Coherence Explorer
What you're seeing
This tool plots the coherence function — the single equation at the heart of Synchronism. It takes a density (ρ) and returns a coherence value between 0 (quantum/random) and 1 (classical/ordered).
γ = 2/√Ncorr controls the transition sharpness. High γ (> 1.4, few correlated particles) = quantum regime, γ ≈ 1 = the boundary where chemistry and biology happen, low γ (< 0.6, many correlated particles) = classical regime.
What to notice: Move γ from 0.5 to 2.0 and watch the curve flatten. At γ ≈ 1, the transition from quantum to classical is steepest — this is where the most interesting physics happens.
Why γ is decoupled from Ncorr here: This tool sets γ directly to explore how curve shape depends on the sharpness parameter, independently of any physical system. The relationship γ = 2/√Ncorr links γ to real systems — use the γ Calculator to enter a physical Ncorr and see where a real system lands.
Adjust γ and ρcrit to see how the coherence function C(ρ) = tanh(γ · ln(ρ/ρcrit + 1)) responds.
Quantum (γ > 1.4)
Higher γ = sharper, more abrupt transition. Lower γ = gentler slope, more collective behavior.
Ncorr = 1.0 — mean-field approximation weakens as Ncorr approaches 1
Lower ρcrit = transition starts at lower density (shifts curve left). Higher = transition occurs at higher density.
Key Values
C(ρcrit)
0.8824
C(10ρcrit)
0.9999
C(100ρcrit)
1.0000