i think we maybe are mixing measuring with the actual evolution of the state. you cannot observe a quantum system without altering its state. also, there is no

i think we maybe are mixing measuring with the actual evolution of the state. you cannot observe a quantum system without altering its state. also, there is no such thing as an isolated quantum system. this is true even for classic mechanics but we are cool with it since the measurement error is insignificant compared to what we measure. i believe that the number of states a quantum system goes through is finite, albeit maybe very very large and the way we are treating it is based mostly on the tools we have not what is happening in reality.