12:08 AM
I am 300% screwed if our professor puts a question from Preskill on our quantum final

Hi everyone :-)

"What is a density matrix?" kil me

I have a not-so-quick question about integrals and polar coordinates. I'm trying to understand the derivation in my textbook for the electric field at a point $x$ distance away from the center, $(0,0,0,)$ of a semicircular disc.
And absolutely nothing is making sense.
Alright, I'll wait for @JohnRennie.

@Kaumudi shoot
@GPhys it's the projector operator onto the state

ded

12:21 AM
?

@dmckee Perhaps, but when I look around my group, I feel particularly bad at it.

@G.Bergeron Really? OK, this is the picture in my textbook:

plus the probability for mixed states..

(They've done it in two different ways, both of which I don't understand at all)

I don't see the pic

12:25 AM
@Kaumudi I can help too if you still need help.

Yep. Still need help, don't understand much.

Well, how far have you gotten?

Not very far, but gimme a minute, I'll try one last time.

@Kaumudi Are you perfectly comfortable with Jacobians?

Nope, that's not a dot product. Anyhoo, I don't understand how that expression came to be, although I know that it is related to the fact that the expression for the electric field at the center of a circular ring of radius R is given by $KQx/{[R^2 + x^2]}^3/2$
@G.Bergeron Not at all. I graduated high school a few months ago and had to google Jacobians.

12:33 AM
@Kaumudi Not a dot product, yes.
@Kaumudi yes and no
@Kaumudi a full ring has more symmetry... and I suppose you want to say on the axis passing perpendicularly through the ring

OK, $dQ$ is given by $\lambda R d\phi$ and there's K and there's that other term, which is what I don't get.
@G.Bergeron Right...

I don't understand what K is either.

K is $1/(4\pi \epsilon_{\circ})$

@Kaumudi hmm... ok, all the "weirdness" of integrating in any coordinates disappear when understanding the Jacobians and such
K is the constant
@Kaumudi That other term is the vector going to the infinitesimal charge element to the point where your evaluating the field

But I don't have Jacobians in my syllabus :-|

12:37 AM
Forget jacobian.
Just focus on the fact that the area you get when you move $dr$ and $d\theta$ is $r dr d\theta$.
Why? Because $dr$ is the length of the the sides of the little square, and the lengths of the top and bottom are $r d\theta$.

@Kaumudi Listen to him, I just mentioned that as a general comment on how to deal with all that properly...

@Kaumudi if you move an the arc of a circle by angle $\theta$, the distance you travel depends on your radial distance from the center. The arc length is $s = r \theta$.
So, for a little tiny square in an integral, the area of the square is the arc length of the top/bottom multiplied by the length of the side.
$dA = r dr d\theta$

Its 1D here

Oh, woops.

@DanielSank We're approximating that little triangle to be a rectangle? OK...

12:39 AM
Well, she can figure it out now anyway.

@Kaumudi arc lenght is $ds=r d\theta$

so bits of charge are $dQ=\lambda r d \theta$

Ik, Ik. I get how the area is $r dr d\theta$ and why $dQ=\lambda r d\theta$.

@Kaumudi not related to this problem
You want to sum up the contribution to the electrical field from all the bits of charge
Hence $\sum d\vec{E}$
Or more $\int d\vec{E}$
Because it is infinitesimal bits of charge

12:42 AM
Yeah. Area integral? (Idk what that's really called :-P)

This would be for a charge sheet

Yeah, sorry, I misunderstood the problem and mentioned area.

But it's a disc.

Here you wave charges spread out over a 1D object

Hahah we're all so confused.
Is it a disk or an arc?
1D or 2D?

12:43 AM
Hang on.

it says ring
so arc
And R is not integrated over so it has to be a ring
1D

Wtf >.< All this time, I've been trying to understand it thinking it was a disc.

It says ring in the question

Good, now we got this sorted out.

So what is $d \vec{E}$?
we know $\vec{E}=q \hat{r}/r^2$
(I ditched the constant)
(... because I'm a mathematical physicist :p)

12:47 AM
Right... (:-P)

If a guy is trapped in a windowless room with only a Foucault's pendulum, how can he tell if he is in Langely, Virginia or Guantanamo Bay without doing any calculations? Is there an easy way that someone can figure out how close they are to the 45 degree mark vs. the 0 degree mark (the equator) without doing any calculations?

so $d\vec{E}=dQ \frac{\hat{r}}{r^2}$

No, hang on.

I know how he can find out by doing a quick calculation, but the guy is not allowed to have a calculator.

@whatwhatwhat By getting the lattitude...
$\omega = 360 \sin \phi$, $\phi$ is the latitude and $\omega$ the rotation per day
$\sin(0)=0$

12:50 AM
Are Langely, Virginia and Guantanamo Bay the only places with Foucault pendulums in windowless rooms?

If it doesn't rotate then it,s the equator
Are you planning on being kidnapped by black ops and are curious to know if you can know where you are after?

@G.Bergeron Right.
Um..?

So now I do $\int d\vec{E}= \int dQ \frac{\hat{r}}{r^2}$, but $\frac{\hat{r}}{r^2} = \frac{\vec{r}}{r^3}$ so $\vec{E}=\lambda \int \frac{\vec{r}}{r^2} d\theta$

@G.Bergeron I shouldn't have mentioned the part about the 45 degrees vs. 0 degrees, I see that it was a confusing thing to ask. The actual coordinates of Langley Virginia is 38 degrees North and that of Guantanamo Bay is around 19 degrees North. The problem is difficult because the locations are both in the Northern hemisphere, so they will rotate in the same direction.

Now find the coordinates of the vector going from the point at $\theta$ on the ring of radius $R$ to a point of z coordinate $x$

12:56 AM
I made a ~30 cm Foucault pendulum when I was an undergraduate
took some fiddling to get the driving magnet stable
more fiddling than it's worth, would not recommend

Technically, the pendulum was built with a cable attached to the ceiling and a bowling ball. Is there another way to tell where he is by taking apart the pendulum??
Which is totally allowed.
Maybe he can roll/spin the bowling ball in a certain way?

Right, and this $r$ is the vector from $(R\cos \phi, R \sin \phi, 0)$ to $(0,0,x)$ so $\hat r = -R \cos \phi i - R \sin \phi j + x k$.

maybe, if you attach a string to the bowling ball and hang it from the ceiling, you can make a Foucault pendulum and measure your latitude!

38 is almost like 45 so $\sin(45)=1/\sqrt{2}=0.7...$

or at least the absolute latitude

1:00 AM
@Kaumudi yes now calculate the norm and integrate each coordinate of the vector integrand separately.

The "norm"?

So if it takes a bit less than a day and a half you are in Langley
@Kaumudi Ugh... the length of the vector
But if you don't know that, allow me to ask why the heck are you trying to do electrostatic and vector calculus?

Okay. (Length of vector = Norm, BTW?)

yes

I see.

1:03 AM
Was it just an issue with translation?
or whatever something like that
Because I don't know your curriculum but I remember fiddling with vectors in high school

No, I actually didn't know what "norm" is. Magnitude is all they teach u in high school.

ah, so just terminology, phew
otherwise you could understand my concern

Lol, yeah x'D

I tend to use this word more because it's shorter and what it is in french
Strictly speaking magnitude is a bit better because norm is when you see a vector space as a normed space
as a metric space
Can you do the problem now?

@G.Bergeron And here we go again. I dunno what a metric space is :-P

1:07 AM
@Kaumudi it's normal
@vzn I could do that, yes. Although I am not sure if people would be interested.

@G.Bergeron yea that makes sense. I'll just add an assumption: "Assume the guy is competent in mental math..."

@whatwhatwhat And assume the guy would understand enough parallel transport of vectors on a sphere... It's not the kind of formula you learn by heart, you rather write them down because you understand the phenomenon.

Alright, I can do it know. Thank you :-)

nice

@G.Bergeron I was going to use $T=\frac{24hours}{\sin(latitude)}$. Were you thinking of a different formula?
Wait a minute, the guy has no way of keeping track of the time!!! Even if the period of Langley should be approximately 39 hours, how can he measure this?!

1:19 AM
@whatwhatwhat why would you know this formula
why I based it on days. I hope he can see the difference between the night and day

@G.Bergeron "windowless room".

well there is no way at all
Unless climate
But if there is AC, and no more tool than a bowling ball and a rope he's toasted
He could try counting/pacing if desperate, it's not as bad as people think
Or use his hearthbeats lying down as a tempo as Galileo

1:51 AM
@G.Bergeron cool, if you have something to say about physics, can assure you ppl will be interested. will be there for 1 at least. can you do 2nd next mtg/ session tue dec 27th 1600Z? chat.stackexchange.com/rooms/info/71/the-h-bar?tab=schedule

@vzn Probably, but I have to check something before knowing exactly. How long is it?

@G.Bergeron crap, now I'm in that limbo/grey area where I don't know exactly what the professor thinks and if I say something like "Assume the guy can keep track of time really really well" then he could respond with "You should have realized that that's allowed/not allowed". Le sigh.

2:06 AM
@whatwhatwhat THIS IS A HOMEWORK QUESTION!?!
This is an awful question!
If it is a mechanic class, he expects a Foucault pendulum

It's a mechanics question that he made up himself....

And you don't need to keep track of time that well, only enough to separate the two. Allow for uncertainty

Yea, I see how it's basically no other way to do this besides using F-pendulum
Could anything be done with the Coriolis force, or no?

@whatwhatwhat Also, "You should have realized that that's allowed/not allowed" you are allowed to argue with the professor about that.

@G.Bergeron in a perfect world, sure. Not with this professor though.

2:09 AM
At uni, they are not gods anymore with respect with grading
You'd be surprised
There are resources for that, ombudsman, etc.

I am teaching a general physics II lab next semester

But you have to have a strong point... If you shake earth and sky for 2 grade points on a homework, well...

I have been informed the students in this lab are ~95% pre-med students
and that this means I should expect complaints about every grading decision I make

@GPhys Hey man, long time no see :)

2:11 AM
at least I only grade their lab reports
@BernardMeurer finals in a couple weeks

Yeah, have my finals this week

chances of failing: Quantum: 100%? Dynamics: Low?
?

I might pass Chemistry

But my advisor asked me not to be TA because I obsess over validity of correction, meaning it ate through a lot of my time

Yeah you should never care whether you're giving students a fair assessment :P
We're scum anyway

2:13 AM
Yeah but that led to no complaints at all
As an undergrad I was constantly seeing the TAs as they didn't know their shit at all

@G.Bergeron I appreciate the TA's like you, I really do
I might not be your student, but thank you ;)

Arguing on some points... sometimes with professors too

I'm just teaching a physics 2 lab and grading lab reoprts
how complicated can it be

@GPhys@G.Bergeron are you both professors?

No problem. But do know that doing this requires A LOT of time. You just want to give everyone zero, but resist the urge. But then, it's trying to rate people on how not wrong they are. I am exaggerating a bit, but it is the feeling I got.

2:15 AM
They're PhD Students

yeah

Oh ok

@GPhys Do something with lasers
and blow something up

Is it just me or is an undergrad physics degree all about appeasement and memorizing things?

Trust me, I'm one
@whatwhatwhat You're probably just in a bad course

2:16 AM
@whatwhatwhat no that's chemistry

It's like my Chemistry

@whatwhatwhat I never memorized a single thing

@G.Bergeron That's a lie and you know it

Or maybe a bad university. But that's all it feels like :(

@BernardMeurer Nope, I also almost never did exercises
@BernardMeurer This is not how I work, I just read and read the books.

2:17 AM
@G.Bergeron Really You really are saying you have never ever memorized a SINGLE THING?
Come on man, that's not true

I was a "bad" student, missing a lot of lectures and such
@BernardMeurer In uni

If you read the books and remember what you read that's memorizing, no?

Does it get more interesting once you do your PhD? I guess the answer is probably an automatic yes based on the definition. My problem right now is that while one can argue that a base level of physics knowledge is important, there are some things that I just. don't. care. about.

Last time I memorized stuff was in grammar courses
@BernardMeurer Ok I thought you meant rote memorizing, but still I cannot recite you the book
If you understand what is going on, you can rederive the important stuff at the beginning of the exam
But anyway most exams you could bring a sheet of wahtever you wanted
or open book

@G.Bergeron I took some graduate math courses like this

2:21 AM
Only some math courses would have required a bit of memorization, but I just lost those grades
I mostly take graduate math class now

@G.Bergeron only 1hr but can go longer if you have time. convention is the speaker posts to meta introducing oneself with bkg, topic, date. this gives notice. the mtg will also be publicized by mods.

And you could always weasel out of learning something by "cheating" on homeworks, but if your still doing that at this point, well, whatever.

I'm disliking undergrad physics so much that I'm thinking of switching to computer science for grad school.
:/

@whatwhatwhat Used to think like that, but at some point you gotta work
I hated homework as I was always doing them in the night alone the day before, while having missed most lectures... So it's you and the book.

@whatwhatwhat cs is totally respectable =D ... drop by chat room sometime if you feel like it

### Computer Science

General discussion for cs.stackexchange.com

2:24 AM
But that got me to understand way better than the large study groups you sometime see

@vzn I will, I have some things I'd love to discuss :D
@G.Bergeron studying only from the book did that?

@whatwhatwhat yes
Mostly impossible in graduate class though

@whatwhatwhat there are a few near-computational physicists who hang out in here too... alas one sharp one CW left, but kyle kanos still visits, he works in comp finance now. what topics are you thinking of? which reminds me, also lots of nice interface between CS & physics these days...

When you miss a couple lectures, even if you show up, you understand nothing, so what's the point?

I prefer book reading already. In lectures, I get distracted when I start thinking about a concept mentioned by the professor. So while I'm thinking about that, the professor goes on of course. But then I've missed so much that it's pointless to try and rejoin. And it's embarrassing to ask something and then the professor says "As I already mentioned,..."

2:27 AM
A ton of graded homework saved me so that I do not do everything the night before the exams...
@whatwhatwhat Until you realize almost nobody really follow the class

@vzn AI/machine learning architectures

Oh exam weeks are BAD memories! 8(

@G.Bergeron then you have just confirmed what I've had to argue with my family about. I just can't follow a lecture for 1 hour and 15 minutes while sitting in a desk and listening.
It's pointless.

@whatwhatwhat ah cool specialize in that myself over the years. see eg vzn1.wordpress.com/category/ai ... alas SE maybe is not so well suited to the topic currently :( ...

I learn better by working through an example and asking question as I go

2:29 AM
@whatwhatwhat but what does it have to do with your family?

Because of my bad studying habits, I ended up sleeping 2-4 hours for like 5 days in a row studying for the next exam each night
It messes with your sanity at some point

@GPhys They would ask me why I wasn't going to class that day and I would try to explain. They never understood.

Yes, but I'm not saying what I did is good
@whatwhatwhat I think this would apply to everyone but then there are not enough resources for that...

@G.Bergeron I know what you mean.
So then I figured that if going to class is pointless, I would only study at home. So I would ask my friends what topics were covered in class so I could Google it later.

bill gates liked to skip his college classes too... took some inspiration from him & found it didnt work too well for me as freshman o_O

2:32 AM
And then the stress, because I wanted grants and needed almost perfect grade... The degree had to come to an end at the end or I'd end up in the psych ward XD

I paid for my own college my family can suck off (wrt whether or not I go to classes)

@vzn I think it's much better to go to class and do exercice even if not graded and all and all, I'm just not able to

@GPhys lol I'm paying for myself but I'm living at home. They like to comment their opinions.

@GPhys Of course

@whatwhatwhat (totally sympathize wrt comatose lectures.) have you tried online content/ courses? coursera etc

2:34 AM
Here university is really cheap so it cost me almost nothing
like 3k$/year @G.Bergeron 3K/year ?!!?!??!?!? WHAT?!?!?!?! LOL ARE YOU TAKING CLASSES IN HEAVEN??? You know it's free in some part of the world, right? .............................................no.................................‌​............... 2:35 AM @vzn I like books omg @G.Bergeron <3 books @vzn I can take as many online courses as possible, but at the end I need a degree. I'm in Canada, in the province of Quebec and education is heavily subsidized @whatwhatwhat they are probably good at reinforcing classroom stuff... fully understand... looking fwd to day when diplomas for passing online courses (eventually?) materialize... 2:37 AM @whatwhatwhat You do know that some states are more socialist, no? Like with healthcare, education, etc. Oh I see. Yea I'll check out some stuff on coursera. My friend did mention something about QM topics on coursera but I'd forgotten (was a long time ago). @whatwhatwhat Grad school is more, but now I have grants @vzn Khan Academy is working on this. @whatwhatwhat you are in the US, I suppose? @G.Bergeron Yea, but I didn't make the connection with the free education part. Would I get in trouble if I leave the country to get a degree and come back? Would my degree even be accepted here? 2:39 AM There are days when I find myself wondering what the highest facepalm multiplicity on the internet might be. Yes I'm in the U.S. @whatwhatwhat its (academia) a very political/ entrenched system. its like the john lennon song. your saying its the institution... And thinking we might need to apply a raising operator to it. @whatwhatwhat it might be accepted by companies (depending on where earned), but not nec by universities for further study... @vzn I agree. It's funny - when you say you don't want a degree, people look at you strangely. But when you say that you want to study high level math/physics without going to college, they still give you the same weird look... 2:41 AM @vzn You can get one today. You can even get one today from an accredited institution which is the real barrier that the existing system puts in front of change. @whatwhatwhat everything is topsy turvy these days, higher edu is going thru major phase chgs. its getting out of control in many ways... have blogged on this... Accredidation is an expensive process and forms one of the basic overheads to being a higher education body that "counts". @vzn Come on it's a Canadian university, of course it is accepted @dmckee youre talking about online-only degrees? what "real barrier" are you referring to? @dmckee yes got in a long discussion about ABET in the cs room awhile back... its the engr degree accreditation org and it is defn not weak/ pushover. @whatwhatwhat The only problem you will have is that as not a citizen, you will pay full tuition over here 2:44 AM Oh well then nvm lol @dmckee huh? @whatwhatwhat Still cheap compared to some places. I think it is around 15k$

Mine is 42k/year with no scholarships and without living on campus

@vzn You can get good on-line degrees from several places now. ASU does one in physics. But they don't save a huge amount relative in-person degrees for several reasons.

@whatwhatwhat :S

2:48 AM
@whatwhatwhat @#%^ o_O ivy league?

@vzn no, just a private school. Illinois Institute of Technology

@whatwhatwhat What is a private school at the university level?

I got into University of Illinois - Urbana (top 20 program in the nation), but couldn't afford it :/
Like, not funded by the govt.

@G.Bergeron A non-state institution that calls itself a university.

Urbana is a public school, for example.

2:50 AM
@whatwhatwhat What it gets to more than 42k?!?!??!

@whatwhatwhat personal question, feel free to skip... are you borrowing money for that?

In this case they do teach graduate courses so the label is deserved.

@vzn Yep, loans and scholarships reduced it substantially, so I'm not starving. Yet.

@dmckee yeah think someone will do it for less money & still with accreditation. but not many students can handle it anyway...

@G.Bergeron My current university is private
one sec, let me check the undergrad cost

2:52 AM
When I see stuff on college education not being worth it on the internet, I subconsciously picture my situation and disagree. But if I had to pay up to over 50k/year just for the tuition, well, I don't know

The first google result says $63,472/yr WTF!!! that sounds low let me check the official website Do most people pay it or most have some kind of backing according to official numbers, the College of Arts and Science yearly cost is$77,409
hahahah the arts school is $82,229 2:54 AM That can leave you with upwards of 300/400k$ in debt O_o

I don't know, I'm in graduate school so it's paid anyway

@GPhys Course fees for the practicals are a bear, aren't they? Of course physics students pay a lot for that sort of thing, too.
But I think the chemists have us all beat.

So the fees vary by degrees also?

@whatwhatwhat lol loans are not exactly a "reduction" esp when you factor in interest :|

@dmckee Unfortunately the living expenses are quite a hit here in Manhattan
I went to an in-state R2 university because it meant I could get a massive scholarship
I was able to pay for 100% of my education without taking loans by applying for competitive scholarships and working over the summer (not even during the school year)

2:56 AM
I still find the notion of a private university funny... Is it a for profit organization?

@G.Bergeron At my place some courses cost extra. In particular all the for the major courses in Chemical and Physical Science have fees attached to maintain the equipment needed.

combined with the large scholarship the state government gave for attending a state uni (and getting some fixed score on a college admission exam)
I figured I could go to a better grad school, and so I did

@G.Bergeron They are often organized as non-profits, meaning that any money they make gets plowed back in.

@GPhys Yeah I live of grants and scolarsip

But they are not run by the government.

2:57 AM
@dmckee But then why so high a fee?
To they have like golden backed blackboards?

@G.Bergeron Low student to professor ratio in class, and even lower overall because the professors get a lot of release time for scholarly activity.
Plus the good ones pay high salaries to attract the best faculty.

What kind of salary are we talking about?

actually that was a pull here
the university has been stealing condensed matter guys

They often have the nicest facilities and they generally offer very good networking to help you build an elite career.

@GPhys Wait a minute I think I have an idea now

2:59 AM
@G.Bergeron Six figures US by the time you get tenure. More in places with high costs of living. Going up to enough to worry about the alternative minimum tax.