What does it mean to be Covariant?

Again, equating vectors with scalars simply doesn't work. I know at least 3 people have told you that, so why do you persist in doing it?

 

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Noted, again.

Why do people insist on asking me trivia questions if they will never be satisfied?

 

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Simply as an observer, perhaps they'd be satisfied if you gave them the right answer.

 

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And if I do give them the correct answer, they still try and pick a fight with it. There is no winning. Such as my post on Hilbert spaces to prove I knew what it was, is a perfect example.

 

A perfect example to show that you have no idea what a Hilbert space is.

I'll break it down for you again: Your post had no explanation whatsoever of what what an inner product space is, or what a complete metric space is. None. Seeing as these are absolutely central to the definition, and that your post was meant to

the only conclusion one can draw is that you do not know what a Hilbert space is. (This is strengthened by the slew of idiomatic errors and non-sequiturs in the post as well.)

Your confusion of vectors with scalars here just serves to show that you don't know what a vector space is, either.

 

I'm basically doing what I asked by giving you this clue, but you need to use that \(\mathbb{1} = \int d^3 x | x \rangle \langle x | \)

The rest is literally one more step, and if you know about Hilbert spaces in the context of quantum mechanics, then you must have seen this at least once before.

 

Well, equating state vectors with complex numbers is certainly not the way to do it, and it isn't even a defined mathematical operation.

 

I never equated anything with anything. I think my response to alphanumeric was more than clear, stating that it was one example I literally pulled out the air for no reason.

 

If these identities are known, Why are you all lynching me? Seriously? What the fuck have I done?

I can't even write a small paragraph on some of the preliminaries of a Hilnbert Space without a hundred questions being posed - I was never here for that, but all of you constantly subject me to it. I don't think I can put up with it anymore.

 

Oh really?

Two examples of you equating vectors (the \(|\psi\rangle\)'s) and scalars.

I have one question for you (not a hundred, just one). Why do you want to be seen as knowing about theoretical physics? Believe it or not, and it's a bitter pill to swallow for all physicists, physics is not seen as being cool by the majority of the population so you're not really doing anything for your cred by claiming it. If you're going to claim something, why not go for an uber cool subject like media studies or something?

 

I never exactly equated it did I? You wanted me to take a wave mechanical approach, and the only ones I had heard of was the above, I even asked you what you had in mind. :bugeye:

Look, it's ok. You can stop your speil. If I ever did have my heart in physics, trust me, I would be studying it alongside you. What I have been doing is doing such on my spare time. I came here as a novice, made that clear, but it still fell on deaf ears, trying to state I made it out to be more.

As I said, I am sick to teeth about these lynching mobs. Even funkstar is trying to make it out you need to know a great deal more about Hilbert Space to say you know what it is - I disagree - I'm not going to start teaching on them, because yes, then I would need to know how the metric fit in to it, but to be honest, I don't think it would be very hard to find out how. As I said, I think I've had enough of this place, for a while.

Well done, you didn't need to get me banned like a few of you have suggested, or even prove I am a sock-puppet, as the theme went for a while.

 

Sorry dude, you obviously don't what a hilbert space is if you don't know how a metric fits into it. I'm not here to lynch you though. which brings me to my point:

I don't think you should leave the site. You're obviously not an idiot, some of your posts on the more philosophical topics are decent. Just do what I do on this site, stick to what you know, or rather, don't stick to what you don't know.

 

I know how a Hilbert Space fits into a metric, that is relatively easy. But, I need to be careful right now. I won't be home until another two days, and I have none of my notes on me. I usually write my work out in jotters in which then I commit them to memory. What I wrote on Hilbert Spaces was purely from memory - but I obviously never wanted to slip up, especially by trying to remember something which I could always go back and check. But I obviously cannot right now.

As for the philosophical side of my posts, thank you. I do try. But I never said I would leave, I said maybe a break would do... I don't know what I want to do. I am just sick generally of being lynched every single day, if not by Prometheus, Guest or funk, it's bleedin alphanumeric who knows exactly how to push your buttons. I think he's became an expert at that since his time here, and perhaps before?

I just don't know anymore. I need some time to think.

 

Green Destiny: the easiest example I know about of an Hilbert space is \( \mathbb C^2 \). I don't know if it is the simplest though, but it's a good place to start.

 

I take it you meant \(\mathbb{C^2}\) (just the latex).

I will have to admit, I've never seen that short hand notation. Can you give me an example?

 

I had a little incline where to look. Apparently the norms I have been speaking about defines an inner product \(|f|= \sqrt{<f,f>}\) which turns the Hilbert Space into a complete metric space.

 

This is a very confused post. The inner product defines a metric, not the other way round. This norm in turn can turn H, the inner product space equipped with the associated product, into a Hilbert space if the metric is complete in the sense of Cauchy sequences.

A Hilbert space is an inner product space that admits a complete norm.

 

You're right, I wrote that a little confusingly. I've been reading a little more nevertheless inbetween.

So... what is the \(\mathbb{C^2}\) notation? I'm interested, as I have not seen it before.

 

You've still been unable to answer my question.

Why do you do this? You've made umpteen accounts on this forum and made the exact-same fool of yourself with each one of them.

 

Have you learned about vector spaces before?