Critical Density
5% Error vs EmpiricalThe critical density ρcrit is the density at which the coherence function transitions from quantum (C → 0) to classical (C → 1). It's not a free parameter — it's derived from the flat rotation velocity Vflat of the system.
The A Parameter
A comes from fundamental constants: α (fine structure constant), G (gravitational constant), and R₀ (a characteristic scale). The derivation yields 0.029, compared to empirical fits of 0.028 — a 5% error from first principles.
Physical Meaning
Every gravitationally bound system has a characteristic rotation velocity Vflat — the velocity at which its rotation curve flattens. This velocity encodes the total mass and size of the system. The critical density is where internal gravitational binding energy equals the coherence threshold.
Below ρcrit: the system is under-dense, loosely bound, quantum effects persist. Above ρcrit: the system is gravitationally coherent, classical behavior dominates.
Connection to MOND
From ρcrit = A × Vflat² and the coherence function, two cosmological results emerge:
MOND's a₀
10% error vs Milgrom's value
ValidatedFreeman's Σ₀
12% error vs Freeman's value
12% Error