hello people, anybody else in the midst of trenches during this here finals week

@0celo7 Never tried it.

@dmckee Hey, a quick question for you

In grad school were your physics exams take home?

@user507974 Some, but fewer than half. Depended on the professor. Take home were much harder.

@dmckee They would have to be of course. Heck they could be a simplification away from an outstanding problem in physics depending on the class. Which did you prefer?

Wohoo APS.

Exams always sucked.

@DanielSank amen. For me it's funny because for most easier classes I feel like I finally learned the material on the test

then again usually i didnt study for them anyways

In physics if I didn't understand it going in it's probably not going to understand it going out.

@user507974 Perhaps.

I learned how an adiabatic demagnetization refrigerator works on my statistical mechanics exam though :)

Analyzing it was a problem on the test.

@DanielSank wait, i actually learned that one on a test too

@user507974 o_O

Where do you go to school?

ucsb

@user507974 Waaaaaat?

@DanielSank u 2?

@user507974 I was a grad student there. I still live in Santa Barbara.

We have to meet.

@DanielSank oh yea, the google labs

You'd the the third Physics SE user I met in real life.

@user507974 Yup.

@DanielSank im down

@DanielSank you'd be the first

for me

im an undergrad here, just finished grad stat mech final today, trying to determine my perspective on life

@DanielSank who did you have for stat mech?

I had that as a question on my undergrad final with Zee.

@user507974 um, lol

DS won't pop your cherry, he's engaged

I think

@0celo7 lol

Hmm...anyone willing to answer a quick question?

maybe

When a white dwarf reaches the Chandrasekhar limit it begins to collapse into a neutron star. But shouldn't the Pauli exclusion principle prevent this?

Electron degeneracy pressure prevents white dwarfs from collapsing

Proof?

Why wouldn't the exclusion principle be enough after it reaches the Chandrasekhar limit?

Lemme find a paper for you

The Chandrasekhar limit represents the point at which it becomes energetically favorable to convert proton to neutron even though you have to push the electron above the Fermi level to do it.

Oh christ

Indeed that is how you arrive at the limit.

forgot

I literally just read that a few hours ago

::chuckles:: We all do that.

@user507974 In UCSB it was Chetan but that's not where I had that question.

I had it in undergrad.

are there two Chandrasekhar limits

Anyway, email me. We can meet up.

one GR and one QM

I'm too lazy to get out the star book

So then electron capture happens and we're left with a neutron star

@SirCumference you dont have electrons in neutron stars. They've merged with the nucleus and you have a neutron soup dont you?

^ That's not true.

There are definitely electrons

And protons

You have many fewer electrons.

Just mostly neutrons

Electron capture is, simply put, when a proton and electron combine to form a neutron

@user507974 Yeah. Which means what I wrote above is partly wrong.

But I think you've got it from here.

@DanielSank Will do, I'm out of town for spring break but I'm probably pretty flexible after that.

@user507974 The capture process happens until making new neutrons starts too cost to much energy because of their Fermi level.

Wait, total moron question, but if a star could reach the Chandrasekhar limit, shouldn't it be too massive to become a white dwarf?

Blah, physics. Who wants to discuss the actual math behind this?

@dmckee What's the femi level of a neutron?

@user507974 It's not of a neutron it's of the bound state. Pauli exclusion limits how many low-energy fermions you can have in a particule volume.

If you want more you have to make them more energetic.

@dmckee Did you see my question?

The Fermi level of <species> is the minimum energy at which you can adding another <species>

@dmckee my bad, meant to word it like that

I thought only stars with $ < 8M_⊙$ become white dwarfs.

Woah crap, mistake

@SirCumference Yeah. You can have a existing white dwarf that gains mass from somewhere.

Oh yeah

Like in a binary system?

Yup.

ooooooooooohh

@dmckee Thats how Type I supernova happen

Thanks!

Wait, in a white dwarf, are the electrons bound to an atomic nucleus?

Wait nvm...

@dmckee Sorry, one last question

If electron degeneracy pressure can't prevent white dwarfs from collapsing above the Chandrasekhar limit, why can neutron degeneracy pressure prevent neutron stars (below $3M_⊙$) from collapsing into black holes?

amazon.com/Variational-Lorentzian-Geometry-Research-Mathematics/…

Just when you thought you've found all the GR books...

@Slereah Did you ever write Ellis an ask him about the boundary stuff and send him Freire's proof?

that sad feeling when a book you got on loan is requested back 9 months early

but you dont even know why they gave you a loan for a whole year so at least it coincided with the end of the quarter

its not, simply put, personally i find a lot of the moderators decisions annoying. Before I've had to put up with some saying a question is too vague and others wanting to close something because they think the question is too specific. It gets pretty silly sometimes

@SirCumference i had closely the same question but what causes that degeneracy pressure ? don't say exclusion principle it say no quantum states of particle can be same but how can that cause any pressure ?

@DeNiSkA It's the exclusion principle preventing the collapse

hey! but what force is there which balances gravity?

exclusion prin. doesn't say which force is that!

gravity isn't even a force

what are you talking about?

ok!! i mean there is always an attractive force between matter (agree or not?)

no

there's no boson with a spin that could have that

oh crap

misread your question

define "matter" and "force"

well somerthing that has a mass is matter

2nd grad student's definition

No

then how do you define it?

Mass simply means how resistant something is to acceleration

Matter isn't clearly defined in modern science

Hi

Hello

Not sure if it'll be an attraction, but neutrons can perturb other charged particles very slightly

If I recall

of course neutrons would have an attraction

Oh wait

ever heard of the nuclear force?

the strong interaction

It's 3:29 man, come on

I'm too tired for this

there are only 4 fundamental forces

how can you forget?

I know all of them

lol

Jeez

I was thinking electromagnetically, for some reason

Anyway, I'm not sure I would call gravity a force

Happens to the best of us

@Mew yes ! so the force is attractive

YEs the strong nuclear force is attractive

Yes

There are no universally repelling forces

so why doesn't neutron star collapse

except the electron-=electron force

hey did you guys try this new apP?

steel bound sky

The Pauli exclusion principle

john rennie gave an explaination to me !

steelboundsky.com

neutrons are fermions

neutrons can't occupy the same space at the same time

*quantum state

yeah

if we're being precise

why? @Mew

because a neutron is in the way

Because they have a half-integer spin

@Mew ok! but there is a huge attractive force won't the neutron get crushed

yeah it's known as the Pauli exclusion principle

Crushed into what?

basically quantum mechanics prohibits fermions (half integer spin particles) from occupying the same quantum state

some theories states that the cores of neutron stars have quark-gluon plasma

that might be the closest thing to what you mean

are you asking why neutron stars don't just form black holes?

Deniska, neutron's won't get crushed

@Mew everyone says the same answer but i want to know what force is that which balances the huge attractive force between the neutrons (::*want to kill pauli*::)

I see what you mean

the "normal" force

wouldn't it be the repulsion force between the quarks

just a gues

I don't know what you mean by "a force that balances the huge attractive force"

There's just the fact that neutrons will not occupy the same space

Unless you raise the mass above 10 solar masses

Deniska is right though, at very very short distances, the internuclear force is repulsive

this is what determines the seaparation distance

Then it overcomes the exclusion principle and a black hole forms

I mean, take 2 neutrons and draw a free body diagram

if the neutrons are inequillibrium, all forces must balance

@SirCumference then why in case of black holes those particles collide?

Thus strong force must be balanced by a repulsive force of some kind

Neutrons consist of quarks that are electrically charged, so when two neutrons get close enough to each other the higher electrical multipole moments will become relevant and cause repelling.

Does a much better job at explaining this than I could

nice

This explains how, if you increase the mass enough, you'll get a quark star

if you increase it even more, you'd get a black hole

i will be back in 5-minutes

Nobody knows if quark stars, exist though

I'll keep looking

and back to work :(

Do you know about neutron stars? @Slereah

No.

I hate to dredge up an old issue, but we (obviously) have a problem with these chat exchanges where somebody winds up insulting somebody else. FYI to everyone involved (@JohnDuffield @0celo7 @Slereah @Danu @ACuriousMind @bolbteppa etc.), please don't get into these exchanges anymore. If any of you find yourselves unable to avoid it, stay out of chat. (Mods reserve the right to enforce this without warning, although we'd rather you manage yourselves.)

Please do ( ͡° ͜ʖ ͡°)

do what?

Enforce.

You realize the first enforcement action would be suspending you?

Would it

Is it a retroactive ruling

The fact that we can impose suspensions without warning is a reminder of how things have always been. We don't usually do it because the point is to educate people rather than to punish them, but technically, there's no fundamental right to a warning before a chat suspension.

Then why the threat at my approbation

It would be nice by the way to have some mod presence more often in this chat.

@Slereah because you were involved in the most recent burst of messages of the type we're trying to prevent. Around here.

@Slereah if you can't keep a conversation decent without moderators around, you're doing it wrong

That I was.

Doing my best!

Got Duffield blocked and all

Hard to not get in the crossfire.

No, it's easy. The easiest way is to not respond. Unlike gun battles, it takes more than one person to have an argument, and the people who "get caught in the crossfire" play just as much of a role in making the argument happen as the instigators.

Easy to say when you are not here, too :p

Is the error function ever something i'm going to want to evaluate by hand, or is it always left up to the computer?

Context: In finding the probability of a particle being between the classical limits of the quantum harmonic oscillator, I have this integral $P_cl = \frac{1}{\sqrt{\pi}} \int^1_{-1} d\xi e^{- \xi^2}$.

where $\xi = \sqrt{\frac{m \omega}{\hbar}} x$

and $P_{cl}$ is the probability of being between the classical limits

Probably use the computer?

Unless the integral bounds are specific values of the error function

I have seen how to solve gaussian integral by changing to polar coordinates, but I haven't seen how that works with limits that aren't $\pm \infty$.

Then it is the error function

The values you can determine with the series for it

The question in the book says to use a table of integrals, so I suppose just recognising that this is the error function, and that it is an odd function is enough for me to say $P_{cl} = erf(1)$

dlmf.nist.gov/7.6

If you want tables

dlmf.nist.gov/7.23

Cool, thank you

The error function is a non-algebraic function - you need a computer/numerical methods

Hell I wouldn't even try to compute a cosine by hand

@Slereah Gauss computed all of his sines and cosines in trig class by hand to 4 decimal places.

What a dork

There's a bunch of stories in Feynman's biography about his mental computations

Apparently a good one to stump those guys is the cotangent

@ChrisWhite know anything about this book? rd.springer.com/book/10.1007/BFb0084027

@Slereah what is $\sum{1/2^n}$

2

Famous one, tho

@user36790 yes

@Slereah proof?

is it geometric or some shit

oh you have to sum from 1

No it's just the series $2^{-n}$

Made famous by the Zeno paradox

@Slereah no to get $1$ you have to sum from $n=1$

Well you didn't specify from where you started :p

But yes

From 1 'twill be 1

Then again it's just a series i know

Not sure I could do one that I didn't know

I vaguely know how to work out geometric series

But not much beyond that

It's easy to see that $\sum_{n=0}^\infty 2^{-n} = 2$ once you know that it converges. Call the series $S$. Then $2S = S+2$. Now solve for $S$.

@ACuriousMind or you just remember the formula for a geometric series?

Well, but remembering a formula is boring compared to knowing a trick ;P

But then, how do you PROVE the formula

DUN DUN DUUUN

IIRC it's like...

@Danu How do you pronounce "Guillemin"

With difficulty.

$\sum a^n \rightarrow (1 + a)^n \sum a^n$

Or something???

Let's see

what

just look it up

Well yes, I could

But

@ACuriousMind you're such a joker

There's a Trick to remember it

@Slereah you call the partial sum $S_n$

Then calculate $aS_n$

then subtract that from $S_n$

then divide by $1-a$

I s'ppose~

then take the limit

Yeah that one

looks like @ACuriousMind got called out by DZ on JD

He's a delinquent

He basically named every active member here

Never thought I would live to see the day when ACM gets called out by a mod

@0celo7 You might want to read that message again.

"Calling out" implies that there is some sort of accusation in there; there's not.

lol :)

that denial.

it's ok

Don't worry @ACuriousMind

Girls love a bad boy

especially 10 yo ones ( ͡° ͜ʖ ͡°)

I feel dirty...

@bolbteppa That's the best feeling.

Hey @user36790!

:: Reads chat logs :: Lol. @ACuriousMind - < insert random question here >!

@Slereah Somehow that reminds me of:

@user36790 huh?

Oh vixra

"Planck’s Theory of Heat Radiation Criticized"

Here is some better nonsense

"The theory of idealiscience is an accurate theoretical model, by the model we can deduce most important laws of Physics, explain a lot of physical mysteries, even a lot of basic and important philosophical questions. we can also get the theoretical values of a lot of physical constants, even some of the constants can not be deduced by traditional physical theories, such as neutron mass and magnetic moment,Avogadro constant and so on. "

HE DERIVES THE AVOGADRO CONSTANT

"Definition 1. $\circ$ denotes origin of truth. Define $\circ$ as all the most complete everything"

This is the best paper ever

"Definition 2. ϑ denotes an alaya. Dividing $\circ$ by dimensions, the total contents of every ℵ1 dimensions of $\circ$ can form an alaya ϑ . The nature of ϑ is the great mirror wisdom, the wisdom has ability to map contents into their mirror images."

@ACuriousMind So you mean to say that quantum fluctuations is nonsense?

@HariPrasad Define quantum fluctuation.

@ACuriousMind $\langle \hat A \rangle^2 - \langle \hat A^2 \rangle $

What's up, @HariPrasad? Embarrased that I found the articles from which you copy-pasted your answer together?

Oh he also derives the natural logarithm from his theory

@ACuriousMind No not at all. I never told that i wrote that myself. I just couldn't provide reference to the original articles

@HariPrasad Why "couldn't" you? Copying content without providing reference is called plagiarism, and the general assumption is that anything you do not mark as citation you wrote yourself.

"Judaism as Science ?"

"The 4th dimension of science is explored from a Judaic point of view."

"The Theory of the Two Sciences: Bourgeois and Proletarian Science"

:D

I am sorry. I couldn't and I deleted my answer because i don't have enough knowledge about what i was saying to support my answer.

And it appears this is not the first answer where you have plagiarized.

I just wanted to say that what the OP is asking for is similar tho what i know about "Quantum fluctuations". I am sorry.

This one is copied from here, for instance. Do not plagiarize answers!

@Slereah I'm very often here.

BUT WHEN WILL YOU ACT LIKE THE MOD THAT YOU ARE

Ban everyone

@ACuriousMind Ha ha lol Thats my own "blog"

@Slereah I try to keep it cool because this is not "my site"

@HariPrasad Still, you should say that you took the text from there.

But that does make it less terrible

If I was a mod everything would be in ruin by now dagnabbit!

@HariPrasad That's not apparent from just looking at it.

@ACuriousMind check the about section: phisyks.github.io/about.html

"Founder, CEO & "Chief phisycist""

heh

LOL

@Slereah yup

@DavidZ Lol, funny (non-)analogy

@ChrisWhite At LMU, it's usually done during the seminars

Now, @HariPrasad, here you just copied the Wikipedia article. You link to it, but still, the impression is that you only cited the blockquoted part. You have to clearly mark citations.

@ACuriousMind I didn't just cite, I said that source of my answer is wikipedia.

@ACuriousMind you could have been little more polite in commenting

Now, what were you sources for this answer, I wonder...

@ACuriousMind Go search for it!

@HariPrasad Ah, yes, this, this and this

I'd say if your answer is just gonna be quoting a website, make it a comment, not an answer

@HariPrasad Why should I be "more polite" to someone who disguises other people's words as their own?

@ACuriousMind Thanks for everything

@ACuriousMind To preserve a generally friendly atmosphere.

@ACuriousMind Now you can ask for deleting my account. Or "BAN" me from all SE sites. :D

What's up with this Choquet-Bruhat woman? She has a lot of textbooks, on wildly varying topics!

She's the one who proved the well-posedness of the Cauchy problem in GR

WAIT

Is the time-orientedness necessary

Aren't all simply connected spacetimes time orientable

@HariPrasad You...find nothing dishonest or bad about copy-pasting answers together without clearly stating which parts are quotes and which ones not?

@ACuriousMind I am sorry and If you are not yet satisfied then I will delte my account. Should I?

Yes.

What? I have no power over you or your account.

@ACuriousMind Then what do you want from me?

Nothing, except not doing that again, and clearly marking (that's what the blockquotes beginning with > are for) all citations in the answers you've already given.

@HariPrasad Copyting stuff like that is just intellectually dishonest. Plagiarism is not cool

@Slereah what are you talking about

Oh the Godel proof?

Do you have a reference for that theorem

Incl. proof?

All simply connected nonconpact...probably