Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
AMA | October 2024
Sean Carroll
Because those are the two states to be in, and you're in one or the other. And so that is the entirety of the Hilbert space. Alpha times spin up plus beta times spin down. So where does the spin in the x-direction come from? If you have the x-direction, maybe you can measure spin left or spin right, right? How does that fit in? you can derive it from spin up and spin down.
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