The h Bar

6:09 PM

You have to admire persistence:

In a torus there is no end. Like I said if u were to walk around it you'd never find an end. Why would the energy? — Dave 1 min ago

0celo7

@JohnRennie what's your opinion of the user Timaeus

John Rennie

@0celo7 a valued member of the site whose only flaw is that he once downvoted me for claiming that the universe is (a) infinite and (b) simply connected. I shall never forgive him for that.

user116211

@0celo7 He is also AI

user116211

He is emotionless.

John Rennie

@0celo7 I take it you want to bitch about his answer to your question

0celo7

6:15 PM

@JohnRennie yes

John Rennie

Frakking, frak, frak, I've just used my last frakking close vote and there are loads more frakking homework frakking questions left to deal with.

0celo7

I hate answers that say "you can't do it"

Because then I want to change my question to be more specific

But he's bitching about that

ACuriousMind

@0celo7 If the answer given is a correct answer to your question as written, but would not be a correct answer to your changed question, that's a bad change.

Edits to questions are supposed to not invalidate existing answers.

0celo7

It's not a good answer though

I'd buy that there is no necessary condition

ACuriousMind

Whether you think it is "good" doesn't matter.

0celo7

6:17 PM

But sufficient?

There's got to be a sufficient condition

John Rennie

I would judge that Timaeus knows considerably more about GR than I do.

0celo7

Wait a moment, does his first spacetime even have the desired property?

Isn't that the Lorentzian cylinder which is totally vicious

If time is going around the circular direction, then that's exactly what I had in the OP

@JohnRennie what do you think

ACuriousMind

@JohnRennie Using all your close votes is still an exceptional occurence for you? :P

0celo7

He constructed the thing weirdly, so I'm a little confused

it's just a cylinder with the time direction cyclical

and the other one is also a cylinder but with slits

Slereah

Timaeus seems like a smart enough fellow but he has a tendency to not actually answer your question

ACuriousMind

6:23 PM

I can't remember the last day where I didn't run out of close votes, excepting days where I didn't really visit PSE at all.

0celo7

so in the one with slits...we can take some timelike curve...and go through the slit...and hit a point with a spacelike separation

John Rennie

Aaaaaaaaaarghh:

if it's in constant motion it isn't halted by anything it's constantly moving. — Dave 2 mins ago

0celo7

ok can someone please help me out here

I don't think either of his spacetimes have the desired property

if time is indeed cyclical

John Rennie

Was it the global hyperbolicity question or the causal separation question?

0celo7

Causal separation

He completely missed the point on the glob hyp one

John Rennie

6:26 PM

Ok I'll look now ...

0celo7

I'm 99% sure his first spacetime is the one in the OP, just finite.

Slereah

@0celo7 yeah what I said

John Rennie

Jesus, the first sentence is a link to an article I have to read just to understand the notation used!

Slereah

heh

0celo7

@JohnRennie It's standard notation...

ACuriousMind

6:27 PM

@JohnRennie It's a duplicate anyway. And I think your drawing is wrong, cf. the answers to the duplicate: The outside field just vanishes.

Slereah

Dude doesn't even know causal sets notation :p

John Rennie

This guy is definitely a rogue chat bot:

In my head, the magnetation would combine into one point in the Torus then what? It gets pushed around in a circle collectively in a ball of energy. — Dave 1 min ago

0celo7

@Slereah to be fair, Wald does not use that notation

or HE either

@JohnRennie Did you read Wald or HE?

@Slereah Got the amazon app on my phone so I can be notified of when Visser and Penrose move

Penrose is slated to arrive Wednesday

ACuriousMind

@JohnRennie I always wonder if these things make sense inside the head of the persons saying them, or if they're as confused as I am by such statements and just don't notice it

0celo7

I miss my cat

John Rennie

6:30 PM

@ACuriousMind Aha, well spotted.

I misunderstood what the OP was asking and assumed he just meant a ring.

Anyway I'm going to delete my answer just to wipe out his comments and annoy him :-)

0celo7

@JohnRennie $p\prec q$ just means that there is a curve connecting $p$ and $q$ that is future directed and nowhere spacelike

oh and $p$ can equal $q$ but that's irrelevant

I need to figure out how to use MS Paint

That way I can spam the chat with spacetimes

John Rennie

MS Paint? Use Google Draw.

0celo7

hmm, what's that

@JohnRennie if I just draw a spacetime diagram you don't need to read the Wiki article

John Rennie

@ACuriousMind: BTW thanks for the answer to my meta question. What would be really nice is a report ranking questions by number of links. I don't suppose you know how to do that do you?

0celo7

oh shit, chrome is letting me draw now

John Rennie

6:36 PM

@0celo7 Google Drive and create a drawing. All my Physics SE diagrams have been done that way.

0celo7

Holy shit teach me

oh man

how do I use this

ACuriousMind

@JohnRennie No idea, sadly. However, if that information is stored in the public data dump, there might already exist a SEDE query for it

0celo7

this is not easy to use

John Rennie

@ACuriousMind I'll have a nose around in the Data Explorer and see if I can find anything.

@0celo7 Google Draw?

0celo7

how do I draw a curve

and have it not delete!

the hell

I can't actually place the damn thing

when I hit esc it goes away

when I hit enter it does nothing

when I hit delete it deletes the other shape

ACuriousMind

6:40 PM

@JohnRennie: data.stackexchange.com/physics/query/191966/…

I'm guessing if you just delete the "where tag..." line, it should get all posts.

0celo7

docs.google.com/drawings/d/…

ACuriousMind

(I don't actually know SQL)

0celo7

20 minutes of work right there

@JohnRennie ok, does that picture make sense

how do I make a point

John Rennie

@ACuriousMind Yes!! I have the second most linked post of all time!

2

data.stackexchange.com/physics/query/edit/454020

0celo7

docs.google.com/drawings/d/…

Ok, now it should be clear

in this spacetime, even though $p\prec q$, they are connected by a spacelike curve

John Rennie

6:47 PM

@0celo7 OK, yes, I see.

0celo7

@JohnRennie now that's the spacetime I talk about in my second paragraph

but I'm pretty sure that it's the one he uses as well

oh...I see what he did

nevermind, he has two cuts

but that's a pretty fucked up spacetime

@Slereah are causal conditions not determined by the metric and topology?

Slereah

They are.

Connection isn't related

0celo7

yeah but if I cut a huge swath out of Minkowski space and preserve the topology

it can mess with the causal structure

Slereah

Well yes

0celo7

and in the cylinder example

Slereah

6:52 PM

It will have a different topology

0celo7

@Slereah no

take the cylinder example

it's totally vicious without any cuts

but if you make those cuts, that's just a homeo

but it's not gonna be totally vicious anymore

Slereah

What cuts

0celo7

cut swaths out of the sides

lemme draw

docs.google.com/drawings/d/…

@Slereah check it

that's just a homotopy

Slereah

I wouldn't say that has the same topology?

0celo7

what's different

Slereah

6:57 PM

Hm

John Rennie

@ACuriousMind: may I edit your reply to my meta question and add the link to the query?

0celo7

@ACuriousMind we need topology help

ACuriousMind

@JohnRennie Sure :)

0celo7

@Slereah the only thing is that maybe while the two are homeomorphic, what's really invariant is $(M,g)$ under the class of conformal diffeos

but he's right, if I tell you the topology is $S^1\times\mathbb{R}$ with a Minkowski metric, there's lots of spacetimes you can give me

Slereah

This one is gonna have incomplete geodesics and all, so obviously not the same

ACuriousMind

7:01 PM

Is saying "the topology is $X := S^1\times\mathbb{R}$" a weird way of saying "it's homeomorphic to $X$"?

Because "the topology" is formally a bunch of open sets.

Slereah

Well

0celo7

@ACuriousMind Yes.

@ACuriousMind I know what "a topology" is

Slereah

Recall when I wondered why in 2D, the hyperbolic plane and the plane were two different things?

0celo7

Yes, I had that question too

Slereah

Despite both of them being $R^2$ and both of them being conformally related

0celo7

7:03 PM

It's because there's no diffeo between them

Slereah

Iunno

Well is there a diffeomorphism between those two

0celo7

that takes the metric of one into the other?

ACuriousMind

The word you seek is "isometry" :P

0celo7

@ACuriousMind No, I don't think so.

They're clearly not the same metric

@Slereah To show that they're not isometric, simply calculate the curvature tensors.

@ACuriousMind can you please make precise what you mean

ACuriousMind

@0celo7 what? Two (pseudo-)Riemannian manifolds are "the same" if there's an isometry between them, no?

Make what precise?

0celo7

7:06 PM

we have the spaces $(R^2,\delta)$ and $(H^2,h)$

then we want a diffeo $\phi :R^2\to H^2$

this is possible

but then the claim is that there is no $\phi$ such that $\phi^*h=\delta$?

I don't see what this has to do with isometry

@ACuriousMind the standard lore is that the physics of GR should be invariant under diff

ACuriousMind

@0celo7 The very definition of an isometry $\phi : (M,g)\to (N,h)$ of ps-Rm mflds is that it is a diffeomorphism such that $\phi^\ast h = g$

0celo7

is it

hubot

Hello!

0celo7

sigh, let's get out a Riemannian geometry book

Slereah

But isn't there an isometry between $R^2$ and $H^2$?

0celo7

7:10 PM

nope

ACuriousMind

@0celo7 Sigh...we talked about this before, the physicist's idea here is to take an diffeomorphism $\phi : M\to M$ and define the metric $g'$ on the target by $\phi^\ast g'\overset{!}{=} g$.

0celo7

different curvatures

@ACuriousMind fucking physicists

Slereah

wait

Are conformal transformations diffeomorphisms in this context

ACuriousMind

@Slereah Conformal transformations are diffeomorphisms such that $\phi^\ast h = \Omega g$ for some function $\Omega$.

Slereah

But conformal transformations don't preserve the curvature

ACuriousMind

7:12 PM

i.e. "isometries up to local scaling".

0celo7

@ACuriousMind Oh, right, I'm retarded.

Damn, I go home and have a few drinks and my IQ drops 5 points

Slereah

So what is @0celo7 talking about

0celo7

wtf

ACuriousMind

I have no idea what either of you two is talking about, really.

0celo7

:D

Slereah

7:12 PM

Oh well

It's late

And I still have my cardio to do

I'd better move my lazy bums

0celo7

I think the issue is that one has to specify "the metric" better

ACuriousMind

But, yes, physicists not only suck at group theory, they also suck at using the same terms as the math-geometers :P

0celo7

@ACuriousMind At this point I'm gonna have to do my thesis on geometry so I can set all of this straight

But there's still the issue: what exactly determine the causal structure

The common lore is that it's the topology + metric up to a scaling

ACuriousMind

The "double-slit cylinder" is a pretty good counterexample, though

0celo7

yes, it is.

Slereah

7:16 PM

I'd say there is no isometry taking between those two cylinders

Or whatever else you call them

0celo7

@Slereah that I believe.

but that's not the issue, is it?

ACuriousMind

@Slereah Indeed, there can't be, they are two different spacetimes.

Slereah

Is it not

ACuriousMind

But their difference doesn't lie in their topology or their metric, really

Slereah

Then what

0celo7

7:17 PM

the combination of topology and metric, right?

ACuriousMind

That was nonsense.

Slereah

I SAW EVERYTHING

You nonsense man

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Me too

;)

ACuriousMind

Oh no! My secret is lifted!

0celo7

did someone take a screenshot

Slereah

7:19 PM

He said the metric was not the same

0celo7

@ACuriousMind Don't worry, the real one is safe with me

@Slereah I know

then something about stretching

Slereah

I think the problem might be that we are using fast and loose definitions of what "the same manifold" and "the same metric" means

ACuriousMind

^

0celo7

Yes, I agree.

ACuriousMind

I think these two objects are not in the same conformal equivalence class.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

7:20 PM

^^

0celo7

Especially the second one.

Slereah

Like I've seen some serious math book on Lorentz surfaces

And there was a bunch of totally different Lorentz surfaces

But

0celo7

Link?

Slereah

They'd be the same under the definition we use

I think it was just called Lorentz surfaces or something

0celo7

Well BEE is a serious math book.

Slereah

7:21 PM

Or another math book title

0celo7

But they don't talk about this issue.

Slereah

Introduction to Lorentz surfaces

On Lorentz Surfaces

Lorentz Surfaces and Me

The time and life of Lorentz surfaces

0celo7

amazon.com/…

Time to get legally

Slereah

yeah probably that

0celo7

my internet is kaput, can't dl

Slereah

7:24 PM

Like these are supposed to be different Lorentz surfaces?

0celo7

can't load the image, thingie kaput

Slereah

They are lorentz staircases, @0celo7

0celo7

define "different"

they are certainly not isometric

Slereah

They are not conformally equivalent

Whatever that means to a mathematician

0celo7

is that from the linked book

Slereah

7:25 PM

yes

0celo7

jesus, when you can't load speedtest to see how fucked your internet is, you know your internet is fucked

ok the metrics are clearly not the same

now they can be the same on the overlap

call the metric on $\Omega_1$ $g$

and the metric on $\Omega_2$ $h$

then $h=g|\Omega_2=\iota^*g$

where $\Omega_1$ and $\Omega_2$ are related by the inclusion $\iota$?

Slereah

Sorry m8

I'm a lowly physicist

0celo7

what

Slereah

I cannot math

0celo7

speedtest refuses to let me test my speed

uh-oh

everything is broken

Slereah

7:30 PM

Are you even connected to the internet

How do you know I'm real

Maybe it's all in your head

0celo7

Literally no internet now

I'm on cell

Help

am I alive

> K. Burns and R. Spatzier, On topological Tits buildings and their classification, IHES Publ. Math. 65 (1987) 5-34.

What

Slereah

good old Tits building

They are named after mathemacian Jacques Tits, @0celo7

Who also did the Tits group

0celo7

Is the internet fixed

@Slereah sounds like a Frenchie

huh internet suddenly works again

@ACuriousMind where were we?

barrycarter

7:51 PM

Who wants to help me with relativity? ;)

0celo7

what kind of relativity

please not spacetime topology

barrycarter

@0celo7 What other kind of relativity is there?

0celo7

there's lots of topics in relativity

barrycarter

@0celo7 OK, special relativity with acceleration.

0celo7

eww, what about it

I can recommend a good book

barrycarter

7:53 PM

@0celo7 I just need answers for the moment :)

I hope to learn how to read soon

0celo7

you can't read?

how are you typing here

barrycarter

@0celo7 No, I mean those weird things made from plants and reeds and stuff

0celo7

what

barrycarter

Never mind, I was attempting to be humorous.

0celo7

@Slereah on what page did you find that image

Slereah

8:13 PM

and back from the cardio

Page 39, @0celo7

0celo7

my internet is ruined

hubot

I have to go

0celo7

...ok

John Rennie

@barrycarter did you see my answer to your question?

John Duffield

@barrycarter : I'll help you Barry. SR is dead easy.

0celo7

8:16 PM

@JohnDuffield lol!!

@JohnRennie you! I need a british person!

John Duffield

@0celo7 : LOL yourself. I'll help Barry, you won't.

John Rennie

@0celo7 They don't get much more British than me!

0celo7

@JohnDuffield haha, sure

@JohnRennie Do Brits not have microwave bacon?

John Rennie

@0celo7 it may exist, but it's not mainstream. I don't recall seeing it in the supermarkets.

Why would you want to microwave bacon? Wouldn't it go soggy?

Slereah

Would American care for terrible food, though

As long as they may drop it in their bottomless maw

John Rennie

8:21 PM

@Slereah there's an article floating around the web somewhere with obscene sounding mathematical terms. The one that sticks in my memory is the Cox-Zucker machine.

Slereah

Oh yeah I remember that one

There's also the Wang machine

John Rennie

Also a Cox ring

Slereah

And of course, there's the Ass-King paper

But that's linguistics

Oh, butt king

Written by

Miriam Butt

Miriam Butt is Professor of Linguistics and Chair of the Department of Linguistics (Fachbereich Sprachwissenschaft) at the University of Konstanz. She is best known for her theoretical linguistic work on complex predicates and on grammatical case, and for her computational linguistic work in large-scale grammar development within the ParGram project. Butt earned her doctorate in linguistics in 1993 at Stanford University. She subsequently held research and teaching positions at the Institut für Maschinelle Sprachverarbeitung at the University of Stuttgart, University of Manchester Institute of...

and Tracy Holloway King

John Rennie

"Butt" is one of those charming colonial expressions. In the UK it just means the end of something e.g. a rifle butt.

Slereah

Sorry I don't know any Arse scientist

I also know that you brits are quite amused by the term "fanny pack"

John Rennie

8:25 PM

Ah yes, I believe "fanny" just means "bottom" in the US

Slereah

yes

instead of a lady's mimsy

John Rennie

According to my niece the current slang term is "foo foo"

Where that came from I have no idea

Slereah

It sounds similar to a french term for it?

Foufoune

Dunno if they are related

John Rennie

@Slereah aaaaaaaaaaaah!!

barrycarter

@JohnRennie Thanks!

@JohnRennie OK, I got your answer, but I still don't see where the missing time goes.

0celo7

8:36 PM

@JohnRennie no, it's pretty good

my internet is ruined, this is ridiculous

$\mathfrak{abcdefghijklmnopqrstuvwxyz}$

barrycarter

"hoochie coochie"

0celo7

huh, $\mathfrak{k}$ looks strange

@JohnRennie only in very polite company

@Slereah had like a liter and a half of soda with my lunch

umad?

Slereah

No

I am comforted in my vision of the world

Upper case Fraktur is the worst tho

$\mathfrak{G}$

0celo7

Let's read this, @Slereah

amazon.com/…

Slereah

mb later

Gotta make my sammiches for lunch first

ACuriousMind

8:41 PM

lunch? It's almost 10 p.m.

Not even I would eat "lunch" at that time.

0celo7

for work tomorrow ACM

wtf is with my internet

Slereah

Well no

But

I must prepare it for tomorrow

John Duffield

9:04 PM

@barrycarter : here you go Barry. Easy peasy.

@0celo7 : LOL. "Therefore, even though locally the speed of light is not to be exceeded, globally the phenomena, such as the existence of closed timelike curves and causality violations may be allowed in principle."

0celo7

9:26 PM

@JohnDuffield Yup, so?

barrycarter

9:43 PM

@JohnDuffield Umm, thanks, but I'm pretty sure that Lorentz contraction and time dilation actually exist.

0celo7

The GR Goblin strikes again!

John Duffield

9:59 PM

@barrycarter : they exist, but maybe not the way you're thinking. Your speed alters you and the way you see things, not the things themselves. When you travel that 8 light years through space to Earth your clocks run slower than mine. But it still takes you 10 years to get to Earth. You arrive at Earth time t=10, not t=6. In similar vein when you accelerate, your measurement of distance changes, but space doesn't change a bit.

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