MOND Unification
Dimensional Analysis — 10% ErrorThe MOND acceleration scale a₀ is related to cosmological parameters. However, this relationship is not unique to Synchronism: Milgrom noted the a₀ ~ cH₀ coincidence in his original 1983 paper. McCulloch (2007) derived a₀ = cH₀/(2π) from quantized inertia. Verlinde (2017) obtained a similar relation from emergent gravity. The 2π factor is the standard geometric factor arising from any argument involving a spherical causal horizon. This is best understood as dimensional analysis with a geometric prior, not a unique derivation from first principles.
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. Multiple frameworks produce the same relation with the same geometric factor. In Synchronism, the coherence function provides a physical narrative for why this relationship holds, but the result itself is shared with other approaches.
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 from dimensional analysis of H₀ and c (shared with other frameworks)
- Uses the standard McGaugh et al. (2016) RAR interpolating function
- Predicts a weaker EFE (~0.3–0.4× MOND) as a distinguishing feature
The External Field Effect
The nonlinear Poisson equation that implements the coherence function produces an External Field Effect (EFE) — a subsystem's internal dynamics are influenced by the external gravitational field it sits in. This contradicts earlier claims in the research archive (Sessions #212, #215) that Synchronism has “no EFE.”
Perturbative analysis shows the Synchronism EFE is approximately 0.3–0.4× the strength of MOND's EFE, with a maximum anisotropy of ~17% at gext ~ 0.4 a₀. This is a concrete, testable prediction that distinguishes Synchronism from both MOND (stronger EFE) and CDM (no EFE).
Tidal Dwarf Galaxy Test
The cleanest discriminator: for a 107 M☉ TDG at gext = 1.0 a₀, Synchronism predicts σ ~ 10.5–14.5 km/s while MOND predicts σ ~ 10.9–40.9 km/s. The isolated predictions differ by nearly 3×. Observable with the NGC 5291 system (Bournaud et al. 2007, Lelli et al. 2015).
Novel PredictionSessions 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.