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Ok, so if you know the interactions, etc., you can calculate from time0 the probabilities for certain results at say time8.

But say, however, we perform a measurement before time8. Will the original predictions for time8 still hold if a measurement is performed prior to that time? Or will it be different - in that case, what information do you need from the measurement, to plug into the unitary operator (which will include interactions, etc.) to find the new probabilities at time8?