2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217149We establish an exact differential equation for the operator describing time-dependent measurements continuous in time and obtain a series solution. Suppose the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured continuously from t = 0 to T, where E is a projector leaving the initial state unchanged and U(t) a unitary operator obeying U(0) = 1 and some smoothness conditions in t. We prove that the probability of always finding E(t) = 1 from t = 0 to T is unity. If $U(t) \neq 1$, the watched kettle is sure to `boil'.10 pages,latexQuantum PhysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext