did einstein really say that?

@skullpatrol Pal you have taught me Theory of Relativity by just one message, OH MY GOD ! You're great

@Loong are you there?

@JohnRennie I hv a question

High Voltage question

Anyone out there? I have a problem

> Don't ask about asking, just ask.

What’s the boundary condition? Griffiths writes $$ \oint_S \frac{x-x’}{R^3} \mathbf{J} \cdot d\mathbf{a’} $$ The essential point is that on the boundary the current is zero*(all current is safely *inside) and hence the surface integral above vanishes

I’m having very hard time in understanding this argument of Griffiths’

Probably yes. Just tell me your question, perhaps I can help.

heya guys, would it be a nice bachelor's project to study some of the representation theory of the Lorentz group?

@ShaVuklia The finite-dimensional representations there are comparatively boring, but I could see someone accepting a detailed workthrough of the infinite-dimensional unitary representation theory, i.e. Wigner's classification, as a bachelor's project.

@ThomasKlimpel I wanted to prove the distribution of union operation that is $$ \left ( A \cap B \right) \cup C = \left ( A \cup C\right) \cap \left (B \cup C\right)$$

ACM are you interested in that boundary condition problem?

@Knight You've given far too little information to be able to tell what exactly you want to know there.

@ACuriousMind Do you got a copy of Griffiths Electrodynamics?

nope

Should I send images?

Or write down the whole the thing from beginning?

Hi

@ACuriousMind Are you around?

@Knight Well, if you want someone to help you you should explain the problem in a manner so that they can actually understand what troubles you. How you should do that depends on what the problem is, which only you can tell right now.

For instance, you posted about an integral that obviously vanishes when the current on $S$ is zero, so presumably you don't understand why the current is zero on $S$. So at the very least you need to explain what the current here is and what the surface $S$ is for anyone to be able to help you.

I don’t think you needed to write such a long message. It would have been better if you would have just asked “what is it that’s troubling you?”

@ACuriousMind Anyway, the problem is when the book wrote $$\mathbf J \cdot d\mathbf a$$ I understood that we need to find the component of vector $\mathbf J$ along the direction of $d\mathbf a$ which points outwards, am I right this far?

@Knight The trick is to use $x \in (X \cap Y) \Leftrightarrow (x \in X \land x \in Y)$ and $x \in (X \cup Y) \Leftrightarrow (x \in X \lor x \in Y)$ together with the distribution law for $\land$ and $\lor$...

@Knight Sure.

@ThomasKlimpel The last sentence things means "x belongs to A and simultaneously to B or x belongs to C"

@ACuriousMind So, why does it matter whether the current is on the boundary or not, we should just care about the angle between the vectors. (wait I'm sending a drawing to explain my point)

@Knight If it's zero then $J\cdot \mathrm{d}a$ is zero, too, no matter the directions.

@ACuriousMind But we got current inside and why not to take it's dot product with the outward normal of the surface?

What does the current inside matter? When you do that surface integral, you compute $J\cdot \mathrm{d}a$ at every point of $S$, not at points inside the surface.

@ThomasKlimpel Can't we do without it? I'm trying to do it only with the help of words not the laws of logic.

@ACuriousMind Oh! Means when we do surface integrals we consider only the points that are at the surfaces? I didn't know that.

@ACuriousMind ah nice, I had also stumbled upon Wigner's classification, and I was very excited when I read about it. many thanks for your answer, I'm definitely going to propose this to my supervisors tomorrow

however, one thing that might bother me:

hasn't this result already been completely worked out?

or would it still be possible to embellish/work out some details of the proof, which could then be considered an actual contribution in my project?

@ShaVuklia Yes. If your supervisors expect you to make an original contribution beyond the write-up itself, this isn't a good project. (To what degree this is expected of a bachelor student varies highly in my impression)

@ThomasKlimpel When we do that truth table proof we actually verify that known result, how can we derive it?

@ACuriousMind Please explain that surface integral thing a little more

@Knight Just pick up any introductory text on surface integrals. To read Griffiths you probably need to understand how to compute surface integrals, and I can't teach you that in a few chat messages, especially not given I have no idea what other calculus prerequisites you might be missing.

@ACuriousMind Hm, well, I have two supervisors. My math supervisor proposed to look at Schur-Weyl duality (but I'm not convinced that the math behind that is worthy of a bachelor's project, as I've already had a semester's course in representation theory). My physics supervisor is fascinated by the fact that we can classify tripartite entangled states into two classes, and he hopes to connect this to symmetries of the standard model (he has written a (not very comprehensable) paper on it).

I feel like my math supervisor's idea is boring, while my physics supervisor's idea is too exotic for my capabilities. Do you happen to know of any interesting topic that relates (lie) algebras and particle physics (that's my physics supervisor's area of expertice) which would be suitable for a bachelor's thesis?

Because this I never thought that we are taking up integral of $\mathbf A$ only at surface points.

So how would you compute that integral there?

I thought we have to find the component of $\mathbf A$ along the outward normal at every point inside and on the closed surface $\sigma$.

like this

@Knight (Wrong, but) and once you've found that? That integral is a number- how do you get the number?

For that we need to know the vector field A

@ShaVuklia How much QFT do you know?

(if none or little, I'm afraid I don't really have any suggestions)

Unfortunately none

did you do a bachelor's thesis on a theoretical topic?

@Knight Well, you could use natural deduction to derive it. That would be related to an actual deeper reason why the distributive law holds (because the implication $B \implies C$ is a right adjoint of the conjuction $A \land B$), but probably much more confusing than simply checking that it holds (which is also a derivation, in a certain sense).

@ShaVuklia Yes, I wrote about 2d Yang-Mills theories (no original contribution beyond writing up in one place what's scattered around about a few dozen papers)

hmm, right

@ThomasKlimpel I don't know why but I find it very very hard to study natural deduction, Propositional Logic is understandable but those horizontal and vertical lines, prop, sub\\ and what not in natural deduction makes everything ....

Please give some suggestion of how can I start my study of natural dedcution

@ShaVuklia As I said, outside of QFT I have little suggestions to offer - you'll have to get your supervisors to come up with something (but if they had been fine with Schur-Weyl, they should also be fine with Wigner's classification - the latter is more ambitious but exactly as "solved" as the first one)

@Knight No, don't study it (natural deduction). There are good reasons why it feels more complicated than the classical laws of logic: It allows to derive all tautologies of intuitionistic logic, but the problem to determine whether a formula is a tautology in inutitionistic logic is PSPACE complete. The same problem for classical logic in merely co-NP complete, i.e. much easier.

@ThomasKlimpel If I want to succeed Bertrand Russell in his enterprise of reducing the mathematics to Logic what should I start with? (I know Godel put an end to it then also I want to make myself capable of at least going to that extent)

@ACuriousMind right right, fair point. though I'm guessing there might be something to say about how to use Schur-Weyl in quantum information estimation problems, which could possibly give the project some freshness (though I'm actually not at all into quantum information)

i still can't install tensorflow ;;;((((((((

@NovaliumCompany You should install Crysis 2 and try to complete it

@ACuriousMind just to be sure; is Wigner's classification ordinary material that is treated at a master's level?

thing is

it's okay to regurgitate results, but my uni doesn't want me to basically do a master's course for my bachelor's thesis

@ShaVuklia Most standard physics courses will state the result but not prove it.

alright, that is very good news for me

@Knight Good question. Maybe you can find something interesting on the materials page for Grenzen der Mathematik. Aslo settheory.net contains quite some material. For following Bertrand Russel, Dmytro Taranovsky's material might be interesting (he certainly tries hard). I started with normal textbooks in my native language, namely by 'Einführung in die mathematische Logik' by Ebbinghaus et. al.

But the English version of that Ebbinghaus book is old and makes you cry, if you compare the well written German book with that poor English translation. There is also the question why one should be motivated to dive into logic at all. One advantage is that you will be able to use the automated reasoning tools after a while, and logic is so expressive that you can tell them exactly what you want to know. Not that they will always be able to help you, but at least they understand your problem.

recommend me movies.

@NovaliumCompany What genre would you like?

@ThomasKlimpel On which mathematical topic you are currently working? Are you doing some kind of research or enterprise? I really liked talking to you.

@Knight nvm, I'll just google (since I've watched most movies and it's pretty hard for me to find something good to watch) thanks anyways

@ACuriousMind Is there a cohomology theory for W-algebras?

@NovaliumCompany No I want to suggest you some movies, tell me the genre

Crime? Romance? War? Noir?

@Knight sci fi,fantasy,thriller,drama... everything except romance

adventure

@NovaliumCompany Would you like psychological thriller?

tell me names

It is somewhat erotic, do you still want to watch it?

But it's a great great movie

tell me names.

Dressed To Kill (Brian De Palma)

Watch and discuss it with me tomorrow

nope

not my type of movies

I like 2010+

Why?

I like new, famous movies.

Adventure, Sci-fi, Fanatasy...

Old movies are great

I don't like them.

Watch The Irishman, but I'm sure you wouldn't understand it

meh, might watch it

Watch Tetro

If you won't like it then you can beat me

@NovaliumCompany

Not my type

Why do you like such weird movies?

They are just great you know

alright...

I can't suggest you any movies, we are too different

Oks, no problems

Hi all, I'm trying to design a lens to collimate the light from an LED light source. I understand that the LED is not a true point source, but I'm not sure what I'd need to do to take this into account. Currently, I'm oversimplifying the design by just measuring the beam angle at a predefined distance and using that angle to calculate the focal length of the lens. But this apparently won't work as the multiple sources of emission will emit at different angles.

I posted this question earlier: electronics.stackexchange.com/questions/481529/…, which is what has lead me to believe I'm oversimplifying the design. Could any of you point me to the right direction in terms of designing a lens for an LED?

According to the comments in that question, an LED cannot be modelled with a single angle

Which courses Nuclear postdoctoral physicists take in their first year?

@NovaliumCompany If you're using Linux, try using Anaconda python -- it is a single install, includes TensorFlow, and I've never had it not work on a system. You can even install it without root access if needed

It probably works easily on Mac also, but I can't vouch for that

@JamalS Probably? I'm afraid I don't know anything about that

@ACuriousMind my math supervisor was enthusiastic about my proposal to study wigner's classification thm!!!!

man, I'm so hyped

he said it sounded fun and relevant

you know, I had been considering Wigner very low key for a while, but I didn't dare to give it a go until you mentioned it yourself as well

somehow that helped me to go into this direction today, and now it seems I might finally have a project

it seems someone else in my country did a thesis on this as well two years ago

but I don't think that will impose a problem, as the topic is very rich

he treated it mostly as a math project, while there is so much to say about the physics behind it. so I'm confident enough that I'll be able to distinguish myself

anyhow, had to share my relief!

either way, the math behind wigner (i.e., mackey's thy on induced representations) is broad enough to spin it in many physical directions

tho wigner would be a somewhat classical approach I guess