Do wormholes increase the GDP

I also like wormholes :p

No

worms probably do

fishing

@Slereah They decrease it, less apples to sell :P

@ACuriousMind wow

you just blew my mind

"wormhole" is kind of a silly name

@Slereah why

then again so is "the big bang"

you mean page one of the Bible

Page 1 is usually the printer's blurb

there is this thing in the west where, as time went on, the age of the universe got older and older

is a universal covering space of a top. space unique? in other words, if $S^n$ is the universal covering space of $\mathbb{R}P^n$ (for $n\geq 2$), then are there other universal covering spaces?

@SirCumference-Pies : a new answer awaits!

I think it's unique?

@Bass Yes

You can rather easily show that all universal covers are homeomorphic.

I would ask for a proof

but I'm not sure I care

@ACuriousMind :o

by the way

The atiyha singer theorem

Totally increases the GDP

It is used for graphene studies

thanks

The word universal is certainly suggestive... ;)

So is the word "hole"

@Bass It follows from the universal lifting property - given two universal covers $C_1,C_2$ of $X$, you can lift the projection $\pi_1: C_1\to X$ to a unique map $\phi_1: C_1\to C_2$, and conversely $\pi_2$ lifts to a unique map $\phi_2$, and you should be able to see that $\phi_1\circ\phi_2 = \mathrm{id}$ and $\phi_2\circ\phi_1=\mathrm{id}$.

@ACuriousMind What if one does not know the universal lifting property?

@0celo7 Then what the hell do you think a universal cover is?

@ACuriousMind Points + homotopy classes

Something like that.

No, not the construction. Constructions are boring. What do you think it does, why is it a relevant object?

@ACuriousMind Not sure. It's used in causal structure, but I don't know what general relevance it has.

Learning topology from Hawking was evidently not the best idea :P

@ACuriousMind I can tell you about Cauchy surfaces in the universal cover :)

@ACuriousMind So what do you want me to know about them?

@0celo7 I don't "want you to know" anything. Learn what thou wilt.

@ACuriousMind cool

@SirCumference-Pies : see above, I've answered it, and in the space of a couple of minutes I've got four downvotes.

@David Z : that's not nice.

@Danu I suppose there are things with a universal property that are not uniquely determined by that property.. but I'm not sure about that

@Bass Nope, the actual definition of a universal property already determines the object with such a property up to isomorphism.

@ACuriousMind What were you looking for me to say?

@ACuriousMind oh, fair enough!

I might have just forgotten it in the last few hours :P

@Bass However, you'll encounter the term "universal property" often much earlier than you can actually understand what a "universal property" formally is.

So, don't worry about it too much, and maybe also explicitly prove it for the universal properties you encounter, but in general, you can trust when something is called a universal properrty, it determines the object with it uniquely

Isn't universal cover just fancy talk for making the manifold into a thing with a trivial homotopy group

Or whatev

@Slereah Yes, the universal cover is the cover with trivial fundamental group.

(aka the simply-connected cover)

Is that what you were looking for?

Because I knew that :P

But you have to prove that it's "the" simply connected cover and not "a" simply connected cover.

@ACuriousMind Hatcher?

Hm, I wonder how universal covers work on non-Hausdorff manifolds

@0celo7 I have not read Hatcher.

@ACuriousMind Now that's a lie

What would be the universal cover of $\Bbb R \sqcup \Bbb R$ with the two extremities identified

@Slereah Is that just the Riemann sphere

@Slereah Universal cover is a topological object, it doesn't require Hausdorffness or a manifold at all.

$(-\infty,-1)$ and $(1,\infty)$

Well yes, but how does it work here

I am wondering

@ACuriousMind but, a universal property is mostly worded as "A C is a D with the universal property that for each E there exists a unique F such that ....". So the thing that is uniquely determined is the F, and not the C. In the case of universal covering spaces, C would be the topological space that is the universal cover, E would be another cover of the base space and F the map $C\to E$

does this always mean that C is uniquely determined, too?

@Bass Yes, this is what you have to show

It almost always works by taking a "different" C' with that universal property as the E in there, and then you get two unique maps which are inverses of each other, so they are isomorphisms.

@Slereah Okay, what is your space, exactly?

What I said

@ACuriousMind oh I see. Same pattern as before

thx as always

Two copies of R with those intervals identified

@Slereah hmm, interesting

does that look like a fortune telling origami thing?

@Slereah Uh...I'm not sure what space that is, is it a line that splits into two lines?

The line splits in two and merges back again

What?

Ah, it's the "line with two origins", but with a thicker origin :P

basically, yes

@ACuriousMind what

It ate too much pie

Hm, I'm not sure that thing's universal cover is something we can visualize. For one, the fundamental group seems to be $\mathbb{Z}$.

So the cover is not finite, which is already kinda bad for visualization

how on Earth did you determine that

I'm thinking it might just be two copies of $R$?

But that's just a vague hunch

How does light behave within a black hole's event horizon? It doesn't behave at all.

@Slereah And that is simply connected how?

naughty light

I guess not!

I think the cover is a weird infinite spiral which has lines sticking out from it every now and then.

Trippy

Think of how the cover of $S^1$ is $\mathbb{R}$, which you can visualise as an infinite spiral over the circle

Maybe that should be a Math SE question

I would encourage a +1 on Lubos and JR's answers, if you like them

Now, your thingy is just a circle with two lines sticking out of it

I don't like Motl :V

He is rude to theories he doesn't agree with

@Slereah he is rude to

INTELLECTUAL GARBAGE

So the universal cover should be the universal cover of the circle with lines sticking out of it :D

@0celo7 : what I said. Follow up on my references. Email Don Koks. I'm not just making this stuff up. Don't blame me if it doesn't square with some Penrose diagram you've been reading about or asking about.

That sounds silly, but the picture in my head looks right

So...

-<-<-<-<-<-?

HAHA

proof by diagram right there

@0celo7 It's just a circle with two lines sticking out. You can just retract the lines, and you're left with a circle, which has fundamental group $\mathbb{Z}$.

@JohnDuffield I don't understand Don Koks. Can you explain that in simple english?

Lemme draw it :D

@ACuriousMind Huh, I think I knew that!

Can't wait to take some classes so I actually remember this stuff :P

Duffield's newest answer is at -5. Wow.

I guess a lot of people disagree with him!

SECRET

OH

wrong person

you have funny a funny b

:D

@Bass : like Einstein said, light curves because the speed of light varies with position. It works like sonar. If light didn't go slower when its lower, your pencil wouldn't fall down. A black hole is where light goes so slow, it stops.

Well, it makes sense I guess!

I like my diagram, I should draw those more often for answers

@0celo7 : I guess a lot of people disagree with Einstein.

draw me a diagram of the Birkoff theorem please

what about

@Slereah gets me every time

You know what diagram I like?

@ACuriousMind cool, the universal cover looks like a treeification of the original space

Diagram of gauge theory

I wonder if the guy did it as a joke

@ACuriousMind Proof?

@0celo7 How did you do with that orbit problem?

@HDE226868 Working on it with my study group tonight

@ACuriousMind what is a universal property ultimately? I mean, when you understand it thoroughly?

@0celo7 By looking at it.

@ACuriousMind Bah

that's called religion

I think he's gone insane.

hehe linear algebra homework has a matrix with 420 in it

BLAZE IT

@dmckee : hello there. We seem to have a bit of a "not very nice" issue again. From people who don't answer questions themselves, but who instead downvote good answers without explanation, and even say that's not an answer.

@Slereah Gee that's a swell image!

John, using stategically worded complaints to disparage your "detractors" is "not nice", and I'm sick of it.

@Bass Hm, well, that's difficult to explain beause the proper formulation of it lies in category theory

@Slereah This one just doesn't make any sense

Category theory again D:

@Slereah: Do these images have a point?

Does anything

@Slereah a needle

@Slereah Yes, a cone, for example. Or a knife.

@ACuriousMind Diabolical shanker confirmed.

You call this a knoife?

everyone thinks ACM is a nice hippy

then he filets you

There must be a whole lot of trolls on PSE. -6 already!

@David Z : see dmckee's comment above. Mine is a genuine point. That answer refers to Einstein and Shapiro and others, it's a good answer. And it was in response to a request from a guy who was dissatisfied with the existing answers. But it got four downvotes in a couple of minutes. Now it's got six, with no explanations. This is not the way the community ought to be working.

Pretty sure there's at least two geometries on Lorentz cylinders

The normal one and the one with CTCs

Not quite sure if the one with a Cauchy horizon would be a third one

As far as I know conformal maps preserve causal structures so probably Iunno

@Slereah they do

it's a theorem

I know

Just wondering if it applies to what I'm saying

that would be at least three conformal metric classes

Hm

You can always build a Lorentz metric from a non vanishing vector field and a riemannian metric

But can you build all metrics out of them

Apparently Fallout works best with no family

@Slereah I've said it before, you can't include NV in the progression because that was Obsidian's writing, not Bethesda's

And it shows.

Yep

That's what happens when you sell out!

Although, Bethesda did Morrowind

I suspect that Ken Rolston was responsible for it being awesome because he is awesome

@ACuriousMind Meaning?

@0celo7 That Bethesda's writers are shit compared to the guys at Obsidian.

MAJOR SPOILERS

reddit.com/r/Fallout/comments/3twp5c/major_spoilers_so_er_shaun

BUT WORTH THE READ

@ACuriousMind is it

I would play fallout NV

but it crashes upon boot

and the solution is very tedious

I wonder when Torment 2 comes out

next year, apparently

It was supposed to come out this year :p

But oh well

For the money I put in I'd rather they polish it nicely

Anyone understand Bloch's theorem?

Probably

kinda

@0celo7 Ok, suppose I have a string with periodically varying mass density.

isn't it just "differential equations with that period are of that form"

Oops, wrong comment. Deleted.

Well, what does it mean that $k$ vectors differing by a lattice reciprocal vector correspond to the same state?

I've never managed to really understand this.

hey @DanielSank

the 95% of PSE is here!

Isn't it just the expression of a discrete symmetry?

@TanMath What does that mean "95%"?

everyone is Daniel Sank

@0celo7 : it's simple. A gravitational field is where the speed of light varies with position, and a black hole takes this to extremis. At the event horizon of a black hole the coordinate speed of light is zero. Hence the vertical light beam doesn't get out. It couldn't be simpler.

I am Daniel Sank

Of course, if you promote Penrose diagrams and other universes you might claim that the above "makes no sense".

we are all Daniel Sank

Woooooo!

@JohnDuffield ?

@DanielSank it has been claimed that 95% of PSE is you and your socks.... the rest are tebels trying to fight the you and your socks off! but who cares? we love being you!

@DanielSank : that was a little poke at 0celo7 for believing in woo like the parallel antiverse. Methinks he said the frozen-star black hole "makes no sense" because he's asked a question that has a very obvious answer.

@DanielSank Just put him on ignore. Makes life a lot easier.

@0celo7 put who on ignore?

@0celo7 you?

@DanielSank What do you mean "what does it mean"? The original crystal/lattice has a translation symmetry. The reciprocal lattice of a lattice is another lattice, which has a corresponding translation symmetry. Saying "Two reciprocal vectors are equivalent if they differ by a lattice reciprocal vector" is just a convoluted way of stating that translation symmetry, isn't it?

@TanMath I am the 1%

@JohnDuffield It's a ghost!

...but a friendly one, of Faddeev-Popov kind ;)

Damn confusions all over & all the time. It doesn't seem to matter if I try to answer; like here; physics.stackexchange.com/questions/161333/… or to ask like here; physics.stackexchange.com/questions/220050/…

$\partial_{\mu}\bar{👻}^{a}\partial^{\mu}👻^{a}+gf^{abc}\left(\partial^{\mu}\bar‌​‌​{👻}^{a}\right)A_{\mu}^{b}👻^{c}$

@Slereah I'm seeing ghosts!

Very spooky

@JokelaTurbine : you won't get much joy on Lesage gravity Jokela. Gravity just doesn't work like that.

You know

i thought Halloween was over!

"Prelude to Foundation" is a bit unrealistic

A mathematician wouldn't say "But my lord, it is impossible to expand this theory as you ask!"

He would say "Why yes that is interesting to study, how about some grant money"

@JohnDuffield ...very instructive :P

@JokelaTurbine : Einstein said light curves because the speed of light is spatially variable. It's like sonar. Simplify a body to a single electron, think of the wave nature of matter, then simplify the electron to a wave in a square path. The horizontals bend down, and the electron falls down, like this:

The Newtonian deflection of matter is half the GR deflection of light for good reason.

See Ned Wright's article.

I think @JokelaTurbine and @JohnDuffield could be good friends :)

Also see what Newton said: "Doth not this Aethereal Medium in passing out of Water, Glass, Crystal and other compact and dense Bodies into empty Spaces, grown denser and denser by degrees, and by that means refract the Rays of Light not in a point, but by bending them gradually in curve Lines?" It's the same explanation as Einstein's.

What's the name for a planet that has an orbit perpendicular to the plane of a (binary star) system, but really just oscillates along it on a line? It's like Stnitkov or something, but I can't remember exactly what.

@JokelaTurbine : once you've read up on this I imagine LeSage gravity will lose its appeal. See paragraph 19 here.

Ah, Sitnikov. That's what I was thinking of.

OK chaps, I'm off to bed. I hope you all feel you've all learned something today.

@HDE226868 nerd

@0celo7 Yep.

nerd porn?

A slide from some galactic dynamics lecture notes.

And no, they aren't the same thing.

@HDE226868 proof?

@0celo7 As always, try google :P

@0celo7 Here, lecture 1. I'm not taking the course, just following along with the notes.