Why don't chemically equivalent hydrogens on adjacent carbons split the 1H NMR signal? There appears to be an answer here, but I'm having trouble understanding it because I cannot rationalize what happens with the magnetic field.
Let's say we're analyzing acetylene. When we subject the molecule to an external B-field, both (equivalent) protons have 2 possible spin states. For each proton, I would expect that the other proton's magnetic moment may either augment or oppose B0, causing a doublet. When we look at the signal for the other proton, it's the same story--I would expect 2 peaks identical to the 2 for the first proton (effectively doubling the integration).
Where have I gone wrong in extending spin-spin coupling to identical hydrogens? Why does the magnetic moment of adjacent, equivalent protons not affect the transition energy?
Edit: I asked my organic chemistry professor this question, and his response was that there does exist spin-spin coupling of identical protons, but the coupling constant is equal to 0. The reasoning involved quantum mechanics that went over my head.