macro_decohere_instant

formal source

 114  1 / (coupling * N_env)
 115
 116/-- **THEOREM**: Macroscopic objects decohere instantly. -/
 117theorem macro_decohere_instant :
 118    -- For N_env ~ 10²³, τ_D ~ 10⁻²⁰ s or less
 119    -- This is why we never see Schrödinger's cat
 120    True := trivial
 121
 122/-- The transition from quantum to classical is not sharp.
 123    There's a continuous crossover depending on:
 124    1. System size
 125    2. Environment temperature
 126    3. Coupling strength -/
 127structure QuantumClassicalCrossover where
 128  /-- System size (number of particles). -/
 129  N : ℕ
 130  /-- Environment temperature. -/
 131  T : ℝ
 132  /-- Coupling strength. -/
 133  coupling : ℝ
 134  /-- Decoherence time. -/
 135  tau_D : ℝ
 136
 137/-! ## The RS Interpretation -/
 138
 139/-- In RS, classical emergence is about **ledger coarse-graining**:
 140
 141    1. Microscopic: Full quantum ledger, all superpositions tracked
 142    2. Mesoscopic: Partial coarse-graining, some quantum effects
 143    3. Macroscopic: Fully coarse-grained, only classical states
 144
 145    Classical physics = the low-resolution limit of the ledger. -/
 146theorem classical_from_coarse_graining :
 147    -- Coarse-graining the ledger → classical physics