# [bi|sur|in]jective coordinates

Discussion in 'Physics & Math' started by RJBeery, Sep 29, 2010.

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1. ### prometheusviva voce!Moderator

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I agree, quarkhead was quite wrong to call you a village idiot. Calling you that does a huge disservice to village idiots everywhere.

3. ### Green DestinyBannedBanned

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Oh, I'm so glad you joined us, afterall, this arguement would have not been the same without you :bugeye:

You're another one who cannot talk. You were practically sucking quarkheads dick in that other thread, remember...? The one you called me rash that wouldn't go away, a bit like herpes?

You are all so full of witt. I want to be just like you one day.

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7. ### AlphaNumericFully ionizedModerator

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At physics, I am better than most but then statistically so would anyone who passed A Level physics.

So you failing on the most fundamental and basic concepts in the mathematics used everywhere in physics is something we should just let slide?

I had to explain it to you. You didn't correct yourself, you whined that I hadn't replied and after several days I eventually got around to replying and only after I pointed it out did you say "Ooops, I was wrong". Up until then you were working with the assumption that if I didn't pass comment on something it was right.

I don't mind people being wrong, I'm wrong all the time. What I do mind is you try to give the impression you're familiar and competent in areas of physics you then proceed to get utterly wrong. If no one here were sufficiently familiar with things like tensors, the Dirac equation and quantum mechanics no doubt you'd have carried on spouting nonsense indefinitely. The fact you wasted time on that pet 'theory' only to have basic mistakes pointed out to you left, right and centre, demonstrates your ability to self correct is not very well developed.

You don't seem to understand the difference between grasping something sufficiently to be able to explain it in your own words compared to blindly copying and pasting someone else's answer.

I didn't come up with the Dirac equation but I grasp the fundamentals of it so if asked to talk about it I could, off the top of my head, and be able to respond to questions someone might ask. Someone who is just reciting from memory the Wikipedia article would not be able to respond to questions or to consider implications or generalisations of the equation. You copied and pasted an answer without reference and hence it might appear to the casual reader that you understood the question well enough to provide an answer you understand the derivation of. If you'd just provided a link no one would have minded, as referencing other people's work is fine and a standard part of science. Neglecting to mention you don't understand the question and you're just copying and pasting is deceitful.

Rpenner, QH, myself, Guest etc provide references when we're just passing on information we don't fully remember or grasp (ie saying things like "Its in Chapter 2 of Polchinski somewhere") and for things at or below degree level we're sufficiently familiar with material to construct our own replies, putting our understanding into our own words.

If you can't see the difference between that and mindless copy/pasting then your grasp of rational thinking and the scientific method is even worse than I previously thought.

Injective means that no two coordinate values map to the same point in the space-time. The standard form of the SC metric includes terms which form a unit 2-sphere, $r^{2}d\Omega_{2}^{2}$. As the discussion in that thread and this one have covered, the unit sphere's standard coordinates have problems at the poles, ie when $\theta = 0,\pi$ because the azimuthal angle $\phi$ becomes degenerate, the points $(\theta,\phi) = (0,\phi)$ all map to the same space-time and likewise for $(\theta,\phi) = (\pi,\phi)$.

Oddly enough rockets happen to be something I am working on. Well, some small tiny part of the enormous set of technical issues which must be worked out in the design phase....

You really have a chip on your shoulder about people who've put in more effort than you in physics, don't you?

Yes, its not because you spout crap and try to convince people you know more than you do, its all because everyone who disagrees with you or corrects you are just brown nosing each other.

Its hardly our fault you spout so much BS. You brought up Pauli matrices in another thread and when pushed you admit you don't know anything about them. That then contradicts your claims of having 'investigated' the Dirac equation and when I call you on it and provide an opportunity for you to prove yourself you throw another hissy fit.

If everyone here is so terrible leave. Like you said you would but then, surprise surprise, you didn't.
Do you really think its wise to play the "Lets link to a post where he says something a little daft" game, given your track record? QH doesn't deny asking the occasional daft question, we've all done it. But unlike you QH tries to learn from his mistakes and puts in some effort. Not to mention he can actually do the sorts of maths he talks about, unlike yourself.

8. ### Green DestinyBannedBanned

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Most people pass their exams, even their physics. What makes you so special? Oh that's right... You are just better than everyone else. Period.

I won't let things slide with you, or quarkhead, or anyone in fact who dares to take this attitude on. I don't mind being corrected. It's when you have that gangly nerdy child in the background armwaving, pointing out every second you made a mistake.

Don't worry, I can do this too.

Em, no. I don't think we are talking about the same thing, unless you are mixing two instances together.

You're wrong all the time? Well my god, are you really?

And how the hell do you deduct, ''I don't learn from my mistakes'' - that was one thread, and I have not had any like that since. I learned from my mitakes, trust me.

I honestly don't remember doing that, but isn't that basically what you or guest, or anyone here does when they spout off hard textbook stuff? Your unoriginality in these arguements are getting tiresome.

Hahahah! Load of hypocritical bullshit now. Are you running out of interesting things to say?

Do you remember only a three or four days ago, you nsaid the Dirac Equation wasn't something you can explain?

Not true. There are many instances you do not pass-off references. I see it happen sometimes, but not all the time.

Temur would seem to disagree.

:sleep:

No, just you specifically. You do afterall, run about, making sure you point out other peoples errors, but never fully admit to your own.

Again, I don't mind being corrected. It's little annoyances like you in the background which pisses me off, and other people.

Again, a complete lie. I said, ''tell me if the theory works, then I will worry about the mathematics''.

You've played this card all too many times. I think the more you go over it in your head, the more you are wishing it said something else.

I'd hate to make you happy.

Why not? Repeated attempts at politely asking you to back off with the snarky comments seem to be, uneffective. So, in reply to this, I can be an annoying little shit too, and start linking to everyone elses incorrect statements. You do it all the time, so why not me?

And yeh, QH played that card too. Truth is, his questions were no more indifferent to mine, nor was I any more reluctant to learn. My back was up however, when the unecessery comments, assinine attacks and blatent trolling was issued left right and center, from you, and others.

So don't worry, you're not going to be singled out in this.

9. ### Green DestinyBannedBanned

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And when I said temur disagrees, I didn't mean with your post, I mean when you posted this:

Originally Posted by AlphaNumeric
you cannot use the Schwarzchild coordinates to describe every point in the manifold, they are not injective or surjective.

10. ### Green DestinyBannedBanned

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Temur said:

''Schwarzschild coordinates are injective but not surjective. They have singularities at the horizon and miss the part of the manifold inside the horizon. So you have to put an extra patch to see the whole picture just like on sphere.''

Contradiction there, would you not say, rocket scientist?

11. ### temurman of no wordsRegistered Senior Member

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Green Destiny, I was trying to speak your "layman" language as you requested, so what I said cannot be used against something that is in a more standard language. In any case I strongly feel that you have to go through more basic stuff first before getting muddled into this.

12. ### Green DestinyBannedBanned

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First of all the qoute wasn't to me, it was a discussion between yourself and RJBeery. Secondly I've never had a problem with you. But if you are telling me you have lied somewhere along the lines, in strictly a layman sense, then I would like clarified why the two statements are in clear paradoxical reference to each other:

''Schwarzschild coordinates are injective but not surjective.''

''you cannot use the Schwarzchild coordinates to describe every point in the manifold, they are not injective or surjective.''

I understand people here need to ''tone things down'', but I think the language here is pretty much clear. Either you are wrong, or he is. Which one is it?

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14. ### temurman of no wordsRegistered Senior Member

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Sorry it seems I confused you with RJBeery. Well it depends on what exactly you mean by the Schwarzchild coordinates, but the issue there was about the Schwarzchild coordinates not being able to cover the entire manifold. So this conclusion is achieved either way. Now since you want to focus on something different, if you take the 2-sphere cross the Schwarzchild radial coordinates then that is "injective", but if you take the spherical coordinates on the 2-sphere with range, say [0,2pi]x[0,pi] then it is not "injective" because of the poles and the "0-meridian" will not have unique coordinates. Note that I used double quotes for "injective" because coordinate mappings are usually understood to be the inverse of what you are talking about. What you are talking about can be said to be a parameterization.

15. ### Green DestinyBannedBanned

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So technically, you are correct.

16. ### temurman of no wordsRegistered Senior Member

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How did you deduce that?

17. ### Green DestinyBannedBanned

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How are you not?

You may need to numb this down for me.

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Oh wait..

19. ### Green DestinyBannedBanned

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''but if you take the spherical coordinates on the 2-sphere with range, say [0,2pi]x[0,pi] then it is not "injective" because of the poles and the "0-meridian"''

Ah I see. So, basically, this does not apply to black holes?

20. ### temurman of no wordsRegistered Senior Member

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I need to ask you what is Schwarzchild coordinates?

21. ### Green DestinyBannedBanned

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If I do, I want you to numb this down for me, explain why your statement concerning injective coordinates cannot be used in the sense alphanumeric used them.

The schwarzchild coordinates are coordinate systems used in the static model of the spherical object in question.

22. ### temurman of no wordsRegistered Senior Member

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How many coordinates (like x,y,z in the case of the usual coordinate system) does this system have? What are the meanings of each of them?

23. ### Green DestinyBannedBanned

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When you started talking about spherical coordinates, and then saying it cannot be injective, I thought you were assuming something, but I have obviously picked you up wrong.

Please explain again. Note, I have never done a lecture course on black holes, so I will require a simple answer.