but never explained. It could be a numerical accident. In Synchronism, it is a derivation: the coherence function, applied at cosmological scale, produces this relationship with a factor of 2π that comes from the geometry of the horizon.
The Derivation Chain
Step 1: Critical Density of the Universe
Standard cosmology. The density at which the universe is flat. This is measured, not assumed.
Step 2: Coherence Transition
At the coherence transition (C ≈ 0.5), the gravitational acceleration from ρcrit over a Hubble-scale volume defines the threshold where dynamics change. The 2π factor arises from the spherical geometry of the causal horizon.
Step 3: The Result
Plugging in H₀ = 67.4 km/s/Mpc and c = 3 × 108 m/s gives 1.08 × 10−10 m/s². Milgrom's observed value: 1.20 × 10−10. Error: ~10%.
Comparison
MOND (Milgrom 1983)
- a₀ is a fundamental constant
- Value determined empirically from galaxy fits
- No explanation for why a₀ ≈ cH₀
- Extremely successful at fitting rotation curves
Synchronism
- a₀ is an emergent scale
- Value derived from H₀ and c
- The cH₀ coincidence is explained, not assumed
- Inherits MOND's empirical success plus adds environment dependence
Sessions and History
Derived in Sessions #87–88 of the autonomous research program. The derivation was independently stress-tested in Session #91, where the same result was obtained from a different starting point (via Freeman's Law). Both derivations agree, providing internal consistency.