The h Bar - 2016-09-29 (page 3 of 3)

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7:03 PM

@vzn : sure, yes. If there was no evidence for an expanding universe, I'd be saying space just has to expand. The BICEP2 talk sounds reasonable, but it's a puff piece. Anybody with any knowledge of cosmology would surely stick up their hand and ask how gravitational waves from the Big Bang can still be detectable after 380,000 years in the "maelstrom" early universe.

Hmm, Sakurai's approach to figure out $W_1$ is a bit different than what I'm used to

What are you used to?

I'm reading Shankar right now.

I think he does it the same way...

We both agree that $$W_0(x)=\pm\int^x p,$$ right?

modulo an $\hbar$

I guess I don't understand what these signs mean either

He said we'll see that in the next lecture but I'm curious now

@0celo7 Do a series expansion of $W = \sum_i \hbar^i W_i$ (note that this $W_i$ is different from Sakurai's), then plug that into the Schrödinger equation and compare the coefficients of order $\hbar^i$ to get DEs for the $W_i$. $W_0$ agrees with his, and for $W_1$ you find $2\partial_x W_0 \partial_x W_1 + \partial_x^2 W_0 = 0$, where you don't get a sign choice for $W_1$ and the sign of $W_0$ is irrelevant because it gives an overall sign. Sakurai's $W_1$ is then my $W_0+\hbar W_1$.

Right, that's how I learned it from Shankar.

I don't see how that's different

It's different because you don't have a $(\partial_x W_1)^2$ term of which you have to take the square root, introducing the sign that's troubling you in Sakurai.

7:07 PM

Right, there's no trouble in Shankar either

@vzn : it's increasingly negative I'm afraid. Especially after reading popscience rubbish like this. "We live in a Goldilocks universe... Now, the idea of the multiverse has been around for a while, but in the last few years, we've started to get the first solid hints that this line of reasoning may get born out..." This is peddling woo to people who don't know any better.

@ACuriousMind So you agree with me that in Sakurai's treatment there's a sign issue?

@ACuriousMind
$\vec{\mu}=g\mu_B \frac{\vec{S}}{\hbar}$, where the spin angular momentum $\vec{S}$ is a vector of pauli matrices. In the einstein de haas, we can see that $\vec{\mu}$ and $\vec{S}$ are parellel. What I mean by theoretical framework is how to explain in terms of hilbert spaces that $\vec{\mu}$ is just some constant multiple of $\vec{S}$ and not some more complicated linear combination that otherwise make $\vec{\mu}$ and $\vec{S}$ not multiples of each other?

@0celo7 Yes. In fact, Sakurai's treatment looks a bit strange to me because he never really formally defines what exactly he's doing to get those n-th order approximations. I think the approach of series expansion and comparing $\hbar^i$ coefficients is much clearer.

@ACuriousMind I agree. See my "this lecture is making no sense" comment :)

The prof has been told to follow Sakurai very closely because he is a new prof

For better or worse (worse I think)

7:16 PM

There's another very clear way to get WKB from the "quantum Hamilton-Jacobi equation" and then neglecting the "quantum" term, which is very nice because it makes the semi-classical character evident in the first step, but that isn't what Sakurai is doing, either

We did that the other day

Sakurai talks about it a little bit like 20 pages earlier

the prof gave some more details

"Economists have used non-standard analysis to model markets with large numbers of agents (see Robert M. Anderson (economist))."

That's a lot of agents

Infinite moneyyy

proof?

Robert M. Anderson (mathematician)

Robert Murdoch Anderson (born 1951) is Professor of Economics and of Mathematics at the University of California, Berkeley. He is director of the Center for Risk Management Research, University of California, Berkeley and he was chair of the University of California Academic Senate 2011-12. == Research == Anderson’s nonstandard construction of Brownian motion is a single object which, when viewed from a nonstandard perspective, has all the formal properties of a discrete random walk; however, when viewed from a measure-theoretic perspective, it is a standard Brownian motion. This permits a pathwise...

that guy apparently

Ok, let me put my question in another way. For quantum experiments, we experimentally observe probabilsitic outcomes of some observables, and our theoretical model is make use of state vectors and hilbert spaces to recover those probabilities.

7:19 PM

@Secret You'll have to define $\vec \mu$ for that, first.

You can't "theoretically" show things about quantities you haven't defined.

that... I don't really know, because classically you define that via current loops, but electrons don't really rotate, thus current loop approach does not work. The relation for magnetic moment showed above is derived from adding hats to the classical case and then putting in the g factor. Thus I don't really know what magnetic moment of an electron is other than it somehow respond like a bar magnet...

@ACuriousMind Stop, you'll break all the physics books

@ACuriousMind ok I'll see what my prof says on tuesday

but for now...

I have another question

@ACuriousMind Do we sweat in hot showers?

I knew that classical, a magnetic dipole moment is because a charge rotates and it is the dipole magnetic field generated by that rotating charge (similarly for current loops). But quantum mechanically, we cannot say an electron is rotating because it is point like, thus the only thing I can say is that it has a magnetic field that is like a bar magnet

@Secret Yep - the point is that you identify the "magnetic moment" as the quantity that couples linearly to the $\vec B$ field. In writing $g\vec B\cdot \vec S$ for your Hamiltonian, you have already defined the magnetic moment to be collinear with $\vec S$. The physically interesting thing is the determination of $g$ (and the quantum corrections that QFT computes for it are one of the most important tests of the accuracy of QFT)

@0celo7 wat

@ACuriousMind That's not my real question, but I have been wondering about it :P

7:27 PM

I mean...I guess we do?

Proof?

How would one know

No idea, though. Seems like a research topic for an IgNobel

O wow, I didn't noticed I have defined the magnetic moment to be collinear to the magnetic field via the dot product, I thought I am just picking out a component of $\vec{S}$ (which is a 3 component thing of pauli matrices) that aligns with B when doing that

There does not seem to be any definitive literature on the topic.

I see it now, thanks!

7:29 PM

@ACuriousMind Huh? That only gives $\mu =S+B^\bot$.

@0celo7 Hmm? We know that the energy of a magnetic dipole in a field $\vec B$ is $-B\cdot \mu$. So when you write down a Hamiltonian with $B\cdot \text{stuff}$ in it, you have implicitly declared that $\text{stuff}$ is the magnetic moment.

No?

the dot product is not invertible...

...we suppose that Hamiltonian holds for arbitrary $B$.

@Secret : the electron isn't pointlike. See this question where I asked for the supporting evidence. There isn't any.

@ACuriousMind Ah, that's a problem I have with physics in general.

So ok.

7:33 PM

@JohnDuffield Regarding the nomination comments: I'm not going to read a paper based on something I know nothing about. That would be a colossal waste of my time, and I have no idea if any of your claims make the remotest bit of sense.

Assuming that principle (which I think I reject), then yes.

@HDE226868 They probably don't.

@ACuriousMind I'm reviewing associated bundles because I want to understand the de Rham decomp. thm. I have a question

@HDE226868 : fine. But if you don't know about something and I do, you might prefer to reserve your opinion.

$(P,M,G)$ is a principal bundle, $F$ a manifold, $G$ acts to the left on $F$

@JohnDuffield See, though, I have no evidence to suggest that you know what you claim to know.

Previous experience would suggest the opposite.

We write $E=P\times_G F$, I think all this is standard

7:35 PM

And currently, your rationale for why ACuriousMind shouldn't be a mod is that he was wrong on one answer - according to you.

@HDE226868 : I didn't invent the wave nature of matter. Or electron optics.

@0celo7 Yes, it is, although $F$ should be a vector space, no?

@ACuriousMind No, we're looking at general associated bundles here.

Dear lord.

But okay

:)

Ok, so we have the projections $\pi_P$ and $\pi_E$ for the two bundles

I'm just wondering about the local trivializations of $E$

We take $U\subset M$ to be a trivializing open set for $P$, that is, $\pi_P^{-1}(U)\approx U\times G$

there is a smooth map $F_U:\pi^{-1}_P(U)\to G$, agreed?

(basically the projection applied to the diffeomorphism above)

7:39 PM

@HDE226868 : it isn't.

@ACuriousMind If you think that's bad, I once tried to understand connections on fiber bundes. Not even principal or vector bundles. It's not nice

@JohnDuffield Well then, tell me why my comments didn't refute your argument.

We then define $F_U^E:\pi^{-1}_E(U)\to F$ by $F_U^E((p,f)G)=F_U(p)f$.

And this supposedly gives a homeomorphism $\pi_E^{-1}(U)\to U\times F$.

I think the homeo is $p\mapsto (\pi_E(p),F_U^E(p))$.

But I'm having a hard time showing this is a homeo

maybe it's trivial

the notation is horrible, yes

it's definitely hindering my understanding

One way to define a associated bundle is to patch it together from trivializing patches, in that definition, there's nothing to show

@HDE226868 : because you've admitted that you aren't in a position to know who's right or wrong in some encounter, and moreover that you don't care to put yourself in that position. If I was in such a situation I'd reserve my opinion.

7:45 PM

That is, you just look at your definition and note that you defined $\pi_E^{-1}(U)$ such that it's $U\times F$ almost trivially.

But I'm afraid you need to figure this out from whatever you're exactly working with because there are so many slightly different notations and conventions

@JohnDuffield No, I said I wasn't able to figure out who was wrong in that one instance.

Tsk, look at the time. I must go I'm afraid. Bye.

God Particle (film)

God Particle is an upcoming 2017 American science fiction thriller film directed by Julius Onah and produced by J. J. Abrams. It is scheduled for release on February 24, 2017 in IMAX and conventional formats. == Plot == A team of astronauts aboard a space station find themselves alone after a scientific experiment causes Earth to disappear. When a space shuttle appears, the space station crew must determine if they are friend or foe. == Cast == Daniel Brühl Elizabeth Debicki Gugu Mbatha-Raw Chris O'Dowd Zhang Ziyi David Oyelowo Aksel Hennie John Ortiz == Production == On March 29, 201...

whaaaat

@HDE226868 : and I said that you need a few more examples where you can.

> J.J. Abrams

7:50 PM

@JohnDuffield No, you didn't say that, and the onus is on you to prove your point.

Oh dear

> A team of astronauts aboard a space station find themselves alone after a scientific experiment causes Earth to disappear.

J.J.!

More trash from the trash master

Ruining Star Trek wasn't enough for him

How do I tell if I am an alcoholic?

Now he wants to ruin physics, too

@0celo7 are you drinking right now

7:52 PM

@ACuriousMind Stupid question, why is $P\times_G F$ Hausdorff? Does it follow from general theorems of quotients by Lie groups?

@Slereah No alcohol allowed on campus

Ahah America

@0celo7 Well, it's locally homeomorphic to the product of two Hausdorff spaces, no?

@0celo7 lol

@ACuriousMind why is that funny?

oh, QM prof sent me an email

@HDE226868 : you've already made the point for me. You said I have no way of evaluating the accuracy of that answer. But you do. You can read the paper. But you won't. You insist on giving your opinion and making a judgement from a position of ignorance.

@ACuriousMind what

7:54 PM

@JohnDuffield Yes, I'll get back to you in a couple weeks, once I've done the reading I need to begin to understand the paper.

that's what I'm trying to prove!

@0celo7 But why do you need to know that it's Hausdorff prior to that?

I'm thinking there should be a nice way of seeing it.

@0celo7 It just is

Ok, a group has to act continuously and properly

wtf that's not a nice condition

7:57 PM

@HDE226868 : good stuff. The main point is that it's an electron optics paper. It concerns the wave nature of matter. If you ask around, a lot of people will tell you the electron is a point-particle. It isn't. See this question where I asked for the evidence and awarded a 300-point bonus.

OK I really must go now. Bye.

@ACuriousMind I did?

I defined $\pi_E((p,f)G)=\pi_P(p)$

@JohnDuffield That's absolutely not what the accepted answer says. It says that the pointlike approximation works, and we don't have evidence to the contrary.

aha, wait just one moment

@ACuriousMind I'm going to write a textbook on differential geometry with notation that's worth a damn.

@HDE226868 : I heard a ping because I hadn't closed down all sessions. What you think is the accepted answer, is wrong. Electron diffraction says its wrong, so does the Einstein-de Haas effect, so does electron motion in a magnetic field. If you beg to differ, show me the evidence that the electron is pointlike.

Guess what? There isn't any.

Over and out.

John, did you read Anna's answer?

Never mind. Logic's not working.

@ACuriousMind @0celo7, sorry for the intermittent interruptions.

It was unwise of me to carry on that conversation.

8:08 PM

I enjoy JD convos

8:19 PM

@0celo7 I look forward to it

@HDE226868 You can do this in chat however you like. I find the red numbers appearing in my inbox from the constant squabbling on my nomination much more irritating :P

user218912

8:58 PM

new qft problem set due in 2 weeks, and we didn't learn the stuff we need to solve it yet ._.

user218912

so that gives only 1 week to do it assuming we learn the stuff next week.

9:12 PM

Nobody can solve QFT

It's a trick

user218912

9:23 PM

@Slereah @ACuriousMind Can you please give me an idea of how to do this?

user218912

he didn't teach us what it means yet, but I want to work ahead.

what part do you not know what it means

user218912

idk what a time ordered product is.

user218912

we didn't learn it yet.

@IceLord It's defined in the very screenshot you posted

9:25 PM

Yes, that

user218912

@ACuriousMind idk what the point of it is.

Basically it means that the operator product is sorted in such an order that they happen in chronological order

user218912

@Slereah oh okay.

A(x)B(y)C(z) is time ordered if x happens after y happens after z

user218912

is this a particularly difficult problem?

9:27 PM

It's alright

Just apply the differential operator, it shouldn't be too difficult

Though remember how time ordering is expressed

user218912

okay I'll do it in a week from now.

user218912

I need to review some stuff we learned first.

$T[\varphi(x) \varphi(y)] = \theta(x_0 - y_0) \varphi(x) \varphi(y) + \theta(y_0 - x_0) \varphi(y) \varphi(x)$

And the derivative of the step function is the delta function

user218912

yep.

user218912

thx

9:31 PM

this + the CCR should give you the result

@JohnDuffield lol "increasingly negative". ps theres 2 talks by nobel prize winners gell mann/ feynman. susskind. heres another on universe expansion by smoot... seem to recall you posted same pic in chat once? ted.com/talks/george_smoot_on_the_design_of_the_universe oh yeah & if thats all too much for you, randall munroe. :P ted.com/talks/randall_munroe_comics_that_ask_what_if

10:14 PM

@ACuriousMind Totally understandable. For the record, I don't think that it's going to be productive in the future either way.

@ACuriousMind No you don't

@Slereah Proof?

@0celo7 $\varphi[f'] = -\varphi'[f]$, for $\theta$ : $\theta[f'] = [f]^\infty_0 = - f(0)$, equivalent to $-\delta[f]$

What exactly is $f$?

a test function

what space exactly?

Test: $\mathfrak S$

jeez

10:27 PM

Smooth function of compact support

10:39 PM

tfw your math book unironically writes a mixed fraction

10:58 PM

@0celo7 You write a mixed fraction

@KyleKanos You're dead.

Who are you?

No, I'm quite alive

The fact that I'm typing this should be indicative of my alive-ness

Your wife or children could be using your account.

Wow Kyle!!

Hey @KyleKanos!!!!

My oldest is 7 years old and wouldn't know what to write

My wife probably doesn't know this site exists

Hi @Danu

10:59 PM

I am your wife

THE RETURN OF THE KING

King of what?

@Slereah I sincerely doubt that

@KyleKanos You're like a rapper, your retirement lasted for all of 6 months.

I got too involved in elections :/

11:00 PM

How are you @Kyle?

@KyleKanos Hah, really?

@0celo7 Basically I saw the "guys" who were running and felt a strong compulsion to make some statements about it

I'm happy that we had some CM guidance in that matter---it was all getting a bit crazy

@Danu I'm doing well. Over-worked, but also paid justly, so it's quite alright

I haven't been following, what happened?

There?

11:02 PM

Yes, thanks

We've been having problems with overzealous flagging.

lol

See the pinned message from Dr. David.

@Danu What is funny?

Just funny that even David now got fed up with this crap

I actually thought of nominating myself due to the less-than-quality names tossed in the hat

11:03 PM

^ do itttt

@Danu I thought I was the flagger, but we've had 12 flags. I think I threw 3.

But I would be kinda like some previous mod(s)

And just rarely show up

@0celo7 And you can't guess where the others came from...?

Duffy?

Oh, right.

I forget about him.

11:04 PM

@KyleKanos Isn't Manish a bit like that? :P I mean, no offense to Manish or anything but I rarely see him around.

That's who he's referring to...

the other 3 mods are active daily

That's why I put the (s) there. There was a mod before him though

????

> previous mod

Ah, okay

mbq, or whatever the three letters were

11:05 PM

Who?

@ACuriousMind German outta nowhere

He became mod over at stats & bascially gave up mod here

I see. What do you think of the current candidate list, Kyle?

It's better now that it's been "cleansed" (not quite sure how I feel about that action, though) but there's definitely a person or two I think would have thrown their names in

Probability homework was not bad at all today. Just some basic analysis/PDF stuff. No dreadful poker hand probabilities.

@0celo7 I occasionally lurk, get used to it :P

11:06 PM

@KyleKanos I see that you thought I would---I did consider it.

@ACuriousMind I never lurk. I constantly feel the need to interject myself into any conversation that's taking place.

^ you really do though

@0celo7 Yes, yes you do

@Danu That was a joke

Oh wtf that was a joke

Wish I could interject in conversations.

11:07 PM

I hate you ppl

Or answer questions.

It's a habit you should try getting rid of :P

lmao @ACuriousMind you and me both feel the pain :P

But working ~11 hours a day for a boat-load of money has it's drawbacks

BOAT LOADS OF MOOLAH

name one time I've done it

11:07 PM

ship some over here

@0celo7 Just now on math.se

@KyleKanos ship some to me, domestic shipping is cheaper

@KyleKanos It also has a boatload of money, though.

(it didn't bother me in this case)

Just find a job in industry. They pay nicely

user218912

do you need to know condensed matter to be a condensed matter theorist? or can you get away with just knowing field theory and stat mech?

11:09 PM

Who else would you like to see run, Kyle?

@IceLord lmao looking to drop your class?

user218912

@0celo7 lol xD

user218912

if the answer is yes I won't drop obviously.

Don't drop it.

Dropping classes out of laziness should be avoided at all costs.

(I'm assuming it's laziness)

user218912

well mostly because the problems in ashcroft and mermin are really difficult.

11:11 PM

Good learning opportunity, no?

@Danu I honestly thought Emilio would (and as much "bad blood" was there, I honestly think he'd make a fine mod). I also think DanielSank and Nathaniel would make fair mods as well

@KyleKanos I think it may still be possible to convince Daniel ^^

Ah, I vividly recall you and Emilio's discussions haha

Is it possible to nominate someone else?

user218912

@Danu bleh... all the other grad students discuss the problems in the lounge everyday but I have to do it all alone (I have you guys but no one knows cmt here).

As in, I nominate Daniel to run?

11:12 PM

Nope, only self-nominations

I also got in a bout with you once, over that tachyon answer, remember? ^^

@IceLord Why not discuss with them?

Darn. Maybe I can hack his account quickly and post a self-nomination for him

Hey @DanielSank Look, an endorsement

Meh, I'll just leave him a note.

user218912

@Danu undergrads can't go to the physics lounge.

11:13 PM

@DanielSank: Run for Mod. Please.

@IceLord what BS is that

user218912

@Danu it's only for profs and grad students afaik.

@Danu All the grad students in my topology class do the homework together in the TA room. No undergrads allowed.

@Danu Separation of knowledge, of course

Can't give all the students the keys...

@IceLord Is there someone controlling the entrance? oO

11:14 PM

@0celo7 #rekt haha

shitty uni's!

@ACuriousMind You probably have to swipe in with your student ID.

in LMU there is just a single student lounge lol... no separation even from the students who are studying to be teachers

@Danu I have the best homework grade.

@0celo7 #double#rekt

or rather #reverse#rekt

user218912

@ACuriousMind no but everyone knows I'm an undergrad, so once I entered and got told to leave.

11:15 PM

But you plagiarize ACM

@0celo7 So it's rather that you don't allow the TAs to work with you? :P

In my algebra class, the "homework group" consisted of trolling Math.SE and Quora for answers.

@IceLord dafuq

@IceLord oO

Assholes

11:15 PM

@Danu Doubtful.

@0celo7 I heard stories like that, also

I can't imagine a student telling another student to leave here because of such a silly thing

ACM has refused to help me with analysis homework from now on.

GET OUT OF HERE YOU PLEBS

He helped me with a topology problem once.

@ACuriousMind Thanks for that.

11:16 PM

Plebs?

Do people really use that word outside of internets?

user218912

@Danu something like that.

@KyleKanos I do

@KyleKanos There's a guy I see around who wears a fedora and has a fountain pen in a holder on the fedora. I bet he does.

epic character

@0celo7 You ask him what year it is....

user218912

11:18 PM

I should have been like... "I am the lord of ice, bow down before me and repent for your sins or I'll freeze you to death"

No

You absolutely should not have done that

I...agree with 0celo7

user218912

perhaps

Wow what a strange thing to say

The sky is blue

Anyone agree?

Nah, it looks pretty black to me right now

11:19 PM

Only during the day time

Dark blue

:(

user218912

@ACuriousMind but isn't it just really really really dark blue?

that's isomorphic to blue

@0celo7 You know what I'm gonna ask.

11:21 PM

what are the morphisms in your category

Color maps

It's possible the sky is colorless

> Hello Ryan,
The +- signs do cancel with each other as I did in class. The reason is the first +/- comes from the zeroth order solution W_0(x), while the second +/- comes from the first order solution W_1(x). The “+” sign holds both for W_0(x) and for W_1(x). The same is true for the “-“ sign. In other words, the sign is chosen to be “+” or “-“ simultaneously for all the terms in the series. If you cannot see this, please come to my office and we can discuss it.

@ACuriousMind Does this make sense to you?

Sounds sensible to me, though I don't know what the W's are.

@Danu :P ACM knows.

11:30 PM

@0celo7 Not if this is supposed to be applicable to the derivation in Sakurai, no

@ACuriousMind My thoughts exactly...

user218912

@0celo7 should I read peskin and schroeder or my prof's notes?

Why are you asking me.

I've told you many times that I don't know or care about QFT.

I decided not to pursue physics specifically because I hate QFT so much.

So stop asking me about it.

user218912

sorry :o

user218912

my university allows me to use lunch money to buy peskin/schroeder.

user218912

11:34 PM

and I have like 300.

From the "Comments not Posted" series:

> You've concluded that the author's of the papers linked by other answers are wrong, have you? Oh. Good. I guess that settles it, then.

::facepalm::

DJ Khaled is writing a book.

11:56 PM

@ACuriousMind "hoping to help their career" Huh? I wonder what mechanism he is envisioning. It's not like I get any credit toward tenure. Nor did I get any toward being hired at a R1.

ACM probably doesnt know what R1 is

Don't read Peskin&Schroeder @IceLord

Read Schwartz for a good basic intro.

@0celo7 It's the highest-rank in research activity by some US university classification scheme

@dmckee hey is ${}^3H+{}^{16}O\to{}^{18}F+{}^1n$ reasonable?

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