short-time quantum evolution is quadratic, not linear.
that difference is the entire reason the watched pot never boils.
left: survival probability P(t) = cos²(t) for a two-level system. each measurement projects the state back to |ψ₀⟩. the quadratic short-time form P ≈ 1 − (ΔH)²t² means frequent measurements freeze the state: P → 1 as the number of measurements n → ∞.
right: hypothetical linear decay P(t) = e−t. the short-time form is P ≈ 1 − t. measurements do nothing — the total decay is the same regardless of n.