The h Bar

Sir Cumference

01:27

@ShaVuklia He's 19...

0celouvskyopoulo7

@SirCumference I'm going to sue you

what did you say?

loltospoon

02:08

Hello all

If I compute the total energy of the particle in a box (potential = 0 inside box) analytically, I don't have to worry about normalization of wavefunction, correct?

Because I am doing it by the equation $E_n=\frac{n^2\hbar ^2\pi ^2}{2ma^2}$

NeuroFuzzy

@loltospoon ?? The quantity $\frac{n^2\hbar ^2\pi ^2}{2ma^2}$ doesn't depend on the wavefunction at all, sooo... yeah.

You set $\langle \hat{x}|\psi_n\rangle=\sqrt{\frac{2}{L}}\sin(\frac{n\pi x}{L})$, in which normalization is important, and find $\langle \psi_n | \hat{H}|\psi_n \rangle=\frac{n^2\hbar ^2\pi ^2}{2ma^2}$.

(IIRC. Might have some factors wrong)

(I guess L=a)

You don't have to normalize an unrelated $f(x)$ before you plug $n$ into $\frac{n^2\hbar ^2\pi ^2}{2ma^2}$, if that's what you're asking :p

loltospoon

02:48

@NeuroFuzzy ok cool, thank you

0celouvskyopoulo7

@Slereah check out figure 7 of Penrose

loltospoon

Another question: I am trying to compute the eigenvalues of the particle in a box with an added potential $V$. To do this, the strategy I decided on was to compute like so:

$$\langle H_{total} \rangle = -\frac{\hbar ^2}{2m}\frac{\partial ^2}{\partial x^2} + V$$
$$\langle H_{total} \rangle = -\frac{\hbar ^2}{2m}\frac{\partial ^2}{\partial x^2} + (V_0 + V_{new}) \quad ; \quad V_0 \text{ is the potential for the particle in a box, which is zero, and }V_{new} \text{ is the added potential.} $$

NeuroFuzzy

03:00

@loltospoon So, this might be better as an actual question on the site, but I can give you a run down.

Well... yikes... do you use Mathematica?

I can give basically a full answer in Mathematica no problem, haha

for numerically discretizing things

It's a fun problem :)

loltospoon

@NeuroFuzzy nah, I'm doing this in Swift, unfortunately

Using Mathematica would be a lot easier I hear

NeuroFuzzy

@loltospoon Yeah, to do it numerically you basically need a program to find the eigenvalues of a tridiagonal matrix.

0celouvskyopoulo7

@NeuroFuzzy whats up

NeuroFuzzy

@loltospoon this is going to be really ugly but, to solve it numerically for the case of an arbitrary potential V, you construct the following matrix (I came up with it using Mathematica):

$$\left(
\begin{array}{cccc}
\frac{\hbar ^2}{m}+V\left(\frac{L}{5}\right) & -\frac{\hbar ^2}{2 m} & 0 & 0 \\
-\frac{\hbar ^2}{2 m} & \frac{\hbar ^2}{m}+V\left(\frac{2 L}{5}\right) & -\frac{\hbar ^2}{2 m} & 0 \\
0 & -\frac{\hbar ^2}{2 m} & \frac{\hbar ^2}{m}+V\left(\frac{3 L}{5}\right) & -\frac{\hbar ^2}{2 m} \\
0 & 0 & -\frac{\hbar ^2}{2 m} & \frac{\hbar ^2}{m}+V\left(\frac{4 L}{5}\right) \\
\end{array}
\right)$$

That's your hamiltonian matrix $H$, with space approximated by 4 points. You can plug it into Schrodinger's equation to find the time evolution of the four points in space or w/e

or you can find its eigenvalues/eigensystem to diagonalize it

loltospoon

@NeuroFuzzy wait, why are some of the values $0$? I thought the entire matrix would be filled

NeuroFuzzy

03:15

@loltospoon oh, it's in the position basis right now

loltospoon

@NeuroFuzzy what does that mean?

Btw, I'm only an undergrad

NeuroFuzzy

So... you have your $\psi(x)$. But because this is in a computer space is discretized and it's actually a column vector: $[\psi(x_1),\psi(x_2),\psi(x_3),\cdots,\psi(x_N)]$

and now your operator $V$ sends $[\psi(x_1),\psi(x_2),\psi(x_3),\cdots,\psi(x_N)]$ to $[V(x_1)\psi(x_1),V(x_2)\psi(x_2),V(x_3)\psi(x_3),\cdots,V(x_N)\psi(x_N)]$

so it's just a diagonal matrix consisting of diagonal entries which are the values of the potential

say $${\bf V}=\left(
\begin{array}{ccc}
V\left(\frac{L}{4}\right) & 0 & 0 \\
0 & V\left(\frac{L}{2}\right) & 0 \\
0 & 0 & V\left(\frac{3 L}{4}\right) \\
\end{array}
\right)$$

eep, one of the V's being a function and one being an actual matrix

loltospoon

So then you're saying that to get it into the state $[V(x1)ψ(x1),V(x2)ψ(x2),V(x3)ψ(x3),⋯,V(xN)ψ(xN)]$

I need to multiply the $\psi(x)$ matrix by your $V$ matrix shown above there?

NeuroFuzzy

Yeah exactly

vzn

hey @NeuroFuzzy havent seen you around in awhile, nice to see you again, whats new? are you still an undergrad? what kind of prjs are you working on lately?

loltospoon

03:24

@NeuroFuzzy Hang on, I still don't understand why the $V$ matrix only have values along the diagonal. I mean, I can totally force my code to do this, but I don't get why

NeuroFuzzy

likewise you come up with a matrix for the kinetic energy, and then you add them, and you have a matrix for your hamiltonian which is of the above form (I actually forgot a factor). If you want to discretize space into 100 points you have a 100x100 matrix, but only the diagonal and immediately off-diagonal entries are zero, so it's a relatively easier problem.

@0celouvskyopoulo7 Nuthin'! Procrastinating!

0celouvskyopoulo7

@NeuroFuzzy me too

vzn

@NeuroFuzzy that reminds me of density formulation of QM...

0celouvskyopoulo7

I have about 20 papers to read and four books

NeuroFuzzy

@vzn Graduated from UCSD with a math and physics degree, accepted for grad school at UCSD! Theoretical condensed matter

7

0celouvskyopoulo7

03:26

Speaking of, I really should be playing Skyrim

NeuroFuzzy

@0celouvskyopoulo7 literally made a graph in mathematica to sort out which books i should read next

@loltospoon :( it would be so much easier to explain if you used mathematica haha. Can you tell me what you're trying to do again?

Write a program to find the energy levels of a 1D quantum particle in a box with an arbitrary potential...?

vzn

@NeuroFuzzy congrats dude great to hear :) ... hey did we ever talk about the Physics guest session? any )( possibility for you? think youd make very excellent choice, tons to talk about, chance to celebrate etc, plz think about it :) physics.meta.stackexchange.com/questions/7783/…

0celouvskyopoulo7

@NeuroFuzzy one of the books is 750 pages, and it's all PDE

I need to be 21 so I can have a steady stream of bourbon

vzn

@0celouvskyopoulo7 yeah whatever, what about the strip clubs? or is that 18? :P (which reminds me...)

0celouvskyopoulo7

I'm 10

NeuroFuzzy

03:30

@vzn ooh neat. I'll look into it!

0celouvskyopoulo7

It's still a way away

vzn

in theory salon, 9 mins ago, by vzn

The doctoral students of Richard Feynman / physicstoday

0celouvskyopoulo7

@NeuroFuzzy what math do you do again?

Condensed matter means algebraic topology

vzn

@NeuroFuzzy btw time to update your SE profile... not that anyone else seems to pay much attn to those... :| ... whats this QM problem with loltospoon?

NeuroFuzzy

@0celouvskyopoulo7 I'm trying to shy away from the math but I'm finishing up some commutative algebra and Lie groups stuff

0celouvskyopoulo7

03:32

Why would you shy away?

vzn

@0celouvskyopoulo7 lol, exactly

NeuroFuzzy

@0celouvskyopoulo7 Because at this point I'm becoming better at math than condensed matter >.>

0celouvskyopoulo7

That sounds perfectly reasonable

vzn

@NeuroFuzzy mathematical physics... if not married at least a LTR

@NeuroFuzzy its yours for the taking if you want it plz let me know am sure itd be great :) caveat: not for the faint of heart or those "shy" in any way :P

0celouvskyopoulo7

The problem with mathematical physics is that physicists think they can do it.

vzn

03:36

@0celouvskyopoulo7 lol you should start your own bumpersticker biz

0celouvskyopoulo7

Nothing against physicists but what they do is simply wrong from a mathematical perspective a lot of the time.

NeuroFuzzy

@vzn I'll think about it for sure, but miiight decline.

vzn

> An engineer thinks that his equations are an approximation to reality. A physicist thinks reality is an approximation to his equations. A mathematician doesn’t care. —anonymous vzn1.wordpress.com/quotes

NeuroFuzzy

@loltospoon LMK if you post a question on this, I'd be happy to answer. If you're writing a program to find the energy levels and eigenstates of a 1D quantum particle in a box with an arbitrary potential, I can definitely provide an answer.

vzn

@NeuroFuzzy awww hard "nos" hurt my feelings, just put it on indefinite consideration instead... :| ... why decline tho?

NeuroFuzzy

03:41

@vzn Lack of expertise and fear of appearing an authority figure and saying something incorrect :)

but i'm leaning towards yes

vzn

@NeuroFuzzy ok. think you will find the crowd very welcoming. we are not here to ding anyone, quite the opposite, think its more about enthusiasm & nearly cheerleading. no preparation reqd although welcomed if you have time. its meant to be low key/ informal by default, guests can take it wherever they want. keep in mind one of the guests was a ~14yr old girl enthusiast. (wonder whatever happened to @heather anyway, havent seen her in ages...)

@NeuroFuzzy theres a regular mtg coming up tues may30th morning (next one is 16th, next tues, too soon to get out advance notice). plz seriously think about it, let me know :) chat.stackexchange.com/rooms/info/71/the-h-bar?tab=schedule

loltospoon

@NeuroFuzzy I actually did, but as the background to a question I thought might help me get going on this. Feel free to respond: physics.stackexchange.com/questions/332594/…

vzn

@0celouvskyopoulo7 even better combine the 2... bourbon + strip club! sort of like Two Great Tastes That Go Great Together™ :P youtu.be/DJLDF6qZUX0

loltospoon

@0celouvskyopoulo7 are you seriously 10?

Avantgarde

03:57

lol

loltospoon

Why do we take time seriosuly? When I look around, I don't notice time passing by, I see reactions happening on the molecular level as a result of a history of events. So What we live in is just a serious of reactions. Therefore, can't we just ignore time?

Avantgarde

whaa

vzn

@loltospoon sure, if you can live forever metrolyrics.com/live-forever-lyrics-oasis.html

Avantgarde

You can ignore time, but then the world won't be Lorentz invariant. No one wants that...

Avantgarde

04:41

wow there's a Christianity stackexchange too

John Rennie

04:56

@loltospoon we can ignore the flow of time, and the result is the block universe. We can't ignore the time coordinate.

37

A: Is there a proof of existence of time?

It's easy to get mixed up between time and the flow of time, and I think you've done this in your question. Take time first: since 1905 we describe any event as a spacetime point and label it with four co-ordinates ($t$, $x$, $y$, $z$). Saying that time doesn't exist means we can ignore the time...

0celouvskyopoulo7

@JohnRennie Do you know the book "Stars and Relativity" by Novikov?

John Rennie

No.

amazon.co.uk/Stars-Relativity-Dover-Books-Physics/dp/0486694240

0celouvskyopoulo7

I am supposed to read it for reasons

Wonder if the library has it

I was told it's quite readable despite being a physics book

the library has a book "relativistic astrophysics"

John Rennie

It looks quite interesting, though I think it's about how matter behaves in relativistic conditions rather than GR itself.

0celouvskyopoulo7

544 pages, jesus christ

@JohnRennie My goal is to understand what sorts of equations of state people usually consider, roughly speaking.

I'm off to bed

cheerio

John Rennie

05:07

Goodnight

Xasel

hey just reaskign his, what's the interpretation of F(x) -g(x) > -infinity. I couldn't make a sense of this statement

John Rennie

Don't know, sorry.

Xasel

that F(x) is original function with domain R^n -> R

whereas g(x) has domain x such that all the values of x for which F(x) has loca/minimas

0celouvskyopoulo7

@Xasel ask me in 8 hours

Slereah

05:50

@0celouvskyopoulo7 wot

NeuroFuzzy

06:11

@loltospoon Had some time and put together an answer! physics.stackexchange.com/questions/332622/…

Sorry if it looks complicated. It literally boils down to writing the matrix D2, writing the matrix V, writing $H=-hbar^2/(2m)*D2+V$, and then finding the eigenvalues and eigenvectors of H.

You'll totally have to use a library or program to find the eigenvalues/eigenvectors.

Or else you can roll your own eigensystem solver... but I think that's a pretty serious amount of work, even just for tridiagonal systems.

Sha Vuklia

Guys, why do they compare the slow decay to $t\sim1/\omega$?

Like, what is the physical meaning of $1/\omega$ in this case?

NeuroFuzzy

@ShaVuklia the period of vibration is $2\pi/\omega$ so that means $t$ being a few periods.

Sha Vuklia

usually I'd say it has to do with the time of an oscillation, since $\omega$ is the angular frequency

yea, but in this case there is no oscillation?

NeuroFuzzy

oh true.

Sha Vuklia

i guess they just wanted something to make a comparison then..

NeuroFuzzy

06:18

I guess it's usually explained as the natural frequency. The frequency which would be there in the absence of damping

Sha Vuklia

yea

NeuroFuzzy

so the physical statement is that the spring creeps back to the origin on a timescale much greater than the natural period.

Sha Vuklia

hm yea makes sense

thx!

NeuroFuzzy

np :)

Slereah

@0celouvskyopoulo7 It's the book that contains the fact that the trace energy condition is rubbish

mathvc_

06:33

@ACuriousMind because there is a general solution for every group lol I did seeking for a particular solution for a space that its fundamental group is isomorphic to S_3. indeed i found the answer by acting S_3 on IR^2 that's simply-connected :)

am I right? S_3 is isomorphic to the group of rotation by angle 120 degrees and reflection?

Slereah

07:26

Hey @BalarkaSen

Balarka-san

Balarka Sen

Hi

@mathvc_ There are many, many ways to do this.

Slereah

Isn't $S^3 \approx SO(3)$

Balarka Sen

SO(2) is just S^1

Slereah

Hence the edit

user228700

Morning, everyone! :-)

Balarka Sen

07:31

m

John Rennie

@Kaumudi.H Morning

Slereah

Hence no reflections for $S^3$

Balarka Sen

@Slereah SO(3) is RP^3, however.

Slereah

You want $S^3 \sqcup S^3$

user228700

@BalarkaSen A minimalist, I see :-P

Slereah

07:32

Oh right, it's $SU(2)$ that's $S^3$

Balarka Sen

I'm a big fan of minimalism.

Slereah

So there's some quotient involved

Balarka Sen

(Waiting for Godot is one of my favorite plays all time)

@Slereah Right.

Slereah

"The Clouds" by Aristophanes is the best play

It's the greatest episode of the Simpsons

Balarka Sen

that's classic tho. i'm thinking of postmodern shits

John Rennie

07:34

postmodern shits ?

Balarka Sen

not to be taken literally

user228700

@Balarka: How is it that you're so enriched in cultures other than your own?

Balarka Sen

although there's a thing called "Artist's Shit" somewhere

John Rennie

@BalarkaSen I was wondering how you would apply moral relativism to going for a number two

Balarka Sen

:P

Slereah

07:35

Greatest joke from The Clouds :

STREPSIADES
What are they doing like that, all doubled up?

STUDENT
They’re sounding out the depths of Tartarus.

STREPSIADES
Why are their arse holes gazing up to heaven?

STUDENT
Directed studies in astronomy.

Balarka Sen

@Kaumudi I think everything is related. I am into my culture too, but I don't talk about that a lot because of obvious reasons.

user228700

Obvious reasons?

Balarka Sen

Different language.

Nobody really reads Bengali. Oh I guess by my culture you meant Indian. I don't really connected to India as much as I do to Bengal.

user228700

Ah, hmm, I see. I was only wondering how you've been exposed to so many different forms of art from so many different parts of the world.

Balarka Sen

@Slereah Huh

Interesting!

user228700

07:38

...it's not typical for a 17/18 y/o brought up in India is what I mean.

Slereah

It's a fun play because it's popular perception of philosophers in Ancient Greece

It's also probably partly responsible for a murder

Balarka Sen

i got teleported from the 60's

@Slereah What kind of murder

Slereah

(Some people back then have said that it may have contributed to Socrates' execution)

Balarka Sen

erk

user228700

@BalarkaSen -_- OK.

Slereah

07:39

Socrates does say that the gods don't exist a lot in that play

in hilarious ways

of course I'm pretty sure I don't get most jokes because I don't speak ancient greek

Nor do I know athenian pop culture

Balarka Sen

ancient greeks were strange

user228700

Anybody around here have BFRD?

Slereah

Not all that much

The play is fairly classic humor

Strepsiades is your classic bumbling dumb dad

Socrates is doctor Frink from the Simpsons

Strepsiades' wife is too good for him

Balarka Sen

lol

user228700

I was reading up about it and it seems that one in 20 people have it.

Slereah

07:44

His son is spending too much money

etc etc

John Rennie

@Kaumudi.H (Google, Google) Body-focused repetitive behavior ?

user228700

Yep.

user228700

Ah, BFRB, not D.

John Rennie

I depends how you define it. We all have mannerisms e.g. drumming fingers or pulling on ears.

I have a tendency to chew my knuckles when concentrating ...

user228700

Ah, I see.

Avantgarde

07:46

what;s BFRD

?

user228700

@JohnRennie I s'pose it would depend on the degree to which it is done.

user228700

Eg: Do u chew on ur knuckles till they start bleeding and can't chew anymore?

John Rennie

@Kaumudi.H Indeed. I just think you need to be a little cautious about statistics like 1 in 20 people have it since there isn't a precise point at which it becomes a problem.

@Kaumudi.H I'm currently typing this with the stumps of my fingers and there's blood all over the keyboard.

user228700

@JohnRennie -_- Nice.

John Rennie

:-)

user228700

07:48

I think it depends on when the habit starts causing serious harm.

John Rennie

In winter I get dry skin on my knuckles and I tend to worry at it. But I have never made my knuckles bleed as a result.

@Kaumudi.H Yes, I'd go along with that.

user228700

I mean, I'm pretty sure I have two of the variations of BFRB mentioned on the list: when anxious, I tend to pick my scalp (till, yeah, it starts bleeding & pains too much to go on) or I chew on the insides of my cheek till either it becomes bleedy and raw/all the skin to chew is gone. (Sorry for the grossness :-|)

John Rennie

Biting your cheek! That's disgraceful! I thought you were a vegetarian!!!

Slereah

she only eats vegetarians

user228700

-_- You're in a nice mood today...

John Rennie

07:51

It was supposed to be a joke - a poor one I guess ...

user228700

Nah, I got the joke and all :-P

Balarka Sen

i could make a self-cannibalization joke but i just woke up

John Rennie

Anyway my morning got off to a bad start.

user228700

Oh? :-(

John Rennie

I forgot to buy milk yesterday so at six a.m. I had to cycle to the supermarket to buy milk.

But ...

This morning MY (LATEST) NEW LAPTOP ARRIVES! :-)

So the day is looking up.

user228700

07:53

Ah, there you go! :-)

user228700

Man, am I glad that I only have to do this revision business for 4 more days.

Balarka Sen

the overwhelming question is, what next?

user228700

Mum says I should get a haircut or something; you know, signalling a significant change in my lifestyle and whatnot but I'm not too sure I will go along with that idea...

John Rennie

Four more days to go
Four more days of sorrow
Four more days of this old dump
And we'll be gone in four days

Traditional English schoolboy song.

user228700

@BalarkaSen I have a list :-P

user228700

07:54

@JohnRennie Eyy, that's fitting! :-D

Balarka Sen

well any list i ever make is trash after i finish my exams

but i guess not everybody is me

user228700

:-P No, no, I've been curating the items on this list for over three years, man. I'm gonna go through with them all.

Mithrandir24601

@BalarkaSen I still have my notes from first year somewhere underneath my bed...

user228700

Anyway, my head's been all bleedy and nice for roughly a month and a half now, so I am looking forward to it not being this way in 4-5 days.

John Rennie

@Kaumudi.H I've always found the post-exam period to be a bit of an anti-climax. You think you're going to feel ecstatic that it's all over, but in the event you just feel numb, tired and very relieved.

I wouldn't try and plan anything amazing. Just chill and do whatever you feel like at the time.

user228700

07:58

Yeah, I completely agree. I just tend to come back home and take a long nap first thing.

John Rennie

Te best moment is when you wake up the next morning and you're in bed thinking "I dont have to get up and work this morning!"

Mithrandir24601

@JohnRennie I believe you mis-typed 'very relieved' and meant to type 'stressed and worried that you are going to fail everything'

Slereah

"Non-vanishing vector field is a section of the spherization of $TM$, a bundle with fiber $S^{n-1}$."

Nooo

Not the sphere bundle

user228700

@Mithrandir24601 No, the exam I'm writing in 4 days is computer-based and displays the result as soon as it's over.

user228700

@JohnRennie I agree! :-)

John Rennie

08:01

@Mithrandir24601 actually no. I find that once you've finished the last exam the die is cast and your fate is out of your hands. So at that point I stop worrying. It's still stressful when the exam results arrive :-)

Mithrandir24601

@Kaumudi.H Huh. Fair enough then. In that case it's 'depressed because everything was a disaster'

:P

Although, really you'll be fine

user228700

:-P Yeah, no, if it doesn't go well, I'm probably going to spend a few hours crying in the corner first.

user228700

...which reminds me that I should get back to that sweet sweet revision :-/

Sha Vuklia

guys, why can't $\phi$ be zero?

John Rennie

@Kaumudi.H Only four days more!!

user228700

08:04

:-D YES!

Mithrandir24601

@JohnRennie Fair enough, I suppose. When I finished my final undergrad exam, I was ecstatic with relief that I wouldn't have to pummel my brain with insane physics that I didn't understand. That lasted until the next day...

@ShaVuklia it can, in the trivial case where everything is zero...

John Rennie

And now ... more coffee!

user228700

@JohnRennie Yeah, same here, I think.

Mithrandir24601

(or where there's no damping, or no driving force)

Sha Vuklia

@Mith why "everything"? As soon as $\gamma\omega_d\ll\omega_d^2-\omega^2$, we have $\tan\phi\approx 0$?

Mithrandir24601

08:08

@ShaVuklia hence no damping, or no driving force. The 'everything' was just because of the order my brain works in is 'check the trivial case first'

user228700

QQ: How to apply strikethrough?

Balarka Sen

@Slereah sphere bundle is pretty good

--- blah ---, without the spaces

~~blah~~

Mithrandir24601

@ShaVuklia But why am I just giving you the answer? (OK, technically, if $\omega_d = 0$)

user228700

~~Coffee! It's lunchtime though but who cares~~

user228700

Ah, yes! @Balarka: Thanks.

Sha Vuklia

08:10

they say the same as you later on

Slereah

@BalarkaSen But the Grassman bundle is $Gr(n,1) = P(n)$ D:

If there's a section of the sphere bundle, is there a section of the projective bundle?

I don't think so

or is there

I don't know

Balarka Sen

A section of the sphere bundle of $TM$ is literally a unit vector field.

Slereah

yeah, but the projective bundle is a direction field

Sha Vuklia

So if $\gamma=0$, then $\phi=0,\pi$. However, if $\omega_d\approx 0$, then only $\phi=\pi$? @Mithrandir

Slereah

Not quite the same

Balarka Sen

08:12

right

Mithrandir24601

@ShaVuklia to be fair, if 'everything' is 0, then the phase is undefined

Sha Vuklia

I still don't see why $\phi\neq 0$ when $\omega_d\approx 0$

Balarka Sen

@Slereah Oh, let me take that back. Grassmannian bundle fibers over the space of 1-dimensional subspaces of the fibers of $TM$ right?

A unit vector spans a 1-dimensional subspace of the tangent space it lives in

Slereah

Yes

Balarka Sen

So that should give a section of $Gr(n, 1)$ just fine.

Slereah

08:15

I guess so!

But is the opposite true

Mithrandir24601

@ShaVuklia First of all, do you mean when $\omega_d \approx 0$ or $\omega_d = 0$?

Slereah

If I have a direction field, does that mean I have a vector field

(non-zero)

Balarka Sen

@Slereah Mhm, should be, modulo a Riemannian metric.

A direction field is the same as a 1-dimensional subbundle of TM

Sha Vuklia

@Mith $\omega_d\approx 0$

Balarka Sen

Give it a Riemannian metric and look at the unit sphere bundle. Unit sphere bundle of the 1-dimensional subbundle sits inside that.

If M is orientable, that's just the trivial double cover. Choose out a section

Mithrandir24601

08:17

@ShaVuklia then, without even looking at anything, why would you expect $\phi = 0$ when, for small $\phi$, $\tan \phi \approx \phi$?

Slereah

but the double cover isn't the manifold, though

If I take the projective plane, there's a direction field, but I'm not sure there's a non-vanishing vector field

Balarka Sen

If M is orientable the double cover has to be M x {0, 1} --> M

orientability is super essential

Sha Vuklia

because $\tan\phi\approx\phi\approx 0$ ? @Mithrandir

Slereah

Because the thing to prove in particular is

A manifold that admits a Lorentz metric always also admits a time-orientable metric

So if I can define a Lorentz metric, I can define a nowhere vanishing vector field

Mithrandir24601

@ShaVuklia which is why I asked if you're looking at the case $\omega_d \approx 0$ or $\omega_d = 0$

Sha Vuklia

08:22

ok yea well i'll ask on the forum i guess, because i'm still confused

Slereah

Because a direction field being equivalent to a Lorentz metric is somewhat trivial to show

I need to check Steenrod I think

Sha Vuklia

I just don't understand why $\phi$ can't be approximately zero if $\omega_d\approx 0$, because if you look at the equation for the phase, it seems that $\phi\approx 0$ is also a solution

Mithrandir24601

@ShaVuklia Where does it say that it can't?

Sha Vuklia

technically, they don't say it can't. but my problem is they don't say it can

if $\phi$ can be $\approx 0$, then there is no reason not to mention that

Kenshin

yo peeps

Sha Vuklia

08:29

hi @Kenshin

Balarka Sen

sup bro

Mithrandir24601

Rytsas @Kenshin

Slereah

Hello

Sha Vuklia

ah i see something

look at this: @Mithrandir

it has to do with the sign, i think

wait

Avantgarde

yo

Sha Vuklia

08:34

hi @avant (again i guess:d)

Avantgarde

Hey @ShaVuklia :)

working through waves again?

Sha Vuklia

oscillations, technically

but yes :P

waves will be the last chapter

Avantgarde

go you

Mithrandir24601

@ShaVuklia I'm going to start again, hopefully better this time: Look at the original expression for $\tan\phi$ and tell me the different ways that it can approach 0

Sha Vuklia

you can have: $\phi\to 0^+$, $\phi\to0^-$, $\phi\to\pi^+$, $\phi\to\pi^-$ @Mithrandir

or do you mean $\tan\phi\to0^+$ and $\tan\phi\to0^-$

Mithrandir24601

08:39

So the question is, what are the different ways of getting $\omega, \omega_d$ and $\gamma$ to get these behaviours?

Slereah

web.archive.org/web/20090320002214/http://www.ecn.purdue.edu/…

Mithrandir24601

the first one :P

Slereah

in defense of the goto

Sha Vuklia

ok let me think

oh I see now

if we have $\omega_d\approx 0$

then we technically have a positive fraction

so we have $\phi\to0^+$ and $\phi\to\pi^+$

but $\phi$ must be $\in[0,\pi]$

so we are left with only $\phi\approx 0$ @Mithrandir

Slereah

Roki Vulovic - Panteri / Mauzer ,English Lyrics

►

Sha Vuklia

08:44

whoa ^

Avantgarde

nice song

GLORIOR BELLI - Backwoods Bayou (Official Video Clip)

►

Mithrandir24601

@ShaVuklia :D Now, what's the physical intuition as to why this is the case?

Sha Vuklia

oh god... the hardest part XD let me think

(i have no intuition :P)

i think you mean this

like yea i get why

we have technically a force that is changing very slowly

so, somehow, the spring force balances this

i don't know exactly why. like they say: the driving force balances the spring force, but that looks weird to me, because the driving force doesn't care about the spring force. i would rather think that it's the spring force that balances the driving force. but i donno

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