The h Bar

Slereah

17:00

I had to do 4th order things once and it was already a nightmare

John Rennie

Gosh, 5 already.

0537

@0celo7 I am lost now... can you help?

John Rennie

I have to slope off I'm afraid

0celo7

@Slereah $$\int\int\int\int\int\int\int\int\int\int\int\int\int\int F(a,b,c,d,e,f,g,h,i,j,k,l,m,n)\,\mathrm{d}a\mathrm{d}b\mathrm{d}c\mathrm{d}d\mat‌hrm{d}e\mathrm{d}f\mathrm{d}g\mathrm{d}h\mathrm{d}i\mathrm{d}j\mathrm{d}k\mathrm{‌d}l\mathrm{d}m\mathrm{d}n$$

Slereah

Nooo

David Z

17:01

I've got to be off too, but I'll get a meta post up about this close-reason thing sometime soon. Thanks for the thoughts everyone

Terry Bollinger

Hey, how is that kitten doing???

ACuriousMind

...which kitten?

0celo7

Probably mine.

John Rennie

@TerryBollinger It's nearly done, five minutes more at gas mark 5

Terry Bollinger

@0celo7 yep.

0celo7

17:02

@ACuriousMind Steiner was unhappy about something earlier.

Well he's sitting on a rug and being quiet...so he's probably fine.

@0537 perhaps

Terry Bollinger

@JohnRennie the acceleration question? cool.

0537

@0celo7 Ok please do the entire calculation and post it as an answer :D

ACuriousMind

@TerryBollinger ...I think he means the kitten :P

Apparently, @JohnRennie's physics prowess is gained by eating kittens. And kicking puppies, probably.

Terry Bollinger

@0celo7 wow that integral was so long it invoked a slider bar on my browser, and now everything is shifty...

@ACuriousMind I never knew, aieee!

0celo7

@0537 Well, do you want a rigorous thing using Lie derivatives or a convincing heuristic argument

because I'm sure it can be done using Lie derivatives somehow

yuggib

17:08

@0celo7 when I was young I also typeset the integration variable with roman d; but when you write papers on a regular basis you quickly understand how valuable time is

0537

@0celo7 I don't mind.

0celo7

@yuggib i have a package where \dd gives me roman d with spacing

yuggib

It's still two characters more than plain old d

David Z

@0celo7 the physics package?

vzn

@yuggib what are you researching these days?

0celo7

17:10

@DavidZ correct, I think you were the one to tell me to get it

David Z

could be

It's getting to the point where seeing italic d in integrals really irks me

(I guess I lied about having to leave, but I didn't feel like discussing the close reason anymore :-P)

ACuriousMind

lol

David Z

I mean, not to stop anyone else who wants to keep that discussion going. If anyone does. But it gets exhausting, and I do have work to do

yuggib

@vzn semiclassical limit of QFT, scattering theory for Lindbladians, some non-perturbative renormalization, classical dynamics of point particles and fields

vzn

@yuggib "classical dynamics"? is that still studied?

Stan Shunpike

17:17

@0celo7 what is four-force? I am having trouble envisioning this concept. Does this mean forces are relative?

Slereah

why not

Isn't four-force just the derivative of the Lagrangian

Stan Shunpike

What lagrangian?

0celo7

beats me

Stan Shunpike

Lol

alrighty

TanMath

hello all!

DanielSank

17:24

@DavidZ Correct. See the meta post. Note also @tpg2114's answer.

TanMath

Hello @DanielSank

DanielSank

Hi.

TanMath

@DanielSank do you know about Fermi's Golden Rule?

DanielSank

Of course.

I wrote about it here.

John Duffield

@DanielSank : I liked Nathaniel's answer.

DanielSank

17:40

@JohnDuffield I specifically explained in my answer why banning actual homework questions is not practical.

It's also not what we want, even in spirit.

A question asked by a student trying to understand physics via a homework problem is not qualitatively different from a question asked by me trying to solve a research problem.

I explain all of this in detail in my post.

0celo7

@ACuriousMind I'm very confused. Every manifold supposedly has two orientations, but what are the two?

An orientation of an atlas is when all the trasition functions have positive functional determinant

DanielSank

@0celo7 False. See Mobius and his strip.

0celo7

@DanielSank every connected orientable manifold

whatever

TanMath

@DanielSank where?

DanielSank

@TanMath Click on the link in the comment you just responded to :\

TanMath

17:46

@DanielSank do you know about response functions correlation functions, liouvillian pathways etc.?

@DanielSank it is not there!

DanielSank

@TanMath Yes, it is. I just didn't call it that. Read my answer on that page.

@TanMath I know what a response function and a correlation function are.

Never heard of a Liouville pathway.

ACuriousMind

@0celo7 Just pick any orientation. You can always reverse it (just invert one of the vectors of the oriented basis of tangent vectors at every point).

DanielSank

^ Yes.

0celo7

@ACuriousMind Well what does that mean

does every transition function have negative functional determinant then

DanielSank

What do you mean by transition function?

ACuriousMind

17:49

@0celo7 Obviously not, since you defined an orientation to come from purely positive determinants.

0celo7

composition of inverse chart and chart on the intersection of chart domains

DanielSank

@0celo7 Ah.

0celo7

@ACuriousMind exactly, so I have no clue what your new orientation does differently

ACuriousMind

@0celo7 It has slightly different charts (one of the directions in the $\mathbb{R}^n$ the chart maps to has been reversed.

It's really obvious if you think in terms of a smooth assignment of oriented bases of the tangent space instead of the transition functions. (Positivity of the determinants is just a convoluted way to say that these bases are not flipped when going from one chart to the other)

TanMath

@DanielSank i still cannot find it...

@DanielSank can you explain them? i can't understand the semi classical theory of light interaction with quantum systems...

0celo7

17:52

Hmm. Why are the signs of the functional determinants constant. I'm sure it's because they cannot cross 0 (using the intermediate value theorem) but why can't they be 0

Is it because the inverse transition function exists and is also smooth

DanielSank

@TanMath That is a very, very broad topic.

@0celo7 What's a functional determinant?

0celo7

@DanielSank Jacobian determina t

ACuriousMind

@DanielSank It's just the determinant of the Jacobian

DanielSank

@ACuriousMind Who the hell calls that a "functional determinant"?

ACuriousMind

@0celo7 If the Jacobian isn't invertible, you don't have a chart!

DanielSank

17:53

^ Yes.

ACuriousMind

@DanielSank some math people :P

0celo7

@DanielSank No shit, but why

DanielSank

@0celo7 Do you have a good geometric understanding of what it means for a matrix to be invertible and/or onto?

0celo7

@DanielSank columns/rows are linearly independent

ACuriousMind

@0celo7 The chart is a diffeomorphism. Are you telling me you don't know why the Jacobian of a diffeomorphism should be invertible?

John Duffield

17:55

@DanielSank : I read your answer, but I'm afraid I think the "problem-solving" label is rather ambiguous.

DanielSank

@JohnDuffield Fine. I don't care about the label.

I care about getting the meaning right.

I agree "problem solving" is not a good label.

However, "homework" is crappy too.

@0celo7 Right.

So suppose I have a function $f:\mathbb{R}^n \rightarrow \mathbb{R}^n$.

Pick a point $p$ in the domain.

0celo7

@ACuriousMind Maybe?

DanielSank

At that point, $f$ has some value.

0celo7

I know it's obvious but I'm drawing a blank.

DanielSank

If $Df(p)$ has linearly independent columns, that means that by moving in various directions away from $p$, I can go in any direction I want in the image.

See what I mean?

That's why the function is locally invertible: no matter what point I pick near $f(p)$ in the range there is some direction I can go away from $p$ to hit that value.

0celo7

17:59

@ACuriousMind Oh, the chain rule.

We've done this before.

@DanielSank All one needs is that the Jacobian of the inverse is the inverse of the Jacobian, which follows from...something

DanielSank

@0celo7 Needs for what?

The derivative of the inverse is the inverse of the derivative whenever an inverse exists.

0celo7

To see that the determinant is not zero

DanielSank

@0celo7 That's an ass-backwards way to think about it, IMHO.

0celo7

Because it's a diff, the Jacobian of the invese exists

But that's just the inverse of the Jacobian

DanielSank

Too many pronouns. Don't know what you're saying.

I'm trying to give you a way of seeing why all this stuff works.

0celo7

18:05

@DanielSank Yes, because $D(f^{-1})=(Df)^{-1}$

DanielSank

Yes, that's true.

@0celo7 suppose I have $f:U \rightarrow V$ where both $U$ and $V$ are subsets of $\mathbb{R}^n$.

Suppose I pick a point $p \in \mathbb{R}^n$, and evaluate $Df(p)$.

yuggib

@vzn well.....not so much

but it is a mixed ode-pde system, and it is interesting mathematically

DanielSank

The direction I move in $V$ if I move a bit away from $p$ by an amount $\vec{u}$ is $[Df(p)]\vec{u}$.

yuggib

(and I am a mathematician nowadays :-P)

0celo7

@DanielSank perhaps

@DanielSank do you know a simple proof of the Jacobian of the inverse thing

I know a proof but it might require some things I'm not supposed to assume

FenderLesPaul

18:25

yeo

0celo7

@DanielSank what, geometrically, does it mean for the Jacobian to be singular

in terms of the map $f$, not the Jacobian

FenderLesPaul

Anyone here have a good intuition for Bosonization in 1+1 spacetime?

DanielSank

18:47

@0celo7 You mean a proof that $(Df)^{-1} = D(f^{-1})$?

@0celo7 It means that there are directions in the target space which you cannot get to (to first order) by moving around in the domain.

Note that theorems like the inverse function theorem have invertibility of the derivative as a sufficient, but not necessary condition.

0celo7

19:05

@DanielSank yas

@DanielSank What do you mean

Inverse function theorem is like if $Df(p)$ is invertible, then $f$ is a diffeomorphism in some nbd of p

does this imply that if $f$ is a diff then $Df(p)$ is invertible

Slereah

19:24

I always confuse the torsion tensor with the contorsion tensor

It's a bit annoying

FenderLesPaul

Yay finished my Penn State application

I am freeeee

David Z

20:18

@FenderLesPaul ooh, in what capacity are you applying?

FenderLesPaul

@DavidZ I'm applying for grad school

Ideally I'd like to work with Ashtekar on some classical GR

or do CMT

DanielSank

@0celo7 No.

That's what I meant when I said that an invertable derivative is sufficient but not necessary.

0celo7

yes

DanielSank

It's pretty easy to construct an example to show this.

0celo7

I think I'll just take it as a theorem of analysis and leave it for my analysis class

No reason to spend time proving it

I've been using it thus far without problems

@DanielSank Like what

DanielSank

20:23

@0celo7 like $f(x) = x^3$.

Bam.

0celo7

Yup.

DanielSank

Even $f(x) = x^2$ on $[0,\infty)$.

David Z

@FenderLesPaul ooh nice :-) good luck with that

I hear the gravity PhD program is not easy

DanielSank

@DavidZ Would you say they're hard to escape once you're in?

0celo7

@DanielSank Wait, that's not a diffeomorphism.

DanielSank

20:34

@0celo7 Sure it is.

0celo7

What's the derivative of $x^{-3}$ at $x=0$?

FenderLesPaul

@DavidZ thanks! Did you do your PhD at Penn State?

DanielSank

@0celo7 Infinity. Does that make it not a diffeomorphism?

0celo7

@DanielSank The inverse has to be differentiable -.-

That's the definition of a diffeomorphism: a differentiable bijection whose inverse is differentiable.

DanielSank

@0celo7 Oh it does? Er, in that case maybe in 1D the inverse function theorem is actually an if-and-only-if...

David Z

20:36

@DanielSank lol

@FenderLesPaul yes I did, though I was in the other building

DanielSank

@DavidZ :: puts a dollar in the pun jar ::

0celo7

I just realized I have not eaten in like 7 hours. wtf

David Z

the IGC (where they do the quantum gravity research) is an adjacent building to the rest of the physics department

DanielSank

@0celo7 jet lag?

0celo7

@DanielSank I'm all sorts of messed up

Woke up at 4AM

FenderLesPaul

20:38

@DavidZ Oh I see, nice!

0celo7

And I've been eating continuously for the past two weeks

So now my eating schedule is messed up as well

David Z

@DanielSank the "funny money"

FenderLesPaul

did you ever get to meet Ashtekar? I've met him once in person and he's a little scary :p

DanielSank

@DavidZ Ouch. I think you owe a dollar now.

David Z

Haha I can see that :-P if he's at a conference or something

I took his intro QG class, actually

so I met him, but not in a personal capacity

FenderLesPaul

20:39

ooh that sounds cool

David Z

He's actually pretty reasonable when he doesn't get too worked up about his research

FenderLesPaul

haha

David Z

@DanielSank owe really?

DanielSank

>.<

David Z

:-P

0celo7

20:40

parents went shopping hours ago and took my car

now I'm going to die of starvation

there's nothing to eat in this house anymore

David Z

There are always some stories going around the department about Ashtekar and Martin Bojowald's ongoing feud about the direction of quantum gravity research

0celo7

I might have to eat cat/dog food to make it through the day

or a cat/dog

FenderLesPaul

Yeah he sounds like kind of an intense person

0537

@0celo7 walk?

FenderLesPaul

I actually have no idea if he's even taking grad students

for classical GR stuff

since he's been doing all that LQG research

0celo7

20:44

@0537 do you not understand how far stuff is in America

David Z

oh, yeah, for classical GR... I dunno. Seems unlikely. I know a few of his current students, I could ask if they know anything.

0537

@0celo7 do you live in the middle of no where?

0celo7

@0537 no

my dad actually took my house keys too

FenderLesPaul

@DavidZ that would be awesome if you could, thanks!

0celo7

@TerryBollinger whatever was bothering him is gone, he's been knocked out like that for a while now

0537

20:50

@0celo7 delicious?

David Z

@FenderLesPaul it may take a few days, but I'll see if I can get in touch with anyone and maybe put you in touch with them. Why don't you email me at [email protected] just so I have your email address.

(no promises)

FenderLesPaul

sure sounds good, I'll do that now :)

Mike Miller

hey, penn state people, cool

David Z

ooh are we making a club? :-P

Mike Miller

nah. i was just there for a semester once and have a friend about to finish his physics BSc there. nice place.

0celo7

20:56

Penn State was waaaaaaay too expensive for me

FenderLesPaul

It's too bad there aren't more GR research groups in the US

Mike Miller

@DavidZ: is there some tie between penn state and chinese labs? friend of mine from penn spent time there too; not that China in the broad is very specific

FenderLesPaul

I basically have to cross my fingers and hope I get into penn state, chicago, or caltech

David Z

@MikeMiller not that I know of

Physics Meta

0

Q: Bonus Points on other sites

What did I do to earn this? Do people get this regularly or its awarded?

discussion

Mike Miller

21:08

I feel like I've seen a bunch of meta questions from this person lately...

dmckee

@0celo7 Strange that latex doesn't offer a \iiiiiiiiiiiiiint command. for situations like that. As it is you should adjust the kernning by hand.

0celo7

@dmckee You should do that, you have mod powers

I can't edit it now

dmckee

$$\int\!\!\int\!\!\int\!\!\int\!\!\int\!\!\int\!\!\int\!\!\int\!\!\int\!\!\int\!‌\!\int\!\!\int\!\!\int\!\!\int F(a,b,c,d,e,f,g,h,i,j,k,l,m,n) \dots$$

0celo7

missing the measures

lol

FenderLesPaul

wait are you back in America?

@0celo7

dmckee

21:13

Well, yeah. I was just exhibiting the improved kerning. But I think three \! might be better.

0celo7

yes

@dmckee Agreed. (assuming you have two there)

dmckee

Yup.

Physics Meta

21:41

0

Q: Not able to flag anyone

I had the privilege taken from me. Is this permanent or is there a place I can see my time for restriction?

discussion support feature-request

Demosthene

22:15

Would anyone familiar with asymptotic analysis care to help me with question 1? I cannot get it right for the life of me -.-

0celo7

23:21

@FenderLesPaul do you have Bredon handy

Huy

23:40

zzz 0cetr0l7

0celo7

Fine, you tell me then

The "who is in chat" is bugging out for me

@Huy why do you think I'm trolling

Huy

cuz that's what you're best at

(this was almost a Luke Starkiller quote)

0celo7

@Huy could you not be an ass for like one second

Huy

It's almost 1am and I'm way too tired to do any maths

what was the question anyway

something something measure zero isolated

0celo7

Basically what are the sets of measure zero on R

Huy

23:51

@0celo7: I don't think it's that easy to give you an answer.

I was going to say countable unions of singletons

but the Cantor set is uncountable

0celo7

Cantor set?

Huy

Cantor set

In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883. Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle thirds of a line segment. Cantor himself only mentioned the ternary construction in...

this is uncountable but has measure zero

0celo7

Hmm, that's awk

PhD analysis

Huy

no, intro measure theory

but harder than other things you consider to be PhD level

0celo7

Seems too advanced for an intro

Huy

23:56

@0celo7: want an accessible intro?

I think we actually looked at the Cantor set as an example in measure theory very early on

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