The h Bar

Semiclassical

17:01

@BalarkaSen similarly, the Lambert W function becomes clearer once one thinks in terms not of $w=W(z)$ but $z=we^w$.

dmckee

@Blue Eh? Not in general. Even the van der Waals gas has a treatment of potential based on the average distance between molecules.

Balarka Sen

@Semiclassical But the branches of Lambert W is a fucking mess

Semiclassical

eh, even that becomes clearer once you look at the plane of complex $w$.

Balarka Sen

For log it's very simple because e^z is an infinite sheeted covering

Semiclassical

lemme find a good picture

CooperCape

17:02

Error bars in a LaTeX graph ezpz?

(tikzz)

dmckee

Not a clue. I make graphs in Root and PDF insert the image in the paper.

CooperCape

Oh fair

Semiclassical

enumaris

So, can someone explain to me clearly the relationship between chirality and spin? I know that helicity is spin dot momentum. I also know that in the massless limit chirality is the same as Helicity so chirality must be related to spin as well right. Is chirality spin dot (some constant vector with units of momentum)?

CooperCape

I just looked it up it's literally just coordinates{(0,1) +- (some,shit)};

Semiclassical

17:04

that's a contour plot of arg(e^w) in the plane of w

Anonymous

@dmckee Do you have any source which discusses the derivation of the real gas (Van Der Waals equation) from the partition function (taking into account potential interactions for all pairs of particles) ?

Balarka Sen

@semi huh ok

Semiclassical

Anonymous

Actually the pairwise approximation is still an approximation

Anonymous

For more than 2 particles, only taking pairwise interactions is not enough

Anonymous

17:06

(afaik)

Anonymous

I would be interested in reading something stating the contrary

dmckee

@Blue Not off the top of my head. But most books do the variations on the coupled-oscillator crystalline solid (which may be the easiest statistical treatment of a system involving potential energies).

Semiclassical

Look for a chapter on virial expansion / cluster diagrams.

Anonymous

@dmckee I probably know the crystalline solid one. Even that is an approximation (taking into account only neighboring particles)

Anonymous

The differential equation they write don't include all the N particles in the system

dmckee

17:10

@Blue Ah. A little googling gives me nyu.edu/classes/tuckerman/stat.mechII/lectures/postscript/… which seems to treat the problem in a perturbative approach.

Semiclassical

@BalarkaSen so, in the first plot, each strip is the image of $w\in \mathbb{C}\mapsto e^w$. So on each strip we can define a one-to-one inverse function.

Balarka Sen

Oh, right, yes, the first one is of course log

Semiclassical

so each strip corresponds to a branch of log(z), with analytic continuation of z moving you between each branch sequentially

Balarka Sen

right, right, sure, i know that

Semiclassical

right.

in the other plot, you still have strips away from the real-w axis

dmckee

17:11

@Blue Uhm. Of course you can't be explicit about $N$ particles int he thermodynamic limit, but you can find the spectral density, and integrate.

Semiclassical

but in the middle you now have a bit different arrangement

Anonymous

@dmckee Interesting. I see lot of approximation there too. But yeah, I should have been more careful when I said "potential interactions are ignored in statistical mechanics." Yes, they can be approximated. However, for the problem Yashas stated, I'm pretty certain we have to ignore potential interactions (as there is not enough data)

Balarka Sen

@Semiclassical I guess the issue is $f(z) = z\exp(z)$ derivates to $f'(z) = (z + 1)\exp(z)$, which vanishes at $z = -1$. So the map is not a covering map at $-1$

Semiclassical

yeah, there's some weirdness there

Balarka Sen

That's why the branches act badly

Semiclassical

17:17

main thing to note, I guess, is that you can cycle between those three regions in the middle by moving around $z=-1$

user929304

@JohnRennie Dear John, if it s not a bad timing, I had a small question: say in a 2D Hilbert space, we pick two kets |a_1\rangle

vzn

Squarepusher × Z-MACHINES

►

user929304

That is, \theta_n = pi/2, where theta_n is the angle between |a_1\rangle \oprod |a_1\rangle ... |a_1\rangle (n times) and |a_2\rangle (also tensored with itself n times).

Is there an easy geometric way of seeing why the angle should approach pi/2?

Semiclassical

use $'s plz

user929304

@JohnRennie sorry one part of the msg got lost. Namely, in the 2D space the angle between the ket a_1 and ket a_2 is theta, with there very small.

@JohnRennie and theta_n is the corresponding angle between their tensored versions (each with itself n times)

Balarka Sen

17:22

Surely robots can learn to play pleasing and cute music, given the massive advancement in machine learning in recent days

Phase

@BalarkaSen are you asking ACM to serenade you?

Balarka Sen

No because I don't like cute music

vzn

@BalarkaSen liked the robots, not the song so much, maybe robots will slowly gain more talent :|

Balarka Sen

robots can never learn to make Death Grips music

Phase

@BalarkaSen death grips IS robot music

vzn

17:25

@Phase lol serenading probably requires empathy o_O

Phase

Are you implying ACM has none? That's just mean

He's an advanced AI / robotman

there's probably a few bytes of room for Empathy

@BalarkaSen is that directed at me?

Balarka Sen

no at vzn

Phase

Or the self referential meme

Ah

John Rennie

→ 10 messages moved to trash

Enough already

Phase

the room owner has spoken, hush or be Shog9'd

[kneels]

Balarka Sen

17:29

get shogd bro

John Rennie

Kickmutes will be handed out if this continues

vzn

geez everything spirals/ escalates so quickly in here these days. not to blame for that o_O :(

Semiclassical

i look away for a moment and the room goes crazy

4

schrodinger's troll?

Anonymous

lol

CooperCape

That was a good read tho thanks lads

Phase

17:32

I don't fancy the idea of being kickmuted, so I'm gonna say one thing [JR pls :( no kill] afaik no-one got annoyed at you for posting a robot video, Sen just made a comment about your self referencing. It's not a big deal and it escalated

Sid

what's up with people always getting into fights here?

John Rennie

→ 3 messages moved to trash

→ 2 messages moved to trash

Balarka Sen

Just to clarify my position, I wasn't commenting at self-referencing. I was commenting at vzn for making vague implications that this room's moderation is dictatorship, a conspiracy theory that has been beaten to dead horse by him, and is quite silly in my honest opinion.

Phase

I probably didn't help it's just that one of his messages, especially pre-edit, struck as me as high-school-bully tier and got my back up faster than it should've. Sorry for contributing folks

enumaris

isn't it more like an oligarchy

after all there are multiple mods aren't there heh

Phase

17:37

If @BalarkaSen has his way he'll seize the means of production and make everyone a mod

damn commie sleeper agent

Balarka Sen

thats more like it

enumaris

we gotta get the poli-sci facts right

Making everyone a mod is kinda the opposite of what communist regimes have done in the past

Phase

Wintergatan - Marble Machine (music instrument using 2000 marbles)

►

This guy looks like he's having the time of his life

enumaris

Communist regimes tend to overwhelmingly be dictatorships lol

CooperCape

Nah Everyone will be a mod but mod privileges won't be a thing and BS will be the site owner and we're all equal and he is our leader.

enumaris

17:38

sounds about right

John Rennie

Why would anyone want to be a mod? You have to clear up everyone else's crap and you get shouted at whatever you do ...

8

Sid

@JohnRennie So, I should start drinking more coffee now?

Balarka Sen

@CooperCape ma nama shog

2

imma ban you all

Phase

@JohnRennie tbf, a few things aside, the more time I spend here the cooler I am with Mod intervention as long as it's just stopping dumb stuff. Some of the flags from regular users though...

Poor 0celo7

Balarka Sen

@enumaris True. A running gag of mine is to meme USSR

I am not seriously a supporter of communism

John Rennie

17:39

@Sid I'm deeply suspicious of these claims about what is what isn't good for you. As a general guide if it feels good you should probably do it.

Balarka Sen

I do like Marx's mathematical manuscripts, however :D

CooperCape

Urban Dictionary is wholly confused on what shog means

enumaris

Communism as an economic idea is oh so different than communism as a political idea and again wholly different than the communism as styled by Lennin, Stalin, Mao and others

Phase

@JohnRennie Finally someone who approves of my heroin hobby

enumaris

It's pretty hard to define clearly now unfortunately :(

Balarka Sen

17:41

I think JR correctly predicted it comes from "Shoggoth", name of a monstrous character in Lovecraft

Phase

@CooperCape I think I prefer "to shit when you jog"

enumaris

the biggest atrocities Stalin and Mao committed were against clear definitions in terminology (/s in case this message gets too much hate)

Phase

"to shit when you jog 9"

Balarka Sen

@enumaris I quite agree. But, unfortunately the people who claim themselves to be anti-left aren't making a good case for support either.

CooperCape

@Phase Dude this is a physics chat room and you're talking about outside activities as a preference wth where do you think you are sports science SE?

John Rennie

17:42

@Phase what a shame you edited that. I was wondering if you liked dressing up as Wonder Woman or Supergirl :-)

enumaris

hmmm

Phase

@JohnRennie I dress up as Supergirl. Then I shoot myself up with crack and heroin

really get's the noggin joggin

enumaris

the terminology the left and the right also leaves much to be desired...

John Rennie

@Phase That's ... a mental image I could have done without :-)

CooperCape

There's a ginger kid on the bus I take to school and we all call him ginger noggin.

God we're cruel :c

Phase

17:44

@JohnRennie I'm confused how you can have a mental image at all when for all you know I'm a 9 foot tall African American gentleman with one arm and three legs

Balarka Sen

@Phase that is digital blackface

enumaris

ban

Balarka Sen

burninate

with fire and hate

Phase

BalarkaSen are you assuming I'm not black

enumaris

MJOLNIR WILL SMITE THEE

CooperCape

17:45

My friend just hit me up with "I don't know what I'm doing anymore" so I replied with "You never did" and apparently that sorted it so I feel like a God...

Phase

@CooperCape not true

Balarka Sen

@Phase irrelevant.

Phase

There's a blissful period as a young child where life is good and simple

@BalarkaSen how many IG followers you got huh? you's irrelevant!

Balarka Sen

you're clearly a ricegum fan

Phase

Welcome to the Ricegum mother______

enumaris

17:47

I'm pretty sure swearing is allowed in this chat right

(not actually sure, I just saw people do it)

Balarka Sen

no this is a christian chat

chrischanchat

Phase

0celo7 politely requested and I feel like I could do with the change of pace

enumaris

hmm

Phase

I swear too much anyway

enumaris

ok serious physics question tho

John Rennie

17:48

@enumaris it isn't a banning offence, but at the same time you shouldn't consider it compulsory

enumaris

please define chirality in a clear and concise manner

Phase

It's how Chiral something is and in what way it's Chiral

enumaris

great

Phase

I'm pretty sure it's handedness of molecules

John Rennie

@enumaris there is no clear and concise way to define chirality. It is a fundamentally difficult concept.

enumaris

17:49

:(

CooperCape

I can chat shit about optical isomers and chiral carbons but idk what it means

Phase

I think Physicists must have another use for it @CooperCape

John Rennie

There is a really good blog post somewhere that explains chirality and helicity. I'll have a quick Google ...

Balarka Sen

Chirality means mirror image is congruent to itself, right?

That's pretty much what it means in math

Phase

Congruent?

Chiral means that it's not equal to it's mirror

Achiral is where mirroring has no effect iirc

Balarka Sen

17:51

Isn't it the other way around?

CooperCape

In chem optical isomers are not equal to their mirror

Phase

I dont think so

CooperCape

So I'd be with Phase on this one

John Rennie

@enumaris This blog is the simplest explanation I've seen

Balarka Sen

Oh I guess rip me then

Yeah that should be non-congruent

Phase

17:51

@BalarkaSen I just mean generally tho

maths might be different

Balarka Sen

By congruence I mean equivalent after rigid motion

enumaris

I'll take a look

Phase

You're the maths guy so

Balarka Sen

@Phase No, no, you're right

enumaris

but as a concrete question

Balarka Sen

17:52

I forgot the right terminology

enumaris

if I have a massive particle

Balarka Sen

I am a forgetful person

enumaris

and I flip its spin

without changing its momentum

CooperCape

I've always been taught chirality is handedness and hands are mirros but neq sooo

enumaris

have I changed its chirality?

John Rennie

17:52

@enumaris no

Balarka Sen

The place where it comes up in math is knot theory.

John Rennie

You just changed its helicity

enumaris

but if the particle is massless then I have in fact changed its chirality correct?

Balarka Sen

The left-handed trefoil knot and the right-handed trefoil knot (mirror images of each other), are not the same knots.

John Rennie

@enumaris Read the blog article - it's complicated

enumaris

17:54

-.-

CooperCape

What is knot theory

Or is that a deep question

Balarka Sen

study of knots

CooperCape

Oh, that was ez

Fair

John Rennie

@enumaris well don't look at me in that tone of voice. I didn't design the universe.

2

CooperCape

(not ez but yano for once I understood something you answered me with...)

Balarka Sen

17:55

@JohnRennie You can see voices? O_o

enumaris

I'm having trouble mostly with the fact that helicity and chirality are supposed to be the same for massless particles, but there doesn't seem to be a nice limiting method to get there?

Phase

@CooperCape it's what boyscouts and amateur sailors learn

CooperCape

I was once both...

Phase

Great shame in that :)

Sorry, had a typo

Emilio Pisanty

this is hilarious

CooperCape

17:56

I thought for once I... I was accepted... and then. then the edit came.

Phase

@EmilioPisanty There was a comment chain moved to chat where people got grumpy

John Rennie

@EmilioPisanty Unix hackers have a sense of humour. Just ... not a very good one :-)

CooperCape

Now I lead Bevers (6-8yos) and get called a 'nonce' an awful lot at school :/

Phase

And basically said "never make an inside joke at the potential expense of some rando"

@CooperCape Beat em up and tie em up with knots

enumaris

Like, if a particle is nearly massless, is its chirality and helicity somehow more aligned in more references frames or something

until you get to actual massless in which case they align in every reference frame...

CooperCape

17:58

@Phase I can do a reef knot...

Balarka Sen

@CooperCape Is that a British thing? I thought that was seriously offensive...

Phase

@CooperCape Just sic the beavers on em

@BalarkaSen iirc it means Pedo

Balarka Sen

yes

CooperCape

@Phase Pretty much that yea

Sad times

Phase

@CooperCape they're just plebs, don't let it get to you

CooperCape

18:01

@Phase Ehh one time the teacher heard an that was an interesting lesson... :p

Phase

did they get punished or something?

CooperCape

Nope

Our physics teacher's too chill it's fine

Balarka Sen

how old are these people

CooperCape

17/18

Why is weird that they're calling me a nonce

Phase

@BalarkaSen let's get ACM on this, he will send them to the cloud and purify their minds

Anonymous

18:05

@CooperCape I thought the 6-8 year olds were calling you that...lol

CooperCape

@Blue Oh my goodness that would be sooo much worse!

Can you imagine them going home to there parents...

"What did you do tonight then...?"

"Well Jordan's a nonce..."

might not go down too well

Anonymous

17-18 is your age group. So I wouldn't bother much :P

CooperCape

Yeah I don't mind really

Phase

It's weird how similar Nonce and Ponce are, I wonder if that stems from old stereotypes

CooperCape

Just weirds teachers out and unnecessarily awkward conversations.

What am I saying all my conversations are awkward lol

Phase

18:08

"balance: -£1.58"

Feels bad man.

CooperCape

:c

I think that's the negative of my Amazon balance

Phase

This is my bank account

Tbh tho I started this month with less than usual and only gotta last 10 days

CooperCape

One more year until I reach the uni bank balance standards

Although I can't get a student loan for like 4 months cause of my age smh

Phase

dang

CooperCape

Idk what I'm gonna do...

Be very poor for a few months I guess

or just owe my parents $$$ but I'd kinda feel bad

enumaris

18:15

911 conspiracy has made it to the physics stack exchange

what is this 2004?

CooperCape

Yeah I've... seen.

Actually when I went to NY I had a fun chat with some conspiracy theorists

enumaris

when I was in middle school I watched that video loose change

and for all of about 45 minutes I was convinced it was an inside job

and then I watched another video debunking every claim

and that was that

lol

Phase

wait where is it

enumaris

-2

Q: Question about the velocity of the alleged plane that hit the Pentagon on 9-11

We (almost) all have seen this video that shows the explosion on the morning of 9-11 at the Pentagon. Now if you play this video image per image there is no plane [an alleged Boeing 757 223, whose length is about 48 (m); see this article)] to see. If we assume that the video displays 18 images p...

velocity

can he not see that the frames/sec on that camera is more like 2-4 at max?

Phase

"I'm not a skeptic, I'm just considering the facts"

"I'm not $a$ but I'm $a$"

enumaris

18:18

the police car goes from going into the shot to exiting the shot in 8 frames

if it was at 18 frames/s that police car be zoomin!

CooperCape

I think we can all clearly see it's no 18fps

More like 1/2fps at best

enumaris

yeah lol

I like the youtube video's comment on it "the real mystery is why is the pentagon using this camera as a security camera" LOL

Phase

FUCKING WOLFRAM

I thought I cancelled it no wonder I'm a quid below ground level

I got charged 90 quid yesterday

enumaris

D:

Phase

what the actual fuck

0celo7

18:22

Lmao

Bernardo Meurer

Lol

CooperCape

At least you can... um... do longer... computations :(

Bernardo Meurer

git rekd

CooperCape

stip by stip solushuns

Balarka Sen

lmao Phase

Phase

18:23

@CooperCape did you look at my screenshot

I'm on a free account being charged

(??????????)

enumaris

maybe they have a cancelation fee?

Sir Cumference

You oughta contact them about it

CooperCape

At least you can feel good you're funding a respectable webpage

Balarka Sen

you're one of the few supporting A New Kind of Science

feel proud dave

CooperCape

we're proud of you

Phase

18:25

I am angery

enumaris

so angry that it's turned into angery?

Phase

THEY ARENT EVEN OPEN BECAUSE ITS ON US TIMES

Sir Cumference

@Phase Perhaps free here means it's open source

Balarka Sen

when you're old you can tell your grandchildren that you supported Stephen Wolfram's Kickstarter Crap

Sir Cumference

Otherwise you're getting scammed

CooperCape

18:26

As a great man once said

'nibba you got fucked;'

Balarka Sen

and they'll look at you with awe

@Cooper l m a o

im crying man

Phase

Do I kill myself or them

HMMMMMMMMMMMMMMMMMMMMMMMM

Balarka Sen

HAHAHA

lootcrates spotted!

CooperCape

dont do it habibi

Balarka Sen

dont you want to feel the sense of pride and accomplishment for unlocking more steps of your calculus homework?

3

Phase

18:29

not the time SEN

CooperCape

@BalarkaSen Response 101

0celo7

@BalarkaSen the point is that branches and branch cuts are more conceptually difficult than anything in analysis

name one topic harder

enumaris

Riemann sheets?

0celo7

I'm including that in there

Balarka Sen

@0celo7 I am not sure I agree, but you might have a fair point in saying analytic continuation is a nontrivial C phenomenon

0celo7

18:31

because the way you're supposed to understand that stuff is via Riemann surfaces

CooperCape

@0celo7 Making good memes.

enumaris

how u include Riemann Sheets in branch cuts...

0celo7

read what I wrote

@BalarkaSen I have spent hours with @Semiclassical figuring out branch cuts

Balarka Sen

Well you really don't have to go that far, you just have to understand taking graphs of holomorphic functions

enumaris

still seems unfair to include it, you only specified branch cuts :P

0celo7

18:32

@enumaris heck it then, just imagine I said Riemann surfaces too

enumaris

XD

victory!

Balarka Sen

@0celo7 C'mon, you can't say a subject is hard based upon the fact that you had a hard exercise to figure out

0celo7

@BalarkaSen the only thing of comparable difficulty in real analysis is function spaces on manifolds

showing those things are locally connected or whatever other BS

those are conceptually hard too

the definitions are so technical

Balarka Sen

I will say though that in a first course of complex analysis branch cuts are not really anything more than a nice show

You never actually use that stuff

All you have to understand is locally log is a well-defined function

how big a neighborhood it's defined on is not really of much relevance

enumaris

my brain freezes anytime complex analysis is mentioned

anytime I see a x turn into a z

integrate some f(x)? Sure no problem (conceptually). Integrate some f(z) along the real axis? Nope.

0celo7

18:40

@BalarkaSen Analysts not understanding $\Bbb C$ is a real issue

Spin structures are already bad, but Spin$^\Bbb C$...

Physicists do some jig with EM fields to explain it

Balarka Sen

I understand spin topologically

@enumaris It's actually quite physical.

0celo7

Analysts don't understand spectral sequences

enumaris

what's quite physical?

0celo7

If you say complex variables are physical you've either turned into @Semiclassical, @EmilioPisanty, or crazy...

Balarka Sen

@enumaris If $f$ is a complex function and $\gamma$ is a path in $\Bbb C$, $\int_\gamma f(z) dz$ represents work done in trying to push an object from $\gamma(0)$ to $\gamma(1)$ against the force field given by $f$.

enumaris

18:43

why not all 3?

Balarka Sen

@0celo7 I meant line integrals, not complex analysis on the whole

enumaris

Line integrals in real space is fine :D

Anonymous

@BalarkaSen Cool. I saw that a few days back in the context of conservative fields. :D

Anonymous

Treating it as complex function makes evaluating the integral easier

Balarka Sen

It's the same thing though. Write $f(z) = u(x, y) + i v(x, y)$ and $dz = dx + idy$, then $f(z)dz = (udx - vdy) + i(udy + vdx)$

Anonymous

18:45

It there is some hole inside, you can use the residue tricks and stuff

enumaris

I'd rather keep conceptual clarity in favor of computational ease

Balarka Sen

Your line integral then decomposes as a complex number whose real part is line integral of the vector field $(u, -v)$ along $\gamma$, and imaginary part is line integral of the field $(v, u)$ along $\gamma$

enumaris

I don't doubt you can make many things computationally much easier by using complex numbers rather than sticking to the reals. But still...I don't like them -.-

Balarka Sen

@Blue I'll tell you more about these when we learn differential forms

It actually becomes a very clean formalism

enumaris

differential forms are fun

Anonymous

18:48

@BalarkaSen Nice. I'm interested!

Balarka Sen

The relation with complex analysis also becomes apparent

enumaris

F=dA <--where else can you have such a nice relationship between electric/magnetic fields and potentials? :D

Balarka Sen

Truly

Semiclassical

the distinction I'd draw between real and complex analysis is between the words complicated and complex

something is complicated if, while it works out correctly, it feels arbitrary and doesn't join together into a coherent whole. something is complex if, despite the apparent complications in its workings, it still acts as one coherent whole

0celo7

If you think that describes real analysis I don’t know what to say

Semiclassical

18:51

i was going to a slightly different conclusion

the trouble is that, seeing someting as 'complex' rather than merely 'complicated' requires a certain depth of insight and experience

I have that for complex analysis, but I don't have that for real analysis. So of the two I would say I feel like real analysis is complicated but complex analysis is complex. But I can well imagine that that's different for another person.

enumaris

not sure how often that distinction between complicated and complex is used..

Semiclassical

eh, I think it shows up quite a bit though perhaps under different words

i think 'complexity' overlaps quite a bit with the notion of 'elegance' in mathematics, for instance

enumaris

Isn't elegance usually more overlapping with simplicity

like Einstein's Theory of General Relativity is extremely elegant because it has only a few simple assumptions (SR + Principle of Equivalence) and from those assumptions it generates a vast plethora of physical implications

Whereas QFT feels more like a hodgepodge of ideas and tricks tacked on over time...

(Is there a QFT fan in here who's gonna start a flame war with me now?)

Semiclassical

well, it's only simple once you see how those assumptions work

if someone just handed you a long list of results of those assumptions, would you necessarily guess there's a simple set of assumptions behind it?

enumaris

(Where's the QFT fan who's gonna start a flame war with me tho?)

Semiclassical

18:59

in that way I'd say that GR is certainly complex.

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