Phase Transitions

Core Prediction

The coherence function predicts three distinct regimes, with transitions between them. The most interesting physics happens at the boundaries — especially at γ ≈ 1.

Quantum
Boundary
Classical
γ = 2 (single electron)γ ≈ 1γ → 0 (macroscopic)

The γ ≈ 1 Boundary

This is where Synchronism makes its strongest chemistry prediction. At γ ≈ 1 (Ncorr ≈ 4), the coherence function has maximum curvature — small changes in density produce large changes in coherence. This is why:

1,703 chemical phenomena were tested. 89% show γ values within the predicted boundary region. See the full chemistry analysis →

Transitions in Cosmology

The same framework applies to larger scales. Galaxy rotation curves show a transition at ρ ≈ ρcrit from Newtonian (high density inner region) to MOND-like (low density outer region). This is the astrophysical phase transition.

What Doesn't Work

Critical Exponents: 2× Off

Real phase transitions have universality classes with specific critical exponents. Synchronism's mean-field-derived tanh gives the wrong exponents by a factor of ~2. The function captures where transitions happen but not how they unfold.

Next: Scale Invariance →Interactive Visualizer

Prerequisites

Understanding these concepts first will help:

The γ Parameterγ = 2/√N_corr: why 2, why √N

Related Concepts

The γ ≈ 1 Boundary1,703 phenomena at the quantum-classical edgePhase Transitions in ChemistryMelting, boiling, superconductivity, superfluidityPhase Boundary VisualizerInteractive γ < 1 / γ ≈ 1 / γ > 1 diagram