> madhadron doens't know what he's talking about.

Not sure why you're saying this when you end up saying pretty much what madhadron said, i.e.: "To be excruciatingly precise, it's a ray in Hilbert space"

I get that madhadron doesn't explain themselves but still... There's some irony here.

Because the difference between a ray and a vector is so minor that the words are effectively interchangeable, and in actual practice the word "vector" is invariably used. No one ever talks about the "quantum state ray." It is always the "quantum state vector."

Also, simply saying "no it isn't" with no further explanation in response to any comment just obnoxious. It's essentially saying, "You're wrong, and I know why you're wrong, but I'm not going to tell you." It's not constructive, and anyone who does it deserves to be smacked down hard, even if there might be a tiny nugget of truth hiding underneath their oblique self-aggrandizement.

> anyone who does it deserves to be smacked down hard

I was trying to hint that there was something you were overlooking in your explanation. Probably not an effective tactic in this medium.

But thanks to your fine example, I will in future make sure to lay out things in exquisite detail while belittling the person I am replying to.

No, I hadn't overlooked it. I was providing an answer appropriate to the audience and the context. And that answer was actually correct. Not only was your answer not constructive, it was also flat-out wrong.

I actually do. It's a spinor. It doesn't transform the way a vector does.

A spinor is a vector. It's not a vector in 3-D space, but that's true of all quantum state vectors, not just spinors.

The way the OP was using vector implied a 3D Gibbs-Heaviside vector, not an element of an arbitrary vector space.

Hogwash. Here is the full context:

> Is it a magnitude or a vector?

Of those choices, vector is clearly the more correct one.

Here is what a constructive response would have looked like:

"Lisper is correct when he says it's a vector and not a "magnitude" (the more common term is "scalar"), but there is an important subtlety: it is not a vector in 3-D space. Instead it is something called a spinor (https://en.wikipedia.org/wiki/Spinor) which is a kind of vector, but behaves differently than vectors in 3-D space in some important ways. For example, if you rotate a spinor 360 degrees you do not get back the same spinor you started with. You have to rotate a spinor 720 degrees to get back to where you started.

And in fact if you really want to get into the weeds, in the mathematical formalism of QM these are actually things called "rays" in something called a "Hilbert space" but no one cares about that, not even physicists, which is why all physicists refer to these things as "state vectors" rather than "state rays" even though there are some formal differences between vectors and rays. But only people who want to publicly exhibit their superior knowledge (as opposed to engaging in effective pedagogy) would ever bring up such trivial details."

How? Take people's word. If they say vector, assume they just mean some element of a vector space. No need to be rude to somebody based on an assumption.

Any textbook exposing this mathematical formalization with rays? I'm interested by the mathematical aspect as well.

Sure, any intro QM text will cover this. Griffiths is the canonical one.