Some do and I repair the answer.

@ACuriousMind I mean, each component is a solution of $\partial_x\phi +\tau\partial_t \phi = 0$, where $k_x=\omega_1\tau = \omega_2\tau$

JEE talk has died down. What's up with that?

Nice: smbc-comics.com/comic/the-uses-of-bureaucracy

@0celouvsky Panic, dread, and depression?

@EmilioPisanty Hmmm

That's right. Then I'm afraid I got nothing for you

ACM the false prophet

@0celouvsky you're in a harsh mood today ...

@ACuriousMind or then again maybe that means that that sum-of-cosines isn't quite as good an analog as I thought

@JohnRennie I am?

@0celouvsky In the spirit of Dirac: There is no god, and I am his prophet :P

What else did I say that was harsh?

the spin states I'm interested in do have an equivalent equation but you can choose $\tau$ consistently

@EmilioPisanty So you could, in particular, choose $\tau = 1$?

@0celouvsky you said I had a sheep as a girlfriend

@JohnRennie that's common knowledge

@ACuriousMind well, that'd be wonky dimensionally, but yes

@0celouvsky no, when I said I was going to eat the sheep I wasn't referring to deviant practices

I mean, $\tau$ is the eigenvalue there

@EmilioPisanty dimension, schimension...well, then the thing would be a joint solution in our sense!

@JohnRennie one of us is going to get banned if this goes any further :p

@ACuriousMind yeah, I think the joint solution is probably the best I can manage

anyways, I need to catch a bus back to civilization

Actually I was thinking about making lamb kebabs ...

cyalater all

@JohnRennie thanks for your help, bro :)

@MohamedZiad You're welcome. Hope it helped!

@JohnRennie yeah it did, thanks, I forgot to consider that both of the two motions don't depend on the same thing ^^

@ACuriousMind do you have any idea if

@0celouvsky no :P

I am alone fighting with around 5 ignorantes on facebook

who say physics is completely wrong

but physics is completely wrong

fight me

Physicists can't even tell me what's on the other side of Mercury

they are using a computer which works becaz of physics

@ACuriousMind I accidentally hit enter

and they talk rubbish about evolution

I will attempt again later

every mutation has to be beneficial is their version of evolution

they don't understand it but talk about it

SO WHY ARE YOU HERE

out. get out.

Smoothie, are you spying on me?

@YashasSamaga That's a pithy summary of the human condition :P

yea

@Kaumudi.H because being a smooth operator is good?

@JohnRennie "I'm not the smoothest operator in my class..."

Finite Simple Group of Order Two.

A classic.

@dmckee Heh, did you know before clicking the link? ;)

Yep.

God dammit can you not link YouTube when I'm in QM lectures

The "smoothest operator" line is pretty distinctive.

Is it so hard?

" You're going for your bachelors in fairytale studies? Good for you!"

huh

I give up

@0celouvsky You could try not clicking them.

these people do not have enough brain cells

@dmckee I cannot know what the link is before clicking on it

@0celouvsky Is it so hard not to click on YouTube links?

when they have no answer, they write some rubbish or quote some text from some random guy

I thought it was going to be a wiki link

@ACuriousMind I don't know if I should click or not

@0celouvsky My browser shows me the url when I hover over the link, but ... why are you clicking links in class when you don't know where they go?!?

^asking the real questions

I'm on mobile

@0celouvsky On android holding on the link will pop up a contextual menu that shows the url as well as options for acting on it.

What even is a smooth operator?

@dmckee I have an iPhone

Derivative to all order, maybe?

Oh, mine does the same

Does it matter?

Who knew

lol

@dmckee yeah, I thought I was going to get a wiki link explaining what it was!

@ACuriousMind I'm glad you think this is funny

WTH

"It seems to me that foolishness is a gift. Common sense seems not common any more"

He insulted me

because I put logical statements

@Kaumudi.H because that's your name

Ok moothie

I am trying to get an idea of how stupid people can be

Incoming "let it go" songs in 3...2...1...

so today I figured out how overly religious people survive

if there is no answer, just insult :)

LET IT GOOOO

@ACuriousMind NSFW (or class)

@Kaumudi.H Yes. Yes.

Oh god, to click or not to click

when someone quotes to show that there is math in the bible and I point out that circumference != 2pi r, the person tells that "scientific mathematics" (that word itself is funny) is wrong

and the bible is correct

So many links

I thought that guy made those numbers up

but it is really there in the bible :|

Haha classic

@Kaumudi.H Actually I really like the Let It Go song from Frozen. Don't tell anyone though :-)

it is a wonderful video

I think I pissed them off by quoting the NSFW video :D

Yellow orange

I would love to have complete freedom to teach a high school calculus class

It would be really fun

Oh well, I have a book to finish and a beer to drink. I'm off to tackle both tasks. See you all at 5 a.m. tomorrow.

@JohnRennie It's a hard job, but someone has to do it.

Hang in there.

When was radioactivity disproved? o0

When d' Nile was found to be just a big river in Egypt, of course.

nature.com/nature/journal/v489/n7414/full/489170a.html

@YashasSamaga I swallowed a Ni-63 capsule and am just fine

So I'm not convinced it's real

One person claimed that radioactivity is wrong and another person claimed that god set the world such that radioactivity measurements would give wrong results about the age of the earth. looool

says god is fooling the scientists

that's the only legit argument I've heard today

I wasted 1 hour fighting with these anti-science people

@0celouvsky For you or the students? :P

:-P

@ACuriousMind Well...I'd have to explain linear algebra first. So not for me, that's for sure.

@AccidentalFourierTransform Wonderfully recursive, that one :P

@0celouvsky They are usually expected to have had the rudiments in precal.

Of course, they go it in a very concrete form, so you probably won't be happy.

@dmckee I don't remember learning about vector spaces, bases, inner products, isomorphism theorems, etc. in linear algebra.

fun fact: if you google "recursion", you get the message "Did you mean: recursion"

Everything has to be understood as an actual grid of values written on the page.

I'd be surprised if any high school teaches linear algebra.

@AccidentalFourierTransform neat

@dmckee Oh god, I'd have to talk about set theory too

The definition of abstract functions...yuck

Why would you need to do that? You don't need to know that for calculus. In fact, you don't need that for anything except for indoctrinating students that set theory is the one true foundation of mathematics ;P

No mathematican really thinks about a function as a special kind of relation

See, I know that.

But I tried explaining that to my girlfriend and it didn't make sense to her

Then she took the intro abstract math class where they did that thing with relations, and then it clicked

@ACuriousMind He wants to do everything formally, of course. Which won't work for about four-fifth of them.

And then she forgot all about it and now a function is just an arrow again

Most of them are still processing math purely as concrete algorythms at that point.

@dmckee First day would go something like this

Which is a shame, because they should be able to handle some abstraction.

@dmckee My point is that you don't need the formal definition of a function to do formal calculus - "A function $f : A\to B$ is something that takes input from $A$ and gives output in $B$" is fully sufficient.

No analyst has ever cared that the proper set theoretical definition of a function is as a special subset of $\mathcal{P}(A\times B)$.

> Hello class. Some of you may have heard that calculus is the study of change or whatever. False. It's the study of the $\le $ symbol. Def. 1 A normed vector space ...

@ACuriousMind I'm not saying that anyone should care, and I think you misunderstood me

I'm saying that one should see it at least once

And if we're doing very abstract things they should know what it is formally

At least in the back of their minds

@0celouvsky Mhhhh, I agree only in so far as it belongs to some kind of universally shared experience among mathematicians.

@0celouvsky So you're going to explain ZFC to them? :P

@ACuriousMind Set theory is wrong anyway

Because otherwise you can just skip the pseudo-formality of defining abstract functions

^ Useful for CS types, too. Of couse, many consider them to be a subset of mathematicians.

@0celouvsky no

@ACuriousMind I said it wouldn't be fun for me. I would of course only explain ZF.

ZFC is inconsistent

That's why we'd start with normed vector spaces and not topological vector spaces. No need to give them the idea that C is necessary for math

@ACuriousMind I don't know how I would motivate them to care about the material

How does it even work?

I recommend "Rethinking set theory", Leinster

I certainly wouldn't have cared about it at that age

(Someone like Axler would've titled that one "Down with ZFC!" :P)

@ACuriousMind Ok, I don't need to explain what a function is, formally. But I need to explain $\cap,\cup,\setminus,\Delta,$ and De Morgan's laws.

Injections, surjections, cardinality, well ordering of $\Bbb N$ (maybe?)

Text of an exam question:

> Explain in words why the interior of an isolated conductor is all part of a single equipotential.

Answer provided by a student:

> Because the electric potential is the same everywhere inside an isolated conductor.

::sigh:: The first rule of Tautology Clubs is the first rule of Tautology Club.

@dmckee On my analysis midterm half of the people answered "prove that a one-dimensional subspace $V$ of a Banach space $E$ is closed" with "it was shown in class that finite-dimensional subspaces of normed vector spaces are closed"

I have a question very similar to physics.stackexchange.com/questions/229366/… . Can I put a capacitor and inductor at "right angles" and intersecting each other to create an antenna?

@StevenStewart-Gallus They are both inefficient antennas to begin with.

Combined they will be—at best—a slightly less inefficient antenna.

And you'll have to control the signal phase bewteen them to achieve that.

@dmckee What do you mean by inefficient? By inefficient do you mean emits lots of heat radiation? Isn't that the definition of an antennae?

I mean you signal strength is smaller that you would get with a good antenna and the same driving signal.

Okay.

I am assuming that by "capacitor" and "inductor" you're talking about off the shelf components designed to be used for their $C$ and $L$ respectively.

@dmckee Definitely no. You'd have to do some clever combination of the two.

Because they are designed to have small fields outside their own volume.

@StevenStewart-Gallus In that case the words "capacitor" and "inductor" don't specify your design.

Any object has a capacitance and an inductance.

usually those words are used for objects that have a large value of one and small value of the other as well as resistance.

That is something you can put into a circuit that acts vaguely like the idealized symbol you learned to deal with in circuits class.

The parallel plate geometry, for instance, is a very good capacitor with low inductance and low resistive losses.

Likewise for the solenoid geometry for inductors. Especially with a core and even more so if toroidal.

@dmckee is the average physicist (not people in this room) aware of things like measure theory or functional analysis?

@0celouvsky That they exist. Yeah, I think most physicist have heard of them and may even have a vague notion of what they are about.

Those able to read (much less) produce arguments in them will be smaller, but non-trivial, sets.

@dmckee A parallel plate picks up changes in separations of charge between it. A loop of wire picks up change in magnetic pulses. A loop of wire in between two parallel plates should pick up fluctuations in both voltage and magnetic pulses.

I probably rememeber a little functional analysis. From math methods in grad school. But I certainly couldn't use it without boning up.

@StevenStewart-Gallus Yes. And a parallel plate capacitor has only weak fields outside its volume if the separation is much smaller than its linear dimensions. By design it is a poor radiator.

Likewise a solenoid inductor has only weak fields outside the interior volume of the coil. Again, by design.

The geometry of these things prevents the possibly very strong changes of fields inside from having much effect on the outside world.

That's why antennas look different from parallel plate capacitors and solenoids.

Another tautological answer to my exam question. The students don't seem to know what to make of "Why ...?" in that context.

Apparently science is just a collection of facts and not a set of interrelated concepts.

::bangs head on desk::

guys 1 year ago i studied about the highest temperature(4 trillion degree celcius) which was achieved in ALICE but now i forgot why the machine don't melt at that temperatre..do you know why?

@dmckee A parallel plate capacitor is two antennae right next to each other. A transformer is also two antennae right next to each other. Could an efficient antennae be made out of a flat plate (half a capacitor) plus a circular loop (half a transformer?)

i also forgot how temperature is recorded

presumably, because that temperature was reached in a region of a few fermis, not in the whole system

^ That. Total energy was quite modest on the macroscopic scale.

and how it is recorded?

they got some sweet gluon-plasma balls that were hot

@dmckee I'm curious, what functional analysis? I don't remember Arfken talking about it

@StevenStewart-Gallus You can certainly regard them as such, but there are complication. The plate geometry is not particularly efficient to begin with and the two plates are running in opposite polarity right next to each: they very nearly cancel one another out making the whole a very inefficient radiator.

I'm not sure why this is bothering you. In a circuit you want to suppress cross-talk so having RCL type components radiating like mad would be a very bad thing.

It follows that the geometry used for ordinary circuit components is likely to be bad for antennas.

I'm sure you can design an antenna that relies on both electric and magnetic modes at once. it might even be useful, but you should design it.

how they recorded the temperature?

Hi, everybody.

probably due to the amount of energy released?

presumably, yeah

I believe there is a statistical analysis of the dispersion of the energy of the products, but don't quote me. I never did heavy-ion stuff.

I had no idea we had a graph-theory on the site.

A significant fraction of uses seem to be spurious but a few look legitimate as far as I can see.

hey all, i have this doubt, sometimes i hear about trying to modify the general theory of relativity, for various reason. Anyway I have no idea how you can do that, how do they work. I mean if you start from the principle of equivalence you can get the geodesic equation and then you can guess the Field equation in such a way it reduces to geodesic equation when it should. Now if you construct GR in this way, how can you modify it? I mean the principle of equivalence looks "too right"

You have a doubt?

yes, isn't it clear what my doubt is? How to people try to modify it, and what they assume maybe. It doesn't look modifiable to me. I'm not asking for reference, just to have an idea about how they do it

I don't know what it means to have a doubt

Do you doubt something someone told you?

@0celouvsky Don't be a jerk, just tell them that "I have a doubt" is not standard English if that's your point.

We've discussed this often enough so you feigning ignorance is clearly deception.

yeah I just googled it, I'm sorry, I badly translated it from my native language. Can't edit the comment now though.

@Runlikehell What sort of modification do you mean? One towards a theory of quantum gravity or one towards a different classical theory of gravity?

The point of all modifications, however, unless they are nonsense, is that they must reduce in the known tested cases to ordinary GR though, as you implied.

But note that "the principle of equivalence holds in all known cases" never means "the principle of equivalence holds in every case", no matter how right you think it looks, so there's always room to modify a physical theory

@ACuriousMind Both, but mainly about a classical theory. They should reduce it to the GR tested cases, ok, but is it possible to modify it without touching the principle of equivalence? I wanted to say "look too right" but I didn't have enough space to put the "" earlier :)

@Runlikehell Whether or not a modification will preserve the principle of equivalence will depend on the specific modification, and that's not my area so I don't know any of them in enough detail to comment.

@ACuriousMind Ok, thanks you still clarified a bit. Maybe I make myself clear, I have no idea ( and that's of course my limit) how a theory that incorporate the PE be different in any way from the general theory of relativity.

arxiv.org/abs/1403.7377

@Runlikehell ^ read that, whenever you have the time

@AccidentalFourierTransform Thanks, I save it.

its a great text

@AccidentalFourierTransform while preparing the exams on GR it's easier to find the time to read it that's for sure

Hi guys!

Suppose $|\mu\rangle$ is the highest-weight state of a highest-weight module of $\mathfrak{sl}(3)$. The module is spanned by the weights $\left(\Pi_\alpha \rho (L_{-\alpha})^{n_\alpha}\right)|\mu\rangle$ for positive roots $\alpha$, i.e. we act with the "lowering operators" $L_{-\alpha}$ on the highest weight to produce more weights.

I read that these states (those who don't vanish) are linearly independent, so they form a basis of the module. I don't understand why that's true. I think they are linearly independent only if we restrict $\alpha$ to the simple positive roots, because if $[L_1,L_2]=L_{12}$, then $\rho(L_{12})|\mu\rangle = \rho(L_1L_2)|\mu\rangle - \rho(L_2L_1)|\mu\rangle$, which means the LHS depends linearly on the RHS. What am I missing?

@ACuriousMind you around?

@Bass You aren't missing anything, that one should restrict to the simple roots is completely correct

@ACuriousMind If you have time, could you please take a look at the top of page 6.5 here?

The author says that such a commutator would lead to a state with fewer operators in front of the h.w. state, so it is not relevant for the inductive argument. But later he writes One can show that all of these states are algebraically independent supposing that they exist.

@Bass The $\alpha_i$ in that text are the simple roots.

god, if only physics didn't involve algebra

@ACuriousMind $\mathrm{cl}(A)=A\cup\partial A$ or is there some trickery that I'm forgetting?

@0celouvsky You could prove it instead of asking me :P

@ACuriousMind I know how to prove it, I'm asking you to double check.

A simple "yes" is a sufficient answer.

How is my "yes" better than a proof?!

...do you never ask anyone stuff just to make sure you're not having a stroke?

@ACuriousMind Not in the notation of that text. See page 5.4: This allows us to classify the roots as either positive or negative according to $\Delta = \Delta_+ \cup \Delta_-$.

@Bass On 6.3 it pretty clearly says that the $\alpha_i$ are the simple roots, unless I'm completely misreading it.

In any case, Wiki confirms it since you're trying to be a butt about it...

There probably is a notational switch between sections 5 and 6

$\mathfrak P(R)$

that's an interesting letter

@ACuriousMind OK, it's the simple roots only. But then I don't understand the argument on page 6.5 at the bottom, which explains why the multiplicities increase "to the left". It says there are $\mathrm{min}(k_1,k_2)+1$ ways of writing it in terms of a positive integer linear combination of [the negative roots]. To me, this argument does not make sense with the simple negative roots only. With all the negative roots it makes sense.

For example, you can write $\rho(L_1 L_2)|\mu\rangle$ in exactly two linearly independent ways: $\rho(L_1 L_2)|\mu\rangle$ and $\rho(L_{12})|\mu\rangle$. The third way $\rho(L_2 L_1)|\mu\rangle$ is linearly dependent on the first two ways, so we have multiplicity 2 right to the left of the highest weight, as we should have.

@0celouvsky Hi, nice name :-D

@Bass Oh, the notation is very confusing: $\alpha_i$ with one index are the simple roots, $\alpha_{ij}$ wtih two indices are all roots.

Yes, I think that comes from the simple roots in the Cartan basis being the $L_{ij}$ with $j=i+1$.

I.e. the matrices which are the identity matrix plus one $1$ in the top-right corner, right next to the diagonal, for example $L_{12} = \left(\begin{matrix}1&1&0\\0&1&0\\0&0&1\end{matrix}\right)$.

@ACuriousMind So why are there any multiplicities? If all the states $\left(\Pi_\alpha \rho (L_{-\alpha})^{n_\alpha}\right)|\mu\rangle$ are linearly independent, how can there be any multiplicities?

@Bass I'm thinking about changing it to Al-O'0celouvskyopolouß

I'm trying to be multicultural

@0celouvsky You forgot dozens and hundreds of cultures. Many people will be offended.

I got the important ones.

@Bass The "multiplicity" means that there are state with the same weight, not that the states created are linearly dependent - exactly the contrary, the multiplicity is the dimension of the space of vectors with a certain weight

@ACuriousMind Let's define $|\nu\rangle = \rho(L_1 L_2)|\mu\rangle$, i.e. the weight which sits immediately to the left of the highest weight in the standard weight diagram. What is the basis of the two-dimensional space of states with the same weight? $|\nu\rangle = \rho(L_1 L_2)|\mu\rangle$ and $|\nu_2\rangle = \rho(L_2 L_1)|\mu\rangle$?

If that's true, then the weight $\rho(L_1 L_1 L_2)|\mu\rangle$ would have multiplicity 3 because there are three ways to write it. But its multiplicity is 2.

I'm pretty sure we need the non-simple negative roots to get the multiplicities right.

@Bass Okay, you are right, your text uses all positive/negative roots, not only the simple ones

Note, however, that $\rho(L_2L_1)\lvert\mu\rangle$ is not an allowed state

Sorry, I meant the negative roots.

You mean that?

Sorry, not sure what you mean?

I agree with you that in your text, they are considering all roots, not only the simple ones

@ACuriousMind Why is it not allowed?

@ACuriousMind But then we're back here.

@Bass Bottom of page 6.4/top of page 6.5

@Bass We're not, your issue there is the same, namely that you think the state $\rho(L_2 L_1)$ and $\rho(L_1 L_2)$ are both allowed

@ACuriousMind Ah yes I see.

Only one of them is - the definition of the highest-weight representation fixes an ordering of the $L_k$

@ACuriousMind OK so the two-fold multiplicity of $|\nu\rangle$ is $|\nu_1\rangle = \rho(L_1L_2)|\mu\rangle$ and $|\nu_2\rangle = \rho(L_{12})|\mu\rangle$, right?

Ah I think I get it. A three-fold multiplicity would then be $\rho(L_1 L_1 L_2 L_2)|\mu\rangle$, $\rho(L_1 L_{12} L_2)|\mu\rangle$ and $\rho(L_{12} L_{12})|\mu\rangle$.

A two-fold multiplicity with three simple operators would be $\rho(L_1L_1L_2)|\mu\rangle$ and $\rho(L_1 L_{12})|\mu\rangle$.

Everything correct?

is there any generalisation of Schur's lemma to infinite dimensional Lie groups?

@Bass Yep, looks good

Once more, thank you!