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**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?