Heisenberg Uncertainty Principle

[edpell]

Is the Heisenberg Uncertainty Principle as statement about the state of a particle or only a statement about what can be observed about a particle?

 

[chafelix]

Rather the second one. Actually it simply says that you start with a state. Acting with an operator on it measures whatever the operator corresponds to (energy, momemntum,position etc) After the measurement the particle is in an eigenstate of that operator(one that corresponds to the eigenvalue you just measured). Now you want a second measurement, so you act with a second operator, different from the first. If the two operators commute, they may have a common set of eigenvectors(i.e. states), so acting on an eigenstate of the second operator with the second operator will measue the eigenvalue of the second operator, but not change the state. If they do not, then you will force the state to CHANGE into an eigenstate of the second operator and after your measurement you know the state and the value of the observable correspoinding to the second operator. But then, you do not know the value of the first, because the state that occurred when you did the first measurement has CHANGED