[maccha]

Okay I'm confused about coupling in NMR.. let's say you have one hydrogen that is adjacent to two equivalent hydrogens... my textbook says that there are 4 possible signal outcomes because the equivalent protons could both be spin up, both spin down, or spin up spin down (and vice versa). What I'm confused about is, wouldn't both the equivalent protons always be in the same state? (ie both spin up or both spin down)

[research]

What I'm confused about is, wouldn't both the equivalent protons always be in the same state? (ie both spin up or both spin down)

I think the equivalent is not the thing that you think the equivalence here doesn't mean they are the same in their spin direction, it means only their chemical environment is the same and we don't know anything about their spins.