The h Bar

3:15 PM

@ACuriousMind lol

that's a thiq dot

@BalarkaSen I have a statement that the functions of the form $h(s,t)=f(s)g(t)$ are "dense in the space of all functions of two variables in the compact $C^\infty$ topology"

Does that mean anything to you?

Sounds like some Hirsch Chapter 2 stuff to me but I'm not sure

Bernardo Meurer

@JohnRennie Are you around?

John Rennie

@BernardoMeurer Hi. What's up?

Bernardo Meurer

@JohnRennie Take a look at the struct branch on the github repo :)

It's looking good

The collapse function is really broken though :P

it will exit with SIGABRT

Secret

One year old news, PR boxes are related to nonunitary

John Rennie

I love the overall structure ...

Bernardo Meurer

3:22 PM

@JohnRennie :)

But... ?

John Rennie

No, there's no but.

0celouvsky

@BalarkaSen It might just be some Frechet topology with uniform convergence of all derivatives on compact sets

John Rennie

Though I note you have single struct/class that does both board handling and game logic.

0celouvsky

So the usual $\mathscr C^\infty$ topology from functional analysis

who knows

what's important is that it's dense, and idk how to prove that one

John Rennie

I might be tempted to restrict the board struct/class to just managing cells on the board. Then use a separate struct/class for the game. That way you could reuse the board for other games.

vzn

3:25 PM

@Secret amazing, looks substantial, thx for sharing, more blurring of the QM/ classical boundary. any reaction yourself?

0celouvsky

@BalarkaSen I can prove the products are dense in the $\mathscr C^0$ topology using locally compact Stone-Weierstrass, but how would I go about it for the $\mathscr C^\infty$ topology?

Secret

@vzn Lubos blog in one of his well answered PSE already showed that electromagnetic fields are fundamentally quantum in nature (otherwise how it can rotate the spin state of an electron), thus it is not very surprising. However, the realisation of PR boxes via beams of light does suggest that we can use lasers to investigate deeper about correlations in quantum mechanics and elsewhere

Meanwhile, I sometimes don't really like people quantifying things with just one number via extremely complicated expressions. For example, just staring at the numbers $2 \sqrt{2}$ and $4$ it is not very clear what are the difference between entangled states and PR boxes

Balarka Sen

@0celouvsky iunno. That's a nice fact tho

vzn

@Secret afaik using CHSH inequalities on classical fields is very new/ cutting edge research (only few yrs old), although this is not the 1st along those lines...

Secret

The calculations a few post back by me on CHSH stuff suggest how little I understood how to pick correct device settings

Perhaps I am unable to get the expected $2\sqrt{2}$ might be because I use the identity operator as an observable

where it has only one eigenvalue and all vectors are eigenvectors

0celouvsky

3:34 PM

@BalarkaSen I think one has to use Stone-Weierstrass (do you know it?) for each multiderivative somehow

Balarka Sen

i do

vzn

@Secret it appears to me it is only a matter of time before someone finds a purely classical system with entirely quantum formalism associated with it... o_O ... have been musing on that myself for years...

Secret

Light is weird, I think it is best described as a relativistic quantum object, no matter how classical it seems...

0celouvsky

@BalarkaSen I'm thinking one has to use the "crazy" version of it for function algebras, not just polynomials. If you try to approximate with polynomials you're just going to run out of derivatives eventually.

AccidentalFourierTransform

@vzn they already did that in the 30's

Balarka Sen

3:39 PM

Ah, you're talking about the version which says certain classes of subalgebras are dense in C^0(X) for locally compact X?

Secret

ok, it seems I get that wrong calculation because I choose the identity as an observable. The CHSH seems to need an observable with 2 eigenvalues to work, but the identity has only one eigenvalue: 1

user228700

@JohnR: Hi :-) Did u check ur mail?

John Rennie

@Kaumudi.H Hang on, I'll check now ...

0celouvsky

@BalarkaSen It's dense for compact $X$, but not quite dense for just locally compact.

John Rennie

@Kaumudi.H Good luck, though you have massively reduced the amount of luck you need by working so hard for the last xxx months!

Bernardo Meurer

3:43 PM

@JohnRennie I will probably do that later tonight

0celouvsky

you can get a sequences that converge "locally," i.e. on each compact set

Bernardo Meurer

Could you check the BoardCollapse function see if you spot anything fishy?

user228700

@JohnRennie Thank you :-)

0celouvsky

but you might not have convergence everywhere

Bernardo Meurer

It's exploding

0celouvsky

3:43 PM

the sup norm is badly behaved on noncompact spaces

Secret

In order to understand the more nonlocal aspects of quantum mechanics, one must understand joint probabilities

and this stuff is currently still too hard for me

John Rennie

@BernardoMeurer I'll have a look at the collapse function. I can't build your code because I don't have a unix box to hand, so I'll have to cobble together some test environment.

Balarka Sen

@0celouvsky Gotcha. This stuff's too hard for me.

Bernardo Meurer

@JohnRennie SDL is multi-platform, it should work just fine on Malwindows

:P

Made by Spycrosoft

John Rennie

@Kaumudi.H here's hoping you get the right questions :-)

vzn

3:46 PM

@AccidentalFourierTransform very interesting thx much hadnt heard of that one! but its probably not purely mathematically equivalent, am guessing it is missing something key eg heisenberg uncertainty principle or something... but would like to see a close analysis of "what is missing"... think the gap could be bridged...

user228700

@JohnRennie :-) Yeah...

0celouvsky

@BalarkaSen you might need sigma compactness too, so that you don't have "too many" compact sets

Physics Meta

0

Q: The amount Tesla may have made for his inventions

I was watching a show on Nikola Tesla where they stated that invention of AC current credit goes to Tesla. And patent licence was given to Westinghouse. After some year Tesla have observed loss of company he have teared the licence. I am curious to know how much money 💰 Tesla may have made if h...

discussion

0celouvsky

Approximation theory is awful

John Rennie

@BernardoMeurer line 578 you used i instead of j

DanielSank

3:51 PM

Hi, everybody.

Secret

Danielsank, is the identity operator not an observable, despite it is hermitian?

DanielSank

@Secret eh?

Bernardo Meurer

@JohnRennie Fixed

SIGABRT

lol

DanielSank

You want an experiment that measures the identity operator?

The problem is that all the eigenvalues are the same, so you don't have to actually measure anything.

You already know the answer.

Slereah

Measure a particle's momentum, then measure its momentum times the identity operator

Bernardo Meurer

3:54 PM

@JohnRennie Ran it on Valgrind

==20605== Invalid write of size 4
==20605==    at 0x401A1E: boardCollapseCells (main.c:584)
==20605==    by 0x401321: main (main.c:179)
==20605==  Address 0x7670ccc is 4 bytes before a block of size 20 alloc'd
==20605==    at 0x4C2CF35: calloc (in /usr/lib/valgrind/vgpreload_memcheck-amd64-linux.so)
==20605==    by 0x40196E: boardCollapseCells (main.c:565)
==20605==    by 0x401321: main (main.c:179)
==20605==
==20605== Invalid read of size 4
==20605==    at 0x401A07: boardCollapseCells (main.c:578)

John Rennie

@BernardoMeurer: this is a minor detail, but you don't initialise buf to EMPTY. Using calloc initialises it to zeros, but if you ever redefined EMPTY to anything other than zero your code would break.

vzn

@BernardoMeurer sounds like buffer overrun... so now youre writing your own malware? o_O :P

4

DanielSank

^ LOLOLOL

Secret

@DanielSank Ah I see. Btw the question arises when I tried to compute the CHSH correlation function for the triplet bell state (setting $\theta = \frac{3\pi}{2}$) is that it for some reason give me a number less than $2 \sqrt{2}$ instead of $2 \sqrt{2}$

DanielSank

rekt

Secret

3:56 PM

2 hours ago, by Secret

$$\mathcal{B}=\{\lvert++\rangle, \lvert+-\rangle, \lvert-+\rangle, \lvert--\rangle\}$$

$$\lvert \updownarrow\rangle=\frac{1}{\sqrt{2}}(\lvert +\rangle+\lvert -\rangle)$$

$$\lvert \updownarrow -\rangle=\lvert \updownarrow\rangle\otimes \lvert - \rangle$$

$$R (\theta)=\begin{pmatrix}1 & 0& 0& 0 \\ 0 & 1& 0& 0 \\ 0 & 0& \cos \theta& -\sin \theta\\ 0 & 0& \sin \theta& \cos \theta\end{pmatrix}$$

$$\lvert m\rangle=R(\theta)\lvert \updownarrow -\rangle=\frac{1}{\sqrt{2}}(\lvert +-\rangle-\sin \theta \lvert -+\rangle+\cos \theta \lvert --\rangle)$$

Bernardo Meurer

Dammit I got rekd

@vzn Good one :P

Secret

and I suspect the calculation fails might be because the identity operator has only one eigenvalue instead of 2 distinct eigenvalues

Bernardo Meurer

@JohnRennie True, indeed

@JohnRennie I suspect there's something fishy on the iterator, more than that I can't tell

DanielSank

@Secret I don't understand what you're trying to do.

If you want to write a detailed question and post it on main, I can take a look.

Secret

ok, I will try to clarify it on the main

John Rennie

3:59 PM

I would use:
for (unsigned int i = 0; i < self->size; i++) {
for (unsigned int j = 0; j < self->size; j++)
and use separate variables for the cell counters. That seems simpler to me.

@BernardoMeurer I have to go. Ping me if you haven't made any headway by the end of today and I'll have a look tomorrow morning.

Bernardo Meurer

@JohnRennie Alrighty, I'm working on my Computer Architecture lab today, should put more work on this tongiht :)

Thanks for all the help!

DanielSank

I have to say this conversation is interesting from the point of view of understanding the advantages and disadvantages of various languages.

DanielSank

4:13 PM

::crickets::

skull petrol

4:29 PM

::tumble weed blows by::

vzn

in theory salon, 22 hours ago, by vzn

universe as a simulation hypothesis, holographic principle, recent developments/ notes/ minisurvey / Tmachine blog

DanielSank

@skullpetrol I actually saw one of those yesterday.

Was eating lunch with my parents in a taco joint near my work.

A pretty big tumbleweed blew into the side of the restaurant. An employee went outside, picked it up, and brought it inside the restaurant.

She took it into the back.

I don't know if that was to use it in the tacos or because it was too big to fit in a normal trash bin.

The thing was like five feet in the long diameter.

heather

@DanielSank hopefully the latter =P

skull petrol

How about trying to get Walter Lewin in here as our next guest on the AMA? @vzn @DanielSank

0celouvsky

didn't he get fired for some sexual shit

vzn

4:37 PM

@skullpetrol all for it easier said than done... heres the place for those great suggestions plz +1 at least physics.meta.stackexchange.com/questions/9068/… ... btw saw that earlier, latest lewin user is not known to be him...

Secret

[Example of a scary integral]

$$\int_{a}^{\int f(x) dx} g(y) dy$$

DanielSank

@skullpetrol Go for it.

Who dat?

@Secret Heheh, I always forget how to take derivatives of stuff like that.

skull petrol

He's an ex MIT physics prof @DanielSank

DanielSank

Hey, non-USA users, here's a really nice example of very traditionally USA music:

Paradise

►

@skullpetrol Think he'd do an AMA?

skull petrol

I'll ask.

Yes @0celouvsky

Secret

4:44 PM

If the function satisfy (forgot) continuous, then fundemental theorem of calculus applies. Let G be the primitive function, then the derivative is $G'(k(x))-G'(a)$.

Secret

@DanielSank Strongly reminds of farm music, nice

skull petrol

^

user228700

@DanielSank: Hi. Exactly what is the purpose of an AMA?

DanielSank

@Secret Yeah, we call it country music.

@Kaumudi.H A chance to spend time asking a noteworthy person questions of interest.

For example, if you were to do an AMA, I would ask about living in India, about the educational system there, etc.

user228700

> Noteworthy

skull petrol

4:46 PM

"Famous"

DanielSank

Obviously I can do that at any time, but in an AMA there is a larger audience.

user228700

Is it OK if the person in question has been convicted of sexual harassment?

Secret

Danielsank: Nah, that's definitely NOT country music, because...
Country music sounds a lot more cliche and clone than what is shared above

Sir Mashalot: Mind-Blowing SIX Song Country Mashup

►

DanielSank

@Kaumudi.H Is it ok? Well, sure, it's ok to ask criminals questions.

Do we want to host a convicted sexual harasser? Probably not.

user228700

@skullpetrol Thanks. I edited it.

Balarka Sen

4:47 PM

country music always reminds me of johnny cash

DanielSank

@Secret Wut? Maybe bad country music sounds cliche.

user228700

@DanielSank Right, well, this is what I meant. WL was convicted of sexual harassment.

0celouvsky

@Secret Let $X$ be a finite-dimensional real vector space. Let $||\cdot||_1$ and $||\cdot ||_2$ be two norms on $X$. Then there exist two constants $c,C>0$ such that $\forall x\in X: c||x||_2\le ||x||_1\le C||x||_2$.

DanielSank

You can't define a genre by it's wort examples!

Balarka Sen

i've got johnny cash on my throat?

DanielSank

4:48 PM

@Kaumudi.H Then let's not host him.

skull petrol

The original man in black @BalarkaSen

user228700

^^ Good idea.

Secret

It annoys me that my timezone is opposite to anyone else, causing me need to sacrifice sleep to enjoy the party in the chat

skull petrol

@Kaumudi.H he is an amazing physics educator, no? Arguably better than Feynman was :-)

DanielSank

@Secret here is some "blue grass" music

Virtual Bluegrass Band - I Saw Her Standing There

►

It is different from "country" in the typical sounds.

user228700

4:53 PM

@skullpetrol Yes, he really is in that his lectures are great. He is not that great of a teacher for having taken advantage of one of his students.

user228700

If that sort of thing doesn't matter then do ahead with the AMA.

DanielSank

This is a very interesting issue.

skull petrol

Indeed.

DanielSank

It is, perhaps, a moral issue.

Then the question for me always becomes: what is the purpose of morals?

For me, "morality" means "set of behavioral patterns/rules which lead to the most productive group of organisms (i.e. us)."

user228700

MIT took down all of his lectures from their website for fear that the platform would be misused by him to contact his students and speak with them in ways no teacher should.

DanielSank

4:55 PM

So then the question is whether or not having a person who is simultaneously an excellent educator and a convicted criminal would be productive.

skull petrol

and what is the purpose of life?

on the internet

user228700

Anyhoo, I'm afraid I can't participate in what seems like a productive discussion because revision. Toodles!

Balarka Sen

Lotta people out there with lotta good qualities (great scientist, great mathematiciac, great artist, great educator) but got surprising issues with their life (marked with immoral or inethical and sometimes illegal convictions). I try not to judge them black and white, but I do not defend the crimes they are convicted with. Whether or not it's appropriate to talk to them in this chat is a different, more complicated matter admittedly

I guess I'm ambivalent about it

DanielSank

^ I think this is largely reasonable.

Because yes, people have all kinds of issues that we never hear about.

skull petrol

Agreed.

user228700

4:58 PM

Alright, I'll be quick to add that he isn't a good educator for having taken advantage of one of his students. That matter is not a personal issue.

DanielSank

However, having been through graduate school my instinct is to not host this person for an AMA.

@Kaumudi.H I agree with this.

Strongly.

I will attempt to explain why in a well-reasoned way.

user228700

And I will come back and read the transcript tomorrow! (:-P) Have a great day, y'all.

DanielSank

The relationship between professor and student is massively imbalanced. The professor holds a lot of influence over the student's future.

Balarka Sen

@Kaumudi Depends on what you mean by educator, I suppose. As a teacher, sure, I agree with this. But does that mean all of his pedagogy is of no use? Nah

skull petrol

Happy birthday @Kaumudi.H

Balarka Sen

4:59 PM

It's a complicated issue, as I said. Being black and white about it is hard

0celouvsky

@yuggib Is $C^\infty(\Bbb R)\otimes C^\infty(\Bbb R)$ dense in $C^\infty(\Bbb R^2)$ in the $\mathscr C^\infty$ topology? (This is the topology of uniform convergence for each multi-derivative on compact sets.) I can't find it online. There's a sketch of this on Math Stack for compactly supported functions, but I don't think the proof generalizes.

user228700

@skullpetrol x'D Thank you.

DanielSank

@BalarkaSen This is absolutely true. A person's contributions are not invalidated by their failures.

Still, I think the issue of abuse in academic situations is such a big problem that it's important to push back against it very strongly.

skull petrol

Perhaps a meta question?

Balarka Sen

Yeah, that's what I meant. Thanks for writing that out clearly.

DanielSank

5:01 PM

^ That would be very, very interesting.

Balarka Sen

I guess I don't have any strong opinions about this at all so Imma back off

DanielSank

I am a six foot tall male and even I felt abused in graduate school.

0celouvsky

Manlet

DanielSank

@BalarkaSen Please continue! This is interesting and important.

I can hardly imagine what it is like for females to deal with a sexually aggressive professor.

skull petrol

Academia meta?

DanielSank

5:03 PM

@skullpetrol Perhaps, but frankly I don't like that site.

skull petrol

Me neither.

0celouvsky

@yuggib The issue is that one can't use Stone-Weierstrass to get the right kind of convergence. One can get uniform convergence in each compact set, but eventually one needs to fix one compact set for a construction. Approximating higher derivatives is possible, but I don't see how to do it without first fixing a compact set...you have to do some integrals.

@DanielSank Why not?

DanielSank

My point is simply this: sexual offence by a professor against a student is part of two hugely destructive problems: the dominance of professors over their students and the dominance of men over women. I am not sure what is the right way to fight against these problems.

One can argue either way:

1) We must communicate with offenders and victims to understand what happened so we can understand how to prevent it in the future.

2) We must not tolerate this kind of behavior at all; ostracizing offenders creates a more productive setting for everyone.

I'm not sure which I believe, and so I would tend to take a conservative approach and not host the person.

Now that said, in most aspects of life, I think #1 is more true.

skull petrol

#2 sounds unrealistic imho

DanielSank

I think that pushing offenders into obscurity may cut us off from avenues of understanding that can lead to improvement.

Another point: I think it's important to find out what other users think of this person. Would e.g. women find his mere presence objectionable? I simply don't know, although @Kaumudi.H's comments make me think that she would.

0celouvsky

5:08 PM

What exactly did he do?

Secret

For me, I will go for 1, if that does not work, 2 has to be enforced. So it's more like a stepwise management, and best to be dealt on a case by case basis as long resources available

DanielSank

@0celouvsky Read Google.

0celouvsky

Never mind then.

DanielSank

@0celouvsky y u so lazy?

Balarka Sen

I think knowing the fact that they are involved in these kind of offenses doesn't stop me from talking to them about physics or physics education (or alike) but I probably wouldn't engage with them casually or too friendly

Just sayin'

skull petrol

5:09 PM

It was "ugly."

DanielSank

@BalarkaSen Of course. This makes sense.

0celouvsky

@DanielSank I'm doing other things.

Balarka Sen

So if this AMA is an official thing there should be no problem. If it's an informal thing maybe it's best not be done?

DanielSank

@0celouvsky Ah, the opposite of lazy.

@BalarkaSen Hmmm, I'm not sure I agree with that reasoning.

AccidentalFourierTransform

I'm not sure I understand the reasoning

DanielSank

5:11 PM

I think the practical questions here are 1) Would users find this objectionable, and 2) Do we think an AMA with this person could happen without digressing into useless fight about his harassment offense.

Balarka Sen

That's 'cuz there isn't a reasoning.

AccidentalFourierTransform

in any case, I dont really find a WL AMA interesting

Id rather have a second heather AMA

:-P

skull petrol

We could label discussion of his offence as "off topic"

The man is guilty

Convicted

0celouvsky

In a court of law?

AccidentalFourierTransform

in a court of love

skull petrol

5:13 PM

Let's talk physics.

0celouvsky

Those are the worst

Balarka Sen

Anyway, I'm off. I think it's best to get a non-controversial person in this AMA. This chat has had enough lulz

skull petrol

Cya

AccidentalFourierTransform

bye

0celouvsky

@skullpetrol ok, how would I approximate a $C^\infty$ function on $\Bbb R^2$ by a product of $C^\infty$ functions on $\Bbb R$

AccidentalFourierTransform

5:14 PM

define approximate

DanielSank

@0celouvsky Why should we care?

0celouvsky

@AccidentalFourierTransform I want a sequence in $C^\infty(\Bbb R)\cdot C^\infty(\Bbb R)$ (product associated with pointwise multiplication) that converges in $\mathscr C^\infty$ to $f\in C^\infty(\Bbb R^2)$

@DanielSank I don't expect you to be able to answer, so you shouldn't care.

AccidentalFourierTransform

for an arbitrary $f$?

are you sure that's possible?

0celouvsky

P. Michor made the claim, and he's a pretty trustworthy guy

skull petrol

On paper :P

Secret

5:19 PM

@0celouvsky Just wondering, I suspect this is an unfinished sentence?

0celouvsky

@AccidentalFourierTransform Oh, wait, I want density of $ C^\infty(\Bbb R)\otimes C^\infty(\Bbb R)$

@Secret I can show you the proof if you wish

Secret

ok

0celouvsky

So linear combinations of functions in $C^\infty(R)\cdot C^\infty(R)$

AccidentalFourierTransform

oh that changes everything

skull petrol

That's what your gf told me :P

0celouvsky

5:36 PM

Let's start small with these approximations

Clearly I'm going to be using some form of Stone Weierstrass

Suppose $\phi:R \to R$ is smooth with subpport $\subset [a,b]$. Can I find a sequence of polynomials $P_n:[a,b]\to R$ with $||P_n-\phi||\to 0$ and $||P_n'-\phi'||\to 0$, where $||f||:=\sup_{[a,b]}|f|$?

vzn

↑ re all the AMA talk ... great to see further/ continued interest. however at this juncture "our" main challenge is getting anyone to agree. can use any help available with that. even with WLs controversial bkg, dont think would personally turn him down. anyway this was triggered by a new user named WL but is likely not him, so its all hypothetical anyway. (and maybe thats why its so much more fun to discuss at extended length...) also 2nd idea of Kaumudi as guest! :)

0celouvsky

Clearly we can find polynomials $L_n,Q_n$ such that $L_n\to\phi$ uniformly and $Q_n\to \phi'$ uniformly

Maybe I just want to integrate the $Q_n$'s

Well, $\phi$ is definitely the integral of its derivative since it's smooth

Aha.

If I write $R_n(x)=\int_a^x Q_n(t)\, dt$, then $|\phi(x)-R_n(x)|\le \int_a^x|\phi'(t)-Q_n(t)|dt\le (b-a)||\phi'-Q_n||\to 0$

AccidentalFourierTransform

I wish I could give a second downvote for the little picture thingies. — WillO 4 mins ago

😂😂😂😂

vzn

in theory salon, 39 secs ago, by vzn

→ rumor of a machine learning prj on standard model particle unification by sebastian thrun/ new yorker mag https://rjlipton.wordpress.com/2017/04/01/the-end-of-human-science/

0celouvsky

Trying to approximate a smooth function on a rectangle with polynomials

It's hard

Secret

5:58 PM

Argh I give up, I need to sleep. I think I need to ask Emilo how exactly PR boxes are more nonlocal than entanglement in a more physical context, besides the fact it reaches 4 in the CHSH

Why people love to cramp so much information on one single number, it removes all the mechanisms on how to explain things

heather

@AccidentalFourierTransform =P

reading the above transcript, I didn't realize what Walter Lewin had done - while I respect the work he's done teaching and working on physics, I think the fact he's done what he's done significantly deters me from even watching his lectures, let alone inviting him for an AMA.

0celouvsky

Maybe I should be using a partition of unity

$f=\sum f_n$ where each $f_n$ is a test function

approximate each $f_n$ in $\mathscr C^\infty$

then somehow make everything work

skull petrol

Come on @heather he's a harmless old man now.

0celouvsky

omg is @skullpetrol actually WL??

skull petrol

-_-

Secret

6:07 PM

$$\large{\sum_{y\in\int^{\int^{\int^{\int^{\int^{\int^{\int \sin (x_{7})dx_7}dx_6}dx_5}dx_4}dx_3}dx_2}dx_1}}\prod_{\prod_{\prod_{i=1}^ni}}e^{y}$$

I really need a more systematic way to handle iterative nonlocal functionals like these

0celouvsky

wtf is that

Hmm...can I metrize $\mathscr C^\infty(\Bbb R^2)$?

Sure can

lol

the proof is in some Austrian master's thesis

skull petrol

6:29 PM

11

Q: MathJax site going offline

The news that MathJax CDN shutting down on April 30, 2017 was recently brought to my attention. I am testing an updated version of ChatJax which uses the alternate server given in the MathJax post. It seems to work well, but if StackExchange is going to host a local copy to use with the sites t...

support mathjax

0celouvsky

@ACuriousMind

2 hours ago, by 0celouvsky

@yuggib Is $C^\infty(\Bbb R)\otimes C^\infty(\Bbb R)$ dense in $C^\infty(\Bbb R^2)$ in the $\mathscr C^\infty$ topology? (This is the topology of uniform convergence for each multi-derivative on compact sets.) I can't find it online. There's a sketch of this on Math Stack for compactly supported functions, but I don't think the proof generalizes.

ACuriousMind

That's probably an interesting question for someone who cares about such things :P

0celouvsky

Sigh...

@ACuriousMind Would you happen to know if Universitat Wien has theses from ~1990 online?

ACuriousMind

No idea

0celouvsky

@ACuriousMind I need to get ahold of the thesis. Is it better to email the Librarian there or the author?

ACuriousMind

6:39 PM

Also no idea, I never needed to do that

0celouvsky

I couldn't find it on their internal search.

skull petrol

Try a librarian first.

0celouvsky

If yugibb can't answer my question then I'll ask some profs at my school

If all else fails I'll just email the author of the book

He's a regular on MO, should be open to emails

Maybe

I just wish I could read this thesis, maybe it would explain this cryptic comment

What if you're Job Smith XXVI

how do you put that on forms?

skull petrol

What?

skull petrol

7:07 PM

Sebastiano

7:42 PM

Hi. Have you seen my question? Why $\textbf{E}\bullet \textbf{B}=\textbf{E}’\bullet \textbf{B}’$?
After

There are distinct possibilities:

$\textbf{E}=\textbf{B}=0$

$\textbf{E}\bullet \textbf{B}\ne 0$

$\textbf{E}\bullet \textbf{B}\ne 0$

$\textbf{E}\bullet \textbf{B}= 0 \longrightarrow \textbf{E}’\bullet \textbf{B}’= 0 $ with $\textbf{E}, \textbf{B}\ne 0$.

What is happen in these cases?

After why, when, $E^2-c^2B^2=0$ is the case of the transversal waves for any referment? There are other case? Perhaps electromagnetic plane wave? With $E^2-c^2B^2>0$ and $E^2-c^2B^2<0$ what is happen? H…

0celouvsky

please use $\cdot$ for the dot product

that fat dot is silly

skull petrol

(removed)

Sebastiano

Hi. Have you seen my question? Why $\textbf{E}\cdot \textbf{B}=\textbf{E}’\cdot \textbf{B}’$?
After

There are distinct possibilities:

$\textbf{E}=\textbf{B}=0$

$\textbf{E}\cdot \textbf{B}\ne 0$

$\textbf{E}\cdot \textbf{B}\ne 0$

$\textbf{E}\cdot \textbf{B}= 0 \longrightarrow \textbf{E}’\cdot \textbf{B}’= 0 $ with $\textbf{E}, \textbf{B}\ne 0$.

What is happen in these cases?

After why, when, $E^2-c^2B^2=0$ is the case of the transversal waves for any referment? There are other case? Perhaps electromagnetic plane wave? With $E^2-c^2B^2>0$ and $E^2-c^2B^2<0$ what is happen? How shall I p…

@0celouvsky done

0celouvsky

merci

skull petrol

Are you racist against fat dots?

0celouvsky

7:49 PM

yup

can't stand their general face shape

Sebastiano

@0celouvsky :) for your opinion how can I put well my question to be put on the site?

0celouvsky

@Sebastiano Uh, what exactly is your question?

What is $E'$ and $B'$?

Sebastiano

electric field e magnetic field

0celouvsky

I mean how are they related to $E$ and $B$

what's the context?

Sebastiano

@Qmechanic good evening

0celouvsky

7:51 PM

are they free solutions or is there a source

Sebastiano

@0celouvsky the source is special relativity. the question are lorentz' invariants

0celouvsky

@Sebastiano ok, so $E'$ and $B'$ are Lorentz transformed fields?

Do you have an explicit formula for $E'$ and $B'$?

I know such a thing exists

Sebastiano

@0celouvsky yes- i am a teacher of maths and physics 42 years. in this period i am following a special course- my professor is very fast during the lesson.

0celouvsky

Classical electromagnetism and special relativity

The theory of special relativity plays an important role in the modern theory of classical electromagnetism. First of all, it gives formulas for how electromagnetic objects, in particular the electric and magnetic fields, are altered under a Lorentz transformation from one inertial frame of reference to another. Secondly, it sheds light on the relationship between electricity and magnetism, showing that frame of reference determines if an observation follows electrostatic or magnetic laws. Third, it motivates a compact and convenient notation for the laws of electromagnetism, namely the "manifestly...

I think that should help

Sebastiano

@0celouvsky but there is not my exact question. anyway thank you very much. See quora.com/Why-is-this-invariant-in-Relativity-E-2-c-2B-2

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