Why homologous proton don't split signal of each other in proton nmr?

[Ahmed Abdullah]

Each proton has it's own magnetic field so it should effect the magnetic field of all nearby proton whether it is homologous (equivalent) or not. I don't understand how this discrimination arise?
How a proton understand - "that proton is like me so I shoudn't ... ... ... " I mean it's ridiculous. In organic chemistry textbooks it says that, non-equivalent proton split signal because they can align either toward or against the magnetic field of a given proton. Now I don't understand why it should only apply to non-equivalent protons? Not to equivalent protons?
I am not really getting it. Please help me.
Can anyone explain the theory, please?

 

[Ahmed Abdullah]

Is it possible that homologous or equivalent protons are somehow connected with each other in the sense that they all change orientation in synchronous fashion and can't do it independently from each other?

 

[DrDu]

Of course the protons see the field of each other. Consider two equivalent protons. As the coupling commutes with total spin, I can combine the two spins into a siglet state (S=0, spins anti-parallel) and 3 triplet states (spins parallel). Without magnetic field, the triplet states will be degenerate but their energy will be different from the energy of the singlet state, because in the triplet state, the spins are parallel while they are anti-parallel in the singlet state.
Swiching on the magnetic field, the triplet will be split up into 3 with M=-1, 0 , 1 which are equidistant. The radiofrequency can only induce transitions within the triplet, so that you only see one line. However, if the two protons are slightly different, then there can also be transitions from the singlet (M=0) to the triplet states with M=+1 and -1.
However these two lines will be very weak for nearly equivalent protons. Also the two transitions within the triplet from M=0 to M=1 and from M=-1 to M=0 will not be exactly degenerate, because the singlet state and the M=0 state of the triplet will "repell" each other. If you try to figure out the situation, you will see that it describes the "roof effect", i.e. two nearly degenerate intensive lines and two lines which are further off and which are very weak.