The h Bar

0celo7

19:01

@ACuriousMind parity reverses the sign of helicity because even though the eigenvalue of $J_3$ does not get changed, the projection along the momentum (which is flipped) is thus reversed?

FenderLesPaul

Why doesn't Mr.Rogers have anything on what you should do when you feel like your research is just an excuse to get out of the apartment?

ACuriousMind

@0celo7 I suppose you could phrase it that way. The deeper reason is that helicity classifies only representations of the identity component $\mathrm{SO}^+(1,3)$, I think, and not of $\mathrm{O}(1,3)$. Representations of $\mathrm{O}(1,3)$ are given by reps of $\mathrm{SO}^+(1,3)$ together with how the $P$ and $T$ operators act.

skill patrol

Because it's a beautiful day in the neighborhood?

ACuriousMind

Who is Mr.Rogers?

0celo7

^

FenderLesPaul

19:05

@0celo7 what the fuck, you don't know Mr.Rogers?

0celo7

no

FenderLesPaul

I can understand @ACuriousMind not knowing

obe

@skillpatrol who are you?

Kyle Kanos

Fred Rogers

Fred McFeely Rogers (March 20, 1928 – February 27, 2003) was an American television personality, educator, Presbyterian minister, composer, songwriter, author, and activist. Rogers was most famous for creating, hosting, and composing the theme music for the educational preschool television series Mister Rogers' Neighborhood (1968–2001), which featured his gentle, soft-spoken personality and directness to his audiences. Initially educated to be a minister, Rogers was displeased with the way television addressed children and made an effort to change this when he began to write for and perform on...

skill patrol

@obe skullpatrol

0celo7

19:06

is he the pedo?

Kyle Kanos

AFAIK, he is not a pedophile

0celo7

never heard of him then

skill patrol

-_-

FenderLesPaul

you have to be lying

Kyle Kanos

He ran a TV show called Mr Rogers Neighborhood for like 50 years

FenderLesPaul

19:07

wait did you grow up in the US? Or elsewhere?

@0celo7

0celo7

@ACuriousMind digesting, I might need some exposition on that

Germany

FenderLesPaul

implying the world is US and not US

@0celo7 ahhh ok

that explains it

I don't think I've met anyone who grew up in the US that didn't know Mr.Rogers

skill patrol

or Canada

FenderLesPaul

Canada <3

obe

idk who that is.

Jimself

19:10

@skillpatrol Where is that? I think you mean Canadia, eh?

0celo7

@ACuriousMind OK

FenderLesPaul

I'm not the man Mr.Rogers wanted me to be

sniff

skill patrol

Waters?

FenderLesPaul

hmm?

Roger Waters?

skill patrol

yep

FenderLesPaul

19:12

I wish I was Roger Waters

except he sings badly now

so modulo that

skill patrol

Too much LSD

FenderLesPaul

haha

0celo7

I wish Weinberg explained why $R^{-1}_2\mathscr{P}$ commutes with a boost along the 3-axis

ACuriousMind

And I wish \mathscr would be exterminated from the face of the earth

0celo7

h8ers gonna h8

Huy

19:15

h8 h8 h8 h8

ACuriousMind

@0celo7 Do you like mathscr?

I mean, look at it!

0celo7

@ACuriousMind I do.

ACuriousMind

It's drunk, and not in a good way

0celo7

@ACuriousMind You're drunk. (This is likely a true statement.)

who here knows the matrix for a half-rotation about the 2-axis?

ACuriousMind

Sadly not

0celo7

19:18

I can't into matrix exponentials

Huy

@0celo7: What's the 2-axis?

0celo7

@ACuriousMind @FenderLesPaul do you know how to prove the first statement on page 79?

@Huy y

Huy

@0celo7: So just $$\begin{pmatrix} \cos \phi & 0 & \sin \phi\\ 0 & 1 & 0 \\ -\sin \phi & 0 & \cos \phi \end{pmatrix}$$

0celo7

@Huy looks right, I'll just do it explicitly then...

ugh

I'll do a back-of-the-envelope calculation on the back of an envelope

skill patrol

That^ brings back memories of @ACuriousMind and Sofia chatting about "shut up and calculate..." :(

0celo7

19:31

yay

Kyle Kanos

@skillpatrol Sofia

0celo7

explicit calculation proves victorious

skill patrol

@KyleKanos thanks

People who have an English language barrier are at a distinct disadvantage in these kind of chat rooms.

Huy

yes

0celo7

people who disagree with people like ACM are at a disadvantage

although Danu is the mean one

@Huy I agree, poor Winston

I suspect Dogeyes will die

Huy

19:37

:(

Doooog aayye

0celo7

that mission was super frustrating

Huy

I sound exactly the same as those guys.

0celo7

to get a gun you pretty much had to run right into the middle of a room and disarm a dude

Huy

Who needs guns when you've got martial arts.

skill patrol

Kung fu?

0celo7

19:38

I found a broken mechanic: leg break + stun shot

grappling is very reliable

skill patrol

Having said that those who read too much into comments are disadvantaged too

0celo7

@skillpatrol you trying to accuse me of something

skill patrol

Are you trying be sarcastic?

Or am I missing something?

0celo7

yes

Huy

Ok YouTube stopped autoplaying the next video.

That means it's time to go to bed.

Good night.

0celo7

19:42

@ACuriousMind what's the TeX command for upright sans-serif font?

skill patrol

later pal

0celo7

night

Huy

@0celo7: i.sstatic.net/eZdhj.png

ACuriousMind

@0celo7 \textup?

skill patrol

(removed)

FenderLesPaul

19:45

removed

skill patrol

re

FenderLesPaul

added

0celo7

way to break immersion

ACuriousMind

$\text{ \textup{P} }$

FenderLesPaul

There should be an option to star your own comments

0celo7

19:46

\textsf{P}

swag

obe

I like \mathfrak{}

0celo7

upshape?

lol that sounds like a bra...

ACuriousMind

@0celo7 It exists :P

skill patrol

lift and separate

0celo7

$$\textsf{P}\Psi_{p,\sigma}=\eta_\sigma \mathrm{e}^{\mp\mathrm{i}\pi\sigma}\Psi_{\mathscr{P}p,-\sigma}$$

that's pretty

obe

19:48

sarcasm?

FenderLesPaul

this chat makes it impossible to get work done

3

skill patrol

welcome to the black hole of productivity

obe

What is the importance of mixed states in qm?

Kyle Kanos

@FenderLesPaul Not sure what you guys will do when I stop showing up :/

0celo7

:(

skill patrol

19:50

:(

ACuriousMind

:)

Jimself

@KyleKanos finally overtake you in rep

0celo7

lol

FenderLesPaul

@KyleKanos why would you stop showing up?

Kyle Kanos

@Jimself I'll answer questions in the evenings, but not during the day

FenderLesPaul

19:51

Don't leave us Kail

Kyle Kanos

@FenderLesPaul Doing that "job" thing

FenderLesPaul

@KyleKanos but Kyle :(

ACuriousMind

@obe They represent statistical states, where we only know the probabilities that the system is in a certain state, as opposed to knowing its state and calculating probabilities for measuring it in a different one.

TanMath

@vzn well, I have progressed a lot.. I am right now modelling open quantum system of the photosystem...It's fun but a lot of work and research...

Kyle Kanos

@FenderLesPaul I can't stay unemployed forever you know

Jimself

19:52

he can't leave us. We know where his frame of reference is

FenderLesPaul

@KyleKanos yes you can

ACuriousMind

@KyleKanos You can! I believe in you!

TanMath

@KyleKanos what's going on? you are leaving Physics.SE?

FenderLesPaul

I'll send you pizzas to eat

obe

@ACuriousMind Ok.

Kyle Kanos

19:53

@FenderLesPaul I have a wife & 4 kids, no I really can't

FenderLesPaul

hmm that complicates things

Kyle Kanos

@ACuriousMind I have a wife & 4 kids, no I really can't

@TanMath Sorta. I'll be getting a job soon & won't be as active

So I'm not leaving per se, just my availability will be reduced

TanMath

@KyleKanos aw.. that's sad..thanks for all the help you've done for all of us...

Jimself

something > nothing

Kyle Kanos

^ that

alarge

19:54

@KyleKanos So you got the Pascal job?

Kyle Kanos

I'll try to be doing the 20 reviews/day

But I think Brandon's going to get that Late Answers badge before me :(

FenderLesPaul

This reflects my feelings atm: youtube.com/watch?v=PFO28_CQQf4

Kyle Kanos

@alarge The offer was extended over the phone, we just have to finalize the details

FenderLesPaul

@KyleKanos

Jimself

he got all the other ones before you too, might as well be consistent

Kyle Kanos

19:55

@Jimself Very true

alarge

@KyleKanos Congratulations. What kind of a job is it?

Kyle Kanos

A quant job

0celo7

quantum?

alarge

In a bank?

0celo7

you're a heretic now

Kyle Kanos

19:56

@0celo7 Yes, I'm in the process of being quantized

@alarge Yes

0celo7

@KyleKanos it happens to the best of us D:

@ACuriousMind was quantized when he took a shitty GR class

ACuriousMind

@0celo7 quant = quantitative finance, I believe. Heresy, but of a different sort :P

FenderLesPaul

lol

we should replace puberty with quantization

0celo7

ACM thought GR is index manipulations

now he knows GR is index manipulations and a cauchy sequence here and there

skill patrol

Slereah

19:58

GR is pretty much index shit

And once in a while, PDEs and integrals

And topology if you are mad

alarge

@ACuriousMind Quantitative analyst

Kyle Kanos

@skillpatrol I've seen that. Considered a few times of being a member

Slereah

The best Stack Exchange

I want to post dumb questions

"How do I get money"

0celo7

@alarge the book list is finally online, but the grad stochastics class is not being offered this semester

obe

@ACuriousMind $A = \sum_{n} \ket{a} a \bra{a}$ is the same as $A = \int \ket{a} \braket{a|a} da$ ?

FenderLesPaul

20:00

"Is Mayonnaise a currency?"

obe

fail latex.

0celo7

@FenderLesPaul yes

anything can be a currency

FenderLesPaul

@0celo7 upvoted

ACuriousMind

@obe Those commands only exist in the physics package, which, for whatever reason, is not active in MathJax

0celo7

in the US, we use "in ~~god~~ government we trust" as a currency

Slereah

20:00

Sometimes I want to go to the meta SE board and ask

obe

@ACuriousMind Ok well, is it right? If A is a hermitian operator.

alarge

@0celo7 Well, advanced ug/grad analysis will get you started with measures and integrals anyway.

Slereah

"I have several stacks and I would like to exchange them for other stacks"

0celo7

@alarge I'm definitely taking the grad Real/Complex analysis modules

then probably functional analysis

FenderLesPaul

haha it's funny because probability theory

0celo7

20:02

maybe stochastics, although I'd have to find a time for the prereq, grad probability

FenderLesPaul

excuses self

ACuriousMind

@obe Well, I'm not exactly sure how the expressions are supposed to look, but no, a sum is rarely the same as an integral

skill patrol

it is only in the limit

alarge

@KyleKanos So what's your role? Say, looking at the wiki article, which description fits the position the best? Also, why Pascal?

ACuriousMind

They may be "analogous", though, in the sense that at some points, you might need to "replace" a sum with an integral, which is caused by the physicist sweeping infinite-dimensional subtleties under a very large rug.

0celo7

20:03

@ACuriousMind sums are integrals -.- did you even take calculus

FenderLesPaul

yeah

you can't spell integral without sum

0celo7

@ACuriousMind a comfy rig

Slereah

they don't even share a single letter

FenderLesPaul

yes they do

egral is synonymous with sum

skill patrol

Sigma?

0celo7

20:04

@Slereah major derp on your part

FenderLesPaul

do you even SAT bro?

0celo7

the integral sign is literally an S

Slereah

But I meant

The word "integral"

skill patrol

means integer

FenderLesPaul

^

Kyle Kanos

20:06

@alarge Pascal was mentioned over the recent phone call, though I was told C++ elsewhen by these guys. More on the Risk Management side of things.

0celo7

@KyleKanos do you have to move?

Kyle Kanos

I will, but I'll still be East coast

0celo7

up? down?

Jimself

closer to Jim?

skill patrol

or self?

:D

FenderLesPaul

20:10

closer to self

wow

deep

Kyle Kanos

Moving north

Jimself

NY?

0celo7

eh land?

skill patrol

Boston?

Jimself

Cuba?

FenderLesPaul

20:11

Bawston?

Kyle Kanos

This has suddenly turned into an AMA...

Cuba is south of me, last I checked

Jimself

lies

FenderLesPaul

Is it though?

CONSPIRACY

Kyle Kanos

skill patrol

Moving north of the north pole?

0celo7

20:12

@KyleKanos give us a hint

hi @JohnDuffield

Kyle Kanos

Cuba is the pink blob that is beneath the Florida wing of the US

FenderLesPaul

Flo-rida

0celo7

right round

Kyle Kanos

Like a record?

skill patrol

get the job finalised first and good luck pal

Kyle Kanos

20:13

^ agreed

John Duffield

@0celo7 : hi, but drat, I'm afraid I have to go.

skill patrol

later pal

nytimes.com/2015/07/26/magazine/…

13 ads blocked on this^

Kyle Kanos

Ghostery found 15

skill patrol

They will not let me star it in the homotopy theory room :(

0celo7

ABP found 27

FenderLesPaul

20:27

"As he talked, Tao carved shapes in the air with his hands, like a magician. "

0celo7

@ACuriousMind Let $U(R_2)=\exp(\mathrm{i}\pi J_2)$. Why does $U(R_2^{-1})$ reverse the sign of $J_3$?

FenderLesPaul

who the hell writes like that?

skill patrol

ny times

Jimself

@Jimself : the speed of light in vacuo is not constant, see my answer here for more references. The locally-measured speed of light is only constant because we use the local motion of light to define the second and the metre, and then use them to measure the local motion of light. It's a cargo-cult tautology I'm afraid. Define the second and the metre the old way, and the locally-measured speed of light isn't constant at all. It varies with elevation, just like Einstein said. — John Duffield 16 mins ago

::eye twitch::

skill patrol

:D))

Jimself

20:29

I'm not sure how many times I can hear exactly the same argument and say "no that, again, is wrong for these reasons"

ACuriousMind

@Jimself I remind you, for no particular reason, of this meta post of yours.

2

@0celo7 ...by the commutation relations of $J_3$ and $J_2$?

Jimself

An accurate post if ever I've written one

0celo7

@ACuriousMind I figured but I'm not smart enough :( halp

what does $J_1$ do here

I'm assuming $J_3 U(R_2^{-1})=-U(R_2^{-1})J_3$, but the commutation relations do not help...I don't think

Slereah

No need to bring up Duffield, we're all having a good time!

0celo7

$[J_2,J_3]=\mathrm{i}J_1$

FenderLesPaul

20:33

The misconception about spatial variation of speed of light is just one of those situations where you have to know the mathematical foundations of the theory

0celo7

I don't see it...

FenderLesPaul

or you're doomed to never understand why it's a wrong viewpoint

ACuriousMind

@0celo7 Isn't the statement "$U$ reverses the sign of $J_3$" that $U J_3 U^{-1} = -J_3$?

FenderLesPaul

doooomed

0celo7

he's backed himself into a corner at this point, he can't take his word back

@ACuriousMind that's exactly what I wrote, with a U moved over

ACuriousMind

20:34

So I guess you get it by applying the BCH formula

0celo7

oh my god that thing

ACuriousMind

@0celo7 Ah, yes, it is

@Jimself Yes, yes it is

FenderLesPaul

Baker-Campbell-Hausdorff?

Jimself

@0celo7 No, all he has to do is say "Huh, wow, I never really saw it that way. I always thought that he meant this." And then change almost every one of his answers

0celo7

I need the one I can't find

the one with the exponents and the things

argh

Jimself

20:37

we would then drop the issue and not make a big deal of it. Face saved

0celo7

where the heck is the one that I need??

FenderLesPaul

@0celo7 I am the one that you need

0celo7

ACuriousMind

All you need is love

0celo7

@ACuriousMind uh, halp?

Slereah

20:41

isn't that like

The Lie Trotter Katto formula?

Or related to it

ACuriousMind

BCH, Hadamard lemma, Lie-Trotter, they're all interrelated

FenderLesPaul

Lie Trotter Katto sounds like a magic spell

ACuriousMind

@0celo7 Well, tbh, my idea wasn't more than "some variant of BCH should give this" :/

0celo7

@FenderLesPaul halp

Jimself

@FenderLesPaul He's a witch!

FenderLesPaul

20:42

Witch!

@0celo7 with?

0celo7

@FenderLesPaul the claim right above eq. 2.6.20 on page 78 of Weinberg 1

FenderLesPaul

Since $U(R_2^-1)$ reverses the sign of..."

that part?

0celo7

yes

oh

I drew a picture

it's like 4th grade :(

$U(R_2)$ rotates the $z$-axis by pi lol

I love how ACM told me to use BCH

ACuriousMind

@0celo7 The last time I gave you an intuitive answer you didn't want it!

skull patrol

Diagrams are your friends

0celo7

20:47

@ACuriousMind got me there

obe

Is it possible to take QM and QFT at the same time?

ACuriousMind

That's about as unadvisable as it gets, I'd say

0celo7

really? try taking GR without knowing vector calculus

"Professor, what's a partial derivative?"

FenderLesPaul

@0celo7 do you want a verification in terms of operators?

because to convince myself I'd just say

0celo7

@FenderLesPaul if you have one

my picture was fine for my purposes

obe

20:52

@0celo7 Though you can learn that in like 5 minutes.

0celo7

@obe you can learn Shankar is 5 minutes

FenderLesPaul

that $U(R_2^{-1})$ acting on a J_3 eigenstate, say with the spin aligned with the z-axis, rotates the x-z plane by pi so it brings the spin to -z

obe

@0celo7 If he would talk less.

0celo7

@FenderLesPaul that's exactly what I did

FenderLesPaul

but I'm not entirely sure how to verify it in terms of operators

0celo7

20:53

exactly

it has to be possible, right?

FenderLesPaul

because my go to method is to use infinitesimals and just work with generators

obe

Anyhow I'm going to be the first to do this, let's see how it turns out in 5 months.

FenderLesPaul

but you can't do that here since it's pi degree rotation

skull patrol

You can't understand it in 5 minutes

FenderLesPaul

@0celo7 it should be possible yeah

so something like $e^{i\pi J_2}J_3 e^{-i\pi J_2} = -J_3$?

skull patrol

20:55

@obe why are you trying this?

FenderLesPaul

or is what Weinberg says only true for J_3 eigenstates and not as a statement about $J_3$ itself?

skull patrol

Without the basics you're wasting your time pal.

0celo7

$J_3$

above 2.6.21 he says the same thing about a $J_3$ rotation changing the sign of $J_2$

FenderLesPaul

yeah he does

hmm

I'm not sure how to use BCH here because the J_3 isn't exponentiated

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