The h Bar

0celo7

06:18

If a book cites an article for a piece of information what citation do I write?

GBeau

@FenderLesPaul just got an email from "Chairman Dept. of Physics...[rest cut off]"

email from school I didn't apply to, suggesting I apply to them

DanielSank

Whoever downvoted this

3

Q: What is the "interaction picture" or "rotating frame" in quantum mechanics?

$\renewcommand{\ket}[1]{\left\lvert #1 \right\rangle}$ In typical quantum mechanics courses, we learn about the so-called "Schrodinger picture" and "Heisenberg picture". In the Schrodinger picture, the equation of motion brings time dependence to the states, $$i \hbar \partial_t \ket{\Psi(t)} = H...

quantum-mechanics

I'd really appreciate knowing why.

0celo7

@DanielSank please answer my citation question

DanielSank

@0celo7 Link?

0celo7

13 mins ago, by 0celo7

If a book cites an article for a piece of information what citation do I write?

DanielSank

06:31

@0celo7 Question unclear.

You are looking for a reference for topic X.

You find it in book B.

Book B simply states X, and refers to article A.

You look at A and find a completely description.

0celo7

Hawking-Ellis cites an article that says spinor equations may always be replaced by tensor equations.

I can't access the article.

DanielSank

I'd cite A preferably, but both if you can, 'cuz why not?

@0celo7 Ah.

Then cite the book and "references therein".

0celo7

It's an obscure-ish journal from 1937.

DanielSank

@0celo7 If you can't read the article don't cite it.

That would be dishonest IMHO.

Cite the book and note that it contains further useful references. It's all you can do in your case.

0celo7

@DanielSank Hmm, maybe you can find inspirehep.net/record/44924?ln=en

I'm dumb

user54412

06:36

What's really frustrating is when a citation trail ends at an article that clearly doesn't contain the claim that everyone cites it for.

DanielSank

^ Yes.

That should be illegal.

0celo7

you have got to be kidding me

fucking paywall

I'm at a research university ffs

DanielSank

@ChrisWhite Astrophysics references to "quantum fluctuations" tend to end like that.

@0celo7 You're on their network?

They can't buy everything.

0celo7

@DanielSank yup, in the dorm

DanielSank

You just said it was an obscure journal.

0celo7

06:38

journals.cambridge.org/action/…

Mike Miller

That's pretty bad, but I also hate when it's personal communication, or an unpublished paper.

0celo7

@DanielSank turns out to be published by Cambridge

DanielSank

@MikeMiller Yeah, citing personal communications is stupid nowadays and I think no longer allowed in most journals. Decades ago before digital storage, it made sense.

0celo7

does anyone else have access to that article?

DanielSank

You couldn't just staple a twenty page supplementary to every article.

Mike Miller

06:39

@DanielSank Everything is field-dependent. It still happens in math.

DanielSank

@MikeMiller Woah, really?

@0celo7 Paywall for me.

Mike Miller

Everything is field-dependent. I bet you couldn't think of very much that isn't.

DanielSank

Sure sure.

0celo7

paywalls

@DanielSank :/

DanielSank

@MikeMiller I'm just surprised that in the age of digital storage any respectable journal would allow citing something you literally cannot ever find.

@0celo7 Yeah, :/ for sure.

Mike Miller

06:40

@DanielSank: vOv

DanielSank

^ shrug?

Mike Miller

Ayup.

0celo7

@DanielSank especially because it seems interesting

Mike Miller

There's also the unpublished papers that nobody ever gets around to writing, even though they know the result.

0celo7

but it also would make a nice footnote in my answer!

DanielSank

06:41

@MikeMiller Given that arXiv now exists, I find that kind of lame.

Mike Miller

It's sometimes amusing in math to see a bunch of papers around a period cite each other in no sensible chronological order, because eveyrone is looking at everyone else's papers.

DanielSank

People should publish their technical notes, etc.

@MikeMiller Heh, yeah.

0celo7

I guess I could ask the librarian to obtain it...that might work

DanielSank

Hey so, @MikeMiller, in a nutshell, what math is humanity working on in the modern day?

0celo7

I doubt the library has a copy of the paper journal

DanielSank

06:42

What do we not understand?

Mike Miller

@Daniel: What do we understand?

0celo7

Library of Congress might have it

@MikeMiller Quadratic equations

Mike Miller

I can tell you about the little corners of math that I know a lot about. I can say some of my favorite problems. If you want a summary, see the Princeton companion.

DanielSank

@MikeMiller Well, I'd say calculus is in the bag for the most part. We've got the whole abstract algebra basics down. Are there outstanding things there? What's the story on the Riemann hypothesis?

0celo7

I think we have compact 2-manifolds covered.

DanielSank

06:43

And where's my proof of the Collatz conjecture, dammit?

Mike Miller

@0celo7 Nah. The mapping class groups people still work on those.

0celo7

where's my proof that spinor equations have equivalent tensor cousins

PAYWALL!!!

I should go Kylo Ren

throw a fit

Mike Miller

@DanielSank It sounds like you might be surprised to hear that yes, people still do work on algebra, given that it's at least 25% of most departments. Riemann is still wide open. It would be cool of Connes would solve it but I'm making no bets.

DanielSank

@MikeMiller What algebra thingies are still out there?

Broad strokes.

Mike Miller

I am not an algebraist.

0celo7

06:46

@DanielSank the conjecture that spinor equations have related tensor equations

I hear it's very difficult to prove

Mike Miller

I would broadly lump people into representation theorists, category theorist, algebraic geometers, number theorists. This is not really correct but it's close enough.

0celo7

in fact, Cambridge university requires a $45 tribute to prove it

DanielSank

@0celo7 Woah, what? Really?

0celo7

@DanielSank yeah $45 of difficulty

DanielSank

^ LOLOLOL

0celo7

06:47

they must sacrifice a goat after all

DanielSank

@MikeMiller I sat in an algebraic geometry course for a week once. I perceived that it was the most interesting thing I could possibly study, and then stopped going because I couldn't follow it all.

I was sad about that.

@MikeMiller got time for a quick math question?

Mike Miller

I have seen that happen before.

The answer is yes, I do have time, but I make no promises I'll attempt to answer.

DanielSank

Ok.

Mike Miller

I do promise I'll stop you before you get too into it if I xpect I won't.

0celo7

great the library of congress does not have the article

meaning I have to hunt down the volume of the journal

DanielSank

06:49

I asked a cute puzzle on the puzzling site a while back. It's the old random walk with absorbing boundary conditions.

The variety of approaches posted is really awesome!

I too posted an answer using generating functions. It should be easy to follow as I included most of the details.

user54412

@DanielSank I actually cited a personal communication for data (though I think it was resolved into an actual publication in the final draft).

DanielSank

In doing the calculation, I had a sum $\sum_n f(n) z^n$, which I was able to.

0celo7

@ChrisWhite can you access the article :/

DanielSank

However, I then took $z \rightarrow 1$ at the end.

user54412

distracted, give me a few minutes

DanielSank

06:52

If you observe the plots at the end of the answer, you see that as $z$ approaches 1, the solution curve goes from being smooth to developing a cusp.

Mike Miller

Does it still converge at 1/2 for z>1?

DanielSank

Aha!

Did you see the plot at the end?

Mike Miller

Yes, but of course I can't say from the plot.

DanielSank

@MikeMiller Oh? I thought the violet curve shows that it does not converge.

Mike Miller

@DanielSank: It says that it grows extremely quickly in the given domain.

But I did not see the bit in your naswer where you say it diverges.

DanielSank

06:54

@MikeMiller Oh, I see your point.

Mike Miller

So I believe you.

Not really making a point, was just saying it wasn't obvious from the picture to me it diverged.

DanielSank

@MikeMiller yes, and now I realize that I'm not sure whether or not it does!

Anyway, I would like to ask if you can offer any kind of insight as to what $z>1$ means.

I cannot come up with a particularly interesting physical intuition.

I find it somewhat compelling that the curve develops a cusp and then "breaks" (assuming it does actually diverge at $p=1/2$).

Mike Miller

I don't have much interesting to say, no.

DanielSank

@MikeMiller Ok, thanks.

Mike Miller

No need to thank me for something I haven't done :D

I have to play the copy of LISA my friend bought me at Christmas tonight.

DanielSank

06:58

@MikeMiller Thanks for your time. I think this is sort of like baby algebraic geometry, right?

The shape of solutions to equations as one varies parameters, etc.

Mike Miller

Mm, I wouldn't say that's what algebraic geometry is, but deformations are certainly part of it for sure.

DanielSank

@MikeMiller I was under the impression that the topology of solution sets as equations are deformed was sort of the basic starting point.

Mike Miller

I would probably not say that, no, since it's not covered in Hartshorne in detail.

But I am not an algebraic geometer.

0celo7

I found 2014 article that cites that article

so someone has access

(or they're cheating)

user54412

07:15

@0celo7 Is there a link to the article? All I find are references that it exists.

0celo7

@ChrisWhite journals.cambridge.org/action/…

or is that what you're talking about?

Sir Cumference

God I love knowing how to integrate functions

0celo7

@SirCumference Want a challenge?

Sir Cumference

Every time I look at something on Wikipedia and see an integral, I know I have a chance at understanding it

...

Um...

Okay?

0celo7

Let $f(x)$ be the function $=1$ if $x$ is rational and $=0$ if $x$ is irrational. What's $\int f(x)\mathrm{d}x$

user54412

07:18

@0celo7 Yeah, I've got it

Sir Cumference

Sigh, I didn't learn how to integrate piecewise functions...

Okay, walk me through it?

0celo7

@ChrisWhite would you mind emailing it to [email protected]?

@SirCumference don't know how to do it

Sir Cumference

._.

Well...anyway, calc is sorta easier than I expected

At least it is for now. All I gotta do is memorize stuff. Not having much difficulty understanding it.

0celo7

@ChrisWhite Thanks, for some reason gmail sent you email to the spam...the webmaster ppl really need to fix that

user54412

Yeah, you guys have issues

0celo7

07:23

@ChrisWhite Hmm?

user54412

We had problems for a little while when everyone had the local cluster email their jobs' progress to their gmail accounts, rather than their .edu accounts.

0celo7

There's an issue with the gmail-.edu interaction

user54412

Google saw all the spammy looking mass emails going from Princeton to Gmail and concluded Princeton was a spam hub.

0celo7

People who use Outlook or Yahoo don't have issues.

Sir Cumference

@0celo7 Oh by the way, I showed a gamma function to my teacher and asked her to do $Γ(1.5)$. She said it had no solution o_0

0celo7

07:25

@SirCumference It's $\sqrt{\pi}/2$. I calculated it for you.

user54412

I'm told the undergrads here get special school gmail accounts or something.

Sir Cumference

I know...I don't know how ya got to it

0celo7

@ChrisWhite I'd assume so. My school does that.

Sir Cumference

When trying to get that infinity part, I end up with weird stuff

0celo7

@SirCumference You mind giving me her email? I'll teach her.

Sir Cumference

07:26

I don't got her email...

Probably should've gotten it...

0celo7

Go to your high school's website and find it!

Mike Miller

@SirCumference 0celo7 is a known troll. Be wary.

Sir Cumference

But I'm afraid you'd get her to fail me...

0celo7

@MikeMiller Seriously?

DanielSank

^ Yes.

Sir Cumference

07:26

So imma say no...but ya can teach me, I guess

0celo7

He asked how to calculate a Gamma function value.

DanielSank

@ChrisWhite What's a special school gmail account?

Sir Cumference

$Γ(1.5)$

0celo7

It's $\sqrt{\pi}/2$, for the last time.

Sir Cumference

I know...how did ya get to it?

How in god's name did pi show up?

0celo7

07:28

Use the factorial property of the Gamma function + the special integral @ACuriousMind and I showed you last time.

user54412

@DanielSank No idea. I'm not a special undergrad.

0celo7

@DanielSank my .edu email goes to a gmail thingie

DanielSank

@0celo7 cuz you forward it?

0celo7

I can use the gmail app on my phone, for one

@DanielSank No, the school does it automatically.

DanielSank

@0celo7 weird

0celo7

07:29

You're the one who works for Google!

@SirCumference $\int_\mathbb{R}\mathrm{e}^{x^2}\mathrm{d}x=\sqrt{\pi}$

Sir Cumference

R = 0 to infinity?

0celo7

no

real numbers

Sir Cumference

Oh, so negative infinity to positive infinity?

0celo7

yes

Sir Cumference

.-.

okay, so e to the power of infinity squared...isn't infinity?

0celo7

07:33

Oh

put a negative there

Sir Cumference

Ooooh

0celo7

$-x^2$

Sir Cumference

Oh then it's $1/e^∞$

Which is 0...

0celo7

what

Sir Cumference

$e^{-(∞^2)} = 1/e^∞$, no?

Sigh...

0celo7

07:35

what?

Sir Cumference

...I'm plugging in infinity...

0celo7

why

Sir Cumference

Because that's how you solve definite integrals?

You plug in their boundries

0celo7

oh?

Sir Cumference

._.

Um...

0celo7

07:37

you discovered the antiderivative of $\mathrm{e}^{-x^2}$?

publish quickly

Sir Cumference

Ohh crud

sigh

All right, I hadn't looked at chain rule so I probably can't solve any $b^x$ stuff

0celo7

protip: there's no known antiderivative

Sir Cumference

Wolfram gives me an error function...

Oh. Well.

0celo7

the error function is literally defined as the definite integral of it

you can't write it down

Sir Cumference

Oh...crud, that's what she said.

"There's no known antiderivative"

I am an idiot...

0celo7

07:41

maybe, but that's not for me to decide

Sir Cumference

Well then...imma do more reading on integrals...

Er, thanks

0celo7

I showed you exactly how to do that integral the other day

Sir Cumference

Yeah, er, I didn't exactly follow it...

0celo7

ok, then you're not ready to be working with the gamma function.

Sir Cumference

Yeah, guess not

Well, it's 2:44 am here and I need to try and get some sleep

'night

0celo7

07:44

bye

yuggib

09:02

@ACuriousMind @0celo7 The interesting thing is that well-ordering and induction are strictly related. If in a set there is induction, then it is well-ordered (and with the Peano axioms, induction is taken as an axiom scheme, so well-ordering is a consequent theorem); and the vice-versa is also true. The definition of the Natural numbers in ZFC is that they are the smallest infinite well-ordered set, with the ordering given by set inclusion (i.e. the smallest limit ordinal).

The well-ordering theorem instead, tells that every set can be well-ordered. This theorem is equivalent to the axiom of choice. So in ZFC, every set can be well-ordered, even the ones for which a well-ordering seems "unnatural". The usual example is the reals, where a well-order cannot be defined in a constructive way, but it exists.

yuggib

09:17

In set theory, I would say that the "well-ordering principle" for the naturals is true by construction, more than by axiom. Take the emptyset $\emptyset$ (whose existence is guaranteed by the axioms of ZF, in particular by the axiom of infinity that guarantees the existence of at least one set, and the axiom schema of separation).

Then you can construct the set $\{\emptyset\}$, and the set $\{\emptyset,\{\emptyset\}\}$. You see that both these sets are well-ordered by set-inclusion.

You can think of going further, and making any finite set of nested empty sets, and stil it will be well-ordered by inclusion: $\{\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\},\dotsc\}$.

You can extend it to an infinite set well-ordered by inclusion defining: $\omega$ is the set of elements of the form above such that: i) $\emptyset\in\omega$, ii) if $\alpha\in\omega$, then $(\alpha\cup\{\alpha\})\in\omega$.

This set is exactly the naturals, identifying $\emptyset$ with $0$, $\{\emptyset\}$ with $1$, and so on; and the ordering $\subseteq$ with $\leq$.

The existence of $\omega$ is guaranteed by the axiom of infinity (it is, roughly speaking, the statement of the axiom ;-) ).

Slereah

13:22

What's an example of a non-parallelizable manifold

Secret

4

Q: Totally non parallelizable manifold

Does there exist a manifold M which all iterated tangent bundles are non parallelizable manifolds? That is$ M, TM , T^2(M), \ldots ,T^n(M)\ldots$ are non parallelizable manifold? What is an example of a manifold which is not parallelizable, but $T^{n}(M)$ is parallelizable fo...

kt.k-theory-homology smooth-manifolds vector-bundles

becko

14:16

Can I use Lagrange multipliers with redundant constrains?

ACuriousMind

15:39

@Slereah $S^2$.

Shown with the theorem whose name you like so much ;)

Bernard Meurer

16:29

@DanielSank Sorry; I had gone to bed at that time. I'm here now though

0537

@BernardMeurer If you're accepted to waterloo will you go there?

knzhou

1

Q: Theoretical magnetic Monopole

I'm trying to solve question B2 on the 2012 USAPHO semifinal exam (last page). The solutions are here on the last three pages. I don't understand the following line: The flux through the loop will then be $\Phi_B = \int \vec B \cdot dA = \frac{1}{2} \mu_0 q_m\int sin\theta d\theta $ If I...

magnetic-monopoles

Is this even legal? I feel so... violated.

The copy-paste job didn't even get the LaTeX right. It's unicode boxes.

Bernard Meurer

@0537 Depends on where else I get accepted. But waterloo is amongst my top 4

Why do you ask?

0537

@BernardMeurer Lol I may go there too if I don't do engineering.

0celo7

@ACuriousMind Picardy Lindenhof?

ACuriousMind

16:34

@knzhou You shouldn't answer in comments. That said, it is exceptionally bad style to just copy-paste together the comments of another users.

Bernard Meurer

@ACuriousMind Do you sleep?

ACuriousMind

@BernardMeurer Sometimes

0celo7

Oh the hairy man bits theorem

Bernard Meurer

@0537 Cool, let's make the first h-bar born research team

@ACuriousMind hahahaha

0537

waterloo is like the best for physics in the world.

@0celo7 look at their books for the undergrad gr course link

scroll down.

Bernard Meurer

16:38

One naively could have said MIT asked that question. Why is waterloo so good?

0537

@0celo7 or look at the syllabus...

0celo7

Literally says advanced graduate course.

I mean shit I can take a course on Ricci flow but that doesn't make it undergrad level.

Or surgery or whatever

0537

no it's for undergrads too.

you need department consent.

0celo7

That's literally every course.

0537

:)

0celo7

16:42

Dr. Freire teaches a class on Lorentzian geometry based out of Hawking-Ellis and O'Neil.

I could take that as an undergrad.

0537

do it then.

0celo7

No.

I have more useful classes to take.

@ACuriousMind Did you know that for every spinor equation there is an equivalent tensor equation?

Danu

What is a spinor equation?

ACuriousMind

@0celo7 I don't know what that sentence means

Danu

^

0celo7

16:47

I don't either. But apparently it's true.

@Danu e.g. The Dirac equation

Danu

So what makes that a "spinor equation"?

As far as I can tell, it is just another differential equation, outside physics contexts.

0celo7

Probably. I'll give the article a read.

Danu

Link?

I think maybe you're thinking about something like the twistor formalism, where you encode everything in terms of spinors

0celo7

@Danu Uh, find it above. I had to get Chris White to send it to me, I didn't have access. It's a Cambridge link.

I'm on mobile.

@Danu Also I don't think that's right. One, it's the wrong way around. Everything is supposed to be expressed in terms of tensors. And it was published way before Penrose came around.

Danu

@0celo7 Lol, notice the word "equivalent" in your statement. There is no "wrong way around".

0celo7

16:56

@Danu Morally there is.

Danu

It seems like it's at least very similar to the twistor formalism.

@0celo7 No.

0celo7

Hawking-Ellis says the resulting tensor equation is usually quite complicated.

Danu

GR in terms of spinors $\cong$ twistor formalism

0celo7

In what category?

Danu

...the obvious one

0celo7

16:59

I don't think that's the name of a category.

Danu

It is, if you're smart enough ;)

I'm going emperor's new clothes-style :)

ACuriousMind

17:16

@Danu ...you're going naked? oO

0celo7

@Danu I'm probably not...

0celo7

17:33

@ACuriousMind When writing a pedagogical answer that leaves out some details as not to become the first chapter of a geometry book, should one try to provide one reference that explains everything or find multiple references, each one of which explains a certain part very well?

I.e. I won't prove that the partial derivatives are a basis or construct the tensor algebra carefully

Some other stuff as well.

Danu

@ACuriousMind Me obviously being the tailor in this scenario

ACuriousMind

@0celo7 Uh...I don't think that question has a unique answer in general

0celo7

@ACuriousMind And for my specific case?

Like Lee explains multilinear algebra well but he constructs tensor fields differently than I want to. Straumann constructs tensors as I do but doesn't explain multilinear algebra.

Other Lee explains both well but uses modules and rings. Both you and DS say that's a bit much.

ACuriousMind

@0celo7 I don't think anyone except you can decide what references you think are best for the way your answer is written

Danu

I guess nobody got my reference :)

ACuriousMind

17:42

@Danu I just didn't find it comment-worthy :P

0celo7

@ACuriousMind Ok. I might just put a "where to read more" section at the end.

@ACuriousMind Are polar coordinates a global homeomorphism from the plane into itself or do they fail?

ACuriousMind

You should know the answer to that. And if not, you should be able to deduce it.

Danu

@0celo7 Think about the origin.

@ACuriousMind Now this is a quote-worthy message ;)

0celo7

@Danu Ah, yes.

Danu

I ought to bookmark it.

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