The h Bar - 2016-06-10 (page 3 of 3)

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5:00 PM

I think we're saying the same thing. I too consider the cardinal sin the failure to keep our own house in order.

Flagging, in my opinion, is for people who don't know how to leave the keyboard :P

So my point is lets try to keep our own house in order first, and resort to flagging when all else fails.

Only when all else fails.

reminds me of this @skillpatrol

user image

@JohnRennie Yeah, that's reasonable. Your earlier message (with the bold) seemed to be saying something different.

My point is when all else fails leave the keyboard.

5:02 PM

@jibe: did you see my comment on your question?

I just being tuned to downright ignore any posts that are not relevant to me, which is why I am often oblivious to any potentially flag attracting content in the chat room

@Secret probably not the worst idea

Ah yes, you did. I've just seen your reply. Glad to be of service :-)

as I often said to my friends, I am such an absent midned person that if something don't interested me, I don't even know they exist

until they told me

@Obliv sorta :-)

5:05 PM

Should I give a hint for this?

sir can you just gimme a hint I am not expecting a whole solution — Archis Welankar 9 mins ago

My hint would be: $a = r\omega^2$ :-)

I wouldn't give anything, but that's just me

Indeed.

For me, it depends..

The trouble is that giving a hint rewards the asking of the homework question just as answering it does.

Yeah, that's my reasoning too.

I guess a hint is less of a reward, but still, it's more than nothing.

5:08 PM

You could chew them out for asking :P

I rarely comment on the main site nowadays, because 1) I don't have any questions coherent (and/or big) enough to post on main site, and 2) I am a perfectionist thus I only post answers if all cross checking it is as perfect as it can be

I do, hwoever post comment that kinda guess what the OPs are asking, especially in cases where acuriousmind find incomprehensible

and ask OP for clarification

Good strategy.

I am expecting, however that waves of QM questions will came from me once I start the QM big self study

@Slereah I found the homotopy

It's the Worst Homtopy, sadly

$(1-t)v+tn$

How disgusting

So anyway

I have three 3D coordinate systems

5:17 PM

@ JohnRennie I think the Bohm interpretation exploded again ever since that 2015 experiment on surreal trajectory.

As for my view on interpretation, I am ok with either the Bohm or hilbert space interpretation. sometimes I found it is important that given two basically equivalent approaches to a topic, one should not only be familiar with it, but also be able to translate between the two languages

In fact, the notion of a quantum potential is very attractive to me for the bohm interpretation

All of which are a somewhat 3D version of bipolar coordinates

I suspect that picking cylindrical bipolar coordinates is the smart move

But I'm not sure

Problem is that the solutions are slightly different

@Slereah really the only trick was proving that that sum is never zero

Cylindrical is $$\psi(\xi,\eta, z) = e^{i\mu z} \sum_r A_r(\cosh \xi) (\cosh \xi - \cos \eta)^{-r}$$

Bispherical is $$\psi(\xi,\eta, \phi) = e^{i\mu \phi} \sum_r A_r(\cos \eta) (\cosh \xi - \cos \eta)^{-r}$$

Toroidal is $$\psi(\xi,\eta, \phi) = e^{i\mu \phi} \sum_r A_r(\cosh \xi) (\cosh \xi - \cos \eta)^{-r}$$

Maybe the different definitions of $A_r$ make it all identical in the limit of a plane, but it is odd

Although now that I think about it

What does it mean for the dot product of two vectors to be negative?

WAIT

the normal vector only has a normal component :D

@Slereah what is that

and how do you know that those converge

Also given a following paper, I think that the solution would be something like $$V^m_n(s,\eta) = \int_{-\pi}^\pi e^{imt} z^l (j_l(x) + i (-1)^{n+1} j_{-l-1}(x) ) dt $$

Where $x$ and $z$ are awful awful functions of $s$, $\eta$ and $t$ and $j$ is the spherical Bessel function

So sayeth the paper

While that is a solution I'm not quite sure I could get a propagator out of it

5:29 PM

@ACuriousMind Let $X^n\subset\Bbb R^n$ be a compact manifold with boundary. I'm trying to show that any vector field $v:X\to\Bbb R^n$ that points outwards on $\partial X$ is homotopic to the Gauss map of $\partial X$. What I found is that the homotopy $$F(x,t)=\frac{(1-t)v(x)+tn(x)}{||(1-t)v(x)+tn(x)||}$$ works.

Can you think of something more elegant?

You need the fact that $v$ points outwards so that the denominator is well-defined so it's actually a map to the sphere.

What would even the propagator look like

Let's see

Here, $v$ is normalized and $n$ is the outward unit normal vector field.

Oh man I don't even know which function I can associate with the creation and annihilation operator

I have the awful feeling that outside of the 4 articles I found, there's about 0 things on the topic

Errrr

Should be about...

@Slereah What are you looking for?

Well I have the solution of the Helmholtz equation for the coordinates (I think)

Trying to figure out what the propagator would be

But it's a large ugly function

5:41 PM

Is the propagator not a scalar

Calculate it in nice coordinates and then transform?

Well the problem is

Either I do it in ugly coordinates where the propagator is hard, but the identification is trivial

Or I do it in nice coordinates, where it's the other way

The identification?

Is it not a scalar???

Well it's for a wormhole thing

This is why you should never use coordinates.

If you can't prove it topologically it's probably not worth much.

The field needs to be such that $\phi(1, u) = \phi(-1, u)$

Also the derivatives need to match up at $\xi = 1$

5:43 PM

What is $\phi$

And what is $\xi$

and what is $u$

Some scalar field

$\xi$ is the radial coordinate in bipolar coordinates

$u$ the angular one

What exactly are those?

user image

How are they defined o.O

$$x=a\ {\frac {\sinh \tau }{\cosh \tau -\cos \sigma }} $$

$$y=a\ {\frac {\sin \sigma }{\cosh \tau -\cos \sigma }} $$

5:47 PM

oh lordie

why are you doing this @Slereah

just do topology like a healthy man

Topology won't give me the singularity structure

It worked for HE

You're just not good enough lol

Tho I'm thinking that for now

Maybe I'll just do the Clifford torus for a bit

Simpler coordinates and metric

Tho I need to induce a fancy time shift

What exactly are you looking at

like what space

$\Bbb R \times T^2$

5:49 PM

What does that look like

a bunch of donuts

Through times

I know that...

Then why do you ask

Though really, one coordinate is pretty much useless

You can suppress one angular coordinate and just do $\Bbb R \times S^1$

1 hour later…

7:00 PM

@Slereah because I'm a little girl

@Slereah what's that

Orly?

@bernard you there bernard?

or @vzn

@Obliv do you not have questions for me

@Obliv Yep, what bothers you son?

I am willing to help you now because I want to avoid my own math

7:13 PM

@0celo7 you can chime in if you want, but i think it's mostly cs related. @bernard you didn't make the program I asked you , right? I don't think I need those last 2 parts (btw) and I currently have a more important matter :D

@Obliv Not yet, because the calculator project took a whole new level

I'm addicted

I'm getting wifi to work

yeah don't worry about it. i'm more interested in this matter: say you have a set of $p$ primes in the set of $n$ integers. (ie 25 primes in the set $\{1,2,...,100\}$) how would I be able to count the amount of integers between $\{1,2,........,1000\}$ that are combinations of only these first 25 primes?

define combinations

$\{2,3,5,...,97\}$ are the set of primes. An integer in the set to 1000 that has prime factors that only contain the numbers in the set described is one of the numbers i wanna count

Ah alright

nice one

That'll be pretty complex

7:18 PM

yep. I'm so behind on CS that I don't have any hopes in making a program like this probably. Or it'd be so convoluted and complicated it would take too long to run lol

user image

Such a bad proof

@0celo7 did you learn the hamiltonian/lagrangian formulation of classical mechanics before learning GR?

and did u learn SR before GR as well?

@Obliv No

No

I still don't know SR

.____.

that really is an unnatural order of learning physics.

I have no need for SR

I'm not a physicist

7:23 PM

you have no need for GR either

True

You can do SR as math

But GR is an ends in itself

@Slereah It's pretty damn boring

@Obliv I think I'll try to implement that

But it'll be only in july

I need my calculator to be solving the halting problem by the end of the month

don't sweat it I might just work this out without a program

7:29 PM

what the hell is a tubular neighborhood, anyway

A neighbourhood

Like a tube

I think it's supposed to be like

A neighbourhood $V\times [-\varepsilon, \varepsilon]$

What

let us check Hirsch

@ACuriousMind Would a mathematician object to the notation $v^2$ for $v\cdot v$

The best comment on a tubular neighborhood I've found is that, just as a tangent space lets you approximate near a point, a tubular neighborhood lets you approximate near a submanifold, in other words you want to analyze the behaviour of a manifold near a submanifold & charts don't let you do that, and there is a generalization of the Weierstrass approximation theorem lurking nearby

@bolbteppa Hmm, it seems Milnor is using it to obtain a manifold with boundary from this compact boundaryless manifold

He first proves a theorem on a manifold with boundary

Then shows it even holds on one without boundary if we consider the tubular neighborhood

7:44 PM

Interesting

specifically

user image

where $N_\epsilon$ is the tubular neighborhood of width $\epsilon$

his notion of it is less general than in e.g. Lee SM

There is some link with Frenet-Serret too, I'm wondering if it's not just a generalization of something to do with that

The thing with frames on 3D curves?

@ACuriousMind How do you pronounce "Brouwer"? It's German

@BernardMeurer I know what FLP's facebook is.

Do you want it

Yeah, maybe it's tantamount to 'existence of a frenet frame on a submanifold' staff.science.uu.nl/~kolk0101/Books/Analysis/tubular.pdf

This is also nice, it shows easy cases of thickening a sphere or a level set math.ucr.edu/~res/math260s10/tubularneighborhoods.pdf

@0celo7 I've tried that before and I've been scarred for life

7:53 PM

@BernardMeurer Ok

Oh shit what's the proof that $\nabla f$ is the normal to level sets of $f$

Ayyy

@Slereah OOOOOOOOOO

The divergence is continuous so it will be positive in a neighborhood

pick a sphere inside of this neighborhood

ayyy

8:09 PM

@0celo7 completely forgot about the proof of that because it's basically just defined to be true in easy books, nice proof here mathoverflow.net/a/154983/38721

@bolbteppa I figured out the proof myself

My proof is this: let $c$ be a curve in the level set with tangent vector $v$ at $p\in f^{-1}(y)$

Then $df(v)=vf=d(f(c(t))/dt|_{t=0}$

but along $c$, $f$ is constant

so that's zero

and by definition, $df(v)=\langle grad\, f,v\rangle$

So clearly the gradient of $f$ is perpendicular to the level sets.

> For a source, there will be some ball around the zero such that every vector is pointing away from the zero.

I have to prove this...

The stupid multivariable calculus notation made it non-obvious, another triumph for formalism :p

@bolbteppa hmm?

I'm not doing calculus...ok well I am

But it's for the purpose of topology :P

Proving the Hairy Ball theorem a different way

8:43 PM

@ACuriousMind Ok, is this even true? If the divergence of a vector field is positive at a zero of the vector field is there a sphere surrounding the zero such that the vector field points outwards everywhere?

8:54 PM

What is energy? (I know this is a very stupid question)

@ramsay do you know what a lagrangian is?

@ramsay It's what KEGOC delivers to your house :p

@3075 no i don't know what it is :(

learn that first then you can learn the most general definition of energy.

@3075 The most general definition of energy is "Magic"

You mean the most general correct definition of energy :p

8:59 PM

Oh I see! Thanks @3075

9:26 PM

@3075 which is?

The capacity to do work :P

@0celo7 you don't know?

@3075 I'm not a physicist

I guess energy is just some conserved quantity associated with time translation invariance of the lagrangian.

because of noethers theorem.

@3075 but what about in theories where there is no time translation invariance?

9:31 PM

@0celo7 idk

The only theory that's so fucked up is GR :P

@ACuriousMind How is it defined in string land

@Obliv your post reminds me of people who complain that watching the news is depressing ;-)

zeroth component of the space-time momentum, I guess

@ACuriousMind I know that

@ACuriousMind Can you please answer my question about vectors

9:33 PM

@0celo7 Then we're at "What the heck was your question?" again? :P

It seems obvious but I'm at a loss for a proof

I probably need measure theory or something stupid to prove it

@0celo7 Which of the like 6 pings in my inbox is that?

@ACuriousMind lol

what are the six pings

50 mins ago, by 0celo7

@ACuriousMind Ok, is this even true? If the divergence of a vector field is positive at a zero of the vector field is there a sphere surrounding the zero such that the vector field points outwards everywhere?

You can probably safely ignore the others.

I'm trying to find the index of a source/sink

I know what the index of a sink is given that of a source.

So I'm trying to find that of a source.

That sounds as if it is true

So anyway

How formal should the AMA be

Do I need to wear pants while doing it

9:38 PM

@Slereah Only if you plan on taking pictures of yourself.

@ACuriousMind You claimed that the index of a source is +1, right?

How are you defining a source

I think I'd define it as a point the field points away from in all directions

@ACuriousMind Ok, then it's trivial :P

OH

I had another important message for you

4 hours ago, by 0celo7

@ACuriousMind Let $X^n\subset\Bbb R^n$ be a compact manifold with boundary. I'm trying to show that any vector field $v:X\to\Bbb R^n$ that points outwards on $\partial X$ is homotopic to the Gauss map of $\partial X$. What I found is that the homotopy $$F(x,t)=\frac{(1-t)v(x)+tn(x)}{||(1-t)v(x)+tn(x)||}$$ works.

4 hours ago, by 0celo7

Can you think of something more elegant?

I have no idea what the Gauß map is

4 hours ago, by 0celo7

You need the fact that $v$ points outwards so that the denominator is well-defined so it's actually a map to the sphere.

@ACuriousMind Wait, how are you defining the index then?

By some algebraic topology thing?

9:43 PM

The index at a zero is the degree of the map from those spheres you've been talking about the whole time, no?

@ACuriousMind The Gauss map maps a point on the boundary simply to the unit normal vector.

@ACuriousMind oh, oops

Yeah :P

Got things mixed up

The Gauss map maps a boundary point to a point on a sphere via the unit normal vector

But I've shown that any outward pointing vector field is homotopic to the Gauss map

@ACuriousMind oh I also asked you how to pronounce Brouwer

@ACuriousMind So if you define a source like you did, then the vector field on some small sphere is clearly homotopic to the Gauss map. But the Gauss map on a sphere is a diffeomorphism, so its degree is +1.

@0celo7 And I would know that how?

The guy was Dutch :P

Then, if $v$ is a sink, $-v$ is a source, so $-v$ has index +1. But since the index is defined via the degree which is defined with a determinant, we get $ind\,(-v)=(-1)^nind\, v$.

@ACuriousMind oh

And Wiki writes brʌu̯ər in IPA, so it's pronounced like an English speaker would pronounce it, I think

India pale ale?

9:52 PM

International Phonetic Alphabet

Have you never looked at those before? They're behind most names and non-English words that are titles of articles

@ACuriousMind Never even noticed it.

@ACuriousMind So no further comments on this?

Should I ask the math nerds

@0celo7 Nope

I know IPA yeah

I somehow had no doubt you would

@ACuriousMind Why did you not doubt that?

10:44 PM

I swear to god if I have to compile one more kernel today I'll die

10:59 PM

Hi guys!

@ACuriousMind I use $\sigma_i$ to indicate a polarization of a particle (i.e. lorentz little group index). If you know, a scattering amplitudes $1_{\sigma_1}2_{\sigma_2}\rightarrow 1_{\sigma_1}2_{\sigma_2}$ is the same of the process where the $\sigma$'s are reversed? For example, consider Weyl spinors and the $\sigma$'s the helicities. Then, If I flip the sign of the helicities, do I get the same result?

0

Q: What is the index of a vector field with positive divergence?

Let $v:\Bbb R^n\to\Bbb R^n$ be a smooth vector field with an isolated zero at $z\in\Bbb R^n$. Suppose that $(\operatorname{div}v)(z)>0$. Can we say anything about the index of $v$ at $z$? I know that if a vector field is a "source" in the sense that the field always points away from the zero, t...

multivariable-calculus differential-geometry differential-topology

11:25 PM

Howdy

Oh 0celo's back

cool

@SirCumference uh, no

No what?

@SirCumference I changed my name in solidarity

Er, no you didn't?

Or, lemme guess what it is

0celo8?

what

11:33 PM

K, guess it's not

@SirCumference what are you up to

know GR yet

Nope, focusing on stellar dynamics

Which is awesome in itself

how can you do that without GR

...or calculus

Okay, and you? Know GR from head to toe?

@SirCumference I know more than you, boy

11:40 PM

I know integration and differentiation. I haven't needed anything else so far

in how many variables?

1...

Goddammit man...

that's a shame, I need someone who knows multivariable analysis

And you thought I'd fit the bill?

Have ya met me?

@0celo7 I know that

Jk I don't lol

11:41 PM

@SirCumference No

@0celo7 That was a rhetorical question

@BernardMeurer ACM didn't even know

so I need someone smarter

@0celo7 I know programming with multiple variables, does that work for you?

I need someone who knows about degenerate gases

or Fermi gases, whatever you call em

I know about degeneracy

11:43 PM

@SirCumference I know about degenerate gases: It's when a gas listens to too much DJ Khaled

it becomes a degenerate

@0celo7 You sure do

Ok, in a partially degenerate gas, will all the fermions still occupy the lowest energy levels up to the Fermi energy?

@SirCumference I wear $100 basketball shoes, is that degenerate

Yes

ok I'm your man

@0celo7 Yes

11:43 PM

XD

I also listen to rap

like, a lot

I changed

A LOT

I'm a soft rock guy...

JEREMIAH

@BernardMeurer what

@0celo7 One time he says that

11:44 PM

@SirCumference Today I've watched a bunch of sneaker vids

When he's in the Bahamas

"I've changed... JEREMIAH"

about to go to the mall and cop some black Jordans

Out of the blue, he's insane man

@0celo7 Did you get sneakers or just watch them?

@BernardMeurer I missed that

@SirCumference Shit these were thousand dollar joints

I ain't about that life

My man Mayor got $25,000 Jordans

11:45 PM

With a thousand dollars, I'd buy a telescope instead of sneakers...

tho he got them for like a few k back in the day

Jesus

With a thousand dollars I can buy enough organs to live twice down here

@BernardMeurer mayor got AF1s with diamonds n shit

the little AF1 thingie is gold with diamonds on his joints

AF1?

11:47 PM

But, aren't shoes made to be dirty?

thas tight

@BernardMeurer Air Force 1, the shoe

@SirCumference Yeah, Mayor a pretty chill dude

@0celo7 I don't know about shoes man

They are the only thing separating you and the crud you just stepped in

He wears his expensive ass shoes

Pretentious

11:48 PM

@SirCumference Nah

There's people who buy shoes and never wear them -- they're shoes, wear 'em

What? Then what's the point

huh?

Of getting shoes you won't wear?

They look nice

It's literally spending money on something you won't use

11:49 PM

Hm

Thinking about it

Maybe my mistake is to use disk-shaped wormholes

I don't follow the logic, not to sound rude

I think square wormholes would go much better for computing field values on it

@Slereah Is that euphemism for weird sex?

(maybe)

"Weird sex"

11:51 PM

no such thing

there's sex and then there's not having sex

Bring your questions over here: sex.stackexchange.com

This is physics

@SirCumference but yeah you gotta have fly shoes

@0celo7 Out of curiosity, what's the question?

Howdy HDE

@SirCumference Hi.

11:52 PM

3

Q: What is the index of a vector field with positive divergence?

Let $v:\Bbb R^n\to\Bbb R^n$ be a smooth vector field with an isolated zero at $z\in\Bbb R^n$. Suppose that $(\operatorname{div}v)(z)>0$. Can we say anything about the index of $v$ at $z$? I know that if a vector field is a "source" in the sense that the field always points away from the zero, t...

multivariable-calculus differential-geometry differential-topology

Found a pretty intuitive site for learning about neutron star weirdness: astronomynotes.com/evolutn/s10.htm

And most of the quantum weirdness of space

Is "quantum weirdness" a term?

no

It should be

@HDE226868 so?

I haven't taken calc 3, this might be a well-known thing

Never mind, guess it is: books.google.com/ngrams/…

11:59 PM

@BernardMeurer How many times

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