The h Bar

0celo7

00:00

@Slereah is time orientable $\Leftrightarrow$ nonvanishing timelike vector

or is it only one way

@ACuriousMind yeah, what's up with that

Slereah

All spacetimes have a non-vanishing timelike vector

0celo7

He goes on the main site regularly, but never comes here :/

Slereah

That's lorentzian metric equivalent to nonvanishing timelike vector

But the trick is

All spacetime manifolds are time orientable

Not all metrics are time oriented, though

0celo7

what does that even mean

the metric is what tells you what is timelike

how can the spacetime been time oriented

Slereah

Given a spacetime topology, you can always define a metric on it that is time oriented

0celo7

00:03

what?

where is the proof

Slereah

arxiv.org/abs/gr-qc/0609119

ACuriousMind

@Slereah Are metrics which generate the same topology physically equivalent?

Slereah

Theorem 2.4.
For any connected smooth manifold, the following properties are equivalent:
(1) M admits a Lorentz metric.
(2) M admits a time-orientable Lorentz metric.
(3) M admits a non-vanishing vector field X.
(4) Either M is non-compact or its Euler characteristic is 0.

Well metrics don't generate topologies

0celo7

Lorentz metrics don't

Slereah

"(1) ⇒ (2) (The converse is trivial.) The time orientable double covering ( ̃M, ̃g), satisfies (3) and hence (4). So, the latter is satisfied obviously by M."

0celo7

00:06

Wait a moment

ACuriousMind

ah, I misunderstood what you meant by "spacetime topology"

0celo7

How the heck are the open sets in spacetime even defined :o

Preimage of open sets of R^4 under a chart?

Slereah

Well yes

It's a manifold

The spacetime metric isn't the same notion as the metric space that the manifold is

0celo7

I must be stupid or something

ACuriousMind

@Slereah How is the manifold a metric space?

That's only true in the Riemannian case

0celo7

00:08

but there's also the "Alexandrov topology"

Slereah

Eh I dunno

I'm not a math guy

0celo7

Ok I must be really dumb

How are open sets on the manifold defined

D:

Slereah

What you said.

Images of open sets in $R^4$

0celo7

@ACuriousMind is this true

Slereah

Well it's true in 4 dimensions

0celo7

00:11

ah, the charts are homeomorphisms

ok got it

derpy moment

AngusTheMan

Evening guys. A classical harmonic oscillator doesn\t have time translational symmetry does it?

Slereah

It does

0celo7

Of course it does

AngusTheMan

does it...

0celo7

The Hamiltonian doesn't have time dependence

Slereah

00:12

$L = m \dot x^2 + \omega x^2$

No time involved

ACuriousMind

@0celo7 Well, the formal answer is, they aren't "defined" at all: A manifold is by definition a topological space that fulfills some extra conditions. But it is true that the topology is generated by the (pre)images of open sets in $\mathbb{R}^n$ under some chart.

0celo7

should that be $H=$

I get the signs mixed up with the SHO

Slereah

w/e

0celo7

@ACuriousMind Exactly.

Forgive my moment of weakness there.

AngusTheMan

well I agree with you guys but look at Qmechanics answer here .. what am I missing?

ACuriousMind

00:14

...where?

AngusTheMan

11

Q: Do an action and its Euler-Lagrange equations have the same symmetries?

Assume a certain action $S$ with certain symmetries, from which according to the Lagrangian formalism, the equations of motion (EOM) of the system are the corresponding Euler-Lagrange equations. Can it happen that the equations of motion derived by this procedure have different kinds and/or numb...

0celo7

@ACuriousMind ^

AngusTheMan

example 3

haha

Slereah

He talks about symmetry in the solution, not the dynamic itself

That is a different thing

ACuriousMind

@AngusTheMan That's time-scaling, not time translation.

AngusTheMan

00:15

embarrassed emoji face

:p

cheers :)

ACuriousMind

@AngusTheMan don't worry, it happens ;)

0celo7

flipping through Lee

he wrote a 700 page diff geo book without talking about connections

Like a personal trainer I taught coke how to stretch. - Jay Z

Slereah

How

I mean

Technically you don't need connections for a metric space

Still feels a bit of an omission

0celo7

get it "legally" and don't look

he only does Riem geom for a few pages

enough to introduct geodesics so he can talk about the exponential map

Slereah

You can't do geodesics without a connection >:|

0celo7

00:20

To be fair the actual book is 600 pages, the rest is review and index

@Slereah lol

no shit...

lemma skim

ACuriousMind

@0celo7 Look at it. It is about smooth manifolds not pseudo-Riemannian menifolds.

And a generic smooth manifold just doesn't come with any kind of connection

0celo7

@ACuriousMind Look at it! I own it!

Not gonna read the whole thing.

ah

I'm really dumb

It's the exponential map of Lie algebras, not geodesics

I just assumed embarrassed emoji face

I wonder what the Lie derivative on twistors looks like

vacuum $\to$ scalar $\to$ vector $\to$ tensor $\to$ spinor $\to$ tensor valued spinor $\to$ twistor $\to$ Xor

solve for X

also why isn't it a scalor

Slereah

I still don't know what a twistor is

Also where is the schwingor

We decided that spin 3/2 fields were schwingors

0celo7

I got a book on twistor

but I returned it to the library

ACuriousMind

@Slereah Not raritars?

0celo7

00:26

chat.stackexchange.com/search?q=schwingor&user=&room=71

is anyone else getting results for that?

Slereah

"Twistor theory is unique to 4D Minkowski space and the (2,2) signature, and does not generalize to other dimensions or signatures."

Oh, so it's boring

Oct 1 at 13:43, by 0celo7

Rarita-Schwingors

Oct 1 at 13:44, by Slereah

Schwingors

0celo7

dude it gives me "zero results"

Slereah

mb u r just bad at it

ACuriousMind

@0celo7 It's case-sensitive

0celo7

@ACuriousMind wow

that's pretty stupid

ACuriousMind

00:28

Yep

0celo7

lies

ACuriousMind

Hm, perhaps it lowercases uppercase but does not uppercase lowercase?

0celo7

ACuriousMind

Hm, no

Ah!

You typed schwingor

But slereah said schwingors

It's the s

0celo7

ha!

ACuriousMind

00:31

Huh?

lol

0celo7

What?

0celo7

01:01

@Slereah I don't need a connection. A geodesic solves $\delta\int \langle v,v\rangle\,\mathrm{d}t=0$

@ACuriousMind why do you hate $\oint$

Even in CFT?

What about all of those loop integrals :o

Slereah

That's not a geodesic >:|

That is just the shortest path!

0celo7

@Slereah Aren't you asking multiple questions in your question

Slereah

Eh

0celo7

Geodesic := shortest path

Slereah

Not if there's torsion >:|

0celo7

01:04

"is this the right action"

"what is the infinite sum formulation"

@Slereah I have yet to read that torsion document you sent me

Slereah

Hm

I recall reading that torsion may have geodesics that are not the shortest path

But I'm not sure

In the geodesic equation IIRC the torsion term vanishes

0celo7

@Slereah it's true

you can calculate it

Slereah

Since it's $T^a_{bc} \dot x^c \dot x^b$

0celo7

well vary that integral

Slereah

And the tensor is antisymmetric in b and c

0celo7

01:06

see what you get

then add the torsion in by hand

and you get a torsion equation

because the connection is different with torsion I think

then you get the shortest path with torsion

the geodesic equation $\nabla_vv=0$ has no torsion in it

right, @ACuriousMind ?

Slereah

It does

It's right in there

$\nabla$

0celo7

no

damn, what the hell is torsion, again?

Slereah

Torsion is the antisymmetric part of the connection

0celo7

[4K UHD] Hard Bass 2015 Frequencerz LIVE

►

ok ok

torsion doesn't appear explicitly in the geodesic equation

actually shouldn't it fall out completely?

Slereah

Yeah that's what I wonder

Since it only appears in a symmetrical term

0celo7

01:10

because you get $\Gamma^i{}_{jk}v^jv^k$

Slereah

"The antisymmetric part of the Christoffel symbols will not contribute here in any case, but the torsion will change the symmetric part (and thus invalidate the conclusion that extremal length paths are geodesics) if and only if $T_{cab} \neq T_{[cab]}$."

Hm

0celo7

torsion changes the symmetric part o.o

where are you reading this

Slereah

I DON'T KNOW ANYMORE

slimy.com/~steuard/teaching/tutorials/GRtorsion.pdf

0celo7

@ACuriousMind why isn't the plural of "album" "alba" and not "albums"

which idiot put that minus there

he should be shot

Slereah

Geodesic for torsion might be a bit more delicate to derive I suppose

I dunno

Hm

$u^a \nabla_a u^b = u^a (\partial _a u^b + {\Gamma^a}_{bc} u^b) = u^a \partial _a u^b + {\Gamma^a}_{bc} u^b u^a = u^a \partial _a u^b + {\Gamma^a}_{\{bc\}} u^b u^a$

0celo7

01:19

f that

Slereah

No it should still be the symmetrical part

0celo7

oh, that's not bad

yes it's the symmetric part

Slereah

Wait

No

I fucked up my indices

0celo7

I've never seen braces on indices

yeah you did

Slereah

a should be on the bottom

(heheheh bottom)

0celo7

01:20

I thought you were some kind of GR guy

can't even indices

Slereah

Braces indicate symmetrization

0celo7

ok so what is the symmetric part of the connection when there's torsion

Slereah

it's the regular old connection

0celo7

no

Slereah

Maybe I dunno

0celo7

01:22

there's something we don't understand going on

Slereah

There's a few different tensors

Let's check

0celo7

> The other is the source of the name
(as I understand it): a “shortest possible path” between any two of its points
(or more generally, an “extremal length path” between them). In the presence
of torsion, these two concepts need no longer be equivalent

that's what we need

Slereah

Oh wait

I might have confused the torsion tensor with the contortion tensor

Maybe

I don't know

0celo7

contorsion tensor?

Slereah

Contorsion tensor is the difference between the Levi Civitta tensor and the general tensor

0celo7

01:24

what?

Slereah

Contorsion tensor

The contorsion tensor in differential geometry expresses the difference between a metric-compatible affine connection with Christoffel symbol and the unique torsion-free Levi-Civita connection for the same metric. The contortion tensor is defined in terms of the torsion tensor as where the indices are being raised and lowered with respect to the metric: . The reason for the non-obvious sum in the definition is that the contortion tensor, being the difference between two metric-compatible Christoffel symbols, must be antisymmetric in the last two indices, whilst the torsion tensor itself is...

0celo7

ah

that last bit is the contorsion tensor

Slereah

yeah the contorsion tensor is a bit different from the torsion tensor

Not the same symmetries

0celo7

ah that's in BBS

you need torsion in string theory

torsion is BS

no wonder Einstein said fuck it

wait why is there no torsion in GR

I always forget it

Slereah

Because nobody cares about torsion in classical mechanics

No classical field carries torsion

0celo7

01:28

why

I still haven't read that torsion thing you gave me

no clue where I put it

Slereah

The torsion equation is roughly $T = \Theta$

With $\Theta$ being the spin tensor

It is 0 for scalar fields

I think it's also 0 for EM fields

Let me check

0celo7

spin tensor

dude gimme a link to that shiz niz

arXiv paper

Slereah

The spin tensor is the variation of the lagrangian with respect to the torsion tensor

(or contorsion, whatever)

0celo7

o.o

Slereah

Scalar fields and EM fields don't use the connection at all

0celo7

01:31

just give me the thing

Slereah

So their variation is 0.

xxx.lanl.gov/pdf/0911.0334.pdf

0celo7

thanks

sigh

Slereah

So there really isn't much point of doing torsion for GR since basically you'll never use it

0celo7

sometimes GR sucks balls

speaking of balls

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Big dog; big nuts. - Lamar Davis

i.4cdn.org/b/1446423548370.webm

Slereah

"Only the symmetric part Γi(kl) of the connection enters the autoparallel equation [...] geodesics do not depend on torsion"

>:\

0celo7

01:46

lelelele

Slereah

Which one is it!

Maybe when they say "In the presence of torsion, these two concepts need no longer be equivalent", they don't actually mean that it's not

dmckee

OK, then. Someone who doesn't understand first semester basics about the centripetal force has been bothering us with endless questions about his efforts to overthrow the current understanding of large scale cosmology. Nice.

Slereah

He has Einstein and the evidence backing him up

Well 3 AM

Best go to bed

0celo7

night

@dmckee Not me!

dmckee

@0celo7 No, someone with much less self awareness than you. Shocking, I know.

0celo7

02:02

@dmckee damn, way to rek me

what did I do to you :'(

@dmckee who is this person

dmckee

That's for you to figure out.

0celo7

@dmckee so I'm not self aware

in what sense

dmckee

@0celo7 In the sense that your buddies, even casual ones, pass casual insults just for the hell of it. I don't know you well enough to hazard a guess about your inner self.

0celo7

> In the sense that your buddies, even casual ones, pass casual insults just for the hell of it.

dmckee

If you want an appology, you can have it. But then I'll think you thin skinned. (And so the "society" of lads is propagated.)

0celo7

02:07

I don't know what that means.

I don't want an apology, I want to know why you think it.

skull petrol

Why ask why?

0celo7

So I can "look inward" and decide if it's something I want to correct.

@dmckee Donald?

skull petrol

What does "self awareness" mean to you?

0celo7

Not sure, that's why I'm asking.

skull petrol

Are you asking for a definition?

0celo7

02:16

Sure + why I lack it

skull petrol

Each person defines it differently for themselves, because of the "self" aspect.

0celo7

ok, so @dmckee has to define what he means by it

skull petrol

No, you have to decide what you think of yourself.

That^ is self awareness.

:-)

0celo7

can @dmckee just explain?

skull petrol

He has not interrupted, has he?

dmckee

02:23

@0celo7 I did explain. It was a pointless dig of no importance. Basic ladismo at work.

0celo7

>ladismo

What?

dmckee

In al seriousness, I'll lay off that sort of nonsense if you want, but I had interpreted some of your actions here as being of the same kind.

0celo7

"same kind"

I have no idea what you're talking about

dmckee

Take "lad" in the slightly pejorative sense the British use and mash the ending of machismo on it...

@0celo7 In that case I might have been right. But that was purely by chance. Think nothing of it.

0celo7

32 mins ago, by dmckee

OK, then. Someone who doesn't understand first semester basics about the centripetal force has been bothering us with endless questions about his efforts to overthrow the current understanding of large scale cosmology. Nice.

The reason I said "not me" is because I thought the first few words were about me or something

then I read on and figured out it wasn't

dmckee

02:25

@0celo7 Donald has been trying to overthrow big bang cosmology for the last few months. But it seems he would have struggled on the test I gave last week.

Of course, my class struggles, too. So he'd have been right at home.

0celo7

But I'm certainly not challenging any theory!

So I don't know what "I had interpreted some of your actions here as being of the same kind" means

What actions, specifically?

dmckee

Several times when you engaged in seemingly pointless rounds of minor insults with other users. Or should I have taken them seriously and move in with my moderator nightstick?

0celo7

They must have been minor enough for me to not remember them at all.

You mind saying which users?

And how does that make me lack "self awareness", whatever that means?

0celo7

02:41

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What is that guy really saying

skull petrol

03:00

Sorry couldn't get past the laugh.

0celo7

@skullpetrol What?

skull petrol

The laugh was too annoying.

0celo7

I didn't notice it.

skull petrol

You are a troll.

Put that^ on your "self awareness" list :P

0celo7

I wish @dmckee responded

JAN ORTS

09:07

anybody here???

This is my problem: The bungee jumper jumps to the water from the bridge that is 24 metres high... First 12 metres of the fall the cord is not extended, it is only the free fall... The next 12 metres the cord is extended and the total fall is 24 metres, so the jumper falls in a way that he almost touches the water... The weight of the jumper is 60 kg. What is the maximum speed that the jumper attains during the fall?

JAN ORTS

09:31

The maxim speed is reached after falling more than 12 metres because the speed is growing as long as the downward force of gravity is greater than than the upward force of extension of the spring. F = m*a , m*g - k*Δx = m*a . The speed stops growing when a=0, when those two forces are equal. At this moment the jumper attains the maximum speed.

The thing is that I don't know how to calculate this maximum speed.

John Duffield

12:48

@bolbteppa : I know plenty of maths. IMHO what's important is to understand what the terms really mean. If you've ever seen any of my stuff you can see how I've looked hard at things like E and m and c and C. As for rotation and reflection, please provide a link and I'll comment.

John Duffield

13:25

@JANORTS : see this for something that might help.

bolbteppa

I see 0celo on a downward spiral :\ linear algebra is a tough subject, would drive anybody down that road, even moreso if they had been studying string theory 2 months before

Slereah

His problem is that he is studying math

He should study physics!

Secret

linear algebra is ok when compared to real analysis

skull petrol

@JohnDuffield if you know "plenty of maths" explain to me right here, without any links why can you never divide by zero?

Secret

bolbteppa

13:36

Well I did a math course so that the time would come when I could learn physics at the best level without math holding me back, so it's a good idea if you are willing to wait 2 years

Secret

RpfnoR 7 (this mathematical structure has some binary operator, and it is its own inverse, it is closed under the operation and)

but it lacks an identity)

I tend to rely on maths to gain insights on the physics problem

bolbteppa

But I did not go off studying string theory books without real analysis or linear algebra, which is like the biggest sin a student could commit in my eyes

@Secret I find it's very helpful at times, but I'm always conscious of that Feynman warning where he says math might ruin everything haha

Secret

Yeah, when you are too relied on maths, you have to be careful that some solutions to the equations can corespond to something unphysical,

Also, ASSUMPTIONS, (ugh I suck at these!)

bolbteppa

@JohnDuffield your profile here science20.com/profile/john_duffield (not working for me at the moment for some reason) says you don't know much math, even the stand up physicist guy was admonishing you on that site, personally I would take it as a sign I may be doing something wrong hehe

Slereah

Maybe the fact that all physicists do would be a warning sign

Secret

13:40

typo: Red should be +-odd number

bolbteppa

@JohnDuffield But you say you've tried hard to understand energy $E$, do you know how to write down the energy in special relativity from a Lagrangian?

I'm not trying to catch you out, merely trying to convince you to study math more thoroughly, and better physics books than the ones you've read

"Something of an analyst and logician, well read on physics, but maths relatively weak and technically an amateur."

Secret

From the above diagram I am suspecting the set {odd, even,+,-} forms some kind of rng

Slereah

I imagine now Duffield frenetically looking up on wikipedia the formula to copypaste it

skull petrol

Lol

Slereah

although odds are low

He will probably just go "The math isn't important!", as usual

bolbteppa

13:44

@Secret I don't get the diagram, looks like you're just permuting $1$ and $2$ and giving a sign to the permutation as odd or even?

Secret

I am trying to illustrate the relationship when you add an odd number to an odd number, and even number to an even number and an odd umber to an even number

It's just something that pops up when I am procratinating because of being frustrated too much by some matlab code

we know that
odd+odd=even
even + even=even
odd + even=odd

I am just jotting these out some some kind of map or graph or something

because I am curious on its structure

bolbteppa

Maybe you can write it out with delta functions as something like $(2n + \delta^i_j ) + (2m + \delta ^k_l)$ haha

So you want the structure of the quotient group of the additive integer group mod 2

Secret

probably, I am just curious on what operations lead to where

Let's use a london subway map as an analogy, what I am doing above is trying to construct something like a guide so that I can see where and how I get to places

Becuase I have a tendency to like to make "roadmaps" of mathematical objects, and then start doing some extra things to it

Slereah

Nooooo

@Secret : This is your mistake :

smbc-comics.com/index.php?id=3892

Secret

uh...

bolbteppa

13:54

haha

$E = RF$

Secret

I didn't say I have a clever analogy, I am just saying how I think about it.
I don't force people to use them, and I am actually pretty dumb

or am I still making That Mistake?

I could have jsut say I want to make a map for mathemtical objects for myself to explore it, but I cannot say that because maths peopel here will think I am talkign about maps as defined in mathematics

Sometimes I just don't have enough volcabulary to express what I am trying to say

hence all that confusing analogy speak

bolbteppa

Secret

One of my personal hobby is to watch a maths object breaks down when you start messing with it and see what pops out

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