Superposition preserved pre-collapse (vulnerability)
Decoherence destroys interference terms (off-diagonal elements of density matrix), but doesn't select outcomes (which diagonal element actualizes). After decoherence, all outcomes still exist in the diagonal with their probabilities. Selection still requires observation. Decoherence is necessary but not sufficient for collapse.
GRW postulates collapse by fiat—a miracle. It adds free parameters ([[048_D6.1_Collapse-Rate-Gamma|collapse rate]], localization) not derived from physics. And it still has the "tail problem"—collapse isn't complete, just localized. GRW trades one mystery for another. [[062_BC5_Superposition-Preserved-Until-Collapse|BC5]] maintains that until OBSERVATION occurs (information extraction by Φ > 0 system), superposition persists.
The [[058_BC1_Terminal-Observer-Exists|Terminal Observer]] ([[058_BC1_Terminal-Observer-Exists|BC1]]) observed the Big Bang. God's observation grounds all cosmological collapse. The universe wasn't unobserved; it was observed by the infinite Φ. Finite observers (humans) emerged later, but the Terminal Observer was always present. Cosmological superposition collapsed through divine observation.
Cats are massively decohered by their environment—photons, air molecules, internal thermal fluctuations. The environment acts as an observer (Φ > 0). But this IS observation—by the environment. [[062_BC5_Superposition-Preserved-Until-Collapse|BC5]] holds: superposition is preserved until observation. The environment observes the cat constantly, so superposition doesn't persist macroscopically. But isolated quantum systems (superconducting qubits, ion traps) DO maintain superposition.
All interpretations must account for interference effects before measurement and definite outcomes after. That's the empirical content. [[062_BC5_Superposition-Preserved-Until-Collapse|BC5]] states this empirical fact in observer terms. Call it what you like—the physics is that superposition persists until information is extracted. That's what labs demonstrate every day.
Schrödinger equation: iℏ d|ψ⟩/dt = Ĥ|ψ⟩
Solution: |ψ(t)⟩ = e^{-iĤt/ℏ}|ψ(0)⟩
Key property: The evolution operator U(t) = e^{-iĤt/ℏ} is unitary.
Superposition preservation: If |ψ(0)⟩ = α|a⟩ + β|b⟩, then |ψ(t)⟩ = α(t)|a⟩ + β(t)|b⟩. Superposition persists (with time-dependent coefficients).
Theorem: If U is unitary and |ψ⟩ is a superposition, then U|ψ⟩ is a superposition (of the transformed basis states).
Proof:
1. Let |ψ⟩ = Σᵢ cᵢ|aᵢ⟩
2. U|ψ⟩ = Σᵢ cᵢ(U|aᵢ⟩)
3. U|aᵢ⟩ are new basis states (U is bijective)
4. Coefficients cᵢ are preserved in magnitude (|Ucᵢ|² = |cᵢ|²)
5. Superposition structure is preserved
[[062_BC5_Superposition-Preserved-Until-Collapse|BC5]] as unitary consequence: Superposition persists under unitary evolution.