Quantum-Classical Criterion

The Quantum-Classical Criterion is the condition that decides when a substrate system behaves classically: when its phase correlation length is shorter than its thermal wavelength. The book uses it to mark the boundary between quantum coherence and classical behavior. The thermal wavelength is built from the Planck constant, the particle's mass, the Boltzmann constant and the temperature, so it shrinks as mass and temperature rise; comparing it with the length over which phase stays correlated tells whether coherence survives. Alongside the Mass-Dependent Coherence Time, with its cube-root mass scaling, it forms the book's framework for the quantum-classical transition and for signatures that set BPT apart from classical decoherence. A related Chapter 7.3 prediction holds the substrate correlation length constant below T▱ = ħ*ω▱/k_B. The formal statement is ξ⟢ < λΘ, meaning the system is in the classical regime, where ξ⟢ is the phase correlation length and λΘ the thermal wavelength. The book gives λΘ and ξ⟢ the dimension [𝕃]. It connects to Mass-Dependent Coherence Time, Thermal Wavelength, Decoherence Transition, Coherence Factor and Visibility Prediction.