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LilArrin In reply to Dragondestruction [2012-09-24 04:46:58 +0000 UTC]

Oh, I try to put a lot of effort into birthday pictures. I wonder what yours will look like...?

Let's just say I'm already studying dragon anatomy and doodling some practice scribbles during lecture to prepare.

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Dragondestruction In reply to LilArrin [2012-09-24 04:52:57 +0000 UTC]

I see, well good luck in the preparation. You've still got quite a bit of time in which to do it. A bit under four months.

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LilArrin In reply to Dermuda [2012-09-24 04:44:25 +0000 UTC]

It's only ceremonial armor set. The tail blade is probably dull.

Or you can pretend it has a perfectly discontinuous derivative at the edge, even if it's physically impossible, and proceed to quake with fear.

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Dermuda In reply to LilArrin [2012-09-24 20:18:33 +0000 UTC]

That would be one effective weapon. Although I get the feeling that there would be some pretty intense static charge buildup on those edges …

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LilArrin In reply to Dermuda [2012-09-24 21:12:45 +0000 UTC]

And one can also wonder how the edges are gonna look like in phase space, considering...the edges have to be highly localized in position.

...I'm so happy I can talk about such silly physics rabble with another person. It genuinely makes me smile when I realize that you can share in the nerdy humor. Only if the grad students I work with were like you.

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Dermuda In reply to LilArrin [2012-09-24 22:06:41 +0000 UTC]

Right back at you! I work with a group of very serious people which is great for research, but I do miss talking about physics like this. You're not the only one who's smiling!

You've got me thinking, though. An infinitely sharp blade is strictly a 2D object, so I think there'll be some problems in even defining a 3D phase space for it. You're going to be dividing by zero somewhere or else you've got Uncertainty problems. Looks like the blade will be infinite in extent …

Not to mention that losing the dimension will mess with any field lines – there's no way of defining direction for them in 3D, so they'll just splay outwards from the edge. So if you build up enough charge, you'll produce a cylindrical discharge – which would look impressive. I think gravity will get a bit confused too!

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LilArrin In reply to Dermuda [2012-09-27 18:00:25 +0000 UTC]

I'm sure we'll have tons of uncertainty problems, considering the localization. We'll have infinite uncertainty in momentum in at least one direction. Probably just one direction at the edge, but in two directions at the tip. Considering that, it'll get dull in an instant.

But yea, just look at how silly physics gets once we consider a hilariously unreasonable system like an infinitely sharp blade, heh.

Still, I don't think having wacky field lines will be too much of a problem, since I'm sure we've both analytically solved problems involving boxes, cylinders, and flat planes...all of which have very sharp edges for the sake of idealization.

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Dermuda In reply to LilArrin [2012-09-28 23:32:56 +0000 UTC]

I guess I was thinking of a very specific case – that of a infinitely sharp edge on the end of a taper that becomes infinitely thin. We can still have a discontinuous derivative on the edge and have it subtend an angle, and yes in that case there won't be any problems with the field lines. Such a system is indeed 3D – and it still functions perfectly well as a blade, so I was generalising too much! I'm still not sure about the tapered case, though. The edge here is locally 2D, and I have a feeling that an object that is locally perfectly 2D will cause all sorts of problems. Although it would also be very fragile in most directions, so probably not actually terribly useful!

But yes, infinity (and, for that matter, zero), is always a fun concept. Situations like this make me think of Renormalization, an approach that I always find slightly amusing as it looks so much like fudging at first glance. You deal with a system that has properties that tend to infinity by considering additional terms that are also infinite and that all cancel to give a finite answer. Hmm. It's all above board in the detail, of course, but still …

As you say, the blade will dull as the momentum Uncertainty 'melts' the tip. However, this isn't necessarily a problem. The tip will only be infinitely sharp for an instant, but if we constantly reform the tip at every instant with new material we could maintain the infinite sharpness without breaking any laws. The actual amount of material we would need to replace would be tiny, so it probably wouldn't be physically impossible to set up a system connected to a small tank of material that does this all in an automatic, dynamic way. Maxwell's demon would have a field day …

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