The h Bar

Sir Cumference

6:03 AM

@MAFIA36790 Done

crap

wait hold on

@MAFIA36790 k now done for real

user116211

Morning @JohnRennie.

John Rennie

Morning

Sir Cumference

It is 2:00am here, so I guess that's morning for me too

user116211

@SirCumference Go to bed; it's no that late unless it is chilly winter; I generally go to bed at 3:00.

Sir Cumference

@MAFIA36790 I can't sleep

Easier done than said

user116211

6:15 AM

Then do maths.

Sir Cumference

@MAFIA36790 Like what

user116211

Brain can't do heavy computations at night; you will get exhausted soon.

user116211

@SirCumference Anything hard.

Sir Cumference

@MAFIA36790 Like what

user116211

Hmm; analysis?

Sir Cumference

6:16 AM

Nope

Gimme a calc problem

Actually, gimme an astronomy problem

Involving calc

JayJay

Find the moment of inertia of a paraboloid

user116211

Well, I can give you a problem on Group Theory or abstract algebra.

Sir Cumference

@JayJay How is that astronomy?

It's barely a problem

Ok, I need help

I was given an explanation on how degenerate gases worked but I still don't understand why my reasoning was wrong

@JohnRennie You know this stuff, right?

I actually had the stomach flu when we learned this in class, so I got screwed over

John Rennie

@SirCumference a bit.What's the problem?

Sir Cumference

@JohnRennie Well my reasoning is that, for a collapsing star, the gravitational potential energy will decrease as the matter moves closer to the center of mass. So will it continue to decrease until the electrons reach their zero-point energies?

At which point the atoms can literally not get any closer?

John Rennie

6:22 AM

The two things aren't related

Sir Cumference

@JohnRennie Ik, but why not

John Rennie

The density controls the spacing between the energy levels

Sir Cumference

So GPE can't decrease the energy of electrons till they reach the ZPE?

John Rennie

Basically it's like a particle in a box. When you reduce the size of the box you increase the spacing between the energy levels.

Sir Cumference

@JohnRennie Huh? Why?

John Rennie

6:25 AM

??? Perhaps we aren't starting from the point I thought we were starting ...

Sir Cumference

@JohnRennie Guess not

John Rennie

Give me a few minutes, I need to deal with a server that's down ...

Sir Cumference

This came out of nowhere. One moment we're learning about orbital mechanics and the next we're learning about degenerate gases

@JohnRennie Okay, but lemme get this straight. If we cool down an object, the electrons will eventually reach their ZPEs, right?

That results in degeneracy for gas giants like Jupiter, right?

Sir Cumference

6:40 AM

Am I the only one still surprised that "Whoa" is the correct spelling and "Woah" isn't?

John Rennie

You know that if you put a particle ina box then it has a set of discrete energy levels. Yes?

Sir Cumference

@JohnRennie Yep

John Rennie

OK. With fermions we can only get two per energy level. So as we start putting fermions in the box the first two go into the ground state, the next two into the first excited state, the next two into the second excited state and so on. Yes?

Sir Cumference

@JohnRennie Yeah, makes sense

That's the case with degenerate gases anyways

John Rennie

So if we put n fermions into the box they have some total energy obtained by adding up the energies of the first n/2 excited states. Yes?

Sir Cumference

6:44 AM

@JohnRennie Uh, example? Why would the total energy be equal to that of the excited states for the first half of the fermions?

John Rennie

Two fermions per excited state remember, so we only consider the first n/2 excited states. However I forgot to say we have to double this total energy to count both electrons.

Sir Cumference

@JohnRennie Oh yeah

user116211

Son your question is just hiddish — Arkaprabha Das 34 mins ago

user116211

0

A: Wormholes, time travel, and time dilation

Gravity has its effect on time as well. Everything we know about matter quality in space is a mere assmption. So I am as well as you sir are assuming about the above question. First before starting with the above mentioned subject we should know a little about time. What is time ? Time is the ind...

John Rennie

This is the lowest possible energy. At any non-zero temperature the energy will be higher than this due to additional thermal energy.

Anyhow ...

Sir Cumference

6:46 AM

@JohnRennie Wait what is

The zero point energy?

John Rennie

If we reduce the size of the box then we increase the spacing between the energy levels so the total energy goes up.

user116211

Is the post making something sense?

user116211

I can't read; it's too long.

John Rennie

@SirCumference there are two possible meanings for zero point energy in this context.

Sir Cumference

@MAFIA36790 What

@JohnRennie Ok?

I thought it only meant the ground state for the electrons

John Rennie

6:48 AM

Normally the zero point energy is the energy of the lowest possible single particle state. And for a particle in a box this energy isn't zero.

Sir Cumference

@JohnRennie Right

That's clear

John Rennie

But you could also take the ZPE to mean the lowest possible energy for all n particles.

In this case I don't think the concept of ZPE is very helpful.

Sir Cumference

@JohnRennie What do you mean, "lowest possible energy for all particles"?

You mean it would be the Fermi energy here?

John Rennie

The Fermi energy is the energy of the topmost filled energy level.

Sir Cumference

@JohnRennie I know

I'm trying to interpret what you're saying. Evidently I am clueless

John Rennie

6:50 AM

The total energy would be the sum of all the energies of all the filled energy levels (times two because there are two electrons in each level)

Balarka Sen

@SirCumference Prove the Kepler's three laws.

Sir Cumference

@BalarkaSen You prove it

I'm in the middle of something

John Rennie

I think you should forget about ZPE - it is not relevant to this discussion.

Balarka Sen

@SirCumference You asked for a calc problem.

Sir Cumference

@JohnRennie I thought it was just a synonym for "ground state"?

@BalarkaSen The second can be proved through integration I'm pretty sure

John Rennie

6:52 AM

It's normally used to mean the energy of the lowest single particle ground state. Not the lowest total energy of the whole n fermion assembly.

Sir Cumference

Not going to indulge it at 3:00am

@JohnRennie That's the part I was confused on

Never heard of it being the "lowest total energy of the whole fermion assembly"

John Rennie

@SirCumference no, I agree, that would be an inconventional use of the term.

Sir Cumference

I misunderstood what you said and assumed you meant the Fermi energy for some reason in my head, but the total energy would be a lot bigger

John Rennie

And the energy of the lowest single particle state is not relevent to this argument. That's why I think you should forget about ZPE.

Sir Cumference

@JohnRennie All right, ignoring it

Balarka Sen

6:54 AM

As you prefer. You asked for a problem and I gave it to ya.

Sir Cumference

So we got a bunch of fermions in a box

John Rennie

Ok, now where did we get to ...

Sir Cumference

Two of opposite spins at each energy level from the ZPE to the Fermi energy

John Rennie

OK, if you reduce the size of the box you increase the spacing between the energy levels.

Sir Cumference

@JohnRennie You do?

I'm trying to figure out why

John Rennie

6:55 AM

Have you done the wavefunction for a particle in a box? Take the 1D box as the simplest example?

Sir Cumference

@JohnRennie Wait, is it related to the Heisenberg uncertainty principle?

John Rennie

@SirCumference Only indirectly. Don't go down that route for now.

Particle in a box

In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum...

Sir Cumference

@JohnRennie Well I've never taken a QM class, we just got thrown this stuff in our faces in astronomy and a bunch of equations derived from the uncertainty principle

user116211

It's covered in Stat Mech too.

Sir Cumference

From which he started asking us to prove things

@MAFIA36790 Degenerate gases are a part of stat mech, yeah

John Rennie

6:57 AM

OK. For a particle in a box the wavefunction must be zero at the walls - just like in the diagrams in that Wikipedia article.

So the (de Broglie) wavelength of the particle is related to the box size.

Without worrying about the details, does that make sense?

Sir Cumference

@JohnRennie Ashamed to ask, but can you explain?

I know what the de Broglie wavelength is, we went over that

Albeit briefly

John Rennie

The problem is that explaining how to solve the Schrodinger equation for a particle in a box will take ages.

Sir Cumference

@JohnRennie All right, I'll trust you that reducing the box size increases the spacing between the energy levels

What next?

John Rennie

Remember that the total energy is the sum of the first n/2 energy levels (times two for both electrons per level)?

Sir Cumference

@JohnRennie Yeah

John Rennie

7:03 AM

So if you increase the energies of all those levels, which is what happens when you shrink the box, the total energy will increase. Yes?

Sir Cumference

@JohnRennie Oh yeah, that makes sense

John Rennie

So that means as you shrink the box the energy goes up, which means you have to do work, i.e. put in energy, to shrink the box. In other words the box has a pressure. And that is what we mean by degeneracy pressure.

Sir Cumference

@JohnRennie Oh. Oh darn.

That makes sense.

John Rennie

It's really just that simple. A degenerate gas has a pressure because compressing it pushes up all the energy levels and that takes energy to do.

Sir Cumference

@JohnRennie Huh, thanks a lot

Now just one more question

How come degeneracy can be achieved through low temperatures?

Like in Jupiter's case

Does lowering the temperature eventually let the fermions reach the ZPE and subsequent energy levels?

John Rennie

7:07 AM

I started out by saying we have two electrons in the ground state, two in the first excited state and so on.

Sir Cumference

@JohnRennie Yeah

John Rennie

But that's the minimum possible energy for all those electrons i.e. every electron is in the lowest possible state it can get to.

So this is only the case at absolute zero.

Sir Cumference

@JohnRennie So you can't have a fully degenerate gas in real life?

All right, you've explained why degeneracy leads to pressure, but why do fermions reach their ZPE from gravitational compression and cooling?

John Rennie

At any temperature greater than zero the fermions will havbe some extra thermal energy so some of them will be thermally excited to higher energy levels.

@SirCumference you're using ZPE in a misleading way again.

Sir Cumference

@JohnRennie Or all of them reaching their lowest possible energy states

John Rennie

7:10 AM

Cooling and gravitational compression are separate.

Sir Cumference

@JohnRennie All right, let's start with cooling

John Rennie

A hot gas won't be in it's lowest possible energy state because thermal excitations promote some fermions to higher energy levels.

So you have to cool the gas to let the fermions relax towards the lowest total energy.

NeuroFuzzy

What's ZPEATLA4??

Sir Cumference

@JohnRennie As I thought

Good, that makes sense

How about compression though?

I assumed it had to do with GPE

John Rennie

The gravitational compression is where it gets really interesting.

I said that a degenrate gas has a pressure just because of its energy levels. But gravitational compression can apply a pressure.

Sir Cumference

7:13 AM

@JohnRennie You mean, besides leading to thermal pressure?

John Rennie

@SirCumference for now work at absolute zero - so ignore thermal pressure

Sir Cumference

@JohnRennie K

John Rennie

As the star shrinks the size of the box decreases (the box is basically the star) so the total energy of the fermions goes up.

NeuroFuzzy

Ok, sorry, let me expand my acronym. What's ZPE A Three Letter Acronym Four?

Sir Cumference

@JohnRennie Yeah

John Rennie

7:14 AM

But that increase in energy can come from the reduced gravitational potential energy

Sir Cumference

But then again isn't that the case with any object that's getting smaller?

@JohnRennie Reduced GPE?

John Rennie

@SirCumference yes, but most objects aren't made from a degenerate gas.

Sir Cumference

Wouldn't reducing the GPE lead to a lower total energy?

John Rennie

@SirCumference energy is conserved remember.

That reduced GPE has to be balanced by an increase in energy somewhere else.

Sir Cumference

@JohnRennie Oh, but if we're talking about conservation here, it'd just be converted to KE, right?

John Rennie

7:16 AM

For conventional matter the decreased GPE is typically converted to KE and the object gets hotter. Just like a regular star.

But for a degenerate gas the energy can go into the increased spacing of the energy levels.

Sir Cumference

@JohnRennie Any reason it wouldn't just be converted to KE?

All right, I'm a bit confused. The energy levels represent the total energies of the fermions, right? So if they decrease in GPE, shouldn't their total energies remain the same?

John Rennie

The energy has to go into the increased energy spacing otherwise the object can't shrink. It can also go into KE/heating.

Sir Cumference

Since it would be converted to KE

John Rennie

Thermal energy in a degenerate gas is the promotion of fermions into higher energy levels, leaving some lower energy levels unoccupied.

Sir Cumference

@JohnRennie So the decreasing GPE isn't increasing the total energies of all of them, but just some of them?

That still presents the same problem. How can GPE decrease but total energy increase?

John Rennie

7:21 AM

If the temperature is absolute zero the GPE goes just into the increased energy levels spacing.

Sir Cumference

@JohnRennie But that would raise the total energies of almost all the electrons, right? So again, how can GPE decrease while total energy increases?

John Rennie

What we're working towards is that the degeneracy pressure balances out the gravitational compression.

As you shrink the star we get energy from the reduced GPE, but we need energy to go into the increased energy level spacing.

Sir Cumference

@JohnRennie I still am stuck on that part. The energy levels represent total energies of the electrons. If some of them are to rise, then others must fall, right?

John Rennie

These two energies don't scale in the same way with the size of the star, so there is a point where you can't shrink the star because the increase in the energy level spacing is faster than the decrease in GPE

GPE and the degeneracy energies are unrelated

Sir Cumference

@JohnRennie Wha?

John Rennie

7:24 AM

GPE comes from the gravitational force

Degeneracy pressure comes from the exclusion princiople

Sir Cumference

@JohnRennie But...isn't total energy just KE + U?

John Rennie

@SirCumference In classical mechanics yes

Sir Cumference

I realized the problem, crap

John Rennie

In quantum mechanics no

Sir Cumference

That won't work

All right, so the decreasing GPE puts energy into the spacing of the energy levels

@JohnRennie All right, I'm thinking of something, tell me whether it's unrelated or not

I wrote in my notes some equation that details how KE becomes more influential in the total energy as size decreases, while U becomes more influential as size increases

John Rennie

7:29 AM

@SirCumference that's a purely classical argument, and gets troublesome when we have to include quantum effects. And since a degenerate gas is a quantum system, quantum effects dominate its behaviour.

Sir Cumference

@JohnRennie Okay, could you show me the equation for total energy in QM?

John Rennie

I already did. It's the sum of the first n/2 energy levels

Sir Cumference

@JohnRennie That's it?

John Rennie

The actual formula would be very complicated because the energy levels for a particle in a spherical box are complicated.

You could Google it if you really want the gory details.

I have to work now for about half an hour. Back ina bit ...

Sir Cumference

K, gonna head to sleep

Thanks again, 'night

or...morning

Mew

7:37 AM

G'day everyone

Anonymous

7:47 AM

@Mew Did you create that website ? How's it going on ?

Mew

@S007, yes it's still early stages

physicsproblems.nfshost.com

Tonight I will work on a privacy policy and meta page

Anonymous

Are you paying for the server or something ?

Mew

and improve spam filters

yeah

I already had a server

Anonymous

Is it a personal server ?

Mew

so I've added this site to it

Anonymous

7:48 AM

Oh

Anonymous

But does it have enough size ?

Mew

YEah

Anonymous

how much?

Mew

enough

I will be changing the url name too when a consensus is reached

it won't be physicsproblmes.com though as that costs $20k

physicsDoJo is available but a bit childish

I have appointed heather an intermin moderator before the election

Anonymous

That seems good. How much does it cost to register the url ?

Anonymous

7:51 AM

Or is it free ?

Mew

the current url with the".nfshost" is free (included in cost of the server)

but the new url will depend on what we choose

every url is different

Anonymous

If you need we can ask for community donations on meta!

Mew

yeah finances isn't a problem yet but if we need

Anonymous

BTW the current questions show no effort

Anonymous

The 3 questions I saw

Mew

7:53 AM

yeah i don't think they were real questions

just ones to populate the site

i think they will be closed

we will define scope once meta is set up

Anonymous

Do change the example questions if possible...and when are you planning to make it public ?

user116211

@S007 No they are not.

user116211

But there is no definition of the scope yet.

user116211

It's just in preliminary level.

Mew

@S007, no set date, when the community is happy with what we have we can go public

Anonymous

7:55 AM

Before releasing just make sure there are atleast about 50 good example questions so that we can direct the public to see them and learn how to post

Mew

yeah that's a good idea

Anonymous

And I can help if you need...in any way

Mew

I won't have the time to write them up myself thoug

Anonymous

@Mew I will do that part of posting 1,2 good questions per day

Mew

some yes, 50 no

that'd be awesome

Anonymous

7:57 AM

Maybe we can release the site on new year :-)

Mew

@S007, I can make you moderator if you like?

at the moment I think new questions have to be approved by a moderator

that way you can post/approve content if i'm not at the computer

Anonymous

Yeah...if you wish you can make me a mod...and just ping me whenever you need some help with the site and when you are setting up meta

Anonymous

I will post 50 good quality questions by december end

Anonymous

i already registered

Mew

ok you're a moderator now

Anonymous

8:00 AM

Thank you..and you are setting up meta tonight ?

Mew

I"ll try, my first priority is fixing the capture

I think the spam filter capture isn't working properly

Anonymous

which capture ?

Mew

that's why so many bots have joined and moderating has been a nightmare

but all content requires approval now so it looks clean

Anonymous

bots ? How are bots joining ?

Anonymous

:O

Mew

8:02 AM

look at how many users have joined

7 pages of users lol

Anonymous

i saw...but how ??

Anonymous

any bug ?

Mew

I think the capture wasn't displaying

the human detector

so I'll fix that in the next hour or so

then work on meta and privacy policy

Anonymous

well good luck with fixing that...maybe you can ask for help in stack overflow...(I know almost nothing of programming :-P)

Mew

hopefully get this done within a few hours

Anonymous

8:03 AM

yes i too wish :-)...And really hats off from my side for the hard work you are doing for us :-)

Mew

ty.

ffahim

What's the difference between S=ut+t^2(a/2) and S= u+(2t-1)a/2

Anonymous

@Mew The site is not rendering Latex...did you notice ?

Anonymous

physicsproblems.nfshost.com/?qa=3/…

Mew

@S007, yes it's a plugin I need to install

it's on the to do list

Anonymous

8:07 AM

Oh...okay :-)

ffahim

@Mew @S007 can u guys tell me?

Mew

@ffahim, yes please post your question here physicsproblems.nfshost.com and show your working/understanding so far

Mew

8:21 AM

@S007, task 1 complete, the capture has been implemented

bots won't be able to get past now

Anonymous

@Mew Great! And I closed swapnil's question as it had no effort :-P

Mew

@S007, while I agree the question didn't have much effort, I think it's best to focus on populating the site with questions of high quality rather than closing the ones of low quality

People may be put off by a site that only has closed questions

So I think as a rule for the early days, before we've properly defined what is offtopic and what isn't, we should aim to at least replace every questionw e close with a high quality one

Then once meta is in place, we can decide as a community what we want and don't want

Anonymous

@Mew Yes, i will add a few good questions today night. Don't worry about the questions now as it is just a prototype...moreover we need a few examples to show people that what type of questions are not encouraged on the site.....

Anonymous

I left a message telling them to edit and then I will reopen :-)

Mew

Yes, but remember we are unelected moderators

Anonymous

8:25 AM

heather's question is good

Mew

We alone can't decide what is and isn't good quality

So I think we should be very hesitant to close questions until area51 is set up and a consensus is derived

Anonymous

sure...so should i reopen it ?

Mew

If you are going to post more questions soon it will be ok

Anonymous

I promise you will get 2 good questions within 12 hours

Anonymous

:-d

Mew

8:27 AM

i'll leave the other question open for now, and once meta is created hopefully tonight we can start a discussion on what we think the good and bad questions are

and then close the ones we think are bad from there

Anonymous

okaies

Anonymous

i left them open

Mew

That way we can refer people to the meta when we close a question and have some objective standards

awesome

Anonymous

i need to go now....bbye for a while

Mew

laterz

user116211

8:31 AM

@Mew They will set an example of what queries would be tolerated prior to the policy making and defining of the scope.

Mew

@MAFIA36790, I agree having closed and open quesitons is good so users can see what they should do

but having 100% of questions closed doesn't show them what to do that's all

I have left one question closed

and I think I'll close more when we have higher quality ones on the site

and once we have a consensus on meta

@MAFIA36790, that said heather's question appears high quality (esp once latex is added)

user116211

Yes, I think so.

Mew

9:06 AM

@S007, latex has now been added

it's not visible in the preview, but it shows in the final post

user116211

great.

Anonymous

9:22 AM

@Mew Awesome. Also add the latex rendering in preview when you get time !

Mew

@S007, i'm doing that now

Anonymous

9:34 AM

@Mew How are my questions ?

Mew

@s007, really good quality thanks!

Anonymous

:)

user228700

Yo @S007: I've a quick question. Dyou mind?

Anonymous

Even I have a question....I am waiting for somebody to appear :-P....meanwhile you can ask

Anonymous

@Kaumudi

Anonymous

9:48 AM

hey

user228700

@S007: Oh, u're gone :/

user228700

@JohnRennie: Morning :-) (? Is it still morning there? I'm a bit late :-P)

John Rennie

09:55 here!

14:25 in Tamil Nadu?

user228700

Oh, OK, counts as morning then :-) It's 15:26

Anonymous

@Kaumudi im here

Anonymous

9:57 AM

ask

John Rennie

Oh, yes, I forgot that our clocks went back last weekend and that added an hour to the time difference.

user228700

@S007 Oh, OK. I was wondering, u know the parametric coordinates of a parabola, yeah? $(at^2, 2at)$.

user228700

@JohnRennie Ah, OK :-)

Anonymous

yes

Anonymous

@Kaumudi

user228700

9:58 AM

Is this only for the parabola $y^2=4ax$?

Anonymous

obviously

Anonymous

put it and check

Anonymous

(2at)^2=4a(at^2)

user228700

OK, just making sure. Thanks :-)

Anonymous

okay :-)

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