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.

Adjust γ and ρcrit to see how the coherence function C(ρ) = tanh(γ · log(ρ/ρcrit + 1)) responds.

0.000.250.500.751.00C=0.50log₁₀(ρ)C(ρ)

Quantum (γ > 1.4)

Key Values

C(ρcrit)

0.8824

C(10ρcrit)

0.9999

C(100ρcrit)

1.0000

Related Concepts

The Coherence FunctionC(ρ) = tanh(γ log(ρ/ρ_crit + 1))The γ Parameterγ = 2/√N_corr: why 2, why √N