The h Bar

12:00 AM

and considers $L(q_i, (q_{i+1}-q_i)/\Delta t)$ t oderive Euler-Lagrange

and that's the same method in Susskind

Apparently, Lagrange was the one who came up with the gross "variation", "variation consistent with constraints" etc.

which to me made absolutely zero sense until I saw Arnold's mathematical methods of physics where he actually defined a functional derivative and derives everything sensibly in the span of two pages.

0celo7

functional derivative: $$\int \frac{\delta F}{\delta f}\delta f\,\mathrm{d}x=\lim\frac{F[f+\epsilon h]-F[f]}{\epsilon}$$

that right?

I just vary shit, it usually comes out right

how does the Russian define it

NeuroFuzzy

@0celo7 oh he actually defines "+O(h^2)" for h a function but that's not the important part

0celo7

working definition: replace fields $\phi$ by $\phi+\delta\phi$ and expand to first order

done!

NeuroFuzzy

the important part, for me, is that the functional derivative (of the action, which takes in a function and spits out a number) evaluated at a function, is an object which takes in a function linearly and spits out a number.

None of this $\delta$ $\partial$ $d$ confusion crap

just a good ol' linear function

0celo7

don't you just love working on a problem for 20 minutes only to realize you misread it and it's actually trivial

NeuroFuzzy

12:06 AM

yes that's like my favorite thing

0celo7

@NeuroFuzzy do you have the page

NeuroFuzzy

right up there with finding how many independent constraints are on a rank 4 tensor

0celo7

I never had your confusion

Mike Edenfield

how do you pronounce $\partial V/\partial t$

0celo7

@NeuroFuzzy hha

@MikeEdenfield dee vee dee tee

wtf is that

lol

Mike Edenfield

12:07 AM

you get the idea :)

0celo7

same

NeuroFuzzy

@0celo7 Like, page number or page link? Also, where did you learn Lagrangian stuff from?

HDE 226868

@MikeEdenfield I fixed that for you. I don't want to scare you about an edit from nowhere. . .

0celo7

@NeuroFuzzy err, Zee and Wikipedia?

I also read Tong's notes on CM

Mike Edenfield

@HDE226868 s'okay, by the time I pulled up the mathjax reference i probably wouldn't have been able to edit it

0celo7

12:08 AM

I have read parts of Arnold

NeuroFuzzy

I started trying to learn it from Goldstein, then from some book by Hand and Finch, then from L&L and it was all just a nonsense confusing mish mash of $d$ $\partial$ $\delta$ and infinitesimals which sometimes aren't infinitesimal

0celo7

@NeuroFuzzy page, I have access to the book

obe

@0celo7 He was really unclear in his derivation of things.

Mike Edenfield

@0celo7 are you asking about the Susskind book?

HDE 226868

@MikeEdenfield You just needed spaces ("\partialV" $\to$ "\partial V").

NeuroFuzzy

12:09 AM

@0celo7 p. 56

0celo7

@NeuroFuzzy ah, wait till you get to string theory and you have $\mathrm{d},\mathrm{d}^\dagger,\partial,\partial^\dagger,\delta,\Delta$

NeuroFuzzy

I ignored the "+O(h^2)" part

0celo7

now that's fun stuff

NeuroFuzzy

@0celo7 oh nooooo

obe

@NeuroFuzzy You should read these mechanics notes, they're very detailed in deriving things.

0celo7

12:10 AM

Kahler manifolds are the best

@NeuroFuzzy will look at later, thanks

@MikeEdenfield no

Mike Edenfield

@0celo7 yeah realized that after I said it :)

0celo7

V.I. Arnold Mathematical Methods of Classical Mechanics

obe

Does he even distinguish the euclidean space $E^n$ with the real vector space $R^n$

0celo7

idk

but the distinction is pretty much irrelevant

the standard topology on R^n defines a metric, so

@obe I probably just skipped it

I know how to derive Euler Lagrange

@NeuroFuzzy I think that's quite opaque tbh

NeuroFuzzy

@0celo7 Well if you read the "+O(h^2) means blah such that for every epsilon [...]" part, which isn't actually even used anywhere if i recall correctly

but, I mean, it's a linear functional. Like a differential or a jacobian

-shrug- but I wasted a lot of time on Goldstein's introduction to it, so that's really what I'm comparing things to.

0celo7

12:22 AM

I like this one. Let $F[\rho]$ be a functional of the function $\rho$. Under a variation $\rho(x)\to\rho(x)+\epsilon\phi(x)$, its functional derivative is given by $$\int\frac{\delta F}{\delta \rho}\phi\,\mathrm{d}x=\left.\frac{\mathrm{d}}{\mathrm{d}\epsilon}\right|_{ \epsilon =0}F[\rho+\epsilon\phi]$$

there we go

actually not given

it's defined implicitly

I can use this to derive Euler-Lagrange if you want

NeuroFuzzy

okay, that's similar.

bolbteppa

@0celo7 I think that GR book you mentioned earlier is actually cool if you view it as an alternative, pedantic, unified run-through of the elements of SR, basic EM & GR up to Schwarzschild in baby matrix notation. With Landau as your classical diff geom run through of those subjects, and Wald/Hawking? as a modern diff geom run through, I like it :D It's so weird to see Christoffel symbol & Riemann-curvature matrices though

0celo7

@NeuroFuzzy too abstract for you?

NeuroFuzzy

@0celo7 Coool. It's in the same vein as linear functionals without infinitesimals!

=good for me!

0celo7

my above definition needs no infinitesimals either

NeuroFuzzy

12:35 AM

I've never actually done anything with lagrangian densities

0celo7

what

NeuroFuzzy

@0celo7 Yeah, so I like it!

0celo7

they're everywhere

NeuroFuzzy

@0celo7 Yeah but we didn't do anything with them in my mechanics a/b, electrodynamics a/b/c, or quantum mechanics a/b/c (though our professor did almost get into field theories at the end of quantum c)

:(

bolbteppa

@NeuroFuzzy the first chapter of Gelfand's CoV gives you a geometric view of Euler's method in section 7

0celo7

12:36 AM

I want JD to give me the term in the Lagrangian density for photon-photon interaction

protip: it does not exist

it's because EM is abelian

nonabelian gauge theories can have nonlinearities

NeuroFuzzy

@bolbteppa CoV?

bolbteppa

Calculus of Variations

0celo7

although off the top of my head

I have no clue what the cubic term is

:O

of course, a derivative coupling.

for EM we have $f\equiv 0$, so no nonlinearities!

@NeuroFuzzy that's the Lagrange density for a general Yang-Mills theory

NeuroFuzzy

@0celo7 Hey look! Something similar to vector potentials and... structure constants?

0celo7

yes

and what do we know about the structure constants of an abelian group?

$A_\mu^a$ is the gauge potential

@NeuroFuzzy oh, I totally forgot about the $\bar \partial$ and $\bar\partial^\dagger$ operators

so yeah

a lot of ds in string theory

NeuroFuzzy

12:44 AM

They... are zero?

0celo7

yes

so what can you tell me about $\mathcal{L}_1$ in EM

NeuroFuzzy

it ain't s**t

0celo7

exactly

and in QFT you will learn that $\mathcal{L}_1$ is what gives you couplings

interactions

so in EM there are no interactions between the gauge potentials, i.e. no interactions between photons

those are the Feynman rules for the vertices: they vanish for EM

NeuroFuzzy

Aren't there very very weak $\gamma+\gamma$ interactions?

0celo7

not direct!

and not in a vacuum

NeuroFuzzy

12:49 AM

Ahh okay

0celo7

you'll always have a virtual electron or positron or whatever

there's a term $\sim A\bar\psi\gamma\psi$

which says you can have a photon, electron and positron vertex

or, by crossing, an electron -> electron + photon decay

obe

1:03 AM

Is dirac notation sometimes redundant?

Like in shankar he uses it exclusively.

0celo7

post dubious equations here

I'm in a homework groove

obe

Ballentine is so much more clear than shankar.

I can understand his line of thought.

0celo7

I'm getting tired of your carping

pick one, stick with it

obe

Sorry.

I'm done shankar.

I'll read ballentine.

0celo7

@JohnDuffield carping is such a nice word

My dad uses it, I should use it more often.

obe

1:12 AM

My feelings were demolished.

@0celo7 What is probability flux for?

0celo7

@obe scattering

It's not used in QFT to my knowledge though...might be for more specialized particle applications

I guess I'll find out

I'm getting a book on neutron scattering from Lang

I think the probability flux tells you about tunneling probabilities

maybe @NeuroFuzzy knows

look up "transmission" and "reflection coefficient"

obe

I think it was discussed in shankar scattering in 1-d.

0celo7

yeah, on the finite wall?

obe

wall?

0celo7

potential wall

obe

1:20 AM

I don't remember.

Too much detail.

0celo7

same, but it's been over a year since I read Shankar

@dmckee what do you know about neutron scattering

@dmckee I swindled my way into a neutron scattering group

obe

You're in a group now?

0celo7

I think the general goal is to look at how intense radiation damages lattices in various solids by shooting electrons at the solids

@obe maybe?

obe

Cool.

0celo7

idk

I sit in the meetings and sent in my preferences for the meeting times

obe

1:25 AM

They would be fools to deny you though.

0celo7

I know jack shit about this stuff!

there's some QM in there, but a lot of condensed matter and chemistry that I have no clue about

obe

Though you definitely have shown the capacity to learn, and fast.

Chemistry :D

What is a non-linear vector space?

0celo7

uh

no clue, never used one?

obe

They don't exist apparently.

0celo7

well you'd have to define it first

obe

1:29 AM

By definition they don't exist?

0celo7

I have no clue

define vector space

obe

whatever.

0celo7

@ChrisWhite neutrons!

what do you know about neutron scattering

user54412

huh?

0celo7

nothing, it seems

electron scattering in solids

also X-ray crystallography

obe

1:33 AM

I did the latter.

user54412

neutron radiation is the one type I've never worked with, and the one type that sort of scares me

user54412

can't shield against the things

0celo7

@ChrisWhite apparently the grad students in one of the labs left some mystery powders out, one of them was ordered to police it up and check if it's radioactive

user54412

@0celo7 you may have heard of this thing called the "double slit experiment" :p -- same thing here

0celo7

@ChrisWhite is that the thing that shows electrons are literally waves

like literally

waves in the ocean

user54412

1:35 AM

fire some electrons at a sample, get the fourier transform of the crystal structure on your detector

0celo7

also photons with tight belts

obe

Ballentine says it's false though.

0celo7

ballentine is a ho

obe

I see, sarcasm.

user54412

who's ballentine? and what's his beef with electrons?

obe

1:36 AM

He says the double slit experiment lead to the wave-like interpretation of electrons because of experimental limitations.

The phenomenon is actually just a statistical pattern made of individual electrons as particles.

Stan Shunpike

@0celo7 dont be dissin ballentine

bolbteppa

Ballentine's book is based on some weird form of probability and is pretty cranky as far as I've seen

I like the math but the rest...

Stan Shunpike

Yeah I suppose

0celo7

@StanShunpike I'll diss yo momma if I have to

but she's a nice lady so don't force my hand

Stan Shunpike

Hahahha

obe

1:39 AM

@bolbteppa Huh what are you talking about?

Stan Shunpike

Nothing like a good "yo mama" joke

dmckee

@0celo7 Not very much. It's a highly energy dependent business and people in it know lots of rules of thumb and heuristics that I've heard of but never internalized.

0celo7

energy dependent?

we use the beam out at ORNL

dmckee

Cross-sectionand final states of most neutron-involved reactions vary hugely depending on energy.

If you are only using one beam you may be in luck: they are often tuned to regimes that are (relatively) easy to understand.

0celo7

I don't know any specifics yet

I was just wondering if you know any good books for an introduction

dmckee

1:43 AM

I do know that at thermal energies they are a real pain to contain. Little bastards get everywhere.

0celo7

like crabs

dmckee

No. Sorry.

0celo7

too bad

hopefully Lang doesn't use some $100 Cambridge book

he said it's an ebook, but no way I use a book for actual research and learning and not mark in it, so I have to get the physical copy

dmckee

Isn't that what the departmental printer is for?

0celo7

yeah but that will be ghetto

I could just put it in a binder I guess

dmckee

1:46 AM

Several of the places I've worked actually had binding machines.

0celo7

whaaaat

dmckee

For those awful plastic spiral things, mind you, but better than nothing.

0celo7

I see

dmckee

Do get some nice firm cardboard sheets for the covers.

0celo7

A $25 springer mycopy would be well spent

dmckee

1:48 AM

That's spiffy. Yeah. Worth the money for anything you intend to keep.

user54412

@DanielSank Not that I recall, besides the occasional "help, my lab report is due [and I clearly messed up taking data]"

0celo7

I don't think I want to really do neutron scattering, but neutrons are a big issue for fusion, so the experience might carry over!

Zinkle explained his work as modeling neutron erosion in the fusion chamber

which is not really what I want to do either

dmckee

You're starting undergrad, right?

So it doesn't matter what you do now. Get some experience in whatever comes along. You don't get even partly locked in until grad school

I did my first experimental work with a guy into macho-microlening and balloon-borne CMB imaging (shortly before COBE returned, natch).

Haven't done an astronomy thing since.

user54412

@dmckee It's interesting that even post-Planck there are still competitive balloon-borne CMB experiments.

dmckee

I heard they were still doing circumpolar launches of those thing. That's very cool. So to speak.

0celo7

2:00 AM

wow

an interesting and bad bun

all in one

dmckee

I remember with the COBE data came out. I was in grad school and we sat around looking at this graph and decided that if a undergrad turned in something like from lab we'd assume they'd made up the data. It was that good.

Then WMAP and then Plank and it just kept getting better. WTF?

DanielSank

@ChrisWhite Heh, ok. I was wondering whether anyone ever managed to crowd-source research here.

user54412

Q: So I was measuring events from my accelerator, and I got this bump that just doesn't correspond to any channel I know of. Anyone know if PDG is missing something at 125 GeV?
A: Looks like you've found a Higgs boson.

FenderLesPaul

2:36 AM

ballentine sounds like English chocolate

0celo7

3:02 AM

@FenderLesPaul

FenderLesPaul

@0celo7 Hello

0celo7

I bet you won't even do a GR talk

FenderLesPaul

3:21 AM

I can tomorrow night I can't tonight because I have to work through a paper for meeting tomorrow

0celo7

3:40 AM

oh reeeeeeally

FenderLesPaul

yus

FenderLesPaul

3:56 AM

studying for the PGRE

is so mind numbing

0celo7

4:20 AM

That's the arsenic :)

FenderLesPaul

5:01 AM

dafuq

David Z

5:33 AM

@DanielSank I'm not sure. I think there might be some content-based notifications on Stack Overflow so perhaps the system is set up to do things like that, but I don't know the details.

@ChrisWhite one then wonders if it's the same Higgs boson CERN found and has probably been keeping in a locked airtight glass case ever since :-P

Slereah

7:39 AM

hey

David Z

7:58 AM

hello

Stan Shunpike

Sup

Slereah

Geometrothermodynamics

In physics, geometrothermodynamics (GTD) is a formalism developed recently by Hernando Quevedo to describe the properties of thermodynamic systems in terms of concepts of differential geometry. Consider a thermodynamic system in the framework of classical equilibrium thermodynamics. The states of thermodynamic equilibrium are considered as points of an abstract equilibrium space in which a Riemannian metric can be introduced in several ways. In particular, one can introduce Hessian metrics like the Fisher information metric, the Weinhold metric, the Ruppeiner metric and others, whose components...

What kind of name is that

Stan Shunpike

LOL

Didnt Wheeler coin the phrase geometrodynamics?

Slereah

yes

That was when he was trying to do QFT from spacetime topology

Stan Shunpike

Sounds like somebody has tried a bit of linguistic funny business with his phrase then

Slereah

8:13 AM

Geometrothermoelectrochromodynamics

Stan Shunpike

Hahahhaha

AngusTheMan

10:09 AM

@NeuroFuzzy yes my fault, the first phi is mant to be the ODE while the second outside the brackets is the function f ...I will write it again as I was very tired last night.

y_i^{(n)}=\phi_i(x,y,y',\dots ,y^{(n-1)}) The nth order ode

(\partial _x+y'\partial _y+y''\partial _{y'}+\dots +\phi \partial _{y^{(n-1)}})f=0 the PDE in n+1 variables

Slereah

you forgot your $!

AngusTheMan

oh snap

does it come up in LaTeX for you guys on chat ? even with the $$ it was still just writing for me?

Slereah

you have to launch a script

93

A: Should chat have TeX support?

I will leave the original post for historical reference, but as mentioned in the Update below, all four bookmarks are located on this installation page. There are four bookmarks: start ChatJax installs MathJax and starts a loop that renders $\LaTeX$ as needed. This is intended for use in chat, ...

AngusTheMan

$y_i^{(n)}=\phi_i(x,y,y',\dots ,y^{(n-1)})$

oh i see

@Slereah thank you for the link :)

$(\partial _x+y'\partial _y+y''\partial _{y'}+\dots +\phi \partial _{y^{(n-1)}})f=0$

obe

10:44 AM

Time for QFT.

Slereah

but @obe

What is time in QFT

obe

whatever.

0celo7

11:49 AM

foxnews.com/us/2015/09/16/…

0celo7

12:45 PM

@Slereah good question

I think it's the direction with the $-$ or the $+$ if you're a dirty heathen

my question is still locked

great

John Duffield

12:58 PM

@WadCheber : you try getting some rep on physics stack exchange. Especially when you have to blow away the fairy tales and make the kiddies cry.

@Slereah : hence most of JD's answers are downvoted like hell.

0celo7

@JohnDuffield define "kiddies"

also no one has ever cried from reading your post...unless maybe out of frustration at the misinformation you're spreading

John Duffield

@Slereah said "Because to put it politely, his opinion on physics don't really align with the mainstream". That's incorrect. I get downvoted for giving good answers backed by robust references because they don't tie in with some popscience garbage that some starry-eyed kid wants to believe in.

See this and this for example.

@0celo7 watch my lips : photons interact with photons. Get used to it. If you have some textbook that says they don't, that textbook is wrong. Capiche? Now stop elevating mathematical abstraction above physics reality.

Slereah

1:15 PM

By "kiddies" he means "Every general relativity specialist since the 1950's"

John Duffield

@NeuroFuzzy : don't listen to 0celo7, he's telling you bad science. Virtal electrons are not real electrons. See anna's answer here.

0celo7

When did I ever say the virtual electron is real?

All I said is there's no photon interaction term in the Lagrangian, which is correct.

Ask any mainstream physicist.

Slereah

did you even ask Dirac, @0celo7

or the evidence

John Duffield

@0celo7 : oh no you didn't. Neurofuzzy asked if there weren't very very weak gamma-gamma interactions, and you said "not direct! and not in a vacuum". That's wrong. Photons interact with photons, and it's been mainstream since 1934. So stop preaching your ignorance and spreading misinformation and making out it's mainstream when it isn't.

0celo7

> that is the emission of positron–electron pairs off a probe photon propagating through a polarized short-pulsed electromagnetic field (for example, laser)

NOT IN A VACUUM

Slereah

1:29 PM

Well it can happen in a vacuum

It just has a very low cross section

Since it's in $\approx \alpha^2$

0celo7

if there's direct photon-photon interaction, provide evidence of a corresponding term in the Lagrangian

John Duffield

@0celo7 : yes, in a vacuum.

Slereah

Not direct, though, most certainly

0celo7

@JohnDuffield no, your references are not robust

Slereah

As said, it depends on $\alpha$

0celo7

1:30 PM

you misuse quotes

Slereah

If the coupling of electrons to the EM field goes to 0 it goes away

0celo7

you use out of date papers

Slereah

I don't think even the papers back then thought it was that

0celo7

I don't think JD even knows that a Lagrangian is

Slereah

But you are wasting your time.

Just stop arguing.

0celo7

1:31 PM

why are we even talking to him

ACuriousMind

@0celo7: Processes $\gamma+\gamma \to \gamma+ \gamma$ and $\gamma+\gamma\to e^+ + e^-$ can happen in a vacuum. You're correct they aren't direct (as in, tree-level).

0celo7

::sigh::

mod invasion again

@ACuriousMind I see, then why do we need lasers to make it happen

is the cross section vanishingly small otherwise?

Slereah

it is.

ACuriousMind

@0celo7 Because the amplitude for these processes is so small you need high intensities to see them

Slereah

Because it's a second order effect

Two vertex are involved

ACuriousMind

1:33 PM

Also, there could be an influence of the coherence of laser light, but I'm not sure about that

0celo7

the Wiki article mentions the polarization of the laser

Slereah

yeah I think some polarizations don't work for that process

or are less likely

ACuriousMind

I think the article describes the experimental setting where the process is relevant, but I don't see a reason why the diagram should vanish in vacuum

0celo7

ok

Slereah

The one that doesn't happen in a vacuum is $\gamma \rightarrow e^+ + e^-$

0celo7

1:35 PM

yeah because kinematics

Slereah

you need a friendly nucleus to do it

0celo7

friendly neighborhood nucleus

ACuriousMind