OK. So your assertion is that an observed system behaves in exactly the same way as an unobserved system?When I leave the living room with the light on, it is generally still on when I come back in.
When I leave the living room with the light off, it is general still off when I come back in.
Or to put it another way; if I determine the eigenstate of a system to have particular value at a particular time, I may assume this system always to have had that particular value in the past and always will.