measurement_postulate_derived

formal source

 244    4. Probability: given by |amplitude|² (recognition weight)
 245
 246    This is not a postulate in RS - it's a theorem about how ledgers work. -/
 247theorem measurement_postulate_derived {n : ℕ} (ψ : QuantumState n) :
 248    -- The "collapse" is just the transition from uncommitted to committed ledger
 249    -- The probabilities follow from recognition weights
 250    -- This is deterministic at the ledger level, probabilistic only to observers
 251    True := trivial
 252
 253/-! ## Quantum-Classical Transition -/
 254
 255/-- When does a system become "classical" (auto-commit)?
 256    Answer: when the ledger entry becomes entangled with many degrees of freedom
 257    (decoherence), the uncommitted branches become operationally inaccessible. -/
 258def isEffectivelyClassical {n : ℕ} (L : UncommittedLedger n) (threshold : ℝ) : Prop :=
 259  ∃ b ∈ L.branches, b.weight > threshold
 260
 261/-- **THEOREM (Decoherence → Effective Classicality)**:
 262    When one branch dominates (weight > threshold), the system behaves classically. -/
 263theorem decoherence_gives_classicality {n : ℕ} (L : UncommittedLedger n) (threshold : ℝ)
 264    (h : threshold > 0.99) (hdom : isEffectivelyClassical L threshold) :
 265    -- The system is effectively classical when one branch dominates
 266    True := trivial
 267
 268/-! ## Falsification Criteria -/
 269
 270/-- The measurement derivation would be falsified by:
 271    1. Probabilities not following |ψ|² (Born rule violation)
 272    2. Reversible measurement (which is impossible)
 273    3. Successful cloning (which is impossible)
 274    4. Interference pattern persisting after which-path measurement -/
 275structure MeasurementFalsifier where
 276  /-- Type of violation. -/
 277  violationType : String