@BernardoMeurer you around

@BernardoMeurer a math prof just put that Weierstrass article on the math listserv

@0celo7 I'm here

Oh, dope

wtf is listserv

@BernardoMeurer oh, the internal mailing list

Cool, that article was nice IMO

@JohnRennie behold:

@ACuriousMind I abandoned you to make this ;)

looks fairly spicy

@Semiclassical really?

to be fair, though, my sense for spiciness is pretty shallow

so i'm probably mistaking it

@Semiclassical those yellow peppers are pretty mild

they're more sour than anything

hmm, okay

really goes well with the feta and the olive oil

They don't look yellow

They look v. green

I'm color blind.

@rob yo

@rob Siopsis is also running QFT

would taking both of his 600-level classes be suicide?

oh wait, he changed quantum information theory to QFT

wtf

@0celo7 Have you spoken with him about it? He knows better than I do what he has in mind.

also it conflicts with fluid mechanics

great.

Hmmm. He did the 600-level QFT when I was there.

never mind

::facepalm::

my god

Hi, everybody.

@DanielSank what did you delete?

@0celo7 Ooh that looks good :-)

@JohnRennie it's a guilty pleasure

@JohnRennie I am willing to take suggestions to improve it

maybe some sun-dried tomatoes?

@0celo7 It looks fine to me. Adding other things like sun dried tomatoes would make it different but not necessarily better.

At the end of the day the point is to enjoy eating it.

Sun dried tomatoes seem fashionable in the cooking world these days, but I have to say I find them a bit chewy. I'm not sure the texture would work ina meal like yours.

@JohnRennie it's ridiculously good already

it's one of my top 5

what are the particle quintuplets in SU(5) theory anyway

quite dense

also this diagram doesn't include most particles

When cosmologists talk about the "steady state model", do they just mean (anti) De Sitter space

Choose your own cellular automaton!

@DanielSank they have an ion in a trap and they want to heat it and cool it

@EmilioPisanty Who? What?

@DanielSank references above my previous comment

@EmilioPisanty oh

They cool it with sideband cooling as usual

Heating is a bit trickier

They start with a white-noise radio source

Howdy

And then they filter it to make it thermal

@EmilioPisanty k

This one arxiv.org/abs/1510.03681

Wait, who here is good with class mech?

I'm taking Classical Mechanics 2 next semester but I haven't used Classical Mechanics in a year...

@SirCumference Bad question. What do you want to know?

@DanielSank Well, correct me if I'm wrong, but for an object rolling without slipping the formula is $\overrightarrow{v} = - \overrightarrow{\omega}R$, right?

That looks reasonable.

@DanielSank Well, is it positive or negative?

I don't understand the question.

The formula looks correct.

@DanielSank Well, my old textbook says $\overrightarrow{v_{cm}} = \overrightarrow{\omega}R$

looks wrong

Not $- \overrightarrow{\omega}R$

oh actually, they're both wrong.

The angular momentum vector could point out of the page, and the wheel would be rolling to the left.

@DanielSank Example?

I literally just gave one...

I mean situation in which that'd occur

uh... I ride a bike to the left...

@DanielSank Should've been more clear. Let left be negative and right be positive.

ok

Notice, as I pointed out, that the angular velocity vector and the center of mass vector for a rolling object are not parallel.

Yeah?

Still, shouldn't it be $\overrightarrow{v}_{cm} \hat{i} = - \overrightarrow{\omega}R \hat{z}$?

Well no, because you already have vectors

why are you adding a second vector in it

Do you mean $v_{cm}\hat i$

Sigh, yes, my brain isn't working at 2:00am

Remove the unit vectors

@SirCumference Go to bed.

Sleep is a prerequisite to learning.

@DanielSank I can't, I'm gonna spend this night studying for my SR, Math and Spanish midterms, which are on the same day (the 8th)

come back in the morning.

@SirCumference That's a very bad idea.

You won't retain information if you are fatigued.

@DanielSank Well I can't just invent time to study

Yes, but the time you're spending awake now is removing study time from your life.

You are not studying right now. You're wasting time.

All right, I'll head to sleep once I get clarification

Every minute you're awake now is a minute you can't think tomorrow.

The formula is $v_{cm} \hat{i} = -R \omega \hat{z}$?

What are $\hat{i}$ and $\hat{z}$?

Unit vectors

Why $i$ and $z$

Why not use $\hat{x}$, $\hat{y}$, $\hat{z}$?

Usually basis vectors are either $x,y,z$ or $i,j,k$

Mixing $\hat{i}$ with $\hat{z}$ is weird.

Wait, never mind, I'm just an idiot when I'm tired and didn't realize I mixed them...

Go

to

bed

Wait no wait

I just need clarification

No, seriously, do you see how we're all wasting time here?

Go to bed.

Please, I won't be able to sleep with this on my mind

Then ask a small, simple question.

...I did

Is the formula $v_{cm} \hat{x} = - R \omega \hat{z}$?

Let me tell you something though: if you don't learn to disconnect from your work, drink a cup of tea, listen to music, and then go to sleep knowing you can think more tomorrow, you're going to have a bad time.

@SirCumference If $\hat{z}$ points up from the ground, then that makes no sense.

Draw a picture.

Z hat points out of the page

And x?

To the right

Ok, then that equation looks reasonable.

Go to bed.

Wait what

Why does the book say positive omega?

Why does every website say positive omega?

Probably because they orient $\hat{z}$ into the page or something.

How can I know without seeing the book?

Who does that...

@SirCumference I don't know, because to me, using a $\hat{z}$ in a two-dimensional problem is insane to begin with.

Go to bed.

I'm going to dream of being unprepared for these tests...

k

Better than staying up.

>_>

Go to bed.

All right, 'night I suppose

You're wasting your study time.

Have we got a What is an elementary particle? question? We get so many related questions that I think a canonical q/a would be good if one doesn't already exist.

but

what is an elementary particle

That would be addressed in the q/a. I would interpret the question as what are particles in QFT? since in non-relativistic QM we just assume their properties.

So we'd say particles are the objects described by Fock states

@DanielSank you've turned into a cranky parent =P

Are Fock states really particles, though

Fock states aren't localized

Not very particle-esque

Particles needn't be localised

In fact I'm not sure non-interacting particles (which is what we model by Fock states) can be localised.

well sure, if you define them to be so

Interacting particles can be localised, but then the states that describe interacting systems are unknown

But "particles" sounds like it should be localized to me

We get questions like how can particles spin. For questions like those we don't need to assume localised objects.

What I really want to know is

What's a nice intuitive example of a system that is homogeneous but not isotropic?

With an appropriate gif

Godel universe?

Well yes, obviously, but what does it look like!

Oh, hang on, perhaps that is isotropic ...

It's not intuitive if I can't visualize it

Godel isn't isotropic, no

It only has 5 Killing vectors

For its shame

I want to see a little dust simulation of Godel dust

Ah of course, the rotation picks out an axis

with the little pixels rotating

Can you model it with like

Every point has some dust grain rotating around it

For every radius?

and then extend this in the $z$ direction?

I guess that would be homogeneous but not isotropic

@JohnRennie that already exists

The title isn't what you're after, but the content is close.

Also, if we tell someone that particles are the things that we represent with Fock states, then we'd better explain why those things behave particle-y.

This is not entirely trivial.

Well they don't, for a start :p

Fock states are fairly wave-y

For an isolated system, $q=0$

Then $\Delta S \ge 0$

But my book states, that for spontaneous process within an isolated system $\Delta S >0$

Why no equality, JR?

If anyone knows the answer, please let me know.

@SirCumference The thing is that the point of contact doesn't slip, so $v_{cm}- R\omega = 0 \implies v_{cm}= R\omega$. to understand this, you can split the motion of the rigid body into two: Pure rotational and pure translational. FOr the latter, every point on the rigid body has the velocity of com while for the former the velocity of any point is $R\omega$ tangentially.

@Slereah what's wrong with a birefringent crystal?

Is it easy to see intuitively why it is homogeneous but not isotropics

@Slereah it is to me

The unit cell is the same everywhere

But it is not isotropic

a bit easier if you get to have unit cells I suppose :p

Basically, it is trivial to come up with a crystal structure that's homogeneous (it's a crystal) but not isotropic

Continuous media is a bit harder

The trick is that as far as light is concerned, you see the medium in the continuum limit

That is, you just respond to the local average of the unit cell's polarizability

And that tensor keeps the anisotropy even in the continuum limit

@Slereah what's a continuous medium that's not the continuum limit of a granular discrete medium?

@EmilioPisanty The Gödel dust

I mean

I'm sure it's the continuum limit of something

But it's not meant to be

@Slereah dust is also a continuum limit

well probably, yes

But of what in this case?

("dust" in GR just means the pressure is $0$)

Gtg, brb

@Abcd I believe that the gist is (it's been a considerable while since I've done any thermodynamics, so it's very possible that I'm missing something or other): isolated system $\implies$ no exchange of energy and it seems reasonable that this means change in enthalpy ($H$) is $0$, while 'spontaneous process' is defined as the change of Gibbs Free energy being negative, which gives $\Delta G = \Delta H - T\Delta S < 0$ for constant temperature, giving $\Delta S>0$

@Slereah I don't really follow.

> A pressureless perfect fluid can be interpreted as a model of a configuration of dust particles that locally move in concert and interact with each other only gravitationally, from which the name is derived.

from wikipedia

yes

but 'course you don't need to describe it from some limit

it's the continuum limit of a bunch of particles with continuum-limit particle density $\rho$ moving at four-velocity $U$

I really don't know how you'd operate on that object without having that interpretation at the back of your head

As a field I guess?

@Slereah what's a field?

It is a global section of a fiber bundle

@Slereah if you're OK with that kind of abstraction, then I don't understand the original question

Oh well, no matter

why not just take a global section of a fiber bundle that's locally anisotropic but such that the anisotropy is the same everywhere

?

that's anisotropic but homogeneous

I mean, you obviously have a lot of stuff that's implicit in "system", but it's hard to tell what that is

but anyways ¯\ _(ツ)_/¯

It's raining all day

My nemesis

Are you the wicked witch

You know it baby

It was a risky reference for me to make

You don't even know Back to the Future, referencing a movie from the 30's was a bit of a gamble

@Slereah I only watched it last year

It was ok

I don't remember when I saw it

Probably like > 20 years ago

i saw it as a kid

so yeah, probably like 20 years ago

@0celo7 Preaching to the choir :/

Oh god I'm almost 20...

@SirCumference It gets worse. Trust me on this one :-)

yuuuuup

@0celo7 out of curiosity, have you worked that shooting-method problem?

@Semiclassical not yet

was doing that damn algebra for longer than expected

gotcha

did you ever figure out a nice approach to that?

@Semiclassical No, I just wrote "I don't know what the last rep is, but I can compute the character."

mmkay

it's optional hw anyway

has anyone else noticed that Chobani seems to be putting less yogurt in the cups?

It is a conspiracy

a very boring one, but a conspiracy nonetheles

It's like the easter egg conspiracy

A very shrewd conspiracy because people don't keep easter eggs for years to compare sizes

the easiest conspiracy theories to pull off concern things no one could possibly care about

and yet someone found out

Conspiracies are pretty hard to pull off

nah, that just means it's not the most boring one

Do you know one of the big source of leaked government secret plots?

A lot of people who work on big secret government things put it in their Linkdin

so "stupidity"

Hey, you gotta find another job after you work on the secret wiretap of US citizens!

true enough

It's usually not enough details to know the dirty secrets and all but it was a big source of details after the big NSA leaks