I'll temper your statement about uncertainty. You can measure whatever you want, but if your observables are incompatible, you can't say it's still in the eigen

I'll temper your statement about uncertainty. You can measure whatever you want, but if your observables are incompatible, you can't say it's still in the eigenstate you measured it in afterward each measurement. Then again, people have to explain what it means when they say "measure at the same time" means. If it means "system A is in eigenstate |1> and eigenstate |a>" where |1> and |a> are eigenstates of different (non compatible) operators the answer is no.