The h Bar

Q: Moving a question to a different forum or asking for more attention

9:24 AM

@DonThomasReyes It seems to me that the force you want is going to be $\frac{20 \text{kg}\cdot g \cdot \sin 30^\circ - 80\text{N}}{ \cos 30^\circ}$. Think about breaking both gravity and your horizontal force into a component that's parallel to the slope and a component that's perpendicular to the slope, and ignore the component that's perpendicular.

Physics Meta

10:52 AM

0

I'm posting in meta for the first time so please don't mind some culturally outrageous thing that I would end up doing here and inform me about my peculiarities. So I have this question on stack exchange physics, about the fermi level of materials and I have not received any assistance on it as o...

support

Anonymous

11:06 AM

@MathematicsAminPhysics So how many have registered? Who are going to be teach? What will be taught ?

user84215

11:22 AM

@Blue You can see them in Registration for the MSE University. As I said, details would be determined by the committee.

I don't understand. If I take this course, I can say afterwards "I got my bachelor's degree from a chat room", right?

user84215

With a good approximation, yes.

And in the future, you'll be offering PhD's?

user84215

Yes.

So I'd be able to call myself Dr Dawood?

user84215

11:33 AM

After defending your dissertation.

I see. May I comment that I find this whole concept incredibly insulting, to everyone who has a genuine degree from a genuine bricks-and-mortar university?

5

user84215

It is really important that you have a genuine phd degree?

user84215

If you like, I can call you Dr Dawood.

I have an actual degree, not a PhD, from an actual university. I worked very hard for it, for a number of years. It's really important that this is not devalued by a proliferation of people claiming they have degrees, when they really don't.

5

user84215

This project is not suitable for those people whose main concerns are earning degree at all.

11:39 AM

question: when referring to this chat room from the outside, do we prefer to say 1) "the h Bar", 2) "The H Bar", 3) "the hbar", or 4) "the $\hbar$"?

@Jim Do you mean "say" or "write"?

@DawoodibnKareem yes

Actually, Rob, I find those insulting too.

1)

@0celóñe7 what's up?

11:40 AM

everybody says 1)?

waaaaaaaaaazzzzzzzaaaaaap

Chiiiiiiillllin

I don't talk about H bar.

@Jim 1), since that's what it is actually named. 4) is also fine, I guess, but you have to expect confusion :P

First rule of H bar.

11:42 AM

@djsmiley2k That is why you failed the first rule

Wait, first rule is 'Gravity is not a force'

Right.

2nd rule then :D

4) requires rendering :P

I don't have whatever it is, that makes stuff appear properly, here :<

h

^Cheap hack

ℏ for the same price.

fileformat.info/info/unicode/char/210f/index.htm - it's very quaintly named.

11:47 AM

@ACuriousMind Too late now

What is Polychromatic Music? - An introduction with comparison of modern microtonal instruments.

►

I ditched measure theoretic probability for Elven lord's modern algebra topics course

@skullpatrol not really, there's also something special about seeing $\$\backslash hbar\$$

@djsmiley2k here

$\bar h$ is just wrong for so many reasons

11:51 AM

:-)

@Jim I have used that symbol a few times, but not to denote Planck's constant :P

@ACuriousMind I've used $\bar H$, but never $\bar h$. It's like using goto in programming; a lot of languages support it, but any time you use it, you become immediately wrong

@Jim In CFT, the conformal weight is occasionally written $(h,\bar{h})$.

And it's lowercase because these two things are just numbers

Uppercase for a number would be just wrong

@ACuriousMind Uh, energy eigenvalue?

Why is it so "wrong" to use goto?

11:57 AM

@ACuriousMind That's too bad. I'm sad to find out that all this time, physicists doing CFT have been wrong

@skullpatrol taboo, look into the history of goto. Essentially it's more trouble than it's worth

@ACuriousMind here is the book www-users.math.umn.edu/~webb/RepBook

@0celóñe7 Yeah, that's wrong.

BASIC started it.

@ACuriousMind what? Everyone writes $E\psi=H\psi$

what should it be?

@0celóñe7 Still wrong.

11:59 AM

@skullpatrol I seriously doubt that.

@0celóñe7 nice

It's clearly named after Kelly.

@ACuriousMind I figured I could take probability next year but he won't be teaching this course again

R. Kelly?

Scott Kelly

@ACuriousMind so is this something you know about?

@ACuriousMind and you didn't say what the energy eigenvalue should be

12:02 PM

@ACuriousMind avogadro's number

@0celóñe7 that book includes a bit more than I know about finite group representations, but yes, it is something I know about

@Jim also wrong

Clearly

atomic number, Z

@ACuriousMind I don't think there's any way we get through the book

@skullpatrol gotoresearch.com/kellygoto

it looks pretty dense

12:04 PM

@0celóñe7 My own group theory course covered roughly the first four chapters before we moved on to Lie groups.

@ACuriousMind wtf, in one semester?

Thnx @DawoodibnKareem :P

@0celóñe7 It was pretty intense (also, a lot of the time-intensive proofs/computations were outsourced to the exercises)

@ACuriousMind Elven lord loves taking one class for some ridiculous proof

CS ed.SE would be interested in the taboos of using goto @Jim

heather

12:08 PM

hypothes.is a great web annotation service. works on arXiv papers too.

@skullpatrol betcha they know all about it

Yeah, that's a good bet.

Thanks for sharing @heather

You should clarify whether the "divergence" of the stress-energy tensor is the ordinary or the covariant divergence. — ACuriousMind ♦ 12 mins ago

@ACuriousMind What?

@0celóñe7 $\partial_\mu T^{\mu\nu}$ vs. $\nabla_\mu T^{\mu\nu}$.

The former is not even defined.

It's defined in the minds of physicists.

12:22 PM

@0celóñe7 Exactly, and this is a physics site, which is why we got questions like physics.stackexchange.com/q/346793/50583 and its followup physics.stackexchange.com/q/348085/50583, where one point of confusion was precisely this.

The second seems to have nothing to do with this

And not sure about the first one either

@skullpatrol stackoverflow.com/q/2545103

Partial derivatives on tensors are not necessary tensors themselves, but can we really do contractions like that?

goto is still a keyword in Java, but will throw a compile-time exception if you use it

Slereah

@0celóñe7 is it not defined on the jet bundle or some shit

12:32 PM

that's some serious hate if you make the program crash for even using it once in your code

@Jim A compile error is not the same thing as an exception.

@DawoodibnKareem yeah, my brain thought error but I wrote exception because I'm used to complaining about the latter

@Slereah I think it is - it's not a proper tensor field, but it does live somewhere

Slereah

The jet bundle is basically Detroit

Where all the worst things live

$\partial_\mu T^{\mu\nu}$ this is not mathematically defined?

user84215

12:38 PM

@DawoodibnKareem Excuse me if I have disturbed you.

@MathematicsAminPhysics Well, if it's not a bachelor's degree, you shouldn't call it a bachelor's degree. Similarly, the so-called PhD.

@ACuriousMind How exactly? Partial derivatives depend on coordinates.

Thanks @Jim I also found this :-)

It lives in some function space over an open set defined by the chart

Pretty meaningless

We can have derivative of matrix functions, so what prevents having a derivative of a tensor function which are multilinear maps?

12:42 PM

@0celóñe7 You claim that e.g. the LL pseudotensor is meaningless?

If so, then you have finally abandoned physics for pure math entirely :P

Are partial derivatives of tensors pseudotensor, I do recall back in the undergrad GR course whenever we tried to transform it into another coordinate, it does not just having a change of sign plus the jacobian matrices that showed it indeed transforms like a tensor?

@ACuriousMind that thing is defined wrt an explicit asymptotic coordinate system

I'm saying that just saying "ordinary divergence equals zero" is completely meaningless

@Secret what

What's what a covariant derivative does

@0celóñe7 So LL's third requirement is meaningless?

I think all physicists should take a good hard look at the axiomatic definition of connections

@ACuriousMind I just said there's an explicit coordinate system in play.

@0celóñe7 No, I am not talking about the covariant derivative, "$\partial_\mu T^{\mu\nu}$" seemed to be the ordinary partial derivative of a tensor that is formally resembling a divergence, That cannot even be a pseudotensor?

12:49 PM

@ACuriousMind But you should know that there are sufficiently bad coordinate systems, like ones where the metric decays as $1/r+1/r^\alpha$, where "invariant" quantities defined by such pseudotensors are in fact not invariant

there are some physicist shenanigans with integration by parts that fail

@0celóñe7 Well, no one is claiming the pseudo-tensor is invariant. What they are claiming is that its 4-divergence is invariant (I think)

And I am willing to believe you that there are some mathematical issues with actually defining these objects to a mathematical standard of rigor

@ACuriousMind Yes, ordinary divergence in a chart, which is specified

I'm saying that writing down $\partial_\mu T^{\mu\nu}=0$ without further commentary is meaningless

right ok

Because you can just go to polar coordinates or something and that's no longer true

You see the same issue in $\Bbb R^n$, really. It's a danger of the compact notation we use for GR

@0celóñe7 True. Still, I think it would be good to explicitly state that the divergence that's meant in Slereah's answer is a covariant divergence. You know how bad physicists are at this, why make it even harder for them? :P

12:53 PM

nvm, I misread, it's not the covariant derivative, all is good

@Secret Actually no, you're right. $\partial_\mu T^{\mu\nu}=0$ has no meaning in special relativity either

You have to specify a Cartesian coordinate system

@Secret y'know, since you deleted the message that refers to, someone reading this after the fact is not going to know what you're taking about at all :P

People like to say that $\partial=\nabla$ when the metric is flat, but that's only true in a flat coordinate system

@ACuriousMind Opps sorry, that's how it is commonly done in the maths chat, looks like I inherited one of their cultural habits...

In some fields (good fields like analysis) it is always assumed to be a Cartesian coordinate system, so we can get away with it

But in GR where people like to have coordinate freedom, they also need to shoulder some responsibility and be more precise

@ACuriousMind trying to come up with some flippant Marie-Antoinette response to that

12:57 PM

I don't think I've ever seen anyone but Straumann fully commit to the coordinate-free notation.

@ACuriousMind Wald

Abstract index notation is a beautiful thing

I think I recall in my undergrad GR course, we wrote something like this for the covariant divergence: $\nabla_{\mu}T^{\mu\nu}$

He does it incorrectly, but still :P

@Secret Yes, and that has meaning

@0celóñe7 Ohhhh, I think many physicsts will defend their notations by claiming it was abstract index notation all along!

That's the "same" object regardless of coordinate system, so you can be forgiven for not explicitly stating that you're using one.

@ACuriousMind But the problem is that $\partial_a$ has no meaning in the abstract index notation.

You need coordinates to define it, and it's a patently different object than another derivative in a different coordinate system.

12:59 PM

I wasn't saying they would be right ;) (I don't really know about abstract index notation :P)

Wald does write things like $\nabla_a V^b=\partial_a V^b+\Gamma^b{}_{ac}V^c$, which is horrendous

@ACuriousMind In abstract indices you denote the argument of a tensor (seen as a multilinear map) by an index. So if $\omega$ is a 1-form and $v$ a vector, then $\omega(v)=\omega_av^a$, etc.

You can use the flexibility of indices without having to define coordinate systems

That being said, often you want to work with Christoffel symbols, etc., and those are not tensors

And this being a notation, you can't really "prove" anything about it, but it's certainly against the spirit to write something like $\Gamma^a{}_{bc}$.

@ACuriousMind Now Straumann is also dishonest. He doesn't use special symbols for abstract indices. He does everything with indices in one style, then says "interpret the indices as abstract when applicable"

Christoffel symbols is like one of the most horrible looking thing under a change of coordinates

$\partial_{\mu}\partial_{\nu}-\partial_{\nu}\partial_{\mu}$ is one of the terms you can get if I recall

1:16 PM

@Secret That's...not a term that appears in the Christoffels at all.

Anonymous

@MathematicsAminPhysics It'll be better if you don't call those "degrees". You might just say that the MSE University you are designing will offer "courses" (like MOOCs do) by voluntary teachers in chat rooms. You can set course timing as events. Anyone who is interested can register themselves there. However, since it is a virtual chat room we can't do anything if the teachers fail to turn up at the right time.

Q: Christoffel symbol transformation law

10

It is known that the transformation rule when you change coordinate frames of the Christoffel symbol is: $$ \tilde \Gamma^{\mu}_{\nu\kappa} = {\partial \tilde x^\mu \over \partial x^\alpha} \left [ \Gamma^\alpha_{\beta \gamma}{\partial x^\beta \over \partial \tilde x^\nu}{\partial x^\gamma \over...

differential-geometry tensors

Sorry I misremembered, it appears I only remember there are 2 terms and one of them is a product

Anonymous

It seems ridiculous when you say the MSE university will be offering "degrees" like "Bachelor/Masters/PhD" :P

Anonymous

@MathematicsAminPhysics

@Blue There is a dedicated room for feedback where most of what you want to say has probably already been said. Maybe have a look there before you start a new discussion

Anonymous

1:19 PM

@ACuriousMind Oh, thanks. I'll see. I don't think I have much more to say about this though.

The whole MSE university idea is a big utopian nonsense. It has already been settled in various lengthy conversations in chatrooms and piles of downvotes on the MSE meta

I don't see why the OP is pursuing this far fetched trash anymore, but if he so wishes.

@BalarkaSen I'm taking a course on finite group rep theory

what's a group

help

Not to mention, I have not even have the chance to launch the ICBM yet! (metaphor)

1:36 PM

Please confine discussion of the "MSE university" to its dedicated chatroom. Thanks everyone.

→ 8 messages moved to Trash

@ACuriousMind What the hell?

user84215

I think it is a dirty work that one wants to criticize an idea in this way.

Yeah, I am surpsied @ACuriousMind

Has someone told you to censor this?

@0celóñe7 What?

You said yourself that some of what I just moved was not "Nice".

And since there is already a room full of discussion about this topic, I see no purpose in having it also spill into here.

Case closed.

1:44 PM

@ACuriousMind Really? What tool do you use to do simple quick stuff with pictures (like cropping) then?

@Mostafaııııııııııııııııııııııı GIMP

Does it have a GUI?

or scripting only?

ahhh I missed the AMA with @Mithrandir24601 :(

Anonymous

@Mostafaııııııııııııııııııııııı Me too. I was sleeping then. :P

Anonymous

It was around 2am-3am over here

Seems you guys have forgotten that bookmarking a conversation is feature that exists @ACuriousMind

Going to bookmark it now

1:50 PM

@Mostafaııııııııııııııııııııııı It has a GUI

Giskard42

@Mostafaııııııııııııııııııııııı Gimp's got a gui

You still there? @0celóñe7

going to bookmark from the beginning of the AMA to this:

yesterday, by AccidentalFourierTransform

later alligator

@skullpatrol sure

cool

:-)

1:57 PM

@Mostafaııııııııııııııııııııııı Heh, tradition must be upheld :P

OK, for the sake of tradition:

I have bookmarked the AMA with Mithrandir

2

Thanks @Mostafaııııııııııııııııııııııı

@skullpatrol no problem ;)

consider a free particle in 1D. Is its Hilbert space separable?

@Mostafaııııııııııııııııııııııı Yes

What do all those lines on your username mean? @Mostafaııııııııııııııııııııııı

2:12 PM

@ACuriousMind but separable means it admits a countable orthonormal basis. considering that to each and every real number is assigned an eigenvector of this Hilbert space, how is this countable then?

@Mostafaııııııııııııııııııııııı Ah, that's because the $\lvert x\rangle$ are not actually vectors in the Hilbert space!

Other than being unique :-)

@skullpatrol nothing. Just a totally random thing

@ACuriousMind What??

Can you explain more?

@ACuriousMind What is the Hilbert space of that system then?

@Mostafaııııııııııııııııııııııı See e.g. physics.stackexchange.com/q/249851/50583, physics.stackexchange.com/a/90261/50583. The Hilbert space is $L^2$, but the $\lvert x_0\rangle$ would correspond to $\delta(x-x_0)$, which isn't even a function, let alone square-integrable. A countable Hilbert basis of $L^2$ is given e.g. by the stationary states of the harmonic oscillator.

@ACuriousMind Seems pretty square integrable to me. Clearly $\delta^2=\delta$ by evaluating at points, so $\int\delta^2=\int\delta=1$.

@ACuriousMind Hmm, are the dirac deltas a basis of the space of tempered distributions in some sense?

2:25 PM

From that answer: a countable set can span a vector space of uncountable dimension. wow!

what are some of the holes in the standard model?

@ACuriousMind but Shankar never talked about these ::feeling betrayed::

@Mostafaııııııııııııııııııııııı That's wrong.

@0celóñe7 that quote? (from ACM's answer)

Anonymous

@Mostafaııııııııııııııııııııııı I guess it should be a "countably infinite set" rather than any "countable set" ? (Pardon me if I'm saying something silly)

2:28 PM

@ACuriousMind Uh, did you really say that $L^2(\Bbb R)$ has uncountable dimension?

@Blue yes he means a countably infinite set

Anonymous

@Mostafaııııııııııııııııııııııı Yeah. Thanks

@0celóñe7 what is wrong?

It's just that span means something different in infinite dimensional vector spaces.

Yeah, ACM is mixing terminologies.

He is using dimension in the Hamel sense but span in the Hilbert sense.

2:30 PM

I think ACM is aware of these. He's just saying it's uncountable dimensional if we take span in the Hamel sense, but countable dimensional if we take span in the Hilbert sense.

I have a possibly silly question about Feynman diagrams if anyone can help ...

"a countable set can span a vector space of uncountable dimension" is just a slogan for that. He's writing an answer for physics.SE, not math.SE, after all.

Anonymous

Wow. This is the first time I'm seeing JR asking a doubt. :P :)

Yes, ACM is aware of these, but I think that most doubts in physics are because of poorly explained math

If you take a diagram representing Compton scattering then you have a photon and electron coming in and a photon and an electron going out. If you rotate the diagram 90º, i.e. swap the time and spaces axes, then you have another diagram with an electron and poitron coming in and two photons going out.

2:33 PM

annihilation

So the second diagram looks like pair annihilation to two photons.

Is it a general rule that if you rotate a Feynman diagram 90º then you'll get another diagram that represents something physical?

Presumably this applies to diagrams with any number of vertices since we're only considering what comes in from infinity and what goes out to infinity.

what the heck is a free module

"In theoretical physics, Feynman diagrams are pictorial representations of the mathematical expressions describing the behavior of subatomic particles."

nevermind

Anonymous

demonstrations.wolfram.com/…

@0celóñe7 But why doesn't Shankar mention this??

WHY

Anonymous

2:40 PM

"You can rotate an vertex into eight different orientations, each describing a completely different physical process. Included are electron-positron creations and annihilations, which contain the essence of Einstein's mass-energy relation ." Interesting. Got to read about this

@0celóñe7 I expressly said "as a vector space over $\mathbb{C}$", in which case the claim is true.

@Mostafaııııııııııııııııııııııı because the math is too hard

I'm done with Shankar's QM

4

@Mostafaııııııııııııııııııııııı It's not Shankar's fault. Almost no physicist discusses these issue unless they come up - otherwise everyone just pretends one is doing linear algebra. Not saying that's the optimal state of things, but that's how it is

@Mostafa loool

2:41 PM

@BernardoMeurer look ^

@Blue hmm, thanks. That implies that rotating a Feynman diagram does always produce something sensible, though it doesn't actually say so explicitly.

@Mostafaııııııııııııııııııııııı there are much better uses for physics books

such as keeping fans away from carpeting

Though note that putting books on string theory near a computer will cause any SSD disks inside it to mysteriously run slow.

@JohnRennie Maybe some of the data is escaping into extra dimensions.

HOLY SHIT YOU'RE A GENIUS

Anonymous

2:47 PM

@JohnRennie I haven't read this well, but it seems to discuss the rotation of Feynman diagrams.

Anonymous

You could check out the book. But well, I don't think I know enough to help you with this. My knowledge is limited to pop-sci Feynman diagrams. I hope to take up a serious particle physics course someday in the near future.

You're not really "rotating" the diagrams because a Feynman diagram doesn't really have an orientation in space - it's just a type of graph

@ACuriousMind pedant

OK so i want to learn about quantum mechanics and GR. I know single variable calculus and classical physics. I know newtonian mechanics and a modest amount of electromagnetism and optics. Can anyone recommend me path to achieve my goal stated above. thx

What this is likely referring to is the different "channels" one gets from diagrams that look as if they are rotated, but which should be thought of as different assignment of "in/out" to the external lines

Anonymous

2:49 PM

@Черенки I'm in the same situation as you. Start with the "for dummies" books and start learning Linear Algebra side-by-side (at least).

Anonymous

I'm doing the same

Anonymous

QM is more about math and less about physics

Anonymous

Same goes for GR

@Blue That's news to me :P

@Черенки read in this order: Abbott, Munkres, Jost (Postmodern), DiBenedetto, Conway (One variable, volume 1), Lee (smooth), do Carmo (Riemannian), Evans (PDE)

2:50 PM

shouldn't i have a solid background in classical physics

@ACuriousMind well, OK, you can take the rotation to mean a reassignment of the in and out channels. Anyhow the book @Blue linked says that yes rotating Feynman diagrams (in the sense I mean) doe always result in a diagram that makes physical sense.

Anonymous

@ACuriousMind Sorry. I shouldn't have said....more "about" math

I do not think QM is any more "about math" than classical physics is.

Anonymous

It includes a hell lot of math

At least not when you understand "classical physics" to consist of Lagrangian and Hamiltonian mechanics, as I do.

Anonymous

2:51 PM

That's what I should have said ^ :P