Quantum Decoherence & Pointer States

How the classical world emerges from quantum superposition
ρ(t) = Σᵢⱼ ρᵢⱼ(0) |i⟩⟨j| · e^{-Γᵢⱼt} — off-diagonals decay
Decoherence Γ 0.050
Initial θ π/2
Initial φ 0
Coherence |ρ₀₁| = 0.500
Decoherence explains why we never observe quantum superpositions in everyday life. Interaction with the environment entangles the system with many inaccessible degrees of freedom — the off-diagonal elements of the density matrix (quantum coherences) vanish exponentially. Pointer states (Zurek 1981): the environment selects preferred "classical" basis states that are most robust to decoherence. Einselection = environment-induced superselection. This is not wave-function collapse — the global state remains pure.