> It doesn't seem to explain why it's a complex Hilbert space. It's surprisingly difficult to motivate complex- (rather than real-) valued quantum mechanics. S

> It doesn't seem to explain why it's a complex Hilbert space. It's surprisingly difficult to motivate complex- (rather than real-) valued quantum mechanics. See eg https://www.scottaaronson.com/blog/?p=4021 https://www.scottaaronson.com/blog/?p=4021, for example. (As they point out, though, motivating "not quaternions" is pretty easy at least.)