For processes of particle decay and inelastic scattering, quantum field theory (QFT) predicts well the probabilities of various final states for given initial states. Technically, this is described by the S-matrix, which is the unitary-evolution matrix describing the transitions from t=-infinity to t=infinity. But what happens in between at intermediate times? How exactly the initial particle(s) get transformed to the final particles? Is that a continuous process or an instantaneous jump? If it is a jump, when and where exactly does it happen? In the detector? Or much before, during the collision itself? Can QFT answer these questions at all? Are these questions really physically relevant? Are they physical questions, or purely philosophical ones? Here, I do not ask you to give, with a confidence, the final answer, but merely to express your opinion and intuition about it.