The h Bar

Sweating on Skype with 5 seasoned developers in a foreign country trying to make a nodejs app run in azure. Haaa I'm doomed . . . . doomed doomed doomed

Slereah

Lots of TV my man

Hardest part of getting another culture btw

Schoolyard rhymes

Not a lot of those even on TV!

What's a good way to think about the vertical space btw

I'm trying to think of a good way

Is it related to the functional derivative?

It's the tangent of the fiber after all

0celo7

The manifold is a horizontal line, the fibers of the bundle go up, and the vertical fibers are tangent lines to the vertical dudes

Slereah

A vector is obtained by varying the value of the field

Or am I mistaken

0celo7

Keep reading Christo

I think you’re basically correct

Maybe

Slereah

12:46 AM

Hurray

It does help

And since there's some mapping between the jet bundle and the vertical space I'm guessing it will be involved for lagrangian stuff

0celo7

1:18 AM

@Slereah the vertical bundle plays a big role in this stuff

it makes it that much harder to understand though

it's another god damn bundle floating around

Slereah

I can sort of see the notion though, I guess?

Vertical bundle for varying the field

Horizontal bundle for the space derivatives

I guess?

Something like that

0celo7

pretty much -- to get the horizontal bundle you need a connection of course

Slereah

Yeah

0celo7

but ideally the connection doesn't really matter

Slereah

I usully try to picture the tangent bundle on $S \times \Bbb R$

It helps a bit

Well, a tangent plane anyway

0celo7

1:21 AM

that seems pretty hard already

I think of stuff on $[0,1]$

Slereah

The $[0,1] \times \{0\}$ bundle?

0celo7

no, like $T[0,1]$ is what I picture as "bundle" in my mind

or $[0,1]\times S^1$ if I need a principal bundle

Slereah

Not much of a difference with R for picturing

0celo7

yeah

so really $(0,1)$

@Slereah the spacetime on page 3 of the 50 years book is too funny

he must have freehanded it

Slereah

It's alright

0celo7

1:31 AM

$V$ being the manifold is French supremacy

Slereah

Une variété

0celo7

@Slereah have you seen anything other than $\beta$ for the shift field?

Slereah

Pretty much always beta

0celo7

1:48 AM

@Slereah hae you seen HBO's Rome?

Cows

2:12 AM

I have another interview next week. This time it's with one of the big tech companies. OMG going have to go over algorithms and data structures. hehe

Sir Cumference

4:06 AM

@EmilioPisanty Oh deer

@ooolb Oh whale

I'll stop with the puns...

skullpatrol

...u so punny

Slereah

6:55 AM

@0celo7 I did not

Sir Cumference

7:48 AM

I'll never understand why people vote on questions with ≥10 score in Area 51 proposals

@JohnRennie Probably a foolish question, but shouldn't it fall into Chemistry, or at least Physics?

John Rennie

@SirCumference the comment wasn't meant to be serious. Physical chemistry questions are generally on topic both here and in the Chemstry SE.

Sir Cumference

Oh...welp 3:00am me is dumb

John Rennie

In this case I would guess Chemistry is better since this looks more chemistry ish than physics ish

But I suspect answering the question would require specialist knowledge of the area, and I doubt anyone on either SE has that experience.

Sir Cumference

@heather For me, sitting in history class was the worst, but now that I'm finally done with high school I wish I had learned more history

Funny thing, once you're done groaning in the classroom, it actually becomes quite interesting

That's at least what I notice with a lot of the subjects I used to hate learning

Slereah

8:15 AM

Euler-Lagrange on the Jet bundle is apparently $(\partial_i - d_\lambda \partial^\lambda_i)\mathcal L = 0$

ooolb

fml

Sir Cumference

Oye, is there any to get an anti-spam bot for an SE site? Just look at this

Slereah

Apparently equations on the second jet bundle

bluh

Sir Cumference

Every other day we get links to sites, usually involving weight loss or testosterone

Slereah

maybe you need to be less fat and manlier

Sir Cumference

8:17 AM

Eheh...

This is my 11th spam flag in the last month...

ooolb

i am not me right now

i still havent gotten over my haircut why the fuck did i do it

Sir Cumference

At the very least there should be a bot to block questions with titles including ".com"

ooolb

i need looooong hair again

Sir Cumference

@ooolb You need @Loong here again?

ooolb

i’ll admit that pun was impressive

Sir Cumference

8:20 AM

:D

ooolb

but your other ones kinda suck no offense

Sir Cumference

;-;

ooolb

you should do more original ones like that

Sir Cumference

I usually am original

I think

ooolb

well i mean the science ones gotta go

John Rennie

8:21 AM

@ooolb perhaps he doesn't like folding paper ...

Sir Cumference

@ooolb But math ones are at least good. You just gotta look at them from the right angle

Eh?

Ehhhh?

John Rennie

Another failed joke. Oh well :-)

Sir Cumference

:(

John Rennie

Attempted pun on original and origami

Slereah

oregano?

Sir Cumference

8:25 AM

@JohnRennie Oh, I thought you were talking about my pun XD

Slereah

Apparently the tangent space of the field bundle defines the exterior derivative of the ~variational bicomplex~

Of which the variation is the part that projects on the vertical bundle

neat

ooolb

@JohnRennie dude you cant do that

those are so different like wtf

John Rennie

@ooolb I just did :-)

ooolb

thats like doing a pun on physics vs physiotherapy

like what

Slereah

Oh no

Also why are those guys defining the Lagrangian on the infinite jet bundle

Do they think I'm gonna do the sine Gordon equation or something

Jesus that paper has the composite bundle $J^r F \to F \to Y \to X$

How many bundles do you need

skullpatrol

9:34 AM

\o @Blue

Anonymous

\o/

skullpatrol

:-D

Mithrandir24601

@Slereah an infinite number of infinite bundles, obviously :P

Anonymous

Could someone tell me what "open" and "closed" cluster mean, in a graph (w.r.t graph theory)? I can't find any relevant definition on the net

Anonymous

They just say it is maximal connected set of "open" edges of a graph....I don't understand what "open" edge of a graph means

Anonymous

9:44 AM

"closed" edge might still make sense

Mithrandir24601

@Blue Isn't an open edge one that only connects to one vertex (and it doesn't loop back to 'touch' the vertex twice)? It's been a few years, so I may be very wrong

(I remember such an edge being used, but I've completely forgotten what it was called)

Slereah

Hm, how do I write the set of open sets on a manifold

$\tau(M)$?

For the topology

Anonymous

@Mithrandir24601 Isn't an edge, by definition, one which connects two nodes/vertices/points of a graph?

Anonymous

Maybe they just mean that edge is absent

Anonymous

And are calling it open edge

Anonymous

9:54 AM

But then the meaning of open cluster is confusing

lılostafa

Mithrandir24601

@Blue generally yes, but in the likes of QFT, you want a way to represent incoming/outgoing particles, which only connects to one vertex, so you need another term for this - I've no idea if this is an 'open edge' or not though :/

Slereah

Good idea, bring up QFT :p

That will simplify things

skullpatrol

have you seen this @Blue?

Anonymous

9:58 AM

Damn, how bad can typography be....

lılostafa

@lılostafa They've changed the text in parenthesis. Yesterday it said something like "completed the annual survey, and provided your stackoverflow account!"

now it says your responses are anonymous

skullpatrol

you have been "anonymized" :P

lılostafa

@Blue I love old physics/math books that I find in the university library..

Mithrandir24601

@Blue are 'r' and 's' two separate graphs that have been connected together or something?

lılostafa

Did you see this‌? @Blue

The story of 4 Indian mountaineers trying to summit Mount Everest, that were abandoned by their guides and left to die on the mountain

and remained there for 1 year

skullpatrol

10:06 AM

How sweet of them.

lılostafa

really great journalism by the NYTimes

skullpatrol

The link is broken, btw.

lılostafa

@skullpatrol Ohhh

nytimes.com/interactive/2017/12/18/sports/everest-deaths.html

Anonymous

@Mithrandir24601 I'm still trying to decipher it. They defined those waaaay back

Anonymous

This book: link.springer.com/book/10.1007%2F978-1-4899-2730-9

Anonymous

10:09 AM

Page 221

Anonymous

You'll get it on libgen :P

Slereah

@Blue Is that how to brew coffee/amphetamines

Anonymous

Yeah, that would be a nice application (as mathematicians would say);)

bolbteppa

So apparently Weyl came up with a lot of this 'affine connection' stuff

pdfs.semanticscholar.org/c5ea/…

Physicist invents abstract math shocker

Anonymous

@lılostafa Ah, that's awful :(

Anonymous

10:20 AM

I didn't know that

Anonymous

Last year several soldiers had died in the Ladakh region due to an avalanche. That plane near the Himalayan range is quite a dangerous place to stay long

bolbteppa

Not fair to say he was just a physicist tbh

John Rennie

10:49 AM

@lılostafa I would be cautious about stories like that. We don't know what happened. There have been similar incidents where climbers insisted on continuing when the guides said it was too dangerous.

Secret

[Random question]

Consider a black hole that is devouring matter and thus the surface area of its event horizon is growing

From the view of the stationary observer orbiting sufficiently far form the black hole to feel no time dilation, taking account of any time dilation that can be experienced near the vicinity of the black hole, how does one calculate the rate of growth in area of the event horizon?

skullpatrol

11:04 AM

Also climbing a mountain because "it is there" is to risk your life doing something you love...

John Rennie

@Secret From the perspective of the external observer no event horizon exists. The horizon takes an infinite time to form.

skullpatrol

How's the weight graph looking these days?

Secret

I see... so the black hole can never grew large enough to reach the orbit of the stationary observer from the stationary observer's frame of reference, but is that also the case when seen in other frames of references?

I am not sure how to ask these questions, spacetime acts in very nonintuitive ways that distance in the usual sense makes no sense so perhaps the notion of how far the event horizon is to any observer simply don't make sense as a notion because to them the black hole event horizon never formed in finite time...

The only best guess I have is that they will see nothing happen until the event horizon (seen in some suitable reference frame) become so large that the observers are now suddenly inside the event horizon

Slereah

11:20 AM

Help I can't reproduce the Michelson Morley formula

Special relativity is wrong

\begin{eqnarray}
t_1 &=& \frac{D}{c-v}
t_2 &=& \frac{D}{c+v}
\end{eqnarray}

So \begin{equation}
t_1 - t_2 = 2D \frac{c}{c^2-v^2} = 2 t \frac{1}{1-\frac{v^2}{c^2}}
\end{equation}

But Michelson gives it as $$\approx 2t \frac v c $$

Michelson–Morley experiment

The Michelson–Morley experiment was performed between April and July, 1887 by Albert A. Michelson and Edward W. Morley at what is now Case Western Reserve University in Cleveland, Ohio, and published in November of the same year. It compared the speed of light in perpendicular directions, in an attempt to detect the relative motion of matter through the stationary luminiferous aether ("aether wind"). The result was negative, in that the expected difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles, was found not to exist;...

"Michelson obtained this expression correctly in 1881, however, in transverse direction he obtained the incorrect expression

$$ T_{t}={\frac {2L}{c}}$$"

Bloody Michelson

lılostafa

@JohnRennie Yeah, in this case, it was actually the climbers' fault, but the guides were more prepared physically and could come down and survived.

@skullpatrol I was quite surprised that a lot of (actually most of) the comments on that article said the same thing! Some even said that no one should be allowed to climb Mount Everest

because, they argued, so what?

skullpatrol

Yeah, I have my doubts about people who do that sorta stuff...

...as adults we should know better, in my opinion.

amazon.ca/Special-Relativity-P-French/dp/0393097935

@Slereah have you seen this^ book?

Slereah

11:37 AM

Why, because it has French in the name?

skullpatrol

Nah, because it's a classic.

:-)

Slereah

I learned special relativity from a book nobody ever heard of

I don't even remember where I got it from

(Book 2 is quantum mechanics)

skullpatrol

French's book begins with the Michelson-Morley experiment.

Slereah

not a bad starting point

if you're going the historical route

skullpatrol

History motivates.

Slereah

11:46 AM

It may be more confusing than anything if the historical solution was wrong

Really I'm not sure I approve of teaching wave particle duality :p

or relativistic mass

skullpatrol

Yeah, relativistic mass is briefly discussed too.

In terms of E = mc^2

lılostafa

@Slereah Nice

Slereah

@lılostafa That was 6 months ago

2

lılostafa

@Slereah Yeah

OK

skullpatrol

:-)

lılostafa

11:53 AM

OK getting back to work after watching this youtube.com/watch?v=VHoT4N43jK8

skullpatrol

The Michelson-Morley experiment was made to measure the effect of the "aether."

Slereah

that it was

skullpatrol

Anyway, it's a good book.

Kane

12:06 PM

Hey I did a refraction experiment with 2 coins and water. I put water in this container and put one of the coins in. I then moved the other coin up and down the container to estimate the height where the two coins looked the same size. If I did this at a few water heights, why would the gradient of this line be the refractive index?

refractive index of water

Slereah

12:55 PM

@ACuriousMind @0celo7 @BalarkaSen is a horizontal curve just a curve that only intersects every fiber at most once

Secret

2

Q: How do Black Hole event horizons grow?

I was trying to understand how matter falls into black holes, and I got confused by this thought experiment. A small mass falls into a black hole (which negligibly effects the Schwarzschild radius) A sufficiently long time later (as measured by a distant observer) a large mass falls into the bl...

hmmm... an expanding horizon in these coordinates may look like this? :

ACuriousMind

@Slereah no - given a horizontal subtangentbundle (I. E. A connection), a horizontal curve is one whose tangent is horizontal at all points

Secret

grr, intuition is completely not helping in trying to understand black holes with growing event horizons...

Diagram description: (Color coding same as that in the PSE quoted) trying to understand what a black hole with a growing horizon due to feeding look like to an external observer and whether the horizon will grow large enough to cause the external observer to be engulfed by the horizon

The trouble is that any external observer of the black hole will not even see the horizon forming, let alone growing, so I guess they will not realise anything happen until the horizon grow enough and cause them to be now inside the horizon?

Slereah

1:14 PM

@ACuriousMind Isn't that equivalent?

Secret

> The case of non-constant mass is described by the Vaidya metric. Mathematically this is described on pages 133-134 of this book.

Slereah

Basically that the curve doesn't go along the fiber

Secret

O whoops, looks like we need another metric to describe a growing black hole...

Slereah

Oh wait

I guess you mean like

100% in the horizontal space

So that it's not a combination of H and V

It's a vector that "points" to the next fiber

normal vector to the fiber sort of thing

0celo7

You need a connection to define the horizontal space

Qmechanic

1:20 PM

0

Q: Do physical models of theories give a good picture of reality?

I'm not sure if this is the right place to ask, but nevertheless, I ask the question. Ther are various physical models to make visible how a theory works, for example: Falaco solitons, see also here, where it is said that the swimming pool model corresponds to black holes and cosmic strings W...

general-relativity cosmology black-holes education models

Primarily opinion-based? Too broad?

Slereah

@0celo7 I know

0celo7

@Slereah I had nightmares about ADM

Slereah

btw if you take the tangent space of $T\Bbb R$, at every point it has several possible horizontal space (parametrized by some angle)

Are they all equivalent via a new trivialization?

Since 1-manifolds are all flat

I am guessing so

@0celo7 time for a break probably

Secret

0

A: Is this answer stating that an external observer can see a black hole mass grow, correct?

The point Luboš Motl makes in the answer you link is that the infinite time to reach the event horizon is calculated using the Schwarzschild metric. However the Schwarzschild metric is a time independant solution i.e. it only describes a black hole that has existed unchanged for an infinite time ...

uh.... still open question...

grrr

Part of the reason why GR is a lot more non intuitive to me compared to quantum mechanics (besides the fact that GR maths involves more entities with a lot more degrees of freedom like tensor algebra) is because the metric is changing. Most of my comprehension of concepts rely on the notion to be able to calculate or mentally estimate some notion of metric between points in parameter space. GR takes away that intuition and thus I cannot even easily check my answers on the back of the envelope.

Slereah

1:43 PM

"The proof of this theorem involves some results about differential equations, which
I will not state here. The words “existence” and “uniqueness” are probably involved.
Perhaps also “Picard-Lindel¨of Theorem”."

:D

Balarka Sen

@Slereah Depends on your definition of horizontal

Slereah

$T_e E = H_eE \oplus V_eE$

Balarka Sen

That's called choice of a connection. That defines one notion of horizontal for general vector bundles.

Horizontal could mean many different things in many different contexts

But yes, in that case it's what ACM said

0celo7

implying Balarka knows geometry

Balarka Sen

Just because it intersects every fiber at most once doesn't mean it's everywhere tangent to the horizontal subbundle, btw

@0celo7 I do?

Slereah

1:49 PM

Yeah I figured

It just means that its projection on $VE$ is zero?

Balarka Sen

What you gave is a 0th order condition. Being horizontal is a 1st order condition :)

On each tangent space, you could say, sure

Slereah

Also more importantly

what the hell does that have to do with a connection

Or do only principal bundles get to have a derivative from a connection

Balarka Sen

If $E/M$ is a vector bundle, a choice of a subbundle transverse to $VE = \ker dp$ is exactly what a connection is

You can show it's equivalent to the ten million other versions

Slereah

I know, but can you define a covariant derivative just from that

0celo7

Since when does one write a bundle as a fraction

Slereah

1:52 PM

is my question

Prathyush Poduval

Hey @JohnRennie are you there?

Slereah

I guess you can maybe do a "derivative" by doing the usual derivative definition along a horizontal lifted curve?

Balarka Sen

@Slereah If $E = TM$, you can indeed.

That's right

0celo7

That’s the covariant derivative

Slereah

Where does the frame bundle factor in

Balarka Sen

1:56 PM

The general point is that horizontal lifts are exactly the parallel vector fields

along the base curve

Slereah

Is the parallel transport of a vector $v \in TM$ just the values that the horizontal curve starting at $v$ takes?

0celo7

It’s the principal bundle associated to the tangent bundle

Balarka Sen

@Slereah Answered by future-sniping

Slereah

Damn time travelers

So is the notion of parallel transport somewhat more primitive than the covariant derivative?

(at least with that definition)

Balarka Sen

So they say

0celo7

2:00 PM

They’re equivalent notions so who knows

Slereah

Do you get that thing where you google a thing and the link contains maybe one of the word you were searching for

Stop trying to second guess me google

Balarka Sen

Did you mean "Stop trying to guess google"?

Slereah

Oh they don't even do that sometimes

They just say "This result doesn't have that word but we include it anyway"

Balarka Sen

google is not a great search engine

use bing

:dabbing in the background:

Slereah

2:16 PM

Sorry I only use Ask Jeeves

The gentleman's search engine

Secret

productforums.google.com/forum/#!topic/websearch/UepymO_Llpg

Balarka Sen

isn't it just called Ask now

Ask is a fucking annoying search engine

Slereah

alas yes

No more jeeves

Too silly an idea for the modern day corporate blocks that are search engines

"In more sophisticated terms, such an assignment of horizontal spaces satisfying these properties corresponds precisely to a smooth section of the jet bundle J1E → E."

wot

Balarka Sen

J E T S

Slereah

@BalarkaSen why did you say that $E = TM$

I thought the point of the connection was to be defined on the principal bundle

Balarka Sen

2:19 PM

If you're talking about covariant derivative

you'd better be working on the tangent bundle

Slereah

'"Suppose that E is a smooth principal G-bundle over M. Then an Ehresmann connection H on E is said to be a principal (Ehresmann) connection"

etc etc

I thought the covariant derivative was on the frame bundle

and that you could then apply it to the tensor bundle

via math wizardry

Balarka Sen

if you have a general vector bundle you don't really call it the covariant derivative anymore

the right notion is the exterior covariant derivative :3

Slereah

Plus the frame bundle isn't a vector bundle :p

Balarka Sen

true

you can always pass between frame bundle and associated vector bundles anyway

Slereah

"A connection on a principal bundle allows us to define a covariant derivative (a.k.a. a Koszul connection) on sections of any associated vector bundle. "

Hm

@BalarkaSen solder form thing?

Balarka Sen

2:22 PM

I'm future sniping you

snipe of the future past

@Slereah Connection form, rather

Slereah

I suppose so, since you're gonna need it for associated bundles in general

Even if it's not the tangent bundle

like the spinor bundle with the gauge bundles

Hm, I guess that's why the associated bundles are actually $(P \times V) / G$?

That way the principal connection acts on it

Hence why gauge fields are $G$ valued and all that business

Balarka Sen

y

0celo7

@BalarkaSen that’s something different

Namely for bundle-valued differential forms

@Slereah gauge fields are g valued

Slereah

That's what I said

Or is uppercase verbotten

Balarka Sen

g means Lie algebra

Slereah

2:29 PM

$\mathfrak{g}$-valued

Balarka Sen

I need to writes n o t e s on the rotation number

Slereah

What is the geodesic for a principal bundle

Is it just the field value along that curve

Or... field lines???

I don't know

0celo7

You’ve gone off the deep end

Emilio Pisanty

Am I the only one who's completely nonplussed by this?

Slereah

I just want the people writing those things to offer a clear list of associations

Emilio Pisanty

2:32 PM

"Stephen Hawking releases graduate thesis, promptly breaks internet"

Slereah

between the concepts and the gauge stuff

Emilio Pisanty

a.k.a. "Stephen Hawking finally gets round to doing something decent with his thesis copyright, the internet somehow thinks this is important"?

Slereah

"In Chapter 1 it is shown that this expansion creates grave difficulties for the Hoyle-Narlikar theory of gravitation."

lol Hoyle theory

0celo7

@Slereah wot

Balarka Sen

you could say that that theory did not go according to Hoyle

Slereah

2:35 PM

@0celo7 What mathematican concept corresponds to what physical concept

0celo7

Read the books by Naber on gauge theory.

Balarka Sen

I would read such a thing too

Slereah

Let me check this legally

Hawking's thesis is the worst

Typewriter + handwritten equation

You'd think he was already in a wheelchair

Naber does seem to have a "physical motivation" part

Balarka Sen

what's a badass font that i can use in sharelatex

Slereah

microgramma

Microgramma (typeface)

Microgramma is a sans serif font which was designed by Aldo Novarese and Alessandro Butti for the Nebiolo Type Foundry in 1952. It became popular for use with technical illustrations in the 1960s and was a favourite of graphic designers by the early seventies, its uses ranging from publicity and publication design to packaging, largely because of its availability as a Letraset typeface. Early typesetters (like the AM Varityper) also incorporated it. Novarese himself later developed Eurostile in 1962, a typeface very similar to Microgramma. Eurostile added lower-case letters, a bold condensed variant...

Balarka Sen

2:44 PM

that does not look like a very professional font

Slereah

it's the Star Trek font

the font of the future

Naber uses $\mathcal P$ for the projection

When they say $\mathfrak{g}$-valued $1$-form, does it just mean that it's a $TP$ $1$-form

One source is implying $$\Omega ^{1}(P,{\mathfrak {g}})\cong C^{\infty }(P,T^{*}P\otimes {\mathfrak {g}})$$

Which seems odd

Doesn't $T^*P$ already have algebra values

Since the tangent vector of a Lie group is an algebra element