no typo :(

No typo

@0celo7 I hear you can do this easily

Can you plz explain

doing things

what do you need?

I can see why $w = y'$ implies $y'' = w w'$

chain rule

Well yes

Hm

Let's see

its derived wrt to y

MATHEMATICIANS DON'T LOOK

hahah

@AngusTheMan differentiated

there we go ;) I can math

Hm no I don't see how to do it for $y'' = w'$

DO WHAT

There is only one term so I can't jury rig a chain rule with it!

SHOW THAT THEY ARE EQUIVALENT

wtf are you talking about

The equation is $y'' + f(y) (y')^2 = 0$

Apparently the variable change to do is $w = (y')^2$

and apparently this implies that $y'' = w'/2$

Not sure how to show this, tho

Hm

$w_x = 2 y'' y'$

And $w_y = 2y'$

If there was an extra w in it it would be fine, but I don't know

This means that $y' = w_y / 2$, but that means it is wrong

why not just $w=y'$

Because there's a $(y')^2$ in the equation

yeah, that's nasty...

@dmckee : collecting good answers to good science questions is doing science. Only this site isn't doing it. Which is why a lot of good posters are ex posters. They didn't vote with their feet because of there's too many homework questions.

@Slereah what

Could you give us the name of those good posters

I get $y''=w'/2y'$

@0celo7

what is $w'_y$

$\partial_y w(y)$

jesus

wait...

that makes zero sense

the partial derivative of $y'_x$ wrt. y is zero

yeah I don't know what they're doing really

I guess I could trust the equation for now and see where it takes me

no, don't

get some other book on ODEs

Like what

idk

AS?

do they have ODEs?

Do not say swears please

I'll ask the math chat

Hm

I remember I did it yesterday for a simpler substitution

$u = y'$

So that $u_x = y_{xx}$

But also $u_x = y' u' = u u'$

I guess it is a similar method

Hm, let's see

$w_x = 2 y' y''$

$w_x = \frac{dy}{dx} \frac{dw}{dy} $

So that $2 y' y'' = y' w'$

Okay I get it

And now it's a first order ODE, yay

oh for the love of crap why is this album not out :(

@Slereah what is it?

because I tried that sub and it didn't work

also I have this...urge to play Skyrim

It is $w' + 2 f(y)w = 0$

dude I got that a while back

what is $f(y)$ now

you have to express it in terms of $w$...

No

y is the variable here

but $w$ and $y$ are not independent.

It is similar to $y' + 2f(x) y = 0$

hmm

oh is the derivative wrt. $y$ there?

yes

ah, carry on

Yawn.

So the result is $y' = \sqrt{K e^{-2 \int f(y) dy}}$

@JohnDuffield Does a homogeneous space have to have 0 curvature?

what is the final substitution, anyway

And I can use whatever function I want, yay

Only one substitution needed for the meridian equation

I could probably solve the generic equation too but it's not that interesting

at least

FOR NOW

dun dun duuun

what is the substitution??

It was $w = y'^2???$

were you not following

ok

bish

I'm doing my own stuff

@JohnDuffield Please respond to the above.

@0celo7 : there's a difference between "a" space and space. The former is typically a mathematical space, the latter is typically physical space, or space as in physics. I'll assume you're talking about the latter. I'll also assume you're talking about spacetime curvature, and that we've set aside the expansion of the universe. The answer is yes. When space is homogeneous there is no spacetime curvature.

Because at all locations your measurements are the same. If they weren't, your plot of measurements would exhibit curvature, and your metric would be curved.

@JohnDuffield ...ah now someone has down voted my answer too :/

So you're saying the metric has to be constant for homogeneous space?

@AngusTheMan : that was me. No offence, but I thought your answer was a stock answer that said nothing. The questioner has already read all that stuff.

@JohnDuffield I don't think you understand what homogeneity means.

It means that the isometry group is transitive.

@0celo7 : yes. The metric is related to your measurements. When space is homogeneous, your measurements are the same at all locations. If the space down there is the same as the space up here, it isn't down there, it's over there. See this: "the curvature of light rays occurs only where the speed of light is spatially variable".

@JohnDuffield Non taken :) thanks for the feedback!

@AngusTheMan FWIW I gave you up upvote a while back.

:D

@JohnDuffield You do know "metric is constant" depends on the chart, and is not physical, right?

What is physical is the algebra of Killing vectors.

And one may show (cf. e.g. J. Jost, Riem. Geom. and Geom. Analysis) that this (homogeneity) implies constant curvature.

@JohnDuffield Let's take a simple example, ok?

Consider $S^2$, the unit 2-sphere.

Do you know what the metric for this space is, in standard angular coordinates?

Let's put aside physics for the moment and look at some mathematics.

I promise we'll come full circle.

I know what homogeneity means, and so did Einstein.

Oh for the sake of fuck.

Stop quoting Einstein.

@JohnDuffield So you're refusing to go along with me at all? You refuse to consider that maybe you're wrong?

@0celo7 : no it doesn't depend on the chart. You can't transform a gravitational field away. And the algebra of Killing vectors is not physical. You're elevating mathematical abstraction above physics. Space is physical. It isn't nothing. When it isn't homogeneous, spacetime isn't flat. It's "tilted", akin to those tilted light cones. When this tilt diminishes with distance, spacetime is curved.

But your condition that the metric is constant is chart dependent! Killing vectors are not!

So guess which one is physical.

@JohnDuffield Do you refuse to humor me with my sphere example?

Ugh

Now to do the worst part of the equation

Integrate everything to get the parametrization

Hm

I guess I don't have to, technically

Wait, I think I do

Grumble

If I do that tho I'll have to solve a trigonometric ODE

Not too difficult I suppose though

The eq's form is pretty short

@0celo7 : the 2-sphere is misleading. Space is more like the ball. There is no higher dimension in which it is curved. Instead on the large scale it's homogeneous, so light goes straight, and there is no overall gravitational field. There never was, the universe didn't collapse when it was small and dense.

A Killing vector is not physical. Can you point up to the clear night sky and say hey look, there's a Killing vector! No. But I can point to the black between the stars and say that's space.

You do know Einstein's universe was $\mathbb{R}\times S^3$, right?

Not a ball.

So it turns out the ODE was trivial!

But now I must stop screwing around and actually give a value to $f$

In any case, you don't know what homogenous means and refuse to learn. So this is rather pointless. Don't bother talking to me until you're willing to learn.

Well stop talking to him jeez

It's not that hard

It's not like you're gonna get a different discussion

He has like 5 different bullet points he will reuse for all situations

The problem is that he spews his nonsense over the main site. I don't know if downvoting him is enough to discourage OPs from believing him.

@0celo7 : yes of course. For some reason Einstein's cosmology was lacking. It's as if he lost his usual confidence. IMHO all he had to do was lose the dust and focus on space itself.

And there's some part of me that thinks he is not beyond saving. But maybe he is...

EINSTEIN WAS WRONG D:

Maybe but do you really want to invest time that could be better spent picking your nose

I can type and pick my nose at the same time. Betcha Einstein couldn't do that.

@0celo7 : like I said, I know what homogeneous means and so did Einstein. You're the one who dismisses Einstein because you think you know better. I answer some question with a reference to Einstein, and you downvote it. LOL, that won't discourage OPs from believing what Einstein said. And LOL, you're cutting and running because I've caught you out with your lost-in-maths Killing vectors are physical.

Whoosh! There goes a Killing vector! And as for "for the sake of fuck stop quoting Einstein" and "you refuse to consider that maybe you're wrong", well, my irony meter just went off the scale.

OK, I have to go. By for now.

Maybe you should reconsider what you think it right when your answer sits at -7.

And the fact that your only source died 60 years ago.

But whatever, I'll continue to downvote your woo and help OPs to overcome you.

Einstein said what he said. Downvotes aren't going to turn it into woo.

Einstein was wrong. Deal with it! It's woo because it's wrong.

Are we playing "Feed the Trolls" today?

That is the problem when you keep a crank around

@DanielSank Trolls? There are multiple trolls?

Periodically people want to show him the error of his way

Oh here we go: Einstein woz wrong and I'm going to downvote his and your woo because I know better, even though I'm just a 17-year-old kid. FFS.

woz?

@JohnDuffield I am curious about something. Most physicists (and scientists in general) have a pretty low regard for authority. This is natural, as science tells us to dismiss any idea, no matter how entrenched, the moment it is shown to be insufficient. With this in mind, it's a little surprising to me that you so often refer to Einstein as a pivot point in discussions about physics topics.

Pretty sad that a 17 18 year old kid knows better than your idol.

Can you explain why, in your opinion, this is a useful approach to debate/discussion?

I don't care to discuss whether or not he was wrong. I am wondering why you personally, John Duffield find it useful to cite him so much.

Hm

@JohnDuffield When I say "homogeneity is not what you think", you immediately post an Einstein quote instead of debating what homogeneity means.

How can I solve $\lambda = \theta(\lambda) - \frac{1}{2} \cos(\theta(\lambda))$

The extra theta kinda fucks it up

And then when I say your quote is wrong you attack my age.

@0celo7 Yes, that is an interestingly common pattern with some users here.

CuriousOne does that too some times.

@0celo7 Yes, this is very poor (textbookly poor) debate practice.

@DanielSank Any instances you care to share?

@0celo7 If it makes you feel better, it is blatantly obvious to all of us in the spectator area that this was a ridiculous distraction from the main issue at hand.

Maybe just drop it. You're not getting anywhere.

@DanielSank It just pisses me off to high hell that he seems so nice in the YouTube video, but the side of him we see here is not that at all.

@DanielSank : it demonstrates that I'm not just making this stuff up. See for example this answer about the speed of light. And note that I don't just refer to Einstein. I refer to other authors too. And more importantly, to the evidence. You might think you have a pretty low regard for authority, but it's not true. You treat your textbook like a bible, and reject any challenge to its authority.

I really don't think he's a malicious troll.

Therefore, I think he can be saved.

@JohnDuffield Ok, I see what you mean about using references as a way to show that you're not making things up. Thank you.

@JohnDuffield Let's take this opportunity to address another thing which puzzles me. Do you understand that you insulted me in the message to which this one refers?

Assuming you do, I would like to know why you chose to do so. I have given you no reason to believe that I take textbooks as ultimate authority.

In fact, @JohnDuffield, would you please click on this link. I believe it will show that I think quite otherwise.

So, given that you had absolutely no reason at all to think that I take textbooks as authority figures, I really would like to know why you chose to interrupt the interpersonal communication process to insult me by saying that I take textbooks as ultimate authority figures.

@DanielSank : do you mean the thing about treating your textbook like a bible? The "you" there was intended to be a generality rather than specific to you. Besides, that's nothing compared to the insults directed at me.

@JohnDuffield Ok, let's go with this idea that you were using "you" to address the masses.

As a member of said masses, I please direct you to the link which shows that at least one member of these masses does not treat textbooks as authority figures.

Perhaps this indicates that other users feel the same way.

I clicked on the link, I'm pleased you don't treat textbooks as gospel.

Do you wish to revise your statement?

@JohnDuffield Yet you direct your insults to the general population of the chat room. Do you see how this could be a problem?

Fine, change you to some people.

@JohnDuffield Considerable improvement, in my opinion.

Language matters. A lot. Even more online where we can't see each other's facial cues.

Remember that, please.

Now, we agree (maybe) that some people take textbooks as ultimate authority figures. Yet, here in this chat room, you are talking with a few specific people.

Could you please direct me to Evidence which shows that one or more of them take textbooks as ultimate authority figures?

It's not so much of a problem as some 18-year-old kid swaggering around sneering at Einstein and saying he's wrong and it's woo and I'm a crank for referring to it.

@JohnDuffield Shall we focus on what was actually said?

Would you mind reviewing for me the points which were made and the counterpoints made by said "18-year-old"?

(Also note that mentioning a user's age discredits your technical points, as it looks like you're trying to draw attention away from the true content of the discussion. This works not in your favor)

@JohnDuffield ::swaggers::

Can't handle my swag?

I guess the conversation is over.

Anyone know any good jokes?

@DanielSank : a day or two ago I was talking to 0celo7 who was quoting Wald at me. He treats his textbook like a bible, so much so that he won't read my references to Einstein and the evidence, and then he says Einstein was wrong and it's woo. As for me pointing out that this is coming from an 18-year-old, that doesn't work in his favour. Now do excuse me, I really must go.

I referenced Wald for the proof technique.

@JohnDuffield Good bye.

Oh buns

I need to find a bump function that is easily integrable and invertible

bump functions aren't invertible...

^ That.

Well it's not a bump function exactly

one-to-one functions are not integrable on $\mathbb{R}$

Or are they...

It is just a periodic function

Bump functions are just easy to make periodic since basic periodic functions are not easy to deal with

Also it's not the bump function that must be invertible, but its integral

What is a nice periodic function that is always superior to 0

$\sin x+1$

I tried using $1 + \sin(x)$, but then inverting $x - cos(x) = c$ proved difficult

Hm

I guess worst case scenario

Maybe I can drop smooth functions and just use $C^2$

Also maybe I should just drop using proper time parametrization

And just use coordinate time

That way no bothers

Oh wait I still need to integrate with respect to lambda

Oh buns

Does the standard bump function have no integral

Ah, my 2011 desktop

lol

Hm

Maybe

No, fuck

I dunno how to solve this

Dang

Oh spacetime, why can't you have degenerate points

Why is $\exp_q$ injective and of maximal rank on the closed ball with radius $\rho$ in $T_qM$?

And why are there so few well known periodic functions

And why are bump functions so terrible

Hm wait

Can't I use a function that vanishes at infinity and bring it to a compact thing by using arctan or something

Not sure it would help a lot tho

dude help me with this normal neighborhood :(

I dunno man

Ask a math

@ACuriousMind is a math

Ask him

@ACuriousMind isn't around

Ask Duffield

no

what the hell

@Slereah Bring me up to speed on your work

what have you been doing

Well I have the solution for the tangent vector of the geodesic

But trying to integrate it proves challenging

integrate it?

I need to find how it depends on $\lambda$

So that I might calculate proper time along the paths

hmm, pls write out equations

It is mostly in my little notebook

pls type

I can help

Well with $g_{\theta \theta} = a^2 f(\theta)$, I have $\dot \theta = \frac{C}{f(\theta)}$

after doing the geodesic equation?

yes

But now I want to find the proper time along that path

But I need the dependance on the proper time for that

I guess technically I don't need to have the outside of the wormhole be a longer path than the inside for any CTC related bee's knees

But I suspect any other attempt at it will encounter the same difficulties

Jesus

'electromagneticism'

Stefan got trolled so hard here

hello @alarge ! long time no chat!

@Slereah what are these pics for?

Looking at

So many paper ideas just end up on a math dead end

Yes, he destroys the motherf*cker at 49 minutes.

Glorious.

BURN HIM

YESSSSSSSS

Hm

What to do now

hm hm

Maybe

Watch this video with me!

Ori spacetime???

Ori spacetime is basically Schwarzschild with some tweaks

Shouldn't be too hard to find solutions for it

I know Schwarzschild has a lot of exact solutions

STUMP HIIIIIIIIIIM

I wonder if there's a theorem about spherically symmetric spacetimes always being causal

(if they are topologically trivial)

I never saw any

dunno man

GR sucks

I don't know what to do with my life now

I don't either, but

New version of Dwarf Fortress comes out soon

And then

boy oh boy

Oh right

Ori metric is defined by several patches

So awful

ugh

poor Frenchie

you know

I'm gonna have some snails when I go to Germany

in your honor

Snails are an odd stereotype

Basically nobody in France eats snails and frogs

Cheese, wine and baguettes are totally fair, though

I like snails and frogs :(

"Ori [5] later presented a time-machine model which is asymptotically-flat and topologically-trivial."

Well yes, you should know

You are Ori

lol

I know it is considered bad style to write in the first person but still

what if Hawking & Ellis said "for details see Hawking & Ellis (1973)"

(unpublished)

(unpublishable)

(unpublished, personal

uhh, what's it called

correspondence

Private corresspondence

private!

yeah that

Is it kosher to quote a stack exchange post in a bibliography

lol what if HE was never published but every GR book in history kept the references to it

lol what if HE was a private correspondence in the shitter at some conference

I wonder what is the most widely cited private correspondance/unpublished work

The paper that you have to be in the know to have seen

Hawking recited a 400 page monograph to Wald on the toilet

Writing a monograph in the toilets with someone else screams "cocaine"

"Wald! I have a great idea now! Get your pen!"

album still not out

it's never gonna be released

this is BS

> 3 page long proof

ayy Jost why

could be worse

At least it's not the statement of the theorem that is 3 pages long

grid.ece.ntua.gr/sites/metamathsite/mpeuni/pm110.643.html

" 1+1=2 for cardinal number addition. Theorem *110.643 of Principia Mathematica, vol. II, p. 86, which adds the remark, "The above proposition is occasionally useful.""

@JohnDuffield I have updated my answer with regards to your comments, you were definitely right, it was unfocused towards the question as it was, cheers for the feedback :)

"In this paper we present a class of vacuum solutions in which CTCs form at some particular moment. "

Neat

Oh wait

I think I get the difference between compactly generated and compactly constructed

dude this proof

what is going on there??

Compactly generated is when the past directed null generators of the horizon remain in a compact region

I guess they form like

Some truncated cone sort of shape

or cone

I dunno

Hm, what's a compactly generated spacetime

I wanna check this

I think basically compactly generated looks at the past of the chronology violating region while compactly constructed looks at the future of the partial cauchy surface?

Apparently the Taub NUT spacetime is compactly generated

And I guess Misner space as well

"The hypersurface H is said to be null (or lightlike ,or characteristic or to be a wavefront) if, and only if, the induced metric q is degenerate."

:O

What's wrong with that?

Nothing

just didn't know much about null hypersurfaces

Oh. Read HE :P

Not too sure what null generators are

Oh so the null generators are the curves orthogonal to the hypersurface?

I think so, yes.

(well null curves)

Hm

how to prove that they remain in a compact region for Misner space