The h Bar

lol

Q: Ricci scalar for a diagonal metric tensor

2

I was wondering if there is a general formula for calculating Ricci scalar for any diagonal $n\times n$ metric tensor?

general-relativity differential-geometry metric-tensor curvature

lol, that comment is pretty troll

wonder who that was, account is deleted

1

Q: Must states on local algebras of QFT be "backwards-compatible"?

I have (what I believe is) a pretty straightforward conceptual question about Algebraic Quantum Field Theory. On local algebras there exist mathematically possible states that are "not backwards-compatible" in a sense I will define below, and I want to know whether these states get excluded from ...

quantum-field-theory

@Slereah for you ^

>using $\mathcal R$ for the algebra

I shiggy diggy

what's wrong with it?

The standard is $\mathfrak{A}$

Q: How to determine light intensity at each frequency in black-body radiation?

8:55 PM

why?

DanielSank

Anyone understand this?

0

I say, when the temperature increase the energy per photon increases which in part decreases the overall wavelengths of the black-body and the intensity increases because of the emission rate. which mean that light intensity at each frequency is determined by the black-body temperature, but this ...

electromagnetic-radiation

It stands for "$\mathfrak A$lgebra"

$\mathfrak{Algebra}$

oh, is that an A

$\mathfrak A$

yes

@Slereah That's the least helpful mathfrak character ever

8:57 PM

$\mathfrak U$

It stands for "I bet yo$\mathfrak A$ can't guess what this character actually is"

It's pretty helpful if you want to write an algebra

why not $\mathscr A$ like most people?

or $\mathcal A$ like plebs

↑ that

↑↑ and that

I dunno

Some people seem to like fraktur

8:59 PM

I said happy birthday to ACM in fraktur

I bet you can't read it

@Slereah most characters are OK

Lower case fraktur is nice

most lowercase is ok, except for $\mathfrak{k,w,x,y}$

Is that $\mathfrak n$?

Hah

wtf is that

$\mathfrak w$

^I've seen that one used somewhere

$\mathfrak t$

$\mathfrak k$

I've seen old russian math papers

They use a lot of fraktur

9:01 PM

mathfrak k is stupid

$\mathfrak{abcdefghijklmnopqrstuvwxyz}$

Rocky $\mathfrak w$

x and y??? @EmilioPisanty why???

Uppercase, any of $\mathfrak{AGHIJOPQSTVY}$ is trouble

@0celo7 $\mathfrak x$ vaguely makes it

@EmilioPisanty the third one is an H

there's no excuse for $\mathfrak y$

9:02 PM

it's a German eta, clearly

What libraries does mathjax have, anyway

@Slereah who knows

why?

wondering what symbols I can make

oh, no idea

I want lower case mathscr

I used to like mathcal but it's pretty bad honestly

$\mathcal B$ is nice

$\mathcal X$ is a swastika

9:06 PM

onemathematicalcat.org/MathJaxDocumentation/TeXSyntax.htm

$\amalg$

Weren't you looking for this

I figured it out

\amalg

this is weird

If I ctrl-F on chrome and put ß on the search bar, it matches all the ss's on the page

$\cal{ABC}\mathcal{ABC}$

I want a mathfrak ß just to mess with people

cal and mathcal seems identical

9:09 PM

what could one use $\bigwedge$ for

@0celo7 Repetition of logical conjunction

ACuriousMind is $\cancel{\text{a wiener}}$ great

$\checkmark$

Aha!

Yes!

@0celo7 $\bigwedge_{i=1}^n P_i = P_1\wedge \cdots\wedge P_n$

Hm, didn't work

@EmilioPisanty why would you ever use such notation though

9:11 PM

in case you are doing logic

for instance

if you are using the Craig axiomatization scheme

$\bigwedge$ that

$\checkmark_{\mu\nu\rho\sigma}$

This is the new notation for Riemann tensors

Craig's theorem

In mathematical logic, Craig's theorem states that any recursively enumerable set of well-formed formulas of a first-order language is (primitively) recursively axiomatizable. This result is not related to the well-known Craig interpolation theorem, although both results are named after the same mathematician, William Craig. == Recursive axiomatization == Let A 1 , A 2 , … {\displaystyle A_{1},A_{2},\dots } b...

$\bigwedge$ would be quite useful here

$\ominus,\oplus$

also $\odot$

9:12 PM

are those circles the same?

$\Cap$ Take a look, it's in a book, a reading rainbow $\Cap$

$\bigodot$

sniper dot?

$\bigodot\bigodot$

yeah what's the double intersection thing?

compact intersection?

@EmilioPisanty Tits! (The mathematician, of course.)

9:13 PM

(before anyone gets a misunderstandin', that's a pair of eyes)

sure it is

$R_{\clubsuit \diamondsuit \heartsuit \spadesuit}$

$\daleth$

$\digamma$

I didn't know there was letters being beth used for math

do people actually use these symbols?

9:14 PM

What is daleth in math?

probably set theory

alarge

@Slereah I seem to remember Evans' book to be full of these. rsc.anu.edu.au/~evans/evansmorrissbook.php

$\Game_{ab}$ is the Einstein tensor

No that is clearly the nietsniE tensor

@0celo7 what the hell is that

9:16 PM

It's the nietsniE tensor

@Slereah that's a great name for a tensor

lol

a.k.a. the 'nothing, never' tensor

Maybe I should write a GR book

I will supplant Sachs and Wu as having the shittiest notation

$\eth$

what

Why does that $\partial$ have a hairdo

9:17 PM

@0celo7 there's some anecdote about Serge Lang complaining about notation

and then someone repeatedly using $\displaystyle \frac{\Xi}{\overline{\Xi}}$ in a lecture to annoy him

@EmilioPisanty yeah?

@EmilioPisanty lol

$\iiiint$

@Slereah Hey! I've seen that one used

Petersen uses it in a double complex somewhere

this done on a blackboard, no less

so no fancy serifs on the xis, either

$\leftrightsquigarrow$

weeee

9:19 PM

I've been unable to trace back that anecdote, though, but I really want to

$\lmoustache$

Yes!

$\maltese$

Illuminati confirmed

$$\bigg\lmoustache_{\mathfrak a}^{\mathfrak b} \mathfrak f(\mathfrak x)\,\mathfrak d\mathfrak x=\mathfrak f(\mathfrak b)-\mathfrak f(\mathfrak a).$$

17th century calculus!

I...really like that integral.

$\newcommand{\mathfrak}{\text{GTFO}}$

$\pitchfork$

Diabolical

$\Pr$

What is this

9:24 PM

@AccidentalFourierTransform you

Prandtl Number

how the hell do you know that?

know what

@AccidentalFourierTransform $\mathfrak{does\ that\ actually\ work?}$

yep

9:27 PM

well, whaddaya know

it's pretty evil

$\newcommand{\mathfrak}{\mathsf}$

huh

wtf I love mathsf now

$\newcommand{\mathrm}{\mathfrak}$ $\newcommand{\mathcal}{\mathfrak}$ $\newcommand{\mathscr}{\mathfrak}$

you broke it

9:29 PM

error

@AccidentalFourierTransform did not

this might, though

Hmm.

Why is the star board different from the messages?

$\newcommand{\mathsf}{\mathfrak}$

STOP

YES

$\mathfrak{broke\ it}$

9:30 PM

great, my equations in the star board are broken

wtf is wrong with you

I don't even know how to un-break it

you cant

itll stay like that forever

you happy?

@AccidentalFourierTransform "forever" is a pretty strong word

it will stay that way until it is removed from the scrollback

you were not here the last time we broke the latex, were you?

9:31 PM

@AccidentalFourierTransform possibly

lots of people from other rooms came here to see what was going on

can't remember the details though

I remember one time it got pretty messy

Jan 16 at 16:58, by ACuriousMind

Dear lord, what is going on in this chatroom?

$\newcommand{\mathfrak}{\mathfrak}$

Hmm

$\newcommand{\mathsf}{\mathsf}$

@0celo7 how's that going to help?

9:33 PM

wtf did you do??/

@EmilioPisanty I have no idea what you did

the only way they can fix it is by deleting this whole thread

@0celo7 \newcommand{\mathfrak}{\mathsf} concurrent with \newcommand{\mathsf}{\mathfrak}

so it's an infinite loop...

Here it is: $\newcommand{\mathfrak}{\mathsf}$ $\newcommand{\mathsf}{\mathfrak}$ in case someone wants to star that and make things worse

dammit

I don't understand this

chat is forever ruined

@0celo7 "forever" is a strong word

9:37 PM

@EmilioPisanty ?? When will it get fixed

ok, it'll be broken until the protons decay

not forever, but close

@0celo7 it is only broken when the offending loop-causing commands are visible on the screen or through scrolling

which is forever

so the ones above will eventually pass out of the reckoning

that star on the right, though

@EmilioPisanty I flagged it. I'll take the ban to save the chat.

@0celo7 you flagged your own message as offensive?

9:40 PM

can we close this room and start a new one afresh?

No, for moderator attention.

I mean, it's you that broke chat forever ::grin::

@AccidentalFourierTransform is it crucial that we discuss mathfrak further?

Well, we can't use mathfrak or mathcal anymore.

@EmilioPisanty No Lie algebras

i guess that's fine by me

fine by me, too

we love discussing mathfrak

9:41 PM

We can still do analysis

now, if you broke $\epsilon$ we'd be in major trouble

its a topic that comes up every now and then

@0celo7 that's just asking for trouble

$\newcommand{\epsilon}{\varepsilon}$ $\newcommand{\varepsilon}{\epsilon}$

$\epsilon$

YOU MONSTER

quiet sobs

$\smalll {\mathscr E}$

Hmm.

\bbig works, why doesn't \ssmall?

oh it's bigg

does LaTeX display in chat for you people? It doesn't for me

9:44 PM

n00b

sorry

$\newcommand{\alpha}{\beta}$ $\newcommand{\beta}{\gamma}$ $\newcommand{\gamma}{\delta}$ $\newcommand{\delta}{\zeta}$ $\newcommand{\zeta}{\eta}$ $\newcommand{\eta}{\theta}$ $\newcommand{\theta}{\iota}$ $\newcommand{\iota}{\kappa}$ $\newcommand{\kappa}{\lambda}$ $\newcommand{\lambda}{\mu}$ $\newcommand{\mu}{\nu}$ $\newcommand{\nu}{\omicron}$ $\newcommand{\omicron}{\pi}$ $\newcommand{\pi}{\rho}$ $\newcommand{\rho}{\sigma}$ $\newcommand{\sigma}{\tau}$

$\alpha$

is there a setting I'm missing or something?

@EmilioPisanty that is a lot of dedication there

this is pretty horrible

can we have some mods in here?

@Loong @ACuriousMind @DavidZ @dmckee @Qmechanic Help please

9:45 PM

$\newcommand{\tau}{\upsilon}$ $\newcommand{\upsilon}{\phi}$ $\newcommand{\phi}{\chi}$ $\newcommand{\chi}{\psi}$ $\newcommand{\psi}{\omega}$

mods are asleep

aaaaand

quick, post swastikas

$\newcommand{\omega}{\alpha}$

$\alpha$

9:46 PM

@AccidentalFourierTransform I just wanted to break the entire alphabet there

$\alpha$

dear god

What. The. Heck?!?

@dmckee uh. hi

fix this mess please :-(

why stop there? I'd do things like $\newcommand{\alpha}{+}$ or something

9:47 PM

@BenNiehoff There is an external script that renders it. All the regular users know it.

we need an adult

we were just playing around a bit.

@BenNiehoff See meta.physics.stackexchange.com/a/5593/520

But right now the regulars are playing games with what is essentially a bug in the way ChatJax works to mess with our heads.

If mods do want to clean up, and it's possible, I'd appreciate code being placed inside backticks rather than outright deleted =)

yeah, technically \newcommand shouldn't be allowed on any of these

it should be \renewcommand :D

9:49 PM

@EmilioPisanty Well, I could go to that much trouble.

@dmckee not so much mess with people's heads

Is anyone actually trying to do some work/learn something in here right now?

@dmckee not really

Then it's too much work for me. But let's not make this game a regular thing.

Slereah was trying to defend mathfrak A as a reasonable symbol to use

9:50 PM

Please.

^

why would it be unreasonable?

noble effort, but doomed, because it's not a reasonable symbol

to use mathfrak A

@BenNiehoff because it looks nothing like an A

9:51 PM

sure it does, if you know anything about typeface history :P

@BenNiehoff yeah, well

mathfrak P is weirder looking

making the history of typefaces a prerequisite for science is not exactly "lowering the barriers to participation", is it

what if I dont want to lower the barriers to participation?

what if I want just a small elite to participate?

what if I want JD back?

@AccidentalFourierTransform You'll have trouble getting NSF funding, of course.

9:53 PM

@BenNiehoff all of mathfrak AGHIJOPQSTVY should be banned

@dmckee you probably want to say ERC there

lol, I use about half of those ones

@dmckee a small, rich elite

Then, you're good to go.

@BenNiehoff and you think your audience understands your notation?

mathfrak S has a long tradition

9:54 PM

beyond the level of "Let (squibble #37) be an algebra..."

@BenNiehoff of bewildering audiences worldwide

hey, after you sit through a few blackboard talks where people use lowercase xi and don't even bother to call it xi, but just call it "squiggle" instead...

then you can learn to appreciate a bit of mathfrak

@EmilioPisanty I've sat through a lecture on getting NSF funding, but not one on getting ERC funding.

We should be raising the barriers @EmilioPisanty

The NSF has a nice sheet they hand out.

Look at what lowering got us. Vixra.

9:55 PM

One side is how to not get your grant funded the fast way.

The other side is how to not get your grant funded the slow way.

@BenNiehoff "why do people keep using this G thing for s-y objects?"

@dmckee it's hard to get NSF funding in Spain ;-)

The first side is stuff the clerical staff will notice and discard without it ever getting to a scientist.

vixra is the pinnacle of elitism

only the best of the best

lol

@AccidentalFourierTransform ???

9:56 PM

@EmilioPisanty Fair enough. I'd probably have a hard time getting ERC funding.

Conservapedia is much better than vixra, science-wise

imagine if one had to write something backwards in order for vixra to accept it

it would have the same content!

conservapedia.com/Counterexamples_to_Relativity

"Despite wasting millions of taxpayer dollars searching for gravitational waves predicted by the theory, no direct observation of gravity waves has occurred.[19] Sound like global warming? Then, in classic liberal claptrap, the liberal media claimed that gravitational waves were discovered when in fact no such direct observation was made."

Every time viXra gets bashed, I feel compelled to bring up Phillip Gibbs' defense of it on Quora.

@Slereah Wait. When did relativity become something politically charged?

It just is.

9:58 PM

I think he does bring up arguments that cannot be dismissed easily.

that shit long

I aint reading that