The h Bar

0celo7

22:00

@Slereah why does $v$ need to be hypersurface orthogonal?

Slereah

So that the hypersurface is spacelike?

0celo7

Cyber - Everything Is God (Official HQ Preview)

►

@Slereah Uh, is timelike always orthogonal to spacelike?

Slereah

I don't knooow

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

I want to say it is

0celo7

22:07

> Any vector orthogonal to a timelike vector is necessarily spacelike or zero.

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

Yes.

It's true.

This book is handy.

amazon.com/…

Wow.

I'm interested.

Slereah

So Frobinius is a handy way to check for spacelike hypersurfaces

0celo7

@Slereah Apparently.

Ok, let's continue.

One of us has to bite the bullet and calculate $v\wedge\mathrm{d}v$.

Slereah

It's already in Godel's paper

0celo7

22:12

I know it is, but we trust that?

dmckee

Er ... @Floris, do you really think that physics.stackexchange.com/questions/216450/… is the kind of homework question we want to encourage?

0celo7

mod super ping power to stronk

Slereah

$\star (v \wedge dv) = (0,0,0,\sqrt 2 / a^2)$

0celo7

what is $a$

Slereah

Parameter of the Godel metric

0celo7

22:13

$\equiv 1$ in HE?

Slereah

Hell if I know

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

In the proof it's a timelike vector field

0celo7

"a"

It has to be the tangent of the CTC, right?

Slereah

No

It's just a generic timelike vector field

$(1,0,0,0)$

Well $(1/a,0,0,0)$

0celo7

22:18

You know (1,0,0,0) satisfies Frobenius trivially...

In every space

So that doesn't make sense.

Slereah

Does it?

Because NOT HERE APPARENTLY

0celo7

Dude, $\mathrm{d}(\text{const.})\equiv0$

Slereah

Well

See

That's $v^a$

0celo7

oh, you have to...yeah

Slereah

The 1-form is $v_a$

0celo7

22:20

Yes.

Slereah

which is... $(a, 0,a e^{x_1}, 0)$

0celo7

Ok, now what is Hawking blabbering about

Slereah

some shit about the CTC having to cross the surface an odd number of time

0celo7

Yes.

Proof?

Slereah

he does not say

0celo7

22:21

I know!

Slereah

And the only references are Godel, which does not use it

0celo7

@dmckee you're a physicist

Slereah

And Kundt, which is some obscure German paper

0celo7

get me that paper dammit

I can translate

Slereah

I can't find it

Kundt, Wolfgang 1956 Tragheitsbahnen in einem von Godel angegebenen kosmologischen Modell, Zeitschrift fur Physik 145, 611-620

0celo7

22:22

>
Kundt,W. (1956), 'Trii.gheitsbahnenineinemvonGOdelangegebenen kosmologischen Modell', Z8.J. PhY8. 145, 611-20.

Slereah

If you want the ref

0celo7

Hmm

the text got messed up

> Zeitschrift für Physik

Magazine of physics?

Wonder if that can mean any periodical

Slereah

a classier translation would be the Journal of Physics

0celo7

I'm not versed in academic German, Zeitschrift means magazine to me.

An odd number of times...

What??

Slereah

Well

A normal curve only goes through that surface once, which is odd

But why necessarily odd for CTCs

0celo7

22:26

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

I'm not big on homotopy, so I dunno about the contraction only changing even numbers of whatever

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

well there's only one angular coordinate

So yes

0celo7

Wtf is up with this space, lol

Slereah

It is quite a weird space

Made by Crazy Man Gödel

0celo7

22:33

> 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

@0celo7 : Godel spacetime is homogeneous

(time to see @0celo7 lose his mind)

0celo7

waaaaaa

Slereah

Homogeneous and rotationally symmetric

0celo7

NO

I DON'T BELIEVE IT

Slereah

Yeah it's kind of a weird spacetime

dmckee

22:35

@0celo7 Well, at a minimum I do a convincing imitation. Why?

0celo7

@dmckee We need another mind

dmckee

Well, that lets me out. I checked mine into a safety deposit box years ago.

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

@Slereah We've established that.

(that we don't know)

Slereah

Hm

Before the Godel universe, the chapter is the Kerr metric

Which has CTCs

Maybe some of the infos are there?

0celo7

22:39

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

Well see the cylindrical version of the metric

It is independant of $\phi$

0celo7

Oh

So not spherically symmetric?

Slereah

No, just cylindrical

But with no center

0celo7

Ok, that makes me feel somewhat better.

Constant curvature $\Leftrightarrow$ homogeneous, isotropic — 0celo7 11 secs ago

@Slereah Is that correct?

Slereah

Hm

Not sure

0celo7

22:44

I'm sure it's in Wald.

Slereah

But then that would be the curvature of the whatchamacallit metric

intrinsic

0celo7

What?

Slereah

It's not maximally symmetric, either

Only 5 Killing vectors

0celo7

Uh, what?

THERE ARE CTCS THROUGH EVERY POINT

WHAT IS THIS MADNESS

Slereah

Eh, it's not the worse

At least not all curves are CTCs

0celo7

22:49

there's a space like that?

Slereah

Sure

$(T^n, \eta)$

Any compact spacetime, really

It's a theorem even

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

All causal curves are closed

0celo7

null curves certainly aren't CTCs...

Slereah

CCCs

if you will

0celo7

22:51

where

proof

Slereah

arxiv.org/pdf/gr-qc/0609119v3.pdf

p. 21

0celo7

is it not in HE?

Slereah

Maybe I dunno

0celo7

compact CTCs are in there somewhere

bottom of page 189?

Slereah

heheheh

bottom

yeah, seems to be

0celo7

22:55

you troll

they never say all curves are CTCs

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

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

OR IS IT

0celo7

Ok, let's continue brainstorming.

an odd number of times

How??

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

23:03

are the Godel CTCs geodesics?

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

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

Even number, I suppose

0celo7

Yeah, what the hell?

Slereah

I think I'll go make a question

0celo7

23:06

alright

I'll answer this noob's question in the mean time.

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

3 hours ago, by vzn

on the so-called “loophole free” Bell entanglement test and other hot developments in QM theory/ applications / Tmachine blog

Slereah

0

Q: Homotopy proof of the lack of foliation of the Gödel metric

A 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...

bam

0celo7

+1

vzn

Oct 18 at 16:58, by 0celo7

the Matrix is mysterious

0celo7

@vzn what?

vzn

23:19

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

what?

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

You know

I once met a guy

He gave me his book

About his theory on QUANTUM MECHANICS

It is all crazy

dl.dropboxusercontent.com/u/19940612/…

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

what they hell are you doing?

vzn

23:25

@0celo7 (isnt it obvious?) quoting you!

0celo7

No, you're spamming the chat.

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

@vzn Are you trying to piss me off or something?

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

@vzn I don't remember discussing this, but you're welcome!

vzn

23:37

@DanielSank :D

0celo7

0

A: Why does the FLRW metric assume constant curvature?

Definition 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

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

hey someone likes my answer :D

vzn

@ACuriousMind whoa! snicker! reminds me of story of polly nomial...

lol finally got your attn... that is exactly correct :P

Polly Nomial: A Mathematical Fable

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

23:47

@HDE226868 as an astronomy nerd you might appreciate my answer above

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

@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

Ok, my answer should be correct now.

HDE 226868

@0celo7 I haven't had the chance to look yet. Reading now.

0celo7

Now it's correct!

Maybe!

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