Question about measuring observables. If have 2 particle system the particle seperation Q=x1-x2 and total momentum P=p1+p2 are observables of the system as a whole and are commuting. How do you measure these observables. It would seem the only way to measure the seperation is to measure the individual particle positions x1,x2 and subtract them. With the total momentum you measure the particle momentum's seperately and add. However, since Q,P commute you should be able to measure Q,P simultaneously. But if do it by measuring individual particle properties you have violated uncertainty principle since you have both position and momentum for each particle. So is there some way to measure Q or P without determining x1 and x2 or p1 and p2 or are Q and P nonmeasurable and only really mathematical fictions.