It is weird to think that Schwarzschild did a whole bunch of things

You only ever hear about him for the metric

"Schwarzschild is the first to introduce the correct Lagrangian formalism of the electromagnetic field"

Nobody calls it the Schwarzchild lagrangian!

@BalarkaSen do you have ted shifrin’s book?

should I go full physicist and call it an action?

@PrathyushPoduval yeah

why would anyone star that

@0ßelö7 what

@Slereah what what

what's with the normalization

@BalarkaSen you bought it or ebook?

Is it to avoid the divergence of the action?

@Slereah It's best to not have to worry about volume terms.

I worry

I just watched the grandayy video

I've never seen it before

because it's useful for math, not physics

@BalarkaSen minecraft’ed

so you watched the original track?

Yeah

lol

@Slereah Also if you fix the volume, the critical points in a conformal class have constant scalar curvature

absolute fire

I didn’t realise he asked to make the song in minecraft😂

Also is "Einstein metrics" fancy talk for vacuum metrics

You have ted’s ebook?

@BalarkaSen

I do

@Slereah you should learn some riemannian geometry

Can you email it to me?

I know some Riemannian geometry

they are Riemannian metrics that obey $\Lambda$-vac equations

$\mathrm{Ric}=kg$

@PrathyushPoduval why can't you pirate it yourself?

But that's not the extremal of this action

@PrathyushPoduval I'm sorry, I can't. Ted sent it to me so it's morally not right for me to redistribute it

@0ßelö7 it’s not available

@BalarkaSen okay it’s alright then, thanks

No one has bothered to pirate it? Lol

Yeah

Yeah it's hard to find a pirated copy

There isn’t any

I was quite surprised at first

@Prathyush Why don't you pick it up at your university library or something

@Slereah what is the critical point then

That's one option

@0ßelö7 Of $R - \Lambda$?

@BalarkaSen I’m not in university yet, I’m in 12th

Oh.

If $E(g)$ is the usual total scalar curvature integral $\int R(g)$, then the functional derivative is $Rg/2 -\mathrm {Ric}$

Our library is shitty as hell, with only jee books

the Einstein tensor

modulo a sign

if you fix volume you have $R=\mathrm{const.}$

I can recommend some other multivariable calculus textbooks

so the functional derivative is $kg-\mathrm{Ric}$

That I liked

Yeah feel free to

I have heard good things about Edwards, but I haven't read it. Try Duistermaat-Kolk

Though I think it's a bit too theoretical

Federer for multiple integrals

What is the practical part in multivariable?

all of it

Actually being able to do computations

You mean problems then

"extensions of Gowdy polarized space-time"

The fuck is Gowdy polarized spacetime

Maybe

I shall check out those books then

@BalarkaSen do you know what the gradient flow of a functional is?

@Prathyush Though, if you go through Ted's youtube series, you will pick up a lot of computational efficiency

@0ßelö7 I know what the gradient flow of a function on a manifold is

whaaaat

@BalarkaSen same difference, just take the manifold to be a set in a Banach space

I see

I need to compute some gradient flows

Wait, Banach? How do you take the gradient if you don't have an inner product?

@BalarkaSen the inner product is the Riemannian one

@BalarkaSen yeah it’s good. But I don’t like YouTube lectures since I cannot proceed at my own pace

"Clarke and Hajicek define space-time as 4-dimensional manifold, with smooth Lorentzian metric. Hajicek 1971a also adds paracompactness, Hajicek 1971b complete separability (= second countability) and Clarke 1976 connectedness."

I guess it's a pre-Hilbert space. Whatever

I am curious about that connectedness paper

@PrathyushPoduval Ted's lectures are reasonably slow

@BalarkaSen that’s the problem 😅

With most video lectures

Apparently Clarke wrote a bunch of spacetime topology papers

And I've never heard of him

Well going super fast through stuff is not recommended

projecteuclid.org/download/pdf_1/euclid.cmp/1103899938

that is the paper

@BalarkaSen I don’t go super fast on things I don’t know :P But his videos did help me understand the inverse function theorem and implicit function theorem, which rudin did mechanically as expectated

"some physicist consider liberalizations of the Hausdorff condition."

Damn liberals

@PrathyushPoduval Ted's proof of inverse function thm is my favorite

"In order to properly formulate local conservation law, energy momentum tensor should be continuous and differentiable. However, this entails that when energy ‘travels’ along bifurcate curve, it has to take both branches, because if it went along only one of them, the tensor on another one would be discontinuous. But then global energy conservation would be violated."

@Blue I just take the topic lectures which I didn’t understand from my books

@BalarkaSen yeah, he goes through it properly

@BalarkaSen inverse function thm is very important for nonlinear PDE.

"The theorem which guarantees existence and uniqueness of maximal solutions of Einstein’s equations (given the appropriate initial data) relies on the Hausdorff condition. The uniqueness result fails if non-Hausdorff branching is allowed – we may attach non-Haussdorffly additional branches at some given moment of time."

Take that Yvonne

@BalarkaSen what do you do in your school math classes?

@Slereah yep

@0ßelö7 I can believe that

have you read chap 7 of HE yet

Still not

Well, I tried

But not very far

@BalarkaSen basically just compute the "derivative" of nonlinear PDEs and show it's bijective

voila you've got existence/uniqueness

@PrathyushPoduval I think about the stuff that happens :P

what do you expect me to do?

@BalarkaSen Make memes :P

Don’t you get bored?

@Prathyush Just because I am interested in mathematics on the large doesn't mean I get bored at "how easy this high school stuff is! Ugh! It's beneath my toes! wiggle jiggle"

@BalarkaSen Well, not that deep :P

I do enjoy a lot of high school math, and do get hard times working out some stuff

hmm, which board are you in?

A lot of it was like

Finding limits of weird functions

wb

That you'd never see in a real situation

@BalarkaSen is it tough?

I wouldnt call it that but its not super trivial

at least to me

okay. many of the state boards is just for namesake (mine is)

The teacherss encourage mugging up shit, and exams are leaked beforehand

eek

When does your session end?

I would say my school is pretty decent

okay, your lucky then :P

@PrathyushPoduval Probably at the end of this month

seriously? when did it start?

Uh, I have forgotten

we have 3 more monoths to go through now

"Gowdy Spacetimes have become useful test cases for studying the dynamics of Einstein's theory of General Relativity. Because they are simple enough to analyze and admit arbitrary wavelength gravitational waves, they provide insights into the full dynamics of general relativity that cannot be provided by homogeneous cosmological models. "

Jesus

How many fucking spacetimes are there

@BalarkaSen for your education i.gyazo.com/b705d7dcd52d2d3f88c56cf91ce7f02c.png

also where the fuck is the original paper of Misner space

I've been looking for it for months

It doesn't seem to be online

adsabs.harvard.edu/abs/1967rta1.book..160M

Ahah!

ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19660007407.pdf

Jesus

Look at that typewritten report

Terrible typesetting

@BalarkaSen Are you giving KVPY?

@BalarkaSen is it K-theory or $K$-theory?

@Prathyush Nope

@0ßelö7 who cares

okay

@BalarkaSen people who care about precision

@BalarkaSen this has given me faith in duistermaat

lol

what is wrong with epsilons and deltas

how do you even minimize the number?

replace with sequences?

ya

@0ßelö7 I have nothing against it. But after seeing the same technique again and again, this book is having a different approach which I would like to know

In analysis you have sequences or epsilon-delta.

Sequences are usually the way to go.

@Blue Where did you see this?

@Blue I have never come across this delta-gamma representation, maybe someone else may be able to help you

But generally, the partition function is $\sum e^{-\beta E}$

might be it's the delta function

Yeah I read that

I think Delta is just the delta function, because if you look at the probability, it has the same property

yeah

but then, if you follow the 2nd point, you get Z as $e^{-\beta E}$

yup

@ACuriousMind just a matter of curiosity really, there's a question that I feel might have some information that could help me with an acquaintance of mine

unfortunately its on software engineering

So no-one I know can send me screenshots

yoooohoooo

hey, German contingent (i.e. @ACuriousMind & @0ßelö7)

why does it say 'separieren' instead of 'trennen'?

did German suddenly forgot its obsession with being Germanic and indulged in a bit of Latinity just for wissenschaftliche Zwecke?

Hmmm

Keine Ahnung. Why does it matter? Just curiosity?

It might be customary to use the Latin word in a math setting.

@0ßelö7 just curiosity

'separieren' sounds strangely wordy and ungermanish

@JohnRennie it does work as a German word, but the language tends to go for the words with native roots rather than their Latin equivalents

the standard example is the shunning of tele+vision for fern+sehen

German word order always got me the most... Not even like it's hard... I just kinda sucked...

And despite studying it for two years two years ago I'm preeeety sure I've forgotten it all already...

You could post on Sabine Hossenfelder's blog and ask her ...

@JohnRennie don't reaaaaally care enough to take it that far ;-)

I'm editing this one to try and pre-empt more people from posting non-answers

Ask on the German Stack Exchange!

so I'm already deep enough into old German papers

@EmilioPisanty the answer to that is simply no isn't it?

@JohnRennie dunno

it depends on what you mean by 'exact'

Using whatever fancy coordinates makes the wavefunction separable but there's still no analytic solution for the various parts.

and actually looking at some of the old papers, there may well be more hidden in series solutions than we give them credit for nowadays

@JohnRennie yeah. Thing is, if there's a series solution to the various parts, does it begin to count?

@EmilioPisanty Whenever I can't remember a German word I say the English one with a German accent. In some cases it works :)

@EmilioPisanty Yes, Latinisms are very common in scientific language

@0ßelö7 Pretty sure I did that for my German GCSE and it worked...

@EmilioPisanty hmm. I'm not sure I'd consider an infinite series an analytic solution.

what if it requires you to solve this little horror for $\mu$?

(that's a continued fraction, btw)

@JohnRennie so why do you think $f'(x)=f(x)$ is analytically solvable?

(it's not a clear-cut distinction, is all I'm saying)

@ACuriousMind so, does it make me sound less scientific if I don't use the latinisms? Does it make me sound more scientific if I do? =P

@EmilioPisanty 'Yes and yes

@ACuriousMind Germans are weird

@EmilioPisanty Expressions involving $e^x$ are normally considered an analytic solution, just like sin, cos, etc. I guess it depends on where you draw the line.

@JohnRennie yeah, the point is, can you find the values of those without an infinite series?

@EmilioPisanty Yes :)

so I'm trying to draw up an answerness criterion on that thread that's a bit more explicit

Yes, but in principle any function can be written as a power series, in which case all differential equations have an analytic solution.

By that criterion the three body problem has an analytic solution.

@JohnRennie does it actually, though?

@JohnRennie lies

i.e. is there, say, a series solution for the $\rm H_2$ molecule?

@EmilioPisanty yes, there's a power series solution for the three body problem. It's in the Wikipedia article somewhere if I could be bothered to look :-)

@JohnRennie oh, you mean the classical three-body problem?

and if you do solve H$_2$ via series, how does the enforcement of normalizability give you quantization of energy and a value for the eigenvalues?

@EmilioPisanty Sundman's theorem

@JohnRennie $e^{-1/x}$ ain't analytic (a common example in most textbooks)

if you meant analytic function

@PrathyushPoduval I suspect what I meant is more properly described as a closed form solution. I was just being sloppy with terminology.

Hi, everyone! This is sort of a question but I think it is not qualified to be posted as a proper question because I know that it can be easily worked out if I shake off my laziness and grab some pen-paper. So, out of curiosity about the final result, I just want to ask the final result if someone knows it or can suggest some references from which I can simply read it.

Ok, so the question is that are there any number of dimensions in which classical electrodynamics doesn't admit propagating degrees of freedom just like gravity doesn't admit gravitational waves in 2+1 dimensional set-up. Thanks!

@JohnRennie Ah okay. I have been doing too much of maths lately :P

what ami doing

@Dvij this looks related:

@PrathyushPoduval You are doing the top subject out there.

@JohnRennie Yes, this perfectly answers my question. Thanks! :-)

@Sid depends on who you ask :P

@Dvij Physics Stack Exchange to the rescue! :-)

haha. Always! <3

It's gratifying how often a Google search gives you links to the PSE.

@PrathyushPoduval my answer to that is: xkcd.com/435

seen that ;-)

@Sid Who wants to be pure? Saints and virgins are pure. Me, I like getting dirty! :-)

savage, thats how you should live life :P

That should be a new xkcd... :P

well, whaddayaknow, there I was looking for an old paper on a journal called Kongelige Danske Videnskabernes Selskab Matematisk-Fysiske, damn afraid it would be in Danish, and it turns out to be in German

petrolium engineering --> chemical engineering --> electrical engineering --> civil engineering --> ... ---> pure mathematics --> theoretical physics

It seems Marx debunked Taylor's theorem yeaaaars ago

marxists.org/archive/marx/works/download/…

@BalarkaSen is this for real?

Ya

He understood Taylor's proof of his theorem is applicable only for analytic functions

And criticized the hell out of him

That absolute madman

...what exactly is "Taylor's theorem"

$f=derivatives+O(r^n)$

@BalarkaSen Wait. Are you saying Taylor's theorem is wrong? The proof is wrong? Or that Marx is crazy?

Well in their times Taylor's theorem was the sloppy statement that $f(x + h) = f(x) + f'(x)h + f''(x)/2! h^2 + \cdots$ for sufficiently small $h$

No Marx was right. Taylor's original statement and proof of his theorem was incorrect.

how does conservation of momentum deal with irreversible processes?

In what way do you think those two conflicts

inelastic collision...anything that creates heat

creating meaning in a sense of kinetic energy turning into thermal energy

nvm

;)

Inelastic collisions do not lose energy

it just goes elsewhere

samuel-lereah.com/db/spacetimedb/Minkowski

Does this seem like a good structure for a spacetime baseball card

The main sections, at least