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0celo7
0celo7
10:00 PM
@Slereah why does $v$ need to be hypersurface orthogonal?
 
Slereah
Slereah
So that the hypersurface is spacelike?
 
0celo7
0celo7
@Slereah Uh, is timelike always orthogonal to spacelike?
 
Slereah
Slereah
I don't knooow
 
0celo7
0celo7
Lol
Great.
Time to get out the bible
of Lorentz algebra
SPECIAL RELATIVITY IN GENERAL FRAMES
where the fuck does he talk about this stuff...
 
Slereah
Slereah
I want to say it is
 
0celo7
0celo7
10:07 PM
> Any vector orthogonal to a timelike vector is necessarily spacelike or zero.
 
Slereah
Slereah
But then there might be a 12 dimensional metric with 6.5 Killing vector discovered by a Nigerian physicist that has a counterexample
 
0celo7
0celo7
Yes.
It's true.
This book is handy.
Wow.
I'm interested.
 
Slereah
Slereah
So Frobinius is a handy way to check for spacelike hypersurfaces
 
0celo7
0celo7
@Slereah Apparently.
Ok, let's continue.
One of us has to bite the bullet and calculate $v\wedge\mathrm{d}v$.
 
Slereah
Slereah
It's already in Godel's paper
 
0celo7
0celo7
10:12 PM
I know it is, but we trust that?
 
dmckee
dmckee
Er ... @Floris, do you really think that physics.stackexchange.com/questions/216450/… is the kind of homework question we want to encourage?
 
0celo7
0celo7
mod super ping power to stronk
 
Slereah
Slereah
$\star (v \wedge dv) = (0,0,0,\sqrt 2 / a^2)$
 
0celo7
0celo7
what is $a$
 
Slereah
Slereah
Parameter of the Godel metric
 
0celo7
0celo7
10:13 PM
$\equiv 1$ in HE?
 
Slereah
Slereah
Hell if I know
 
0celo7
0celo7
It's related to $\omega$ in HE.
I think I'll get the above book eventually.
If I'm gonna focus on PDEs, might as well really understand the EFEs.
@Slereah Uh, what is $v$?
 
Slereah
Slereah
In the proof it's a timelike vector field
 
0celo7
0celo7
"a"
It has to be the tangent of the CTC, right?
 
Slereah
Slereah
No
It's just a generic timelike vector field
$(1,0,0,0)$
Well $(1/a,0,0,0)$
 
0celo7
0celo7
10:18 PM
You know (1,0,0,0) satisfies Frobenius trivially...
In every space
So that doesn't make sense.
 
Slereah
Slereah
Does it?
Because NOT HERE APPARENTLY
 
0celo7
0celo7
Dude, $\mathrm{d}(\text{const.})\equiv0$
 
Slereah
Slereah
Well
See
That's $v^a$
 
0celo7
0celo7
oh, you have to...yeah
 
Slereah
Slereah
The 1-form is $v_a$
 
0celo7
0celo7
10:20 PM
Yes.
 
Slereah
Slereah
which is... $(a, 0,a e^{x_1}, 0)$
 
0celo7
0celo7
Ok, now what is Hawking blabbering about
 
Slereah
Slereah
some shit about the CTC having to cross the surface an odd number of time
 
0celo7
0celo7
Yes.
Proof?
 
Slereah
Slereah
he does not say
 
0celo7
0celo7
10:21 PM
I know!
 
Slereah
Slereah
And the only references are Godel, which does not use it
 
0celo7
0celo7
@dmckee you're a physicist
 
Slereah
Slereah
And Kundt, which is some obscure German paper
 
0celo7
0celo7
get me that paper dammit
I can translate
 
Slereah
Slereah
I can't find it
Kundt, Wolfgang 1956 Tragheitsbahnen in einem von Godel angegebenen kosmologischen Modell, Zeitschrift fur Physik 145, 611-620
 
0celo7
0celo7
10:22 PM
>
Kundt,W. (1956), 'Trii.gheitsbahnenineinemvonGOdelangegebenen kosmologischen Modell', Z8.J. PhY8. 145, 611-20.
 
Slereah
Slereah
If you want the ref
 
0celo7
0celo7
Hmm
the text got messed up
> Zeitschrift für Physik
Magazine of physics?
Wonder if that can mean any periodical
 
Slereah
Slereah
a classier translation would be the Journal of Physics
 
0celo7
0celo7
I'm not versed in academic German, Zeitschrift means magazine to me.
An odd number of times...
What??
 
Slereah
Slereah
Well
A normal curve only goes through that surface once, which is odd
But why necessarily odd for CTCs
 
0celo7
0celo7
10:26 PM
Ok, do we understand why that's a contradiction though?
The fundamental group for $\mathbb{R}^4$ is trivial, so all curves are homotopic to zero.
 
Slereah
Slereah
I'm not big on homotopy, so I dunno about the contraction only changing even numbers of whatever
 
0celo7
0celo7
@Slereah Well, that's the other part.
Ok, this diagram is confusing me.
What is the angular coordinate in the plane pictured?
$\phi$?
 
Slereah
Slereah
well there's only one angular coordinate
So yes
 
0celo7
0celo7
Wtf is up with this space, lol
 
Slereah
Slereah
It is quite a weird space
Made by Crazy Man Gödel
 
0celo7
0celo7
10:33 PM
> The diagram does not correctly represent the fact that all points are in fact equivalent.
What the fuck?
@Slereah I think this is hopeless.
 
Slereah
Slereah
@0celo7 : Godel spacetime is homogeneous
(time to see @0celo7 lose his mind)
 
0celo7
0celo7
waaaaaa
 
Slereah
Slereah
Homogeneous and rotationally symmetric
 
0celo7
0celo7
NO
I DON'T BELIEVE IT
 
Slereah
Slereah
Yeah it's kind of a weird spacetime
 
dmckee
dmckee
10:35 PM
@0celo7 Well, at a minimum I do a convincing imitation. Why?
 
0celo7
0celo7
@dmckee We need another mind
 
dmckee
dmckee
Well, that lets me out. I checked mine into a safety deposit box years ago.
 
Slereah
Slereah
Also I'm not quite sure where the "a continuous deformation can only change the number of crossings an even number" comes from
 
0celo7
0celo7
@Slereah We've established that.
(that we don't know)
 
Slereah
Slereah
Hm
Before the Godel universe, the chapter is the Kerr metric
Which has CTCs
Maybe some of the infos are there?
 
0celo7
0celo7
10:39 PM
You're telling me the metric on page 168 is...rotationally invariant?
Proof?
I didn't read this section when I went through HE the first time
I might read it again now
And finish it
 
Slereah
Slereah
Well see the cylindrical version of the metric
It is independant of $\phi$
 
0celo7
0celo7
Oh
So not spherically symmetric?
 
Slereah
Slereah
No, just cylindrical
But with no center
 
0celo7
0celo7
Ok, that makes me feel somewhat better.
Constant curvature $\Leftrightarrow$ homogeneous, isotropic — 0celo7 11 secs ago
@Slereah Is that correct?
 
Slereah
Slereah
Hm
Not sure
 
0celo7
0celo7
10:44 PM
I'm sure it's in Wald.
 
Slereah
Slereah
But then that would be the curvature of the whatchamacallit metric
intrinsic
 
0celo7
0celo7
What?
 
Slereah
Slereah
It's not maximally symmetric, either
Only 5 Killing vectors
 
0celo7
0celo7
Uh, what?
THERE ARE CTCS THROUGH EVERY POINT
WHAT IS THIS MADNESS
 
Slereah
Slereah
Eh, it's not the worse
At least not all curves are CTCs
 
0celo7
0celo7
10:49 PM
there's a space like that?
 
Slereah
Slereah
Sure
$(T^n, \eta)$
Any compact spacetime, really
It's a theorem even
 
0celo7
0celo7
wait, aren't there spacelike curves
or null cruves
@Slereah no
It's a theorem that compact spacetimes have CTCs
not that every curve is a CTC
 
Slereah
Slereah
All causal curves are closed
 
0celo7
0celo7
null curves certainly aren't CTCs...
 
Slereah
Slereah
CCCs
if you will
 
0celo7
0celo7
10:51 PM
where
proof
 
Slereah
Slereah
p. 21
 
0celo7
0celo7
is it not in HE?
 
Slereah
Slereah
Maybe I dunno
 
0celo7
0celo7
compact CTCs are in there somewhere
bottom of page 189?
 
Slereah
Slereah
heheheh
bottom
yeah, seems to be
 
0celo7
0celo7
10:55 PM
you troll
they never say all curves are CTCs
 
Slereah
Slereah
Oh yeah
I'm confusing non-chronological and non-totally vicious
(Totally vicious is when all causal curves are CCCs)
On the other hand :
"Theorem 3.3. [47] Any compact spacetime (M,g) which admits a timelike conformal Killing vector field K is totally vicious."
 
0celo7
0celo7
Hmm, I wonder if the math department would let me do my senior thesis on the Cauchy problem/causality issues.
This stuff is interesting.
 
Slereah
Slereah
OR IS IT
 
0celo7
0celo7
Ok, let's continue brainstorming.
an odd number of times
How??
 
Slereah
Slereah
I don't knooow ;w;
It might be something like
It basically has to be like a regular geodesic
With 1 passage through the surface
 
0celo7
0celo7
11:03 PM
are the Godel CTCs geodesics?
 
Slereah
Slereah
But the closed curve can add arbitrarily many 2 passages
No
They're just curves
that's a pretty vague argument, though
I'd like to see math
 
0celo7
0celo7
Is there some general principle here??
A closed curve can cross a surface how many times?
Don't think about Godel or anything for a sec
 
Slereah
Slereah
Even number, I suppose
 
0celo7
0celo7
Yeah, what the hell?
 
Slereah
Slereah
I think I'll go make a question
 
0celo7
0celo7
11:06 PM
alright
I'll answer this noob's question in the mean time.
 
vzn
vzn
@DanielSank @ACuriousMind @0celo7 @dmckee et al thx for the discussions/ thoughts/ refs on bells thm, reality as simulation etc, some folded into this :D
 
Slereah
Slereah
0
Q: Homotopy proof of the lack of foliation of the Gödel metric

SlereahA common proof of the lack of foliation of the Gödel universe, apparently mostly copy pasted from Hawking and Ellis, goes thusly : A closed timelike curve must cross a spacelike hypersurface without boundary an odd number of times A continuous deformation of the curve can only change the numbe...

general-relativity topology closed-timelike-curve
bam
 
0celo7
0celo7
+1
 
vzn
vzn
Oct 18 at 16:58, by 0celo7
the Matrix is mysterious
 
0celo7
0celo7
@vzn what?
 
vzn
vzn
11:19 PM
Oct 22 at 16:38, by 0celo7
I guess my commentary is that we live in the matrix :D
Oct 25 at 15:04, by 0celo7
You're forgetting the loophole that quantum mechanics = glitch in the matrix.
 
0celo7
0celo7
what?
 
vzn
vzn
Oct 18 at 16:54, by 0celo7
Methinks quantum mechanics is itself a consipracy to cover up mistakes in the Matrix. In particular, $\hbar$ is just a rounding error.
Mar 13 at 23:25, by 0celo7
@ACuriousMind ""Could QM be describing a non physical reality of information"...I have no idea what that means. " Translation: is QM the matrix?
 
Slereah
Slereah
You know
I once met a guy
He gave me his book
About his theory on QUANTUM MECHANICS
It is all crazy
 
vzn
vzn
Aug 5 at 1:02, by 0celo7
@ChrisWhite sounds like a simulation
Aug 5 at 0:44, by 0celo7
QM is an artifact of being in a larger, classical simulation
Oct 16 at 19:03, by 0celo7
Is "the world is a simulation" considered conspiratorial?
Aug 5 at 0:53, by 0celo7
From a purely aesthetic standpoint, the simulation idea is second to none
Mar 14 at 23:03, by 0celo7
@ACuriousMind Don't worry, it's hardly likely that our programmers were able to make gravity classical. Although, perhaps they had to start out simulation without working out all the bugs (bugs=QM).
 
0celo7
0celo7
what they hell are you doing?
 
vzn
vzn
11:25 PM
@0celo7 (isnt it obvious?) quoting you!
 
0celo7
0celo7
No, you're spamming the chat.
 
vzn
vzn
@0celo7 oh geez/plz, this from someone who talks endlessly for months on end :|
collected this link section on your own interests expressed numerous times in chat (universe as simulation!)... yw!
 
0celo7
0celo7
@vzn Are you trying to piss me off or something?
 
vzn
vzn
@0celo7 lol you remind me of eminem on colbert :P
dont you think your own ideas are worth pursuing? or was it all just a long running joke?
ok, maybe admit could have handled this all with more finesse, but have been planning this post for months, esp in response to regulars here :|
sigh :(
 
DanielSank
DanielSank
@vzn I don't remember discussing this, but you're welcome!
 
vzn
vzn
11:37 PM
@DanielSank :D
 
0celo7
0celo7
0
A: Why does the FLRW metric assume constant curvature?

0celo7Definition 1. A spacetime is said to be spatially homogeneous if there is a one-parameter family of spacelike hypersurfaces $\Sigma_t$ foliating the spacetime such that for each $t$ and for any points $p,q\in\Sigma_t$ there is an isometry of the spacetime metric $g$ which takes $p$ to $q$. Defin...

 
vzn
vzn
DS we discussed it back in mid sep. even linked to your comments in the post. dug them up/ excavated them.
(ahem though) obviously, the pov expressed is my own :|
even cited your recent bell/ weak measurement paper. awesome stuff. :D
 
0celo7
0celo7
hey someone likes my answer :D
 
vzn
vzn
@ACuriousMind whoa! snicker! reminds me of story of polly nomial...
lol finally got your attn... that is exactly correct :P
 
HDE 226868
HDE 226868
@DanielSank What's the connection to experimental physics here? Is it that the cables could be used for transmission in experiments?
Actually, did I ask you this before? I apologize if that's the case.
 
0celo7
0celo7
11:47 PM
@HDE226868 as an astronomy nerd you might appreciate my answer above
 
DanielSank
DanielSank
@vzn Lol. My first moments in the limelight are me ranting about how old school quantum is kind of janky.
I guess that's fitting though ;D
 
vzn
vzn
@DanielSank whoa, janky, did not even know that was a word. but sounds cool whatever it is :) ... surely where you would like to have your work immortalized, on a hardcore "QUODS" page...? :D ("limelight"?!? yeah right!)
 
0celo7
0celo7
Ok, my answer should be correct now.
 
HDE 226868
HDE 226868
@0celo7 I haven't had the chance to look yet. Reading now.
 
0celo7
0celo7
Now it's correct!
Maybe!
 
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