PolyHedral

Nothing endures but change. I needed to change it again.

I was sober, but very bored. Then again when I'm bored, bad things tend to happen.

You bad person. A few weeks back I actually ended up watching Avatar again because of your signature.

I love paradoxes too! My love for always being right is just more powerful.

Thanx for the great gorilla frubie!

If you know your way around metric tensors, energy conditions are usually put in terms of frame fields, which have a simple relationship to metric tensors.

Depending on how far along you are, you may already have the tools that you need to at least rudimentarily understand energy conditions. (I'm afraid that's the level I'm at; they haven't even been mentioned in classes yet!)

From what I understand it would normally be alarming if, say, the Casimir Effect satisfied negative energy conditions, but then they invented a cool lil' workaround to find the average energy condition for the Casimir Effect -- which turns out positive, thus saving the day. Now, the problem is that I don't sufficiently understand what it means to have an "average energy condition" (not specifically), but I do know that averaged energy conditions use the same tensors (stress-energy tensors) but rather than calculated with indefinite integrals they have definite integrals, but I'm really not sure what the area being calculated represents. As I said, we haven't done this stuff in my classes yet.

That one is actually seriously discussed in the literature and I've heard it talked about in my department (though, granted, by fresh faced interns and underdocs). I don't know what properties a negative mass particle would have aside from a different sign in front of its mass, but they're not supposed to be "permissable" due to our expectations of energy conditions -- but the reason they're still seriously discussed is because energy conditions are rules of thumb to rule out grotesquely unrealistic conceptions of matter; and since we know of a few things that do end up with negative energy conditions (dark energy, casimir effect) we know there are at least some exceptions to the rule of thumb already.

Otherwise, though, I can't offer anything really juicy. I could maybe find out by logging in to Linda Hall if my password still works between semesters. I'm actually pretty interested now in what what sort of particles could conceivably exist.

You make kitty sad. Very well, no more silly messages

That smells like a challenge, sir!

Pew pew pew pew!

What the hell do you think you're doing, son?

If you go back to the n-1 hypersphere example, let's say we have a north point and a south point. You could topologically see this as a square piece of paper (as in my drawing below) where the north point actually looks like a point but the south point is actually the entire perimeter of the square.

Essentially, but the two points are distinct -- it doesn't imply a cyclical universe, though exactly what is MEANT by that is vague. (For instance given infinite time if Poincare recurrence occurs with exactly zero delta^2 we end up with the same universe we had before; but is that the same universe?)

The infinitely large space is exactly the same thing as a point in projective geometry, but it's a different point than the one that actually looks like a point. Not different in principle, but you know what I mean -- it's a distinct, OTHER point.

Also there are concerns about the arrow of time and entropy: for instance, does time flow on both sides (or all available directions) from an entropic minimum? A timeline may not be able to encompass that, you'd start having it (imaginary time)

So, even though the linearity of a logarithmic timeline will have a "small" infinity at one end (a point at infinity), the other end will have a "large" infinity -- but that's also a point at infinity, even though it doesn't "look" like it when drawn linearly.
Ultimately an infinite logarithmic timeline is projective, so like in a painting, there will be a point where lines converge and then a "point" (i.e., the borders of the page) where lines ALSO converge.

Re: logarithmic time, either side you're hitting infinities of different sorts; but that means they're infinities of the same kind looked at from different perspectives. For instance, think of an (n-1)d hypersphere or something.

If you were to, say, define some increasing area (maybe by taking some definite integrals), you can see this visually by "coloring in" the defined area: inside an n-1 hypersphere you might start coloring in, say, green (on a white manifold). You'd start with a dot of green that grows and grows with white all around the outside, but as you keep going -- you'd suddenly find yourself pinned in a white dot surrounded by all the green outside!

http://i641.photobucket.com/albums/uu137/scarletdeliriums/infinities.jpg

I totally dominate your visitor messages. Looking around at penguin's, bird's and others, I think I'm a bit chatty in visitor messages. Maybe I should stop :X

After 7 CST sir, after 7 CST. Then there's only one supervisor to worry about rather than five!

I'm at work fool! That would be foolishly foolish!

Oh man, I totally understand. That's serious business that can't be avoided.

http://troll.me/images/victory-baby/internet-serious-business-thumb.jpg