The h Bar

if I understood this correctly, it seems at least for systems with translational symmetry and described by scalar fields, nearly all the entropy of the system is being locked up in the zero mode

2:01 AM

@ACuriousMind Let $\mathfrak g$ be a real Lie algebra and $\mathfrak h$ a complex one. If $\phi:\mathfrak g\to\mathfrak h$ is a Lie alg. homo, then there's a unique extension $\phi:\mathfrak g_\Bbb{C}\to\mathfrak h, X+\mathrm i Y\mapsto \phi(X)+\mathrm i\phi(Y)$.

Why is it unique?

I'm probably being stupid, but doesn't $X+\mathrm i Y\mapsto \phi(X)+2\mathrm i \phi(Y)$ work too?

Does the requirement that the extension be a homomorphism pin it down uniquely?

Alfred Centauri

@peterh all that's missing is the cape.

@ACuriousMind Ok, that doesn't look like it's a homomorphism.

But I don't see an actual uniqueness proof.

user228700

3:58 AM

Hello :) Does anybody around here know anything about the Dulong Petit law?

4:10 AM

Sounds made up

user228700

@0celo7 Haha no! It's real: answers.yahoo.com/question/index?qid=20110402153458AAWlX6d

4:48 AM

@KaumudiHarikumar Yes. Why do you ask?

@JohnRennie I can't do high school geometry :(

I'm trying to find a circle through three points

user228700

@JohnRennie Oh, I was wondering how this is a law.

@KaumudiHarikumar Because the houses of congress approved it and the president signed it into law

@KaumudiHarikumar Thermodynamics was largely empirical in its early days so the laws were baesd on observation rather than a theoretical understanding. The Dulong Petit law dates from those times. Although you'll still find it mentioned in books it's a historical artefact these days.

I have to solve a system

4:55 AM

It's mentioned in books because it's explained by the Einstein (yes that Einsten :-) theory of specific heat.

user228700

@0celo7 :P BTW, I know a slightly long way to find that circle of yours.

$(a_1-x_1)^2+(a_2-x_2)^2=r^2$

$(a_1-y_1)^2+(a_2-y_2)^2=r^2$

$(a_1-z_1)^2+(a_2-z_2)^2=r^2$

user228700

@JohnRennie Oh, wow, OK. Thanks sir :)

It's """"easy"""" to solve this.

But the solution is pretty horrifying.

Maybe it's not easy.

$-2(x_1-y_1)a_1-2(x_2-y_2)a_2+x_1^2+x_2^2-y_1^2-y_2^2=0$.

$-2(x_1-z_1)a_1-2(x_2-z_2)a_2+x_1^2+x_2^2-z_1^2-z_2^2=0$

I should be able to solve that for $a_1,a_2$.

user228700

@0celo7 Sadly, I dunno what u're typing. Mathjax not on; using phone.

4:58 AM

And somehow get $r$.

Just plug everything back in I guess.

Pretty horrible.

@JohnRennie Any ideas?

Hmm, I can't solve that in general.

Could be degenerate.

@0celo7 Take a pair of points and compute the perpendicular bisector of the line joining them. Do the same for a different pair. Where the bisectors intesect is the centre of the circle.

@JohnRennie I can use Google too.

I didn't Google that, it came out of what I laughingly refer to as my memory.

I don't know how to find the intersection of two lines.

hmm, how do I pick the coordinate system?

the bisectors could be orthogonal and one of them might be undefined

5:19 AM

Hi, everybody.

@KaumudiHarikumar In physics, a "law" is a well established pattern which may not have any real roots in a deeper theory. Many things were discovered historically before they were understood as consequences of more fundamental principles, and so were called "laws", even though they're now "obvious consequences of other stuff".

Now if only we can construct a system full of these majonara zero modes, then we can have basically a very large heat sink in a small lump of material

5:35 AM

hey everybody

Morning.

SO anybody had their 'aha ' momet(Having epiphany/intuition about some physic problem) today?

Not physics

But math, sure

user228700

@DanielSank Hello! OK, thanks for clearing that up :)

share with us then

hmm..quite inactive

Hari Prasad

5:44 AM

hi

@Xasel uh

I don't remember

but I usually have one every day

Hari Prasad

@0celo7 what does your profile pic mean?

Cruel Summer (GOOD Music album)

@HariPrasad it's an album cover "Cruel Summer"

Cruel Summer is a compilation album by recording artists of American record label GOOD Music, released on September 14, 2012, by the label and Def Jam Recordings. American rapper Kanye West, head of the label, first revealed plans for a label collaborative album in October 2011. The album produced four singles—"Mercy", "Cold", "New God Flow", and "Clique"—that charted on the US Billboard Hot 100. The album features appearances from West himself, along GOOD Music signees Pusha T, Big Sean, Teyana Taylor, Cyhi the Prynce, Kid Cudi, John Legend, Common, D'banj and Malik Yusef, and also feature...

Hari Prasad

@JohnRennie Oh thanks

It is a striking image. It looks a bit like some image of a goddess. Something that might have come out of ancient Rome or Greece, or possibly the Asian subcontinent. It was designed by Virgil Abloh and Joe Perez, but Googling has failed to discover any clues as to what inspired them.

user228700

6:10 AM

@JohnRennie Speaking of profile pictures, you said @DanielSank looks like a mad scientist the other day. I can't help but notice that you look a little like an evil genius :-)

user228700

(I hope you won't take offence to that. I'm sorry if you did; was only joking of course :-) )

@KaumudiHarikumar In my younger days (20 years ago!) I used to be a member of an operatic society. Once of the operas we did was Die lustige Witwe by Franz Lehár, and the picture is of me as a Pontevedrin nobleman.

I'm a lot older and more wrinkled now and I no longer have the beard.

user228700

Oh! I don't even know what an "Operatic society" is! Will have to look it up.

Opera

Opera (Italian: [ˈɔːpera]; English plural: operas; Italian plural: opere [ˈɔːpere]) is an art form in which singers and musicians perform a dramatic work combining text (libretto) and musical score, usually in a theatrical setting. In traditional opera, singers do two types of singing: recitative, a speech-inflected style and arias, a more melodic style. Opera incorporates many of the elements of spoken theatre, such as acting, scenery, and costumes and sometimes includes dance. The performance is typically given in an opera house, accompanied by an orchestra or smaller musical ensemble, which...

user228700

@JohnRennie Oh! Yes, I've heard of this, although I have never attended one, of course. It sounds beautiful :-) Thanks for further illustrating the point that physicists aren't confined to labs all day!

7:17 AM

[Reading This Idea Must Die] Bruce Parker probably don't understood entropy: Entropy in NOT disorder, and complexity does not imply low entropy

@JohnRennie what are you describing?

@KaumudiHarikumar How could I be offended of being called a genius?

@KaumudiHarikumar Oh you mean @JohnRennie looks like an evil genius.

Agreed.

By the way, @JohnRennie there are few mad scientists. Most are mad engineers.

7:44 AM

Ok nvm, johnrennie, tugging and danielsank, after some more extensive reading, I don't think majonara zero modes can fulfill the desired role I want for making heat flow uphill exploiting the second law. Their entropy is too small, $k_Bln(2)$ per mode, and once the normal entropy of the system reached this value, they cannot be generated anymore thus no way for cooling the system to subzero temperatures

@DanielSank 0celo7's avatar aka the album cover for Cruel Summer by Kanye West et al.

Typo: iPhone autocorrect yuggib to "tugging"

@DanielSank I found scientists to be a disappointly normal lot. Despite rumours to the contrary I've also found mathematicians to be pretty normal as well. Having said that I have met John Conway (when I was at Cambridge) and he's absolutely barking.

user116211

@JohnRennie Great! Did you two talk about some topic?

user116211

@Secret weird ;P

MonaLisaOverdrive

10:46 AM

'lo again all

Hello everybody. I know this is going to sound like "ugh, another dilettante" :) because I'm going to sound clueless, but I am deeply involved with physics.

MonaLisaOverdrive

RE: recommendations from two weeks ago, given the preface I read I don't think the Shankar book will work for me, unfortunately

and I wanted to know...

@Parabola Yes? Don't keep us in suspense :-)

if anyone has any ideas how to go about I don't know doing research, or working in a lab, considering that I'm in high school and have virtually no clue how to do the "real stuff"

you know, in the field

10:50 AM

@Parabola Are you asking about research you could do now? As opposed to asking how to get a career doing research in the future?

yes, research I can do know

What country do you live in?

India

Ah, I know nothing about how the educational system works in India.

In the UK a lot of universities run courses for schoolchildren to get experience doing research.

I would start by looking to see if anything like that is available to you.

I'm afraid it isn't very "do" oriented, more "think" oriented.

I've talked to physics teachers at school, but apparently there aren't any programs where one can work building/experimenting, although the admins are thinking about building a workshop that will probably be ready by the time I graduate :(

10:59 AM

Even in the UK any practical work you do while learning physics at school isn't real research. It's just a way of getting you used to doing experiments.

Have you tried looking for this sort of thing using Google?

user116211

Hey @JohnRennie, did you see the curriculum of 1st year Physics course in Oxford?

@JohnRennie I would like to continue our discussion

The matter wave is a wavefunction that describes the particle. Actually I wouldn't use the term matter wave as I think it's obsolete. A propagating particle is described by a wavefunction and you can calculate things like the energy and momentum from the wavefunction. So I think you should forget about matter waves and learn about wavefunctions. — John Rennie 7 mins ago

user116211

I did notice there was complex analysis in the very first year O.o

user116211

I never actually can imagine of that in the first year.

@OsheenSachdev the wavefunction isn't an oscillation in any medium.

Wave function

A wave function in quantum mechanics is a description of the quantum state of a system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters ψ or Ψ (lower-case and capital psi). The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the wave function can be derived from the quantum state. For a given system, the choice...

11:06 AM

@JohnRennie and how does it propagate?

@OsheenSachdev I'm not sure that question means anything. The wavefunction is a function of spacetime (so it varies in both space and time) that describes the particle.

A wavefunction can have a non-zero momentum associated with it, in which case it will describe a moving particle.

But a wavefunction can describe, for example, the electron in a hydrogen atom, and (on average) that electron stays in the same place so it isn't propagating anywhere.

@JohnRennie okay...so basically I should just ignore this...blob:web.whatsapp.com/e4a1f521-5693-45b7-a887-a87808eff4de

wait

@OsheenSachdev .....

Phone problems :-)

user116211

@OsheenSachdev You can delete it.

@MAFIA36790 thANKS

11:17 AM

→ 1 message moved to Trash

That is complete rubbish.

well Indian books

Well not complete rubbish - the de Broglie wavelength is indeed $h/p$.

lol yeah but the rest

Can you plz send a good source to read from

11:21 AM

@OsheenSachdev there are rubbish books everywhere and I doubt India has more than most :-)

or some online website

user116211

@OsheenSachdev There are many; go to our Big List.

You want an elementary book on quantum mechanics. I don't know any offhand, but I bet lots have been mentioned on the site.

@MAFIA36790 something I could refer to for cbse too...

8

Q: Popular books on QM

After some discussions with my friend about some "popular" aspects of quantum mechanics, my friend asked me whether there exist any books that could convey the basic ideas in a non-technical way (my friend is not in any technical field). I am in mathematics, so I'm not aware of any such texts in ...

user116211

11:23 AM

You can go with Feynman Lectures Vol.III for introduction; it's available online in the Clatech site.

Ok guys I this is off topic for physicist but still(I guess you guys have enought mathematical training for answering this)

resource-recommendations faq

208

Q: Book recommendations

Every once in a while, we get a question asking for a book or other educational reference on a particular topic at a particular level. This is a meta-question that collects all those links together. If you're looking for book recommendations, this is probably the place to start. All the question...

Q: Approximating a polynomial to a piece-wise function

1

I was going through my introductory calculus book(for high-school student) by a Russian author(N.Psikunov) where I encountered a theorem without proof named: Weierstrass Approximation Theorem So how can we apply this theorem and apply it to piece wise functions?(any general approach?)(say a sim...

calculus real-analysis sequences-and-series complex-analysis polynomials

Ok guys I this is off topic for physicist but still(I guess you guys have enought mathematical training for answering this)

Any suggestion orppointers

MonaLisaOverdrive

@JohnRennie: As a non-physicist, I'd have to chuck in How To Teach Physics To Your Dog…if it's not there already

user116211

@OsheenSachdev If you want a clear conception, you need to consult through those books mentioned; I don't think any high school book in india has ever done that.

11:26 AM

@MonaLisaOverdrive it's there already :-)

user116211

There are many introductory books like Feynman, Schiff, Schwabl etcetera which you can go through. The only prerequisite is you know a bit of classical mechanics and electromagnetism and a bit of linear algebra and pde.

Okay Thanks @JohnRennie and @MAFIA36790

user228700

@OsheenSachdev I dunno your background but having JUST passed out and been through the same stuff, I'd recommend YouTube; it's a great place for beginners like us :-)

user228700

11:43 AM

@OsheenSachdev Unfortunately, none of the books mentioned above will be of much use for the CBSE exams. I reccomend you to borrow(/buy) "Principles of Physics" by Halliday, Resnick and Walker. It's an eye opener compared to a lot of rubbish that we're taught at school. If you're following the NCERT books, although they are extremely detailed, the writers, I assume, couldn't have elaborated more on some topics which did need much more elaboration.

@KaumudiHarikumar Thank you

btw this is chem Structure of atom

so I need a book for chem

user228700

Ohh, chemistry! Regardless, what they teach in that chapter is what you'll learn in the last few chaps. of 12th Phy :-)

okay...thank you!

user228700

You should definitely get your hands on Resnick and Halliday if you're one of us, meaning you want to actually learn. Personally, the physics syllabus of 12th was much better explained in those books. Also, H.C. Verma. That book/many YouTubers saved my life.

Gert

www-thphys.physics.ox.ac.uk/people/JamesBinney/qb.pdf

James Binney and David Skinner (link above) I would warmly recommend to anyone wanting to understand "matter waves".

user228700

11:52 AM

@OsheenSachdev I'm rambling but one of the reasons I decided that I absolutely need to become a teacher someday is because I had terrible teachers in 12th and it screwed up my grades a lot. So, I relied on these books and YouTube to pass and pass I did. Couldn't score a centum but managed to get 95% :-)

@KaumudiHarikumar I do have HC Verma...will refer to it. Just btw even I have teaching as a profession in mind!

Q: In what sense can a complex number be a scalar?

2

A definition of a scalar like A scalar is a one-component quantity that is invariant under rotations of the coordinate system (see http://mathworld.wolfram.com/Scalar.html) seems to exclude complex numbers from being scalars, because complex numbers are generally expressed as two-component ...

symmetry group-theory definition complex-numbers

What, vectors are tensors of rank 1, not rank 2. The rest look fine to me

user228700

@OsheenSachdev Oh, that's awesome! (Both-that you already have the book and that you want to become a teacher!). There's a chap. for atoms in that book so go on and look this up in it!

user116211

@OsheenSachdev Peter Atkins' Molecular Quantum Mechanics; totally a self-contained book and if you want to dig deep, you can go with the older but quite popular Modern Quantum Chemistry by Szabo and Ostlund. The mathematics needed is developed there; so also another self-contained book.

user228700

@MAFIA36790 I'm afraid that if @OsheenSachdev is looking for help with the CBSE syllabus, these books wouldn't help :(

user228700

12:03 PM

@OsheenSachdev Which book was it? Just so I can steer clear :P

Pradeep

user116211

@KaumudiHarikumar You can skip the part you don't require; but these literatures can provide far more better insight than those high school craps; at least they helped me during my high school time.

John Duffield

@DanielSank : all points noted. No reply necessary.

user228700

@OsheenSachdev Oh, crap, really?! That sucks; it's actually supposed to be a good book :/ In any case, post questions on this website if you're unable to understand concepts and also, all those books. Some YouTubers such as Tyler Dewitt, M learning, Bright storm and Khan Academy have great vids. All the best! :-)

user228700

@MAFIA36790 Oh, I see. Well, in my 12th, it was a struggle to keep up with everything and I didn't think that there'd be enough time to read advanced books.

user228700

12:09 PM

@OsheenSachdev Also, Doc Schuster. That guy's so awesome! (For physics)

Space Otter

1:06 PM

So in the very early universe there was huge clouds of helium ect. And these gravitated into clumps which condensed and formed stars?

1:54 PM

Who wants some laser smoke rings?

John Duffield

"Spatiotemporal optical vortices, or STOVs (thin, gray ringlike objects), are newly described three-dimensional light structures that strongly resemble smoke rings".

What goes round, comes round.

Next time when your immune system is fighting the disease, perhaps it is worthwhile to check how the microbes interact with it, as there are ways to handle it without exposing the pathogens to high selection pressures

@SpaceOtter hydrogen

2:18 PM

We are in a world of information. Measures need to be taken to prevent someone stealing your 3D printed blueprints

Rewiring photosynthesis for chemical synthesis

vzn likes solitons, may find this feeding behaviour of stokes soliton interesting

2:37 PM

I wonder what it will mean for espionage when quantum networks are mature in the future...?

Since we're posting links, I found this interesting. Maybe WIMPs don't exist ...

NASA Scientist Suggests Possible Link Between Primordial Black Holes and Dark Matter

Well, whatever they are, wish one day I have a bag filled with them for me to play with on my table

Meanwhile, a new way to fusion for the inertial confinment fusion appraoches. Inertial confinemnt is not as popularly disucssed compared to stellarators and tokamaks

Here's something Danielsank and my chemistry professors will be interested in: A metric that shows the influence of an article, a possible way out of the journal impact factor metric problem

Research like these (fans make relieving the heat of elderlys worse), reminds us of an art friend of mine, that we have to always see what the data said and avoid putting too much expectation of some patterns to ensure we are not being mislead by how beliefs and preconceptions

Hey, try to induce some kind of zero modes like states in these structures so we can soak up as much heat as we can for better thermoelectrics

John Duffield

3:00 PM

WIMPs don't exist, but "dark matter" does.

Meanwhile, the LHC guys are using the 2012 data to formulate a new boson model. A 270 GeV boson predicted to mediate the interaction between dark matter

...why are you posting so many links, @Secret?

vzn style sharing (and currently the chat is not active enough for me to be in communication mode)

@JohnRennie Maybe your conception of "normal" isn't quite normal ;)

I do predict myself will have questions coming up in a few days but I just started reading about lagrangians in susskind's book, and PSE have been doing pretty good at explaining the lagrangian concepts

3:07 PM

@ACuriousMind :-)

By the way, here's something I saw in an exhibit today

I thought I saw a scifi energy reactor of some sort. I then realised I am mistaken when I read about the artist who build this thing is because he want to explore human interactions with engineering components

The exhibit is about how 3D printing and computer aided design have tranformed the way we create art forms and visualise scientific data

Q: Matter waves require a medium for propagation

We have been visited by some high schoolars lately and we get to learn a bit about the various things that happened in India's physics curriculum. Johnrennie has the details

0

I have read: Matter waves require a medium to for propagation. Matter waves do not leave the moving particle, i.e. are not emitted. But when a particle is moving with some velocity in vacuum, what happens to the matter wave? Matter wave can neither leave the particle nor can th...

waves vacuum matter

user116211

3:23 PM

@Secret That's why i never followed the curriculum; my first book was Feynman and I'm fortunate about that.

user116211

@Secret Simply rubbish.

user218912

classes start tomorrow ;o

user116211

@3075 good!!

user116211

Oh, you changed your avatar, I see.

For me, I tend to cross check what is taught by the curriculum with my professors. We sometimes do foudn stuff in the curricum is wrong and the professors just reminds us to bear in mind of it for the rest of your studies, even though we still need to answer those answers in the exam

user218912

3:25 PM

I'm kind of screwed because I have a small (but wide) scratch right in the middle of my face and I look ugly now.

user116211

@3075 So?

user218912

bad first impression.

user116211

C'mon your knowledge creates the impression and not your face; you know that; isn't it? No one will think you are from some gang because of the scar ;P

user218912

lol

user218912

If only classes started in a week it would heal.

user218912

3:29 PM

oh well

user116211

@yuggib o/

@ACuriousMind cmon fam I asked you a rep theory question :(

@0celo7 1. I've got a terrible hangover. 2. I don't know what exactly the question is - if you have a map on $\mathfrak{g}$ and you want it to extend to $\mathfrak{g}_\mathbb{C}$, then requiring it to be the original map on $\mathfrak{g}$ and to be $\mathbb{C}$-linear already fixes it, it has nothing to do with Lie algebras or representation theory.

3:45 PM

1. is an excuse to do more mathematics, not less

@ACuriousMind I don't understand 2.

@0celo7 For any real vector space $V$, if I give you a linear map $\phi: V\to W$ and a linear map $\psi: V_\mathbb{C}\to W$ with $\psi\rvert_V = \phi$, then it follows directly that $\psi(v+\mathrm{i}w) = \phi(v)+\mathrm{i}\phi(w)$.

@ACuriousMind You know I don't know enough linear algebra to see that...

No, I don't know that

Because you don't need to know anything other than what I wrote there

The only things you need to know are that the maps are linear and that $\psi\rvert_V = \phi$.

That description looks like complexification to me

@Secret What? Yes, we are talking about the complexification of a vector space.

3:53 PM

@ACuriousMind What?

ACM: nothing, it's just I recognised it to be describing complexification back in my linear algebra course

How does one prove it

@0celo7 Since $\psi$ is linear, $\psi(v+\mathrm{i}w) = \psi(v)+\mathrm{i}\psi(w)$. Since $\psi\rvert_V = \phi$, this is the same as $\phi(v)+\mathrm{i}\phi(w)$. QED. I honestly don't know how this is not obvious.

@ACuriousMind Why doesn't $\psi(v+\mathrm i w)=\psi(v)+2\mathrm i\psi(w)$ work?

Then $\psi$ is not linear, $\psi(\mathrm{i}w)\neq\mathrm{i}\psi(w)$.

3:57 PM

Ok, but how do you prove that what you said is the only choice

I didn't make a choice

I just assumed that $\psi\rvert_V = \phi$ and that both maps are linear and out fell that formula

There is no choice here, that was the proof of uniqueness already

What?

I have no idea what confuses you.

I don't see the proof of uniqueness.

Please state exactly which statement you think needs to be proven.

4:06 PM

@ACuriousMind I don't understand what complex linearity means.

I don't believe that.

I wouldn't address or reply to questions of the form "What?" without further clarifications if I were you @ACM.

What?

Q: About the notion of the self-interaction of a field

1

In QFT it's very common to hear (read) about the self-interactions of a field. e.g. there's the self-interaction terms of the Higgs field, that come with $\lambda^3$ and $\lambda^4$, right? But I still don't understand what it means? In my mind fields only interact with things around it, like gra...

quantum-field-theory lagrangian-formalism terminology field-theory interactions

Hmm, that's a huge blow to my usual "A interacts with B" mindset. Seems I am going to spend a lot of time wrapping my head around quanutm fields when I start reading QFT

(My current (potentially flawed) mental picture that is based on possibly half baked understanding of gauge theory in wikipedia is that if we have some free field, it is the same everywhere in spacetime hence global. Interaction terms, however introduce "wrinkles" in the field thus making its operator value differ from spacetime point to point, and thus the field now becomes local)

yuggib

4:33 PM

@MAFIA36790 \o

is the gravatar issue going to be resolved?

However, I am pretty sure thinking of interacting quantum fields as "after some time, operator valued wrinkles that spread outwards bounded above by the speed of light" is still too classical to be the correct description...

@yuggib This is the relevant meta.SE thread, it doesn't seem that gravatar is very responsive on this issue

@ACuriousMind I guess I'll just mark it down as another "linear algebra is weird"

(For those who are wondering what I meant by "wrinkle", consider a scalar field of binary numbers as follows: At t=0 it looks like this
111
111
111
However at t=1 interaction occurs and now it becomes something like this
010
000
101

later at t=2, it might look like this
101
001
100

Now imagine replacing the binary numbers with operators, and then you will arrive at what I talked about as "wrinkles"

4:50 PM

From this week's New Scientist:

Wait till it discovers it's going to be crashed into Saturn :-)

and crushed by the atmosphere

user116211

@JohnRennie ;_;

Oops, Saturn not Jupiter.

dmckee

@Secret Alternately we might be forced to finally come to grips with the fact that the digital world is a different place than the analog one with respect to intellectual property and start trying to figure out how this new world can be made to work on its own terms instead of trying to force it into the mold of the old world.

But I'm not holding my breath.

Agreed. The digital world is a very different place. If you have been keeping an eye about those occulus rift demonstrations becoming more widespread, the scientists talkign about big data more frequently, the impacts of 3D printing and CAD on art forms and modelling, and then how facebook and google are basically have the power to control what we read form news itself (The last item I read from last week's newscientist)

then perhaps we might need to start to learn its rules, just as how we might need to eventually forget about the notion of particles completely in order to better understand QFT

>This also works with angular momentum when coordinate is theta. Hence, let's define a generalize momentum this way: $p_k = \frac{\partial T}{\partial\dot q} =
\frac{\partial}{\partial\dot q}\sum_i\frac{1}{2}m\dot x_i^2 =
\sum_i m\dot x_i\frac{\partial \color{red}{x_i}}{\partial\dot q_k}$

Based on chain rule, shouldn't red words be $\dot{x_i}$?

Source

5:06 PM

@JohnRennie Here is a more miserable version.

@BalarkaSen ;_;

@JohnRennie Travis Scott Through the Late Night ft. Kid Cudi.

Manfred Mann - Blinded by the Light

@0celo7 song from my youth, recently rediscovered:

►

@JohnRennie Dunno if you can even listen to that song

it might be an Apple Music exclusive

but it's pretty trippy

if you don't like autotune humming you'll think it's shit, of course

5:33 PM

@JohnRennie meh

5:47 PM

Hopefullly after reading Emmy Noether's paper, I will understand how to build all Lagrangians...

@JohnRennie :(

@Secret $L=T-V$...

No, that won't prepare me for QFT

@0celo7 Interesting. Now give me the Lagrangian for a spin 1/2.

@DanielSank $\bar\psi (\mathrm i{ /\!\!\!\partial} -m)\psi$

hmm

I've forgotten how to Feynman slash.

5:56 PM

$\not{\partial}$

No, that's terrible.

@BalarkaSen Not quite.

@DanielSank This question I am not sure if it is thermdynamic level or stat mech level. In a lot of macroscopic systems, they can be characterised by V, S, U,n. V and n can sometimes change without other variables changed. But I also recall that there's something called Gibbs–Duhem equation that said the 4 parameters are not independent. In thermodynamics You can either wrote a fundamental equations in the form of S(V,U,n) or U(S,V,n), and in stat mech, U and S can be

derived from the partition function. Therefore is it true for the most general systems (e.g. up to QFT level and condensed matter quasiparticles) that whenever an entropy change took place, at least one other parameter that describes the system must change with it, that is, you cannot just have S changed alone?

(NB I would like a stat mech level explanation as thermodyanmics is not very clear on the details of the entropy)

@BalarkaSen $/\!\!\partial$

hmm

:P

Aha!

$\mathrm i\,/\!\!\partial$

Got it!

6:10 PM

That's the Feynman slash?

Yeah

Weird. I'd rather prefer it passed through the middle.

...it does.

It doesn't on my screen

Neither mine.

6:12 PM

It does on mine.

@BalarkaSen Do the gold letters on your GP's spine look faded?

I haven't used mine that much that they would be faded

No

Compared to my Cheeger and Ebin, they look pretty bad

@ACuriousMind So, what does "Dünnschliffen" mean?

I have scribbled stuff up on most pages in G&P.

6:20 PM

@0celo7 I haven't heard that before

But Wikipedia tells me what it is :P

wtf

I haven't heard of the English term for it either.

And I'm supposedly good at making these things.

lol

Transmissionselektronenmikroskopie

good lord

@ACuriousMind German is such a meme language

@0celo7 I don't know what that is supposed to mean

Also, that's a perfectly fine word. A bit short, perhaps ;)

[On Noether's paper] Will figure out how to derive $\sum_{i}\psi_i\delta u_i = \delta f -\frac{d}{dx}\left(\frac{\partial f}{\partial \left(\frac{d u_i}{dx}\right)}\delta u_i\right)$ from $\int \delta f (x,u,u') dx = \int \sum_i \psi_i (x,u,u') \delta u_i dx$ tomorrow mornign as it is getting late. (overlooked something in the 2nd fundamental theorem of calculus)

6:30 PM

2nd?

there's more than one?

Fundamental theorem of calculus

1st fund is $\frac{d}{dx}\int f(x) dx= f(x)$ 2nd is some kind of chain rule involving expressions like the 1st

The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral. The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the indefinite integral of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions. The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral...

@ACuriousMind Can "Präparaten" mean "samples"

@0celo7 Yes, a Präparat is a (somehow prepared) sample

good

"Andererseits besteht natürlich die Möglichkeit, diese sehr
dünnen Präparate in vertretbarer Zeit mit sehr kleiner Leistung und sehr spitzem
Winkel zu ätzen, was bei sehr empfindlichem Material wünschenswert ist, um
Gefügeschäden durch Ionenbeschuß zu vermeiden."

Such a long sentence, gosh

@0celo7 Found another typo on Guillemin-Pollack (fortunately on Ted's list). For a good few minutes I thought I forgot calculus.

6:43 PM

@BalarkaSen Which one?

Page 138 problem #1.

I am going to print out the list and stick it to the front of my book for real now.

oh, what's the typo?

I didn't do the problem

@0celo7 $h_t(z) = e^t z$, not $tz$.

@BalarkaSen Good idea.

@BalarkaSen Ah, the flow ODE is just $h'=h$?

(something like that)

Right, which is obvious because $v$ is literally $(x, y) \mapsto (x, y)$.

6:46 PM

Ye

But for some reason I still thought I was being silly for a couple minutes.

Oh well, better stop complaining and print it out. Bubye.

"Basisstück ist ein

Messinghalter in Form eines „T “s, an dessen

Querbalken (60 mm) zwei mittels Schrauben in der

Höhe verstellbare Teflonfüße (Ø 3mm) im Abstand von

32 mm angebracht sind"

sigh

I've forgotten German

@ACuriousMind I literally have no clue what this sentence is saying

The best I can do is "The base piece is a brass holder in the form of a “T.” On the horizontal piece (60 mm) there are two screws that control the height of two teflon feet (diameter 3 mm), which are mounted at a distance of 32 mm."

But that doesn't make sense given the picture

It's an adequate translation, though.

Are the two screws controlling the Teflon feet or the Brass holder?

the next line is "Die Höhe der

Teflonfüße wird über ein Feingewinde (M8 x 0,5)

verändert."

So the screws don't control the feet

Although a closer translation would be "The base piece is a brass holder in the shape of a "T", on whose horizontal piece there are two teflon feet with a distance of 32 mm whose height is adjustable through two screws."

6:56 PM

@ACuriousMind No, the screws don't control the height of the feet

Which is why I'm confused

It pretty clearly states that they do, though

Then what the hell is the Feingewinde

It's the mechanism through which the screws are connected to the feet

what's M8 x 0,5

No idea, probably a specific type of Gewinde

6:59 PM

"Die Gewinde sind geschlitzt und mit einer

Schraube soweit gespannt, dass die Justierschrauben sich gerade noch bewegen

lassen."

yo, what is even going on now

now there's multiple threads?

@ACuriousMind what does "Gewinde" mean in this context

what kind of "thread"

Uh...it's the receptacle in which a screw turns, I think

so what the heck does "Die Gewinde sind geschlitzt" mean?

is the tightness of the threads adjusted around the screws?

I can't tell just from that description

that's exactly what's happening.

7:16 PM

@DanielSank Balarka Sen's version is even worse!

HDE 226868

Are there any guidelines for whether a computational physics question should go to Physics or Computational Science?

I've also reasoned that it could go to Astronomy, although I'm more confident that it could find a better audience here.