The h Bar

Sir Cumference

12:14 AM

Optics is fun

But complicated as hell

Well, rather there's so much to wrap my head around

dmckee

12:56 AM

@SirCumference Candidate for "understatement of the week".

Bernard Meurer

@ACuriousMind Halp!

ACuriousMind

@BernardMeurer What's up?

Bernard Meurer

@ACuriousMind I'm about to ask a possibly very stupid question so beware

Can an $n$-dimensional shape be mapped into an $n-1$ dimensional space? Or maybe $n-y$ actually

ACuriousMind

@BernardMeurer Yes

You might want to make that question more precise ;)

Bernard Meurer

I can't :v I can barely put in words but it works in my head

Sir Cumference

1:06 AM

@ACuriousMind Can you answer a question about neutron stars?

Or rather Fermi gases?

Bernard Meurer

Do you mean precise about the meaning of 'mapping'?

ACuriousMind

@BernardMeurer Yes

Since all $\mathbb{R}^n$ are of the same cardinality, there are always bijections between them

@SirCumference Probably not

Sir Cumference

Dangit

Bernard Meurer

I was thinking something akin of let $z$ be the volume of a 3 dimensional shape for example, is there a $j$ in a 2 dimensional space such that $j \equiv z$ somehow?

Sir Cumference

Screw neutrons stars and their complicatedness

But I love em

ACuriousMind

1:10 AM

@BernardMeurer Sure, choose $j=z$ :P I suppose you meant to include some conditions on $j$ there...

Bernard Meurer

Oh, yeah hahahaha

Sir Cumference

@dmckee Oh wait, you know things, right?

Bernard Meurer

@ACuriousMind There, edited, also; what would you call the "volume" of an n-dim shape?

ACuriousMind

@BernardMeurer Well...I'd just call it "volume". Unitwise, you already run into trouble with your equation there - do you really mean to equate an area to a volume?

Bernard Meurer

Well kind of yes, like we map the globe, 3-dim, into map 2-dim

HDE 226868

1:15 AM

@SirCumference Not that I can help, but out of curiosity, what is your question?

ACuriousMind

@BernardMeurer 1. A sphere is not a three-dimensional object. 2. There is no "good" (continuous, injective) map from the sphere to the plane - you always have to omit at least one point.

Sir Cumference

@HDE226868 If the Fermi energy rises when a neutron star compresses, how do all the neutrons occupy every energy level up to the Fermi energy?

Bernard Meurer

@ACuriousMind wait wat. A sphere is not 3-dim?

ACuriousMind

@BernardMeurer A ball is three-dimensional, but its surface/boundary, the sphere, is not - you can describe every point on it by just two angles.

Sir Cumference

@HDE226868 Yep, neutron stars are easily one of the most complicated astronomical objects I've ever seen

Because everything about them is based on QM

And as someone who doesn't know much QM...

Bernard Meurer

1:19 AM

@ACuriousMind Game of Thrones is on, can we continue tomorrow, I have more questions:)

FenderLesPaul

QM + GR + fluid mechanics in fact

Sir Cumference

I'm kind of at a loss

FenderLesPaul

hardcore subject

Sir Cumference

I've heard fluid mechanics are even more complicated

I'm keeping my distance

ACuriousMind

@BernardMeurer Of course (although I'll probably not be here this late tomorrow). And no spoilers!

Sir Cumference

1:27 AM

@dmckee Halp!

dmckee

@SirCumference Allegedly.

Sir Cumference

@dmckee About Fermi gases and neutron stars?

dmckee

Uh ... sorta.

Sir Cumference

All right, good enough

If the Fermi energy rises when a neutron star compresses, how do all the neutrons occupy every energy level up to the Fermi energy?

Rob Jeffries would know this, actually

dmckee

The same way the electrons in an atom occupy all the energy levels up to the valence level: when there is a hole, something will spontaneously settle into it.

Sir Cumference

1:36 AM

Yep, I understand that.

dmckee

The trick is, after equilibrium is reached, how does the system compress.

Sir Cumference

So, when a neutron star compresses, every neutron raises in energy?

So why does it take so much energy to compress a neutron star?

dmckee

@SirCumference I'm not sure. That's one for Rob. But it doesn't matter, because in order to compress you have to convert a proton to a neutron and stick it in a empty spot above the pre-existing Fermi-level.

Sir Cumference

In a neutron star, most of the protons should already be converted into neutrons

dmckee

But the proton has a lot less energy than that. So the energy has to come from somewhere.

Sir Cumference

1:39 AM

Usually by the time a neutron star could form, it's energetically favorable for electron capture

dmckee

@SirCumference A neutron star exists in an equilibrium with two degenerate gasses: electrons and neutrons.

Sir Cumference

Wait, really?

I thought it was mostly neutrons

dmckee

@SirCumference Yeah. It is.

Sir Cumference

Lemme see if I got this straight: White dwarfs are made of a ton of degenerate electron gas. But when it gains enough mass (past the Chandrasekhar limit), electron capture is favorable and the degenerate electron gas becomes a neutron gas, right?

dmckee

But there are electrons in there two, and about one proton per electron, too.

@SirCumference But that process only proceeds until further captures would cost energy. There is an equilibrium there.

Sir Cumference

1:41 AM

Which makes the star much smaller

@dmckee Oh man, seriously?

Dang. So if you kept increasing the mass, could you eventually get a pure-neutron star?

Before it becomes a black hole?

Wait, bad question

90%-neutron star.

And how can you find the ratio between the amount of degenerate electron gas and degenerate neutron gas in a neutron star?

dmckee

@SirCumference The population ratio is set my the mass-ratio. With a little thinking I could even figure out how that goes. But there are a lot more neutrons than electrons because the mass ratio is ~1800.

Sir Cumference

I'd imagine it would be different depending on the mass of the neutron star

dmckee

The basic deal is the two gasses will have the same Fermi-energy, but the whole thing is regulated by the energy balance.

Then you throw in neutrino processes and the system gets a way to cool.

Sir Cumference

.-.

Jesus christ this is nuts

dmckee

Rab really is the guy for this stuff. I've never taken the time to study it as deeply as I'd like.

Sir Cumference

1:45 AM

So wait. A neutron from the neutron gas could have the same energy as an electron from the electron gas?

Essentially in the entire star, more than two particles can occupy the same energy level?

dmckee

@SirCumference Well, the ones at the Fermi surfaces. But of course, neutrons are much more massive which is why you have to have more neutrons to get that energy balance.

Sir Cumference

Er...what "energy balance"?

dmckee

@SirCumference Electrons and neutrons are distinguishable. Pauli exclusion doesn't apply between them.

Sir Cumference

@dmckee I probably should've figured that out...

dmckee

The Fermi levels being the same.

Sir Cumference

1:46 AM

But yeah, what energy balance?

dmckee

Because if they weren't either beta-decay or electron-capture would be energetically favorable.

Sir Cumference

Er...I'm sorry, what do you mean?

user54412

@SirCumference A good chunk of most neutron stars is 10% protons. They have noticeable effects on the superfluidity properties. And the n-p ratio varies with depth in a given star.

Sir Cumference

@ChrisWhite Yeah, on the surface there are a good chunk of protons

And electrons

But I'm wondering, is there a good amount of electron degenerate gas in the core?

Or just at the surface?

I imagined only on the surface

user54412

The core density is 10^14 times that of solid rock. Even if the n/p ratio was a billion, that's a pretty impressive concentration of electrons.

Sir Cumference

1:51 AM

True

But compared to the amount of neutron degenerate gas, the amount of electron degenerate gas in the core is extremely small, right?

One could say there is a balance of NDG and EDG in a white dwarf too, right? Even though there is much more EDG

Bernard Meurer

@ACuriousMind I'd never spoil you, I benefit far too much from our friendship to risk it like that :p

@ChrisWhite You broke my heart with that email[

user54412

...

vzn

2:52 AM

via reddit

Experimental test of the free will theorem / Liu et al

on the contextuality/ nonlocality connection/ tradeoff

> This reveals that quantum non-locality can be produced when single-particle contextuality is combined with correlations which are not non-local by themselves.

John Rennie

6:21 AM

@MAFIA36790: gosh you're fussy about all those d's :-)

user116211

@JohnRennie eeee....

user116211

@JohnRennie however, if you've problem, you can rollback it :)

user116211

John Rennie

No, the edit is no problem and thanks for putting the effort in. I just find it hard to care whether someone writes $ds$ or $\mathrm ds$ :-)

user116211

After 10 years? Or am I seeing it wrong :P

John Rennie

6:29 AM

Whose account is that?

user116211

@JohnRennie I discussed once with David about the difference between $d$ and $\rm d$...

user116211

The former is variable and the later is operator.... though interchanging it doesn't make anything wrong apart from beauty ;P

user116211

Valentin Tihomirov

1 7

user116211

@JohnRennie: ^^^

user116211

@JohnRennie: What do you think SE would be after 10yrs o.O

user116211

6:33 AM

An AI?

user116211

Anna V would still be the oldest physicist....

John Rennie

Valentin Tihomirov has been a member for 8 months ...

user116211

John Rennie would still be at the mountain top....

user116211

ACM would be the most popular guy....

user116211

QM would silently make most of the edits ;P

user116211

6:35 AM

Nothing would change :))

skill patrol

Member for 1 year, 5 months on ELU...

user116211

Does the number of years of being a member count in the amount of days of suspension?

skill patrol

Sometimes, depends on your record.

user116211

@skillpatrol Even Ron didn't get that amount of suspension....

user116211

Let it off....

skill patrol

6:42 AM

It must have been serious spamming.

user116211

@JohnRennie: What books did you follow for SR?

John Rennie

@MAFIA36790 I have to drop out for a few minutes - I'm at work and something has come up. Back in ten minutes.

user116211

@JohnRennie o/

user116211

::stopwatch counting 10min::

David Z

@MAFIA36790 nope

user116211

6:57 AM

-__-

skill patrol

In all cases? @DavidZ

David Z

Yep

skill patrol

-__-

John Rennie

@MAFIA36790 I originally learned SR as a student in 1980 (36 years ago !!!) and I have no idea what book I used. When I became interested in physics again (after I retired) I picked up SR just from surfing the web.

SR is very easy once you've grasped the basic idea, and I'm unconvinced you need a book on it.

Just, for God's sake, ignore everything you've read about light clocks! :-)

user116211

@JohnRennie Yes, I'm quite enlightened after reading your answers yesterday.... Now I'm reading Feynman....

John Rennie

7:09 AM

@MAFIA36790 good to know my efforts haven't been in vain :-)

I've never read Feynmann's physics books (shock horror! :-) though I've read his bio and popular science works, so I can't comment on how good they are.

user116211

I just didn't get why we treat time as scalar in NM.... you told me yesterday but still confused.... let me complete Feynman first... (am reading your time-dilation post)....

user116211

@JohnRennie O.o

John Rennie

@MAFIA36790 Consider the different between position and distance. If I say you're at the position $x = 99$ then $x$ is just a number that labels the point where you are.

user116211

@JohnRennie They are free now; thanks to CalTech; you can download them from their site.... Amazon also sells them cheaply.

John Rennie

If I say the distance from me to you is 99 metres that distance is a vector i.e. the vector that starts at my position and ends at your position.

user116211

7:13 AM

@JohnRennie ya... I got that from your answer... time is not vector; time-interval is

John Rennie

@MAFIA36790 and exactly the same is true of the spatial coordinates

user116211

or more formally, component of vector.

John Rennie

So there's nothing special about time in this respect.

One of the mental hurdles in learning SR is understanding that time is just a coordinate like $x$, $y$ and $z$.

3

dmckee

Albeit one taking a funny sign when computing lengths.

user116211

@JohnRennie That's the basic message you gave in what is time post. That was pretty clear actually.

John Rennie

7:16 AM

@MAFIA36790 then you understand SR - congratulations :-)

user116211

:))

user116211

Still, I need to complete Feynman and your post first.

John Rennie

@MAFIA36790 actually I'm pleased at least one person found the what is time Q/A useful. The post got a lot of votes mainly because it got onto the hot questions list, but I doubt many of the upvoters understood it let alone found it helpful.

user116211

And the most evil superstition was the Arrow of Time concept... @john, you shunned it away :)

user116211

I don't know, although, what JD believes :(

user116211

7:20 AM

@JohnDuffield: o/

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

\o

John Rennie

@MAFIA36790 I thought he and I agreed about the arrow of time, i.e. that the block universe idea is basically correct, though he still managed to find something to disagree with me about. Oh well :-)

John Duffield

@MAFIA36790 : read some of my answers. I believe in things that are supported by hard scientific evidence.

user116211

@JohnRennie That's my point... he believes time doesn't flow.... but I can't understand what he is against with in your answer ;/

John Duffield

@JohnRennie : can you see time flowing? No. Pendulums move, cogs move, light moves, and so on. The flow of time is just a figure of speech.

John Rennie

7:23 AM

@MAFIA36790 John has been asked not to discuss physics in this chat room, so it's unfair to involve him in this. I guess you could set up a separate chat room if John is willing.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

After you finish Newtonian mechanics; French does a good book just on Special Relativity @MAFIA36790

John Duffield

I have to go to work. Read my answers to the time-related questions.

John Rennie

@JohnDuffield yes, I agree. I thought we agreed on this.

user116211

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ yeh... I've djview on it.

user116211

But it is rather history-oriented and quite loooooong :(

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

7:26 AM

You will need the background for the second book

user116211

I want to have a grasp on SR before starting my undergraduation.... in that case John's answers including others and Feynman would suffice, I suppose.

user116211

23 hours ago, by John Rennie

Time is invariant under Galilean transformations, so time intervals are also invariant regardless of whether we treat them as vectors or scalars.

user116211

@JohnRennie: What did you want to mean by that?

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

The Feynman lectures are ancient compared to French.

user116211

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ o.O

user116211

7:28 AM

No!

user116211

French wrote it at nearly the same time when Feynman & co. published his lectures.

John Rennie

@MAFIA36790 a Galilean transformation is an ordinary Newtonian mechanics transformation.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Stick with French. It will pay off in the end.

Bernard Meurer

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ You're the physics version of that kid who thinks "The Police" is really old music :p

user116211

@BernardMeurer: o/

John Rennie

7:29 AM

e.g. if you're moving along the x axis at velocity v then in your frame I'm moving at -v.

user116211

@JohnRennie agrees

John Rennie

So my spacetime point $x$ corresponds to your point $x - vt$.

user116211

agrees

Bernard Meurer

@MAFIA36790 Heya

John Rennie

In Galilean transformations time is invariant i.e.

t' = t

user116211

7:31 AM

@JohnRennie spacetime? I thought time is absolute in NM

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Have you @BernardMeurer read any of French's books?

Bernard Meurer

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ Obviously not; I'm just messing with you :D

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

:D

user116211

:D

Bernard Meurer

Glad I brought some happiness

Because I'm off to bed

See you all later

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

7:32 AM

Cya later

user116211

@JohnRennie yes, that's right... but does invariance in Galilean transformation mean the quantity is scalar?

user116211

@BernardMeurer g'nite.

John Rennie

OK if time can only move along one axis then the time interval vector only has one component $\mathrm t = (t)$. A vector has magnitude and direction, but in 1D the direction of a vector is always along the axis.

So there isn't any useful difference between a vector and a scalar.

Time intervals are still vectors, but in 1D a vector is rather a trivial object.

user116211

@JohnRennie: How could I forgot time is same in all reference frame! It is absolute in NM. It is indeed scalar in NM.

John Rennie

I have to get back to work for a few minutes ...

user116211

7:35 AM

But that breaks down in SR... since there is nothing absolute....

user116211

@JohnRennie okayish.... meet you at the afternoon :)

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Get yourself a copy of French's Special Relativity @MAFIA36790

user116211

12 mins ago, by MAFIA36790

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ yeh... I've djview on it.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

What is "djview"?

I mean a physical book.

user116211

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ oh.

user116211

7:39 AM

Don't have money now.... books are rotting in my wishlist in Amazon, dman ;(

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Start on page 1 and do all the calculations.

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