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So basically I'm wondering why the different protons in ...let's say trans-stilbene do not couple with each other. I'm aware of the fact that they are chemically and magnetically equivalent. They can be interconverted via C2-symmetry operation and should therefore just give a singlet in the spectrum.
Nevertheless, according to my actual knowledge about NMR theory the splitting of a signal derives from a proton A that experiences the magnetic field of an adjacent proton B. Therefore it results that according to the spin state of the neighboring proton B (alpha or beta-state) a higher and lower energy level exists for A. One in which the magnetic field of the other nucleus is aligned parallel one in which it is aligned antiparallel to the nucleus B.
Therefore I don't really understand why in for example stilbene the protons do not experience this additional force from the other proton at the double bond.
I would be very grateful for any explanation!