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3:06 PM
I've never watched Star Trek
@BalarkaSen I didn't realize it was so bad until I learned functional analysis
and the mathematical approach to QM
long story short, none of what you see in the physics literature is correct
the end results might be right, but none of the stuff in the middle is
not even close
 
Although of course, @0celo7 says this without having done a QM class
I assured him that it was much worse in classes
 
@Slereah I am currently in second semester QM
I can send you my homeworks as proof
we are doing time independent perturbation theory
 
QM classes basically don't explain shit about any of the mathematical structure
 
which is all wrong too I bet
 
at least the ones I did
 
3:11 PM
> The Hilbert space for a particle in R3 with spin is the tensor product of L2(R3) with a finite-dimensional vector space V, where V carries an irreducible action of the rotation group SO(3). In this setting, the proper notion of “action” is a projective representation of SO(3), meaning a family of operators satisfying the relations of SO(3) up to phase factors (constants of absolute value one).
 
Though I think the worst I did was my GR class
 
My body is so ready to understand spin
 
The GR class that didn't explain the Einstein equation
 
what?
 
(well it was cosmology class, but still)
I think there was like one slide that showed the EFE
and then bam, FRW forever
 
3:12 PM
to be fair, they could do a course out of HE, Penrose, and BEE and never mention the field equations
 
True
 
never mention gravity either...
 
I don't think I've even seen the EFE in O'neill yet
 
are they even in there?
 
Let's see what chapter it is
 
3:13 PM
has to be if he proves singularity theorems
 
The EFE is page 336
and he writes it in the worst way
 
$G=8\pi T$?
What's wrong with that
 
He writes the Einstein tensor as $Ric - \frac{1}{2} Sg$
 
yeah, that's standard.
 
Basically the worst way to write it short of writing it in Penrose notation
 
3:15 PM
why can't we set $G=1/8\pi$ to get rid of that damn $8\pi$
 
Many books do redefine the constant
So that you only have $\kappa$
With $$\kappa = \frac{8\pi G}{c^4}$$
 
then set $\kappa=1$
> The angular momentum operators are unbounded operators and are de- fined only on a dense subspace of L2(R3)
jesus, not this again
 
There are several definitions of natural units, and in some of them $G = 1$ while others have $8\pi G = 1$
 
@ACuriousMind how would I show that $J$ is unbounded?
 
@0celo7 By observing the spherical harmonics are in L^2 and $\ell$ is unbounded for them
 
3:20 PM
take a really really spinny quantum system
that too
 
@ACuriousMind so directly from the spectrum?
that's cheating
 
@0celo7 Why?
 
@0celo7 how so?
 
Isn't $L = x \wedge p$
Which is pretty unbounded already
 
@Slereah The product of unbounded operators is not necessarily unbounded
(Consider the product of an operator and its inverse)
 
3:22 PM
@EmilioPisanty because it's very indirect
it would be nice to construct a wave function violating $||J\psi||\le C||\psi||$
Also, to apply the spectral theorem I would have to analyze the domain carefully to make sure it's self-adjoint.
I guess one could restrict the domain right off the bat
 
I want to say "Take $L$ and boost it" but I'm guessing that won't fly here :p
 
to something like $D(X_1)\cap D(P_1)\cap D(X_2)\cap\cdots$
or $D(X_1P_2)\cap\cdots$
 
@0celo7 precisely. so take an eigenfunction.
 
You can boost L to be as big as you wish!
 
@EmilioPisanty assume I don't know any eigenfunctions
 
3:25 PM
@0celo7 ..what are the spherical harmonics if not that?
You can just directly check that they're eigenfunctions, no?
 
@ACuriousMind never heard of them
 
@0celo7 welcome to a wonderful world, Dorothy
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations that commonly occur in science. The spherical harmonics are a complete set of orthogonal functions on the sphere, and thus may be used to represent functions defined on the surface of a sphere, just as circular functions (sines and cosines) are used to represent functions on a circle via Fourier series. Like the sines and cosines in Fourier series, the spherical harmonics may be organized by (spatial) angular frequency...
 
what is that website?
Will I get a virus
 
It is called the wikipedia
 
Stop playing dumb :P
 
3:27 PM
@0celo7 yes
it's called knowledge
 
nawlidge
@BernardoMeurer ^
 
it is a repository of all the most important informations of mankind
Nose-picking is the act of extracting nasal mucus with one's finger (rhinotillexis) and may include the succeeding action of ingesting the mucus picked from the nose (mucophagy). This action is condemned in most cultures; societies try to prevent development of the habit and attempt to break it if already established. Mucophagy is a source of mockery and entertainment in the media. However, some scientists argue that mucophagy provides benefits for the human body. Friedrich Bischinger, an Austrian doctor specializing in lungs, advocates using fingers to pick nasal mucus and then ingesting it, stating...
2
By the way
 
Nose-picking is not offensive, please don't flag that again.
 
Wikipedia still has the worst article on Misner space
Misner space is an abstract mathematical spacetime, discovered by Charles Misner of the University of Maryland. It is also known as the Lorentzian orbifold R 1 , 1 / boost {\displaystyle \mathbb {R} ^{1,1}/{\text{boost}}} . An intuitive analogy may be drawn with a video game screen, where a screen element exits the frame through the right side, only to re-enter the frame right away through the left...
 
@ACuriousMind This.
 
3:28 PM
"An intuitive analogy may be drawn with a video game screen, where a screen element exits the frame through the right side, only to re-enter the frame right away through the left side."
 
@ACuriousMind who the hell flagged that?
 
doesn't matter who :p
point is, don't flag it again.
 
I know who it was
 
@EmilioPisanty How does that joke go again? Knowledge is like an STI, it makes you unsuited for some jobs and you feel the urge to pass it on.
 
@ACuriousMind who calls it STI?
 
3:30 PM
@ACuriousMind never heard that one
 
We all know who flagged it
 
duffield?
 
(It was you)
J'accuse
 
@0celo7 I do, apparently
 
nope
it would have a blue thing next to it
 
3:31 PM
@0celo7 The blue thing disappears when the flag is dismissed
 
thrilling conversation, this
2
 
@ACuriousMind Can one flag twice?
 
I can prove my innocence by flagging it now.
 
Let's not dwell on who flagged it (but if that user makes a habit out of it (and yes mods can see who cast a flag), we'll need to have a word).
 
3:33 PM
@ACuriousMind can you please clear my name
it was not me
I'm being attacked
 
@0celo7 I think so, yes
 
crap
 
can I flag my own posts?
 
please help me out here
 
(and if so, why?)
 
3:35 PM
I just did
ACM don't ban me, that was a test
"Your recent moderator chat flag was inappropriate and declined. Please use moderator flags in chat only in very serious situations."
sorry!
 
@EmilioPisanty Yes, you can, I think mainly if you posted something you need to have deleted (like accidentally revealing PII)
 
@ACuriousMind ok
I'll flag my own post as offensive some day
 
sad
 
It's kinda like the peer-pressure badge
 
Never really understood the reasoning behind that one. "Hey, look, I made a post so bad that I thought it better to delete it!"
 
3:40 PM
I deleted one of my own post once
I just realized the answer after I posted it and it was dumb
 
well, it really sticks out on my choose-your-next-goal gathingammy
makes for quite a contrast
heck, if there's four of us we could all get one with only a marginal intrusion on the front page
also possibly an undue abuse of the system
 
That much effort for a lowly bronze badge? :P
 
The badge of being bad at stack exchange
Quite the coveted badge
 
By "post" do they mean question or answer?
I could easily get that one
 
@0celo7 Either, I think
 
3:45 PM
either way, really
I'm on it.
I just have to ask JD how do write an answer :)
 
Einstein Haas
 
Please don't post purposefully bad material to get that bedge (that's why I said I don't understand why we even have it)!
 
Photons round a Moebius strip
what else was there
 
I had one or two wrong answers where I think I could've gotten it if I had just waited longer to delete them
 
wow, you had wrong answers?
 
3:47 PM
I have plenty of wrong answers but usually they don't generate that much interest
 
@0celo7 I'm pretty sure I also have upvoted ones which are wrong and just no one has pointed it out to me yet
 
Well, you can't really stop me from getting the badge
brb
0
Q: Is thermal conductivity constant in Fourier's law?

Sourav DalaiIn Fourier's law we take thermal conductivity as constant in a particular direction, but if there is different temperature at two ends then intuitively there will be a temperature gradient, which means different temperature at different point throughout the solid. Also thermal conductivity is dep...

 
So I bought a whole bunch of beef tallow
 
my victim
 
Gonna make some good french fries tonight
 
3:49 PM
@ACuriousMind happy to downvote if they're at -2 and you briefly undelete them =P
 
@Slereah ...isn't that for making candles?
 
also for making french fries
Put it in the frier
Bam
Delicious fries
you can also eat it raw, of course
575 calories per 100 g
quite a filling meal
 
Is that a hypothetical or are you actually eating raw beef tallow right now?
 
'fraid not
I don't think raw animal fat is very good
 
what even is beef tallow
jesus
 
3:55 PM
@0celo7 don't ask
 
people eat that?
 
it's better if you eat it and don't ask what it is
 
Well it is used in the preparation of some foods
 
> Nutritional value per 100 g (3.5 oz)
Energy 3,774 kJ (902 kcal)
Carbohydrates
0 g
Fat
100 g
Saturated 42 g
Monounsaturated 50 g
Polyunsaturated 4 g
Protein
0 g
Other constituents
Cholesterol 109 mg
Selenium 0.2 mg
fat 100 g
my god
 
well it is raw fat
It's like drinking a tall glass of oil
 
3:58 PM
@Slereah I'm a red-blooded American, I drink oil every morning to remember what I'm fighting for.
 
Beef tallow used to be what McDonalds used for french fries, speaking of America
They switched it in the 90's though
 
the best fries are from Chick Fil A
do they even have that in Europe?
 
I don't think so
There aren't that many big American fast food chains in France
McDonalds, KFC, some Burger Kings
 
Hmm, if 2016 is the year of physics, is 2017 the year of chemistry...?
http://www.sciencealert.com/forget-what-you-learned-scientists-might-have-just-created-a-stable-helium-compound
 
why was 2016 the year of physics?
 
4:00 PM
I dunno
 
gravitational waves for starters
 
Was there a big physics thing in 2016?
 
I'm tired of hearing about those
 
Yeah we never hear any really fun physics news
I'd like some SUSY confirmation
Or topological defects
 
@Slereah maybe gravitational waves …
 
4:03 PM
@Ramanujan 0celo7 just said he is tired of hearing those
 
@Slereah That'd be nice!
 
Or better yet SUSY proven wrong
Take that string theory
 
@Slereah The annoying thing is that you can't really prove it wrong except by not detecting it, ever
 
Well we're well on our way to proving it wrong, then!
 
@Slereah ...actually, it's perfectly possible to get non-supersymmetric 4d theories from string theory, they're just much harder to understand so most people do SUSY compactification
F-theory has some good progress on fluxed models that aren't all supersymmetric I think
 
4:05 PM
@ACuriousMind get on that pls
I want faster phone internet
 
How do you generate fermions from string theory without SUSY?
 
2016 also have some kind of trailer sounding things in particle physics such as that Hungary proton experiment, the proton size puzzle deepens as well other possible hints of beyond SM physics
 
@Slereah Well, the 10d theory is still a SUGRA, but if you compactify on something that's not a Calabi-Yau, supersymmetry just gets completely broken.
Still, the 10d theory has the fermions already, and the KK reduction of fermions is fermions.
 
haha yes good conversation
 
Quite unfortunate I don't understand string theory so I don't have a clue about all that
 
4:09 PM
@AccidentalFourierTransform ???
 
Btw, Slereah, recall we had that Deutsch Polizer spacetime discussion the other day? It appears a computer algorithm has computed something similar as a resolution to one model of grandfather paradox
 
@JamalS : I'm not misunderstanding anything. Don't think you can weasel out of the crucial point via some Humpty-Dumpty claim that existence doesn't mean existence. I made the crucial point, it stands, and I await my 500-point bounty. — John Duffield 2 hours ago
 
> The computer’s second solution is more interesting. The snag is it only works if the father also has the ability to travel in time.

The story goes like this.

In 1954 Marty’s father George travels forward in time one year to 1955, when he impregnates Marty’s mother Lorraine before immediately returning back to 1954 – just as his future son, Marty, arrives and kills him.

Because George’s quick foray into the future allowed him to already conceive his son, the paradox disappears.
 
@AccidentalFourierTransform JD is awesome
Almost at Lumo's level
 
@AccidentalFourierTransform I already said it to Jamal earlier, try to not discuss chat-banned users in chat.
 
4:10 PM
I didnt say anything
I copied and pasted
his words, not mine
 
I'm not saying you'll get banned or something, but it creates unneccessary friction
 
@ACuriousMind This is the moderator version of "I'm not saying you'll lose your kneecaps in a freak accident"
 
@0celo7 lol, no, it isn't. If you don't violate Be Nice I won't kick anyone for mentioning users (or quoting them), I just think it'd be better if we didn't talk about chat-banned users here.
 
4:14 PM
those animal fat fries are pretty good
 
(he's frying them in animal fat, not making fries out of fat)
Or is he??
 
that's what you think
 
yes
 
I only fry things in pure water
2
 
4:15 PM
 
@AccidentalFourierTransform Your meals must be sad affairs
 
@AccidentalFourierTransform typical british food
 
boiled fries sound pretty bad
 
did you flag that? really?
 
4:16 PM
(removed)
 
worse than microwave fries
 
who flagged?
 
$\color{gray}{\text{(removed)}}$
 
@AccidentalFourierTransform the queen shall not be disrespected!
2
@EmilioPisanty you need to make it sans serif
 
@0celo7 ah, yes
$\color{gray}{\mathsf{(removed)}}$
 
4:18 PM
it's too dark, hmm
 
oooh, yeah, that's not quite the sans serif I was hoping for
 
...I look away from the chat for one freaking minute and AFT manages to get auto-suspended?
 
@ACuriousMind he had a vile gif up
 
I see it
Oh, well
 
@ACuriousMind well, he did say he only fries things in water
puzzling statement for a spaniard to make, but oh well
 
4:19 PM
how do you know he is Spanish?
never mind
 
the maracas
 
I see it
 
@0celo7 The cat looks decidedly Spanish, don't you think?
 
@ACuriousMind does my cat look German?
or Swiss? Where was Albert from anyway
 
As I remember, it mostly looks bored
 
4:21 PM
savage
 
$\color{silver}{\mathsf{(removed)}}$
 
are you saying my cat does not get entertainment?
 
oooooh, there we go
 
@0celo7 Spin structures are good
 
@BalarkaSen what do you know about them
 
4:22 PM
@0celo7 It didn't seem impressed with most of the books
 
I know what they are; I also know a bit about why we care
 
because I only have math books @ACuriousMind
Einstein was bad at math
 
You know what book has cats in it?
Category theory book
Mine has a drawing of a kitty in it
 
Did you draw it?
 
in Mathematics, Nov 13 '16 at 7:08, by DHMO
physicsists always abuse maths
@0celo7 I think it was okay
 
4:27 PM
 
@ACuriousMind Maybe you knew this, but if $\alpha:\Bbb R\to\mathscr B(\mathscr H)$ (bounded ops on Hilbert space), and if $\alpha'=A\alpha$ for some $A\in\mathscr B(\mathscr H)$, then $a(t)=a(0)e^{tA}$ is the unique solution.
 
Any physicist could have told you that!
Even for unbounded operator! :D
 
Does not look commute to me
2
 
@0celo7 ...isn't that just Stone's theorem?
 
@ACuriousMind You and Stone's theorem. No, it's not.
 
4:29 PM
Oh, no, you're not imposing self-adjointness
 
Where's the unitary operator?
I actually proved uniqueness of solutions for linear Banach-valued ODEs last night.
As in the finite-dimensional case, you just need that $\alpha'\equiv 0$ implies $\alpha$ is constant
And that just follows from the mean value theorem for Banach spaces
So, not that hard, but it does show that the usual derivation of BCH carries over for bounded operators.
@BalarkaSen I remember how to do the natural transformation problem.
 
cool
 
(I will tell you in a minute)
A natural transformation $T\to T^*$ descends to a natural transformation of the identity functor and the dual functor on each tangent space
but such a natural transformation cannot exist
That is, there is no natural transformation from the identity functor on $\mathsf{Vec}_\Bbb R$ to $D$, which sends $V$ to $V^*$ and $f$ to $f^\text{tr}$
I don't remember how to show that one
@ACuriousMind nlab link?
 
4:45 PM
Hm
I guess I also need a physicky book on fiber bundle for gravity
With frame bundles and solder forms or whatever
I think I have one somewhere
"The gauge treatment of gravity"
There we go
 
ok im back
did I really suspend myself?
 
Wrong move
 
23 hours ago, by AccidentalFourierTransform
im hella smart
 
vzn
@AccidentalFourierTransform trying to follow your cartoon, what does it mean? hard to interpret
 
We're almost at 9000 starred comments
2
 
4:50 PM
@BalarkaSen I have a proof that there is no natural transformation from the identity to the dual!
 
someone say something funny
 
It is probably known to you already
@Slereah MAGA
crap
ITS OVER NINE THOUSAND
 
No
It is exactly at 9000
3
 
Hey @AccidentalFourierTransform now that you're back, this is the sort of stuff I was looking for. I looked in Organigraf, Abacus and Servei Estació (+ El Corte Inglés) and they all said "don't have it, never had it"
 
get rekt
 
4:52 PM
Barcelona discriminates against my stationery choices =(
 
If I clear some stars does it go back down?
 
you can try
but we will star back
 
@vzn its surrealism. Dont try to understand it.
 
@JohnRennie why is it a bad thing?
 
@EmilioPisanty thats bullshit
a lot of people in my class use those
 
4:53 PM
I was just curious ...
 
@AccidentalFourierTransform so I can keep up hope, then?
I was about to give up and order on amazon, ridiculous as it sounds
 
what's wrong with Amazon?
free shipping and quick delivery
 
@EmilioPisanty whats ridiculous is that you havent been able to find them yet
 
@0celo7 ordering stationery on amazon?
 
@EmilioPisanty yeah?
 
4:54 PM
@AccidentalFourierTransform that's what I think, too
 
I don't see the issue
 
@EmilioPisanty what exact words are you using?
I mean, at the store?
 
is this some spanish thing?
 
because if el Corte Inlges didnt have it, bad thing
 
what on Earth is the problem with just buying online?
I buy everything on Amazon
food, drinks, books, paper, pencils
 
4:55 PM
@AccidentalFourierTransform they usually have the one similar pad but with really strong squares, so I show them that and I say I want rayado instead of cuadriculado
 
What is the link between the frame bundle and the symmetric tensor (0,2) bundle anyway
 
@Slereah $FM$ is related to $TM$
 
There has to be one since you can define the metric from both
 
not to $S^2M$
 
@EmilioPisanty thats weird, they should have them
dont know what to say tbh
 
4:56 PM
you want the orthonormal frame bundle
 
@AccidentalFourierTransform maybe some big shop near Zona Universitaria, then?
 
But then how do you get $g = \eta(e, e)$
 
@EmilioPisanty @AccidentalFourierTransform Can one of you please tell me what's going on?
 
From the bundles
 
@0celo7 Barcelona discriminates against my stationery choices.
 
4:58 PM
Buy online!!!
 
@0celo7 I'm not sure asking for a natural transformation between the dual and the identity is well-defined, since the identity preserves the direction of morphisms while the dual reverses them, the latter is formally a functor on the opposite category (or a contravariant functor, whichever terminology you prefer)
 
@0celo7 I kinda wanted to go the support-local-business route and all that, but it increasingly looks like that, yes
 
Natural transformations, however, go between functors of the same variance, so I'm not sure what the exact statement is
 
@ACuriousMind Natural transformations can be defined between functors which go opposite ways, just reverse the arrows in the relevant diagrams.
Now, they might never exist. That's another issue.
But one just wants to show that there is no "natural" way of identifying TM and T*M.
 

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