Hi, I have a question, As it is said in QM, if two operators commute, they have so many common eigenstates that they form a basis. And the inverse is right. Now there is the question, if A,B,C are operators, [A,B]=0, [A,C]=0, then is "[B,C]=0" also right? If we simply say A and B, A and C both have common eigenstates, so B and C have common eigenstates, so [B,C]=0, it seems to be right. But in QFT, if x,y spacelike, then [\phi(x),\phi(y)]=0, if the above is right, then we can find a point z which is spacelike according to two non-spacelike point x,y to make any non-spacelike [\phi(x),\phi(y)]=0. It looks like a paradox. thank you!