Quantitative Laws of Quantum Decoherence in Confined Biological Nanoscale Systems: A Localized Model of Compressible Vacuum Medium

This paper proposes a localized effective model of compressible vacuum medium to explain the anomalous long-lived quantum coherence observed in hydrophobic protein nanocavities. Four quantitative scaling relations are derived from geometry and density constraints of nanoscale confinement: coherence lifetime scales with cavity radius as τ=Arτ=Ar, decays quadratically with anesthetic concentration, increases quadratically with decreasing temperature, and exhibits a two-stage Gaussian-to-exponential decoherence transition. All predictions are directly testable by femtosecond ultrafast spectroscopy. The model introduces a saturation density bound for localized vacuum media, which also provides a physical cutoff preventing the stable formation of infinitely subdivided spatial structures analogous to abstract Kakeya sets.