I have always wondered about applications of Algebraic Topology to Physics, seeing as am I studying algebraic topology and physics is cool and pretty. My initial thoughts would be that since most invariants and constructions in algebraic topology can not tell the difference between a line and a p...
See this Edinburgh topology and geometry website? The blue torus is meant to be an electron. See stuff like this and this and this. Hu talked to Atiyah about that at ABB50/25. Atiyah is at Edinburgh.
That the heuristic defintion of the characteristic as "corners-edges+faces" for a polygon gives this is very easy to see in the cellular and simplicial approaches to homology.
And see this TQFT website? See the blue trefoils at the top? (They're always blue). Well, start at the bottom left and go round clockwise calling out the crossing-over directions: up down up. Now where have we heard that before?
@JohnDuffield Do you really think the fact that some websites/videos show blue pictures has anything to do with whether or not they're talking about electrons? It seems quite irrelevant to me
@0celo7 I don't get what that has to do with your profile picture or you hating cats
But it's funny :D
user54412
7:56 PM
@JohnRennie Re: that MO question. Note that mathematicians who don't do physics define "local" w/ regard to neighboring points, whereas in GR "local" means "can be done in the tangent space of 1 point (and then extended to nearby tangent spaces with epsilon error due to continuity)." I think one way of explaining all this to the mathematicians is that there is an interchange of limits going on in the background.
@JohnRennie (con.) I'm pretty sure you can't physically measure the Riemann tensor or its derivatives without an extended region of spacetime -- just as you allude to with the bit about parallel transport. You can then take limits of this result as the region shrinks to a point. But since each and every region contained some points inside the horizon and some points outside, it's no surprise that you can construct a quantity that "detects" the horizon.
@0celo7 : go and read about it. Do your own research.
user54412
@HDE226868 I don't see why not. Except be careful -- M-sigma applies to the bulge of spirals, not the whole galaxy. The bulge is essentially a small elliptical at the center (so FJ applies). While the spiral part is dynamically cold (everything moving orderly in the same direction), the bulge is dynamically warm ("pressure" support against gravity, rather than rotational support).
@ChrisWhite That's just between physicists though. And no, I'm pretty sure it's not. I talked to a bunch of people who are involved in it, and they don't seem to think so.
I do think that it may be based on a bunch of imprecise/hand-wavey arguments that might turn out to be false
I don't see how that excludes the case where each side mistakenly thinks the other one's standpoint is different from theirs when it is only because of incommensurable assumptions/terminology. (I'm not saying it is the case in this specific debate, but two sides thinking they have a rational debate is not sufficient to exclude miscommunication)
I have experienced this on a couple of sites (and I'm not the only one) :
You look through the question list. You see a pretty bad (or at least not-so-good) question heavily upvoted.
Or even worse, a very poor answer to a good question - upvoted to stratosphere.
Or even worse, a very poor/inc...
Probably because Munich is so big you have a higher number of old people taking courses because there simply are more old people near enough to consider attending
I really hope that once the theory of everything is made, we will call it the Dirac-Maxwell-Einstein-Schroedinger-Gell-Man-Weinberg-Klein-Gordon-Higgs equation
I have experienced this on a couple of sites (and I'm not the only one) :
You look through the question list. You see a pretty bad (or at least not-so-good) question heavily upvoted.
Or even worse, a very poor answer to a good question - upvoted to stratosphere.
Or even worse, a very poor/inc...
