The h Bar

0celo7

12:02 AM

@GPhys that's pretty standard. I guess no one looked in books if they all got bad grades

A GR expert knows that stuff, or at least where to find it

GPhys

it says you can't look in books on the first page!

pls

0celo7

How is the second problem not in Carroll?

GPhys

all the calculation part of the second problem I thought was the easy part

bolbteppa

Says you can look in Carroll's book

0celo7

@GPhys do people actually listen to those rules?

GPhys

12:03 AM

probably? I don't think there's really enough motivation not to

maybe it would make more sense if it was an undergrad course

bolbteppa

A GR expert would probably not be taking a class in GR

0celo7

@bolbteppa maybe not a basic course

GPhys

@0celo7 I still don't understand why on the second problem part (iv) the formula derived holds in any coordinate system, and not just ones where the background is locally inertial

0celo7

it's a tensor

GPhys

@0celo7 if the background is locally inertial can't I replace the | with , then?

0celo7

12:07 AM

don't think so. Is the claim that you can?

wait what is the $|$

background derivative

so what's the issue?

GPhys

Why is replacing with , wrong? I'm not making proof claims I'm asking because this was a part of the exam I didn't understand

0celo7

because the covariant derivative wrt. $\bar g$ is not the same as a partial differentiation

GPhys

why is it true that $g_{\mu\nu,\lambda}=g_{\mu\nu |\lambda}$

0celo7

where does it say that?

GPhys

as far as I can tell you minimally need that to be true to do the derivation

Mithrandir24601

12:12 AM

@ACuriousMind Heh. Yeah, I remember one of my GR exams going terribly (as in, there was no way I got more than ~60%), only it turned out that that was ridiculously well :)

0celo7

I think it's true modulo higher order terms. Does that sound right?

GPhys

@0celo7 this is in a locally inertial background metric, mind you

because $g_{\mu\nu}=\overline{g}_{\mu\nu}+h_{\mu\nu}$, $g_{\mu\nu |\lambda}=h_{\mu\nu |\lambda}$

0celo7

So it's not stated there but you needed it?

GPhys

so the result in the question only follows if $g_{\mu\nu,\lambda}=g_{\mu\nu |\lambda}$

0celo7

which result? Which part?

GPhys

12:16 AM

part iv of the second question, maybe we're looking at different things

$S^{\rho}_{\mu\nu}\equiv \Gamma^\rho_{\mu\nu}-\overline{\Gamma}^\rho_{\mu\nu}$

0celo7

yes

GPhys

in a locally inertial background metric

0celo7

let me think

GPhys

$S^{\rho}_{\mu\nu}= \Gamma^\rho_{\mu\nu}$

0celo7

(I'm eating, sorry)

GPhys

12:18 AM

right?

0celo7

at a point

oh, I remember this

GPhys

and

$\Gamma^\rho_{\mu\nu}$ is equal to the result in the question only if $g_{\mu\nu,\lambda}=g_{\mu\nu |\lambda}$

0celo7

did you not learn the Palatini formalism?

GPhys

since $g_{\mu\nu |\lambda}=h_{\mu\nu |\lambda}$

I've never heard of that

0celo7

it's a program that does all of this rather easily

the equation there seems to be correct

let me see if I can explain this succinctly

GPhys

12:21 AM

okay but why is $g_{\mu\nu,\lambda}=g_{\mu\nu |\lambda}$ but not $h_{\mu\nu | \lambda}=h_{\mu\nu , \lambda}$

0celo7

chill

@GPhys I assume you wouldn't want a calculus of variations argument?

GPhys

You can make it if you want?

0celo7

I am writing your answer on paper, give me a bit.

0celo7

12:34 AM

@GPhys oh crap, you're not supposed to assume that $h$ is small for (iv)?

@GPhys Ok, you still here? I think I have it.

GPhys

yes

0celo7

So you pick a coordinate system in which $\bar\Gamma =0$, so $S=\Gamma$

Call the stuff with the derivatives in the Christoffel symbol $\gamma(g)_{\mu\nu\rho}$

GPhys

yes

0celo7

So $$2\Gamma^\sigma{}_{\mu\nu}= g^{\sigma\rho}\gamma(g)_{\mu\nu\rho}= g^{\sigma\rho}\gamma(\bar g)_{\mu\nu\rho}+ g^{\sigma\rho}\gamma(h)_{\mu\nu\rho}$$

GPhys

okay

0celo7

12:41 AM

If the first term is zero, you're done.

Do you see that?

Because you can replace the derivatives in $\gamma(h)$ by $\bar g$-covariant derivatives.

GPhys

@0celo7 why

0celo7

Covariant derivatives are partial derivatives in normal coordinates

The Christoffels are all zero

GPhys

covariant derivatives are tensors but partial derivatives are not tensors?

oh

0celo7

No argument here. It holds at a point in special coordinates. It doesn't always hold because the partials aren't tensors.

GPhys

okay

isn't the first term just zero though for the same reason?

by requiring the covariant derivative to be the one compatible with its metric the first term becomes zero

0celo7

12:46 AM

So then use the fact that normal coordinates implies $\partial_{\mu}\bar g_{\rho\sigma}=0$, and the first term is zero.

@GPhys Yeah that works too

And that's it.

GPhys

@0celo7 picking locally inertial coordinates of background metric feels like cheating

0celo7

It's the number one trick in GR and RG

GPhys

RG?

riemannian geometry?

0celo7

Riemannian geometry

@GPhys does that resolve the issue?

GPhys

@0celo7 yes I think

Fawad

12:57 AM

😡

0celo7

1:20 AM

> It is my pleasure to thank several friends and colleagues at T.I.F.R.
for their comments and encouragement, and in particular H. M . Antia,
who made my interaction with computers so much easier.

Balarka Sen

hahaha

who is this

I was in TIFR for a month and a half

0celo7

@BalarkaSen How does a high school student do the things you do

P. Joshi

Balarka Sen

is this a physics person

0celo7

I am a physicist (on odd-numbered days)

0celo7

3:14 AM

@rob Yuri's explanation for the strange letters in shell models i.gyazo.com/7f01457242f0df472421bd4fa7e035b3.png

@Semiclassical paging QM help desk

@user685252 It appears so.

user685252

:(

0celo7

3:44 AM

GOD DAMMIT AN HOUR OF STUDY TIME LOST TO A TYPO

Bernardo Meurer

3:56 AM

@BalarkaSen Were you born in 2000?

Balarka Sen

I was born in 1984 biatch

Bernardo Meurer

I doubt that

Balarka Sen

I eat dystopia, I breath dystopia, I feel dystopia

Bernardo Meurer

So, today I had a long discussion on the concept-containment with my prof

Learned some more stuff

Balarka Sen

Woo cool what did you learn

0celo7

4:02 AM

@BalarkaSen can u ask your group theory friends what a good short intro to metric geometry is

Bernardo Meurer

Well, firstly that Leibniz would argue that you can't take a subject-concept and take away one single element/characteristic off it. He believed them all to be interconnected in away, and that taking a single one out made no sense

0celo7

Praseodymium

Praseodymium is a chemical element with symbol Pr and atomic number 59. It is the third member of the lanthanide series and is traditionally considered to be one of the rare-earth metals. Praseodymium is a soft, silvery, malleable and ductile metal, valued for its magnetic, electrical, chemical, and optical properties. It is too reactive to be found in native form, and pure praseodymium metal slowly develops a green oxide coating. Praseodymium always occurs naturally together with the other rare-earth metals. It is the fourth most common rare-earth element, making up 9.1 parts per million of the...

wtf, I've never heard of this

Balarka Sen

@0celo7 I can try. But I am about to sleep now

@BernardoMeurer Hm

Bernardo Meurer

Leibniz is really weird

Let me show you my notes

0celo7

@BalarkaSen the conditions for spin and spin^c are the same, right?

Bernardo Meurer

4:10 AM

Balarka Sen

@0celo7 I don't think so

0celo7

@BalarkaSen yeah there are some homotopy conditions

Balarka Sen

@Bernardo Hm

0celo7

algebraic topology is awful

Bernardo Meurer

@BalarkaSen Ignore that definition of universe there, it's wrong, existence can't be given as a predicate-concept

i.e. can't be contained in the subject-concept

Balarka Sen

4:20 AM

So these are Spinoza's views on the theory of truth and reason?

Bernardo Meurer

No, that's Leibniz

Balarka Sen

Ah ok

The idea of universe looks damn close to that of God (which is by Spinoza, isn't it?)

Bernardo Meurer

I don't know whether Spinoza commented on Leibniz's theory, although I do know Leibniz went to the Netherlands to visit Spinoza and that they corresponded

@BalarkaSen Well noted! Exactly!

Leibniz dies being a Spinozist, but it's very clear from his points that they arrive at extremely similar conclusions

Alas Spinoza will argue that there is only one substance, and Leibniz will argue that there are many

Balarka Sen

Very interesting

0celo7

there is only one

strings

@BalarkaSen is a string

@BernardoMeurer is a string

Balarka Sen

4:22 AM

ur face is a string

Bernardo Meurer

I'm writing a post on my blog about this, and improving the notation a bit too

0celo7

yup

so is ur mom

MOD ABUSE

Balarka Sen

I don't hang around in the beaches of Rio like a filthy capitalist pigdog

Bernardo Meurer

@0celo7 It was that flipping Artofcode

I bet

@BalarkaSen Lol, beaches? I have a pool dawg

(not true anymore)

rob

> For reasons best known to nineteenth century spectroscopists, $\ell=0$ is called $s$ (for "sharp"), $\ell=1$ is $p$ (for "principal"), $\ell=2$ is $d$ ("diffuse"), and $\ell=3$ is $f$ ("fundamental"); after that I guess they ran out of imagination, because it now continues alphabetically ($g$, $h$, $i$, but skip $j$ - just to be utterly perverse, $k$, $\ell$, etc.). --- D.J. Griffiths, in his introductory QM text

2

Bernardo Meurer

4:27 AM

Lol

0celo7

@BernardoMeurer If I do do that thing, and don't see you before, I will bring a copy of Shankar. Although by then you should have it memorized, really

You need to get cracking on that

Bernardo Meurer

Memorize Shankar?

I'm going into Logic now

0celo7

Yeah, basically

Bernardo Meurer

once I'm done I'll go to QM

Balarka Sen

Bernardo needs to learn homotopy type theory

0celo7

4:31 AM

There are three books every respectable STEM student should memorize: Wald, Shankar, and Evans.

Bernardo Meurer

@BalarkaSen I actually do

@0celo7 What about Rudin?

0celo7

Rudin is a meme.

And analysis is trivial anyway.

Bernardo Meurer

What's Wald and Evans?

0celo7

GR and PDE

Balarka Sen

@BernardoMeurer If you're heading down that path, soon you'll become the world's biggest expert on Grothendieck topoi

Bernardo Meurer

4:33 AM

Ah, I'm not that interested in GR, at least not yet

@BalarkaSen Grothendieck is my ultimate life goal

Balarka Sen

Good

Bernardo Meurer

Being like him

0celo7

completely insane?

locked away in a dungeon in the mountains?

Bernardo Meurer

Yes

Balarka Sen

flamboyant like a french, insane like a russian

a perfect combination

Bernardo Meurer

4:34 AM

Yep

Exactly

0celo7

I guess Gromov took the insane pill twice.

Balarka Sen

Gromov is beyond insane

Bernardo Meurer

Look at him lol

Grothedieck you fiend

0celo7

Balarka Sen

plot twist Grothendieck = Gandalf

Bernardo Meurer

4:36 AM

What's wrong with Gromov?

0celo7

look at his eyes

or read one of his papers

Balarka Sen

gromov is utterly incomprehensible

Bernardo Meurer

He and Hegel should chat

Balarka Sen

Rokhlin said that the reason Gromov turned out this way is because he gave then-postdoc Arnold the responsibility to be an advisor to Gromov

IIRC

0celo7

is Arnold insane too?

Bernardo Meurer

4:40 AM

Arnold from Hey Arnold!?

Balarka Sen

Well there are stories about Arnold

0celo7

Yeah. Turns out that guy was a physicist too

Bernardo Meurer

Balarka Sen

He became massively angry when a French kid he was teaching in his middle school math class raised his hands when he asked "What's 2+3?" and said "2+3 is 3+2 because addition is commutative"

The legends say his rage was beyond comprehension

0celo7

that's fake story

has to be

Bernardo Meurer

4:42 AM

@BalarkaSen Why was post-doc teaching middle school?

0celo7

or maybe the kid was Grothendieck

Balarka Sen

Nope. There's a small exaggeration but it's true. There's a post in MO where the kid (now a mathematician) responded

Bernardo Meurer

@BalarkaSen Link!!

Balarka Sen

The kid meant it as a joke, and Arnold asked it as a tease question

But Arnold did get very mad

0celo7

I have read the thread

It's well known math lore

I don't believe it

Balarka Sen

4:43 AM

@BernardoMeurer Oh I mean this was after Arnold was famous and all. He used to teach mathematics to a lot of different levels

Let me see if I can find it

There's also the story about how Arnold publicly shamed Bourbaki

0celo7

I will never understand the hate for Bourbaki

I must be the only one who's actually tried to read their stuff

TVS is a perfectly fine functional analysis book

Balarka Sen

@Bernardo mathoverflow.net/questions/153604/the-arnold-serre-debate

0celo7

So is general topology

Balarka Sen

lots of juicy drama in that question

0celo7

Russians be crazy

I see where you get it from Komrade Balarka

Balarka Sen

4:46 AM

I am a proud Soviet

Bernardo Meurer

I have to say, Tarski's notation is annoying me

I hope Kleene is better

Balarka Sen

You should read more modern books on logic, imo (I can't recommend one though)

0celo7

read Jech's set theory and tell me why anyone bothered to write that crap

Bernardo Meurer

I wanted to get Hilbert and Ackermann later too

I heard Ebbinghaus is nice too (from online reviews)

I don't know any logicians to go talk to though :(

Kaplansky's Set Theory and Metric Spaces seems interesting

0celo7

dude, learn some manifold stuff

Balarka Sen

4:52 AM

cool story brother — Wicht Jan 5 '14 at 23:21

I love this comment

Bernardo Meurer

I didn't like manifolds when I did it :/

I thought it was boring

0celo7

they are boring at first

Bernardo Meurer

Logic is really exciting and cool, at least for now

0celo7

but then you realize you can do PDE on them

and then they're cool

Bernardo Meurer

I also suck at Analysis

Balarka Sen

4:52 AM

@0celo7 omg stop u pde theorist

Bernardo Meurer

I have Mendelson's book on topology, maybe I should bother reading it

0celo7

just read Munkres

it's a meme but really good

Balarka Sen

Yeah I think set theory, logic, point-set topology are a good mix

Bernardo Meurer

I don't own Munkres though

Balarka Sen

Munkres is a huge ass tome

0celo7

4:54 AM

Munkres is expensive too

Bernardo Meurer

@BalarkaSen I'm going to be a certified nutjob

0celo7

@BalarkaSen It is?

Balarka Sen

You don't need to read that stuff

0celo7

It's slim

Bernardo Meurer

Add homotopy type theory to the mix

Balarka Sen

4:54 AM

@BernardoMeurer Slowly, slowly :)

0celo7

@BalarkaSen what is wrong with Munkres

I will fight you

Balarka Sen

It's an extremely good book

But I don't think it's appropriate for Bernardo

Bernardo Meurer

Topics I'd like to dab in: Logic, Abstract Algebra, Set Theory, Homotopy Type Theory

0celo7

ok I think Homotopy Type theory was a joke, right?

Balarka Sen

no it isnt

Bernardo Meurer

4:56 AM

I actually want to dab it

0celo7

hott.github.io/book/nightly/hott-online-1075-g3c53219.pdf

Balarka Sen

is that the HoTT book

0celo7

what the hell is this font

Bernardo Meurer

Today in the library I told a bunch of kids that ZFC is broken and they all bought it

2

0celo7

esucc

osucc

Bernardo Meurer

4:58 AM

wtf is that notation

Balarka Sen

welcome to the world of univalent foundations

I really wish I knew something about it

0celo7

I have no idea what this is even is

Is it algebraic topology?

Balarka Sen

It's actually very interesting. I think I ranted about it in the past on the math chat, let me find it and get back to you lol

0celo7

The algebraic structure of paths and homotopies is represented by the natural ∞-groupoid
structure on types, which is generated by the rules for the identity type.

Bernardo Meurer

scottaaronson.com/busybeaver.pdf

I gotta read this again

0celo7

5:01 AM

@JohnRennie late today

Balarka Sen

@0celo7 Well it's like, say you are proving $a = b$. There are many ways to prove that statement, if it is true. You can also talk about "equivalence between two proofs of $a = b$". That's like a homotopy between two paths with the same endpoints

Bernardo Meurer

Morning John!

0celo7

@BalarkaSen That seems like something someone thought while really high.

Balarka Sen

That's what makes it so cool!

0celo7

@BalarkaSen I think I've figured something out

John Rennie

5:03 AM

Morning

0celo7

The fundamental difference between algebra and analysis is that the former needs many drugs to motivate, whereas the latter is natural.

I don't like drugs, so I'm an analyst.

You're a coke fiend, so you like algebra.

Balarka Sen

~~Hey, that's pretty good!~~ Greetings, that's moderately adequate!

0celo7

What?

@BalarkaSen I've been thinking about this a lot lately because I'm taking algebra

Balarka Sen

It's a verbose meme

0celo7

I don't know any memes

Balarka Sen

5:06 AM

well sucks to be you then

0celo7

Do memes increase GDP?

Balarka Sen

According to Fantano, they can be used as a very effective advertisement

So yes, they have the potential to increase the GDP

0celo7

entertainment isn't real GPD

it doesn't create wealth

Balarka Sen

you clearly don't understand economics

effective advertisement => more sale => more wealth

0celo7

no

there might be secondary wealth creation

but someone making a CD and getting paid for it does nothing

Balarka Sen

5:10 AM

the worldwide money gained from selling mixtapes can change the face of modern economy as we know it

you need to change your viewpoint from the capitalist economy to the revolutionary ecanamay

Marx debunked GDP years ago

0celo7

I am considering becoming a revolutionary communist.

@JohnRennie I need QM help

Bernardo Meurer

GDP is kind of BS tbh

Balarka Sen

5:25 AM

@Bernardo math.cornell.edu/~hatcher/Top/TopNotes.pdf

this is a good point set topology learning source

Bernardo Meurer

I'll print it tomorrow with Aaronson's paper and read them

Balarka Sen

(y)

0celo7

look at that awful font

Balarka Sen

look at that whiny guy

this is the best font of all time

lucida is the best

Bernardo Meurer

I'll agree this is a weird font

At least it's not Times New Roman :P

user685252

5:29 AM

"A calm and modest life brings more happiness than the pursuit of success combined with constant restlessness." https://winners-auctions.com/en/content/professor-albert-einstein-regarding-fitting-way-life-imperial-hotel-tokyo-japan-1922

Tweeted by benjamindickman on October 25, 2017 at 11:29 PM

Sir Cumference

Howdy

0celo7

6:09 AM

@JohnRennie I was serious.

John Rennie

@0celo7 sorry for the slow response. I've been sorting out some server issues.

I suspect you know more about QM than I do, but I'll help if I can.

Bernardo Meurer

7:07 AM

@BalarkaSen meurer.xyz/articles/2017/10/25/on-leibnizs-truth.html

Starting the rewrite

Balarka Sen

@Bernardo Coolio

Phase

7:54 AM

Question

what's the deal with signatures

is it just related to defining the scalar product?

John Rennie

Metric signatues?

John Rennie

8:13 AM

Steven Hawking's PhD thesis is online in the unlikely event anyone wants to see it.

Bernardo Meurer

8:24 AM

Trying to get SEO to work on my website

Harder than I thought it'd be

John Rennie

SEO?

Bernardo Meurer

Search Engine Optimization

Qmechanic

9:13 AM

@JohnRennie : Copy-pasted your link here (which is essentially riemannium's answer).

John Rennie

@Qmechanic ah, I hadn't realised it had already been asked about on the site :-)

Mithrandir24601

10:18 AM

@JohnRennie You're late: I knew about this yesterday :P

John Rennie

@Mithrandir24601 I saw it on Facebook this morning. It turns out the thesis has been available for ages so I'm not sure why it's suddenly news.

Mithrandir24601

@JohnRennie Nor am I to be honest...

Maybe it wasn't public before?

user685252

that^'s what i thought

Mithrandir24601

Yeah, by the looks of things, before this week, you had to request access, so that does make sense

user685252

21 hours ago, by user685252

is anyone planning on watching the hawking lecture on friday?

Mithrandir24601

10:36 AM

@user685252 There's a Hawking lecture on Friday?

Depends what it's on I suppose...

user685252

@Mithrandir24601 here

0celo7

12:23 PM

@JohnRennie Sn115, 117, and 119 all have spin 1/2+ but the shell model predicts the latter two having 3/2+. Why?

Mithrandir24601

12:45 PM

@user685252 probably not, to be honest

0celo7

1:19 PM

@Semiclassical I just used the nodal theorem

Semiclassical

1:39 PM

Nice

0celo7

@Semiclassical I am actually completely and hopelessly confused though

Consider the first eigenfunction of the Laplacian $\Delta\phi_1=-\lambda_1\phi_1$

$\lambda_1>0$

$\phi_1$ isn't supposed to change signs, so $-\lambda_1\phi_1$ is $\ge $ or $\le 0$

then by the maximum principle, $\phi_1$ is constant and $\lambda_1=0$ :/

oh, the stupid numbering game. Most people call $\lambda_1$ the first nonzero eigenvalue but in this case $\lambda_1$ should be zero.

ahhhhhhhh

I understand the world now

Semiclassical

Lol, I go away and you figure it out

But yeah, huzzah for scattering states

John Rennie

@0celo7 absolutely no idea ...

Semiclassical

It sounds analogous to the question of why certain transition metals don’t behave as you’d expect from Hund’s rule

There the reason is that the “rule” is not really more than a heuristic, expresssing some facts about how energy levels of hydrogenic atoms tend to work

But ultimately it’s quantum mechanics which has the final say

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