Experiment description: Let us have a slight modification of the famous thought experiment, in which the cat is killed only if a particle decay is detected in a fixed time interval, say from 0 to 1 s. Let the box with the cat, the deadly device, and the radioactive sample with the detector be an isolated system, which at t = 0 s is in a pure quantum state (the initial state), which is known (although very complicated and practically impossible to determine). The quantum state of the system at t = 1000 s (the final state) is given by the time evolution operator, so it is a known pure state as well. Let us have an observable A indicating, whether the cat is alive or dead, but no measurement is going to be made. Question: Is it true that for a majority of initial states meeting the experiment requirements (i.e. the radioactive substance amount is with high probability in the "interesting" range, etc.), the expectation value for A in the final state is very close to one of the two discrete values, getting even closer to that discrete value as time advances? Of course, it will be "alive" for some initial states and "dead" for others. Motivation: I feel that the mutual interaction of the parts of the system will cause some sort of quantum decoherence, so no observer is needed: The isolated system will make the "almost-decision" itself. Am I right?