Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
AMA | October 2024
Sean Carroll
So that's the thing you have to be careful about, but we're putting that aside for right now. And the short answer is, one way of choosing the basis vectors for your spin is spin up in the z-direction and spin down in the z-direction. So in Hilbert space, spin up and spin down are orthogonal to each other. They're not pointing opposite, they're pointing perpendicular, okay?
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