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00:00 - 19:0019:00 - 00:00

00:10
maybe i should just consider particle in a box
hmm
two electrons in one atom will be the non-linear example right
why do you think so?
i mean i don't really see why
it does not change the structure of QM
i just said that because to my knowledge nobody has solved the equation for that case right
00:14
i guess actually i should do particle outside a box lol. let's see if i can do a bvp~
@SillyGoose hehe good luck
this would be a good undergrad qm exam question xD
wait, the mass is the difficult part about the helium atom??
am i understanding this correctly
i'm not sure i have
which part is the difficult part?
@TobiasFünke i'm reading the wiki page, and it says, "The inequality at the heart of the uncertainty principle of quantum mechanics follows from the properties of Fourier integrals and from assuming time invariance."; which, very well, but why does the constant in that equation have the value that it has?
if that value is in our magnitude, then we would have quantum behaviours right?
(i mean u could also say that atoms would not exist, or atoms would be scaled up to our magnitude, so we would have existed in an even higher magnitude, etc.)
00:37
Sorry, I cannot quite follow your thoughts. In any case, consider this PSE thread:
21
Q: Why do universal constants have the values they do?

user4552This is meant to be a generic question of the type that we get repeatedly on this site, in different versions: The origin of the value of speed of light The gravitational constant G theoretically? What if Planck's constant were smaller or bigger than it is? Why do universal constants have the...

what did ohm say when his circuit blew
2
ohm no
and also this
The fine-tuned universe is the hypothesis that, because "life as we know it" could not exist if the constants of nature – such as the electron charge, the gravitational constant and others – had been even slightly different, the universe is tuned specifically for life. In practice, this hypothesis is formulated in terms of dimensionless physical constants. == History == In 1913, chemist Lawrence Joseph Henderson wrote The Fitness of the Environment, one of the first books to explore fine tuning in the universe. Henderson discusses the importance of water and the environment to living thin...
@Relativisticcucumber ohm y god
@Relativisticcucumber "aaaRRRR"
hehe
@qwerty I skimmed through some of your answers, and I couldn't see something "bad" which IMHO would require a downvote or so. Don't worry too much
:) thanks @TobiasFünke
00:48
I'll go to sleep. See you around :) good night
good night!
01:24
Lol
01:57
Trying to better understand the discussion in this question: https://physics.stackexchange.com/questions/819825/generators-of-rotations-j-i-j-j-epsilon-ijk-j-k-and-j-i-jk-e

It seems to be pointed out that it is "special" that in $SO(3)$ the adjoint and defining representations coincide. But I can't see why this wouldn't be the case for any Lie Group? The defining representation always has the same dimension as the group right? Does the adjoint representation not also have the same dimension?
In question form:

- For a Lie Group/Algebra, do the defining representations and adjoint representations always coincide (that is are they always isomorphic)? If not, why?
02:15
@Jagerber48 What do you think the dimension of the representations tells you?
I feel like this is a leading question leading me to the possible point that maybe it IS true that the adjoint and defining representations always have the same dimensions, but that doesn't necessarily mean they are isomorphic?
yes. dimensionality of representation is a necessary but not sufficient condition for two representations to be isomorphic.
I'm really only used to representation theory of like SO(3) and SU(2) and in those cases I think there is only one representation of each dimension. So if two representations have the same dimension they must be the same. But perhaps this doesn't hold for all lie groups
you are correct. for representation theory of $SU(2)$ (and $SO(3)$) it conveniently turns out that all same dimension irreducible representations are isomorphic.
this is not a generic fact
Ok. SO then am I also correct that for ALL Lie groups the adjoint representation has the same dimension as the defining representation?
02:18
i think at least for matrix lie groups this seems true.
since the defining representation of a matrix lie group would be something like $\pi: G \to GL_n(\mathbb{R})$ and the adjoint representation would be $\text{Ad}: G \to GL(\mathfrak{g})$ and $\text{dim} \mathfrak{g} = \text{dim} \mathbb{R}^n$
Ok. This coincidence feels like the key to helping me understand the equation in the title of this question. https://physics.stackexchange.com/questions/819552/how-to-prove-ei-theta-2-hatn-cdot-sigma-sigma-e-i-theta-2-hatn

Namely that we can implement a unitary transformation of a pauli vector either by conjugating by exponentiated pauli matrices, or by doing regular multiplication with a rotation matrix (the matrix exponential of a 3x3 skew symmetric matrix)
02:38
Is it true that there is only one representation of each dimension for SO(N) and/or SU(N)?
 
4 hours later…
06:27
@HerrFeinmann why would miao miao wanna stop a nice magnetic field discussion?
 
1 hour later…
07:27
@Allie Miao miao just got green lit a mini project that might become a paper. YAY! The professor we've consulted felt that it is doable, but gave the most laugh-cry warning: That the paper could be really well-done, yet face cryptic reviewers who dont understand the point of the paper's existence, and elect instead not to publish
exciting stuff nI :)
07:48
@naturallyInconsistent nice. can you reveal the very rough topic?
just out of interest. if not, I can fully understand
08:01
@Jagerber48 no. take e.g. $SO(3)$ (for the sake of example). Then it has its defining representation "3D rotation matrices" and there always exists the representation which maps all elements to the identity (map) (say, here in 3D). So you have two representations of the same dimension.
@TobiasFünke wouldn’t the trivial representation be 0-D compared to 3-D for the defining representation?
no. it is a representation on any finite-dimensional vector space, in particular you can choose $d=3$
for the case of irreducible representations, see e.g. this answer
3
A: Dimension of representations of Lorentz Group

Luke PritchettNo, the loss of uniqueness does not have to do with the non-compactness of the Lorentz group. The fact that there is only one irreducible representation of any given dimension is special to the group $SU(2)$ (and by extension, to $SO(3)$). It is not true even for other compact semisimple Lie grou...

08:38
@TobiasFünke nookooliar fooshun. There had been plenty of noisy ppl going on and on about the cold one, which, as everybody who actually knows about the topic, also knows that the low energy probabilities are of no practical importance, because even if you increase it by 10000x, the ridiculously low cross section would still make it useless. So, miao miao found a thing that might help pin the numbers down. Hopefully to shut them up
@naturallyInconsistent nice. good luck with that!
ooooor...during your research you find it is possible and change the teams hehe
I'm definitely not thinking it is going to work. The numbers are SOOO out of whack. Like, they have been arguing non-stop for decades about the amount of electron screening that will be helping. The cheap estimate miao miao furnishes, says that it is only about 550eV at best, vastly insufficient compared to what is needed.
But the nice thing miao miao is gonna do, is to bring the analytical + numerical approximations to the problem. Make every computation obviously numerically stable and convergent, so that there is nothing to argue about the result, as long as one still accepts the standard assumptions that make the chemical elements a useful concept in itself.
When miao miao read Hagelstein's papers covering the nookooliar-phonon interaction, and the papers assert that it is some nano- whatever units it was, miao miao had too much to laugh and nearly went to work late because of that.
08:59
hehe
09:22
@Jagerber48 The defining representation is not always the adjoint. It's already not the adjoint for one of your two examples! SU(2)'s defining representation is 2d complex, but it's a 3d (real) Lie group (the adjoint is isomorphic to the defining rep of SO(3))
@Jagerber48 No, this is already false for SU(3), where you have (at least) two irreducible representations of each dimension since they are not isomorphic to their conjugates. Look into Young tableaux if you want to understand the rep theory of SU(N)
@qwerty You need to be careful about the notion of "local" there (many aren't): It is not true that you can find a neighbourhood of any point such that that nbd is isometric to Minkowski space (if you can, your manifold is flat), it is only true that you can find an isometry such that at one point in the nbd the metric is the Minkowski metric (cf. Riemann normal coordinates).
The "in a patch it looks like Minkowski" that physicists often use sounds like the former, but they only mean the latter
@ACuriousMind would it be correct to say I was not being rigorous enough: I guess what I meant is that you can approximate your lab to be Minkowski? I guess on reflection if I wanted to pin down what's going on I would have started talking about tetrads which live on the tangent space at the point, rather than a local patch? or do I misunderstand you?
if it's so I will edit my answer to be more precise
09:44
@qwerty it's correct that you can approximate your lab to be Minkowski if you're not in a strong gravitational field, but it's an approximation, you are not just "picking the right coordinates"
In Riemann normal coordinates there are non-Minkowski terms of second order and higher away from the one point where the metric is Minkowski, and the approximation is that you're just dropping them (and it would not be good to do that in a strong field e. g. while falling into a black hole :P)
"you are not just "picking the right coordinates"" - I don't think of coordinates per se? whenever I think about this stuff I just think it's a kinda 4d version of approximating a curved line by a tangent straight line at a point.
But your answer talks about coordinates for a "small patch of Minkowski spacetime" without the caveat that the existence of such a patch is an approximation
you're right there's the inbuilt assumption of it being weak field and I should state the assumptions: i suppose I was thinking that if you "zoom in" for shorter length(?) scales for your lab as the field strength goes up, the principle of the idea still holds
Sure but in very strong fields it breaks down - a blackhole will spaghettify even very small things
And zooming in beyond the size of elementary particles is a questionable solution :P
@ACuriousMind mhm, you're right. I think I was blurring the language with reading some basic diff geo last month that talks about local coordinate charts ('patches') and defining manifolds. I'll think about how to reword things.
10:13
I think that spaghettification depends on the BH
I'm not sure a RN BH or a Kerr BH would spaghettify you. A Schwarzschild BH will
Do I misremember?
I have never studied BHs really xD
Trivial application of GR :P

-some guy in a MIT OCW
@HerrFeinmann The spaghettification is a measure of the tidal forces.
And RN and Kerr black holes also have tidal forces at their (outer) horizons.
Okay, I see. Don't you need to fall into the singularity to be completely spaghettified, though?
RN and Kerr will sure stretch you
Apparently I misrembered, or I had a wrong idea of being spaghettified in the first place :P
When you hit the singularity you get farfalle'd instead
10:30
The tidal forces become infinite at the singularity, though note that for the RN and Kerr black holes the interior isn't stable to perturbations and those geometries would never occur in real life.
The tidal forces at the horizon are finite but for stellar mass black holes they are plenty strong enough to ensure your (messy) death!
 
1 hour later…
11:57
I would guess once the length scale of the curvature is getting smaller than the length scale of the energy of your field, shenanigans happen
Probably some weird shit like graviton pair production
Saying that it's locally euclidian doesn't mean that much considering "locally" means literally "at a point"
If it's significantly curved in a region of a picometer it's still gonna have a lot of effects
12:21
@ACuriousMind Your pasta knowledge is impressive. Can you show me more? :P
Slereah, please check out my paper 'naive perturbation analysis of general relativity'. As you said, gauge invariance of the operators is preserved if the curvature is smaller than the length scale of energy. However, the naive analysis is only possible if gauge invariance is abandoned.
@HerrFeinmann 'Spaghettieis' :p
This is my test for you, ACM. What do you think of penne lisce?
This one question will decide if I can keep being your disciple
Or if I have to join the dark side to annihilate you
@qwerty Spaghetti, tonnarelli, linguine, tagliatelle. Only a wise (wo)man could employ each of these properly
Long pasta is a big deal
Spaghettieis (German pronunciation: [ʃpaˈɡɛtiˌaɪs]), or spaghetti ice cream, is a German ice cream dish made to resemble a plate of spaghetti. In the dish, vanilla ice cream is extruded through a modified Spätzle press or potato ricer, giving it the appearance of spaghetti. It is then placed over whipped cream and topped with strawberry sauce (to simulate tomato sauce) and either coconut flakes, grated almonds, or white chocolate shavings to represent the parmesan cheese. Besides the usual dish with strawberry sauce, one may also find variations like ice cream with dark chocolate and nuts, simulating...
OH GOD WHAT IS THIS MONSTROSITY
Why is there ice cream on spaghetti... WHY?!?!
Oh, not real spaghetti
12:27
@HerrFeinmann I thought the usual test is pineapple on pizza.
german hybridisation of two of italy's most cherished foods: spaghetti and gelato
@Loong ACM is no fool. It wouldn't work on him. Incidentally, you might want to read this:
Nov 2 at 16:39, by Mr. Feynman
Incidentally, there was a famous pizza chef in Naples who made pineapple pizza to show that sometimes people speak out of prejudice :P
> initially, children who were served spaghettieis broke into tears because they wanted ice cream and not a plate of spaghetti.
@qwerty At least it just resembles it. It's funny. There is actually a Michelin star restaurant (if not more) in which they make these "fake" dishes
The US way of doing would be more like: oh, spaghetti taste good and so does gelato. Let's mix them :P
@qwerty hahahahhahaha
12:32
we clearly need to send gelato into a black hole for the real deal
wait. qwerty, how come you know so many german things (apparently)?
@HerrFeinmann uh...I prefer rigate, I think?
it's the season finale. We're about to learn the plot twist that qwerty was German all along
@ACuriousMind good boy
@HerrFeinmann ACM's sock puppet account
hehe
Well, now that you mention it I have never seen ACM and qwerty in the same (real) room
12:37
yes. very suspicious
@TobiasFünke I love learning about different cultures all over the world - mostly wikipedia and youtube. I also have a couple of German acquaintances/ex-colleagues/friends :) but I don't think it was that much through them
@TobiasFünke Our investigation is far from over :P
in my early 20s I spent a short amount of time in the south of europe, but that was more generalised european culture shock :p
I have a history at accusing people of being someone's second account and failing miserably
12:39
hehe
Am I in my early 20s?
@HerrFeinmann at some point you will succeed
What's the boundary?
@TobiasFünke a broken clock is right twice a day
<25 I'd say
I'm in my early 20s
12:41
maybe even <24 hehe. then 24,25,26 would be "mid 20s" and 27,28,29, late 20s or so
Oh god I'm an old boy
Am i crazy, or the graphs that are even are NOT closed?
A Closed graph is one that loops right? like $v^3$
12:59
@Madder depends on what notion of "closed" you mean, but in the sense of "closure" of graph theory (cf. en.wikipedia.org/wiki/…), all those graphs are their own closure
That is, I don't know what the text means by only the even ones being closed either
13:31
Well that does not help much.
 
1 hour later…
14:49
how come perturbation theory is not done in classical EM?
@HerrFeinmann Lol
@TobiasFünke do you know what all the rage is with fractons? To my searching, they don't exist (yet). So why are people investing and incentivizing so much theoretical work into them?
hi
no, sorry, no idea. but then again I barely have read something about this topic
15:13
I'm a little confused in the derivation of London equation (probably this is a textbook level question): as I understand there are two relevant electron densities: $n_s$ for SC electrons and $n_n$ for normal ones
Why in London equations only $n_s$ appears?
It seems that even when using Ampére's law we only consider the magnetic induction generated by the SC current
15:51
Could this be the reason? Does short-circuit mean that they do not intervene here?
16:07
0
Q: Where in the world does GPS time proceed at one second per second? Is there a map?

uhohThe definition, measurement, and distribution of what time it is is a complicated thing, and only certain sturdy folks have the patience to understand it really and fully. It suddenly dawned on me that GPS time (for example) is a purely artificial construct. Zillions of things on Earth depend on ...

16:37
I was discussing with someone about Nobel prizes and field medals, and to my surprise I found out that Germany has a low nr. of winners in field medal, while france which is right at the border, is like nr.2 with only 4 less than the US. How did this happen, considering the leagues of mathematicians Germany had before?
17:00
France is quite good in STEM, and particularly math. I cannot give a precise reason, but they have pretty good unis/grand écoles
Germany has, of course, Bonn as a flag ship; I guess it is the most famous uni for math here
and what do you mean with "before" exactly? Before WWII, indeed Germany was a hotspot for STEM, especially physics and math
17:25
Yes, that's what I mean. Up until then, a big chunk of mathematicians where from Germany.
But to see the big disparity right now (with france) I find it quite odd.
What's everyone favourite textbooks?
17:41
@TobiasFünke baguette is the reason
@TobiasFünke sauerkraut
I wish you mentioned italy so I could say spaghetti
@imbAF well, at least they came to Germany to study/do their research
Also. But a large amount where from Germany.
Unless the education system and the way the French approach STEM was developed so fast that was able not only to catch up but overcome that of Germany's. Then a clear decline is evident
Though a more thorough research need to be done one the matter, I suppose
Sure, over the history there were many extremely famous german mathematicians; but the same holds for nearly every other country, and especially France.
I am not saying otherwise
France was always strong in math/physics
17:46
I merely pointing out the fact that the disparity between the 2 countries wasn't as big as it is right now
So either one was able to sky rocket in the way they were conducting science, or the other one regressed or stagnated
@imbAF ...do you not know why a lot of leading scientists left Germany around, uh, 1933-45???
I know but that is irrelevant to the discussion
no, it is very much the reason why Germany lost its leading role in the sciences
But it is not
If the system is there, people can come and go
As long as the system works as it should
You should produce the same quality of product
I have no idea what you're trying to say. Most of the scientists that left didn't particularly want to come back.
17:51
The system
And people follow the big names, so the next generation of scientists - their disciples - was raised elsewhere
@ACuriousMind I don't know about that
But the system is not the same as the product. If you have a well established way of making STEM fields desirable and accessible and you have developed efficient and good ways of "discovering" potential
you should be able to, regardless of period
produce a high nr. of scientists.
@imbAF this is so uncontroversial that it's in the intro of the Wiki article on Science in Germany
17:54
No, I mean
I don't necessarily think, that people follow where famous scientists go
@imbAF I don't know what you think "the system" consists of. The primary component of the academic system is academics, i.e. well-established scientists who teach their skills to the next generation
And post-WW2 Germany didn't have a lot of excellent scientists/teachers left.
Germany if ACM didn't leave academia:
And you are saying that, that is the main reason for Germany not being at the same level as it was in the turn of the 20th century or even before?
if you wanted to be a great scientist, you wanted to be the doctoral student of the greats who had emigrated (or their students) and so you followed them instead of staying in Germany (of course not everyone did this, but it's the principle at work)
same level = producing STEM field graduates
18:00
@imbAF Yes, Nazi Germany driving out large parts of the scientific elite as fugitives and destroying Germany's prestige as a nation of scientists and thinkers is the well-established reason for Germany's decline in terms of "top scientists" winning Nobel Prizes or other honours.
It's not a particularly mysterious event :P
I would assume so, giving the fact that there was a war going etc
But, one would think
That would be something that would impact the period when that happened. But for something like that to have such long lasting affects it's kind of hard to imagine.
When I asked my friend
what do you mean low amount, I expected him to tell me that there was a difference
but I never imagined it to be like 13 to 2 or something like that
I was baffled
Which them, made me question, what is it that the french are doing that they can produce so many field medal winners, in a, one can say, consistent manner
that Germany ain't
18:39
I'm not seeing France staying that strong in the sciences for much longer tbh
Bad science financing
They benefit from the fact that nobel prizes lag far behind periods of good science activities but that won't last forever
@Slereah i.e. they're not giving you money? ;)
The most important part, yes
@Slereah shouldn't that be the same for every country?
why would France be the only beneficiary ?
Many countries have a hard time doing it!
and do not typically want to that much
giving money to a bunch of lazybones like scientists is typically not a high priority for most states
and when they do they typically want immediate results
So industrial science stuff
You're not getting a good scientific culture like that
So not the real impactful deal
then
18:43
The solution is to just give money to scientists but most states are pretty tight fisted wrt research money
But that should be the priority in a proper functioning society
Though perfect and reality are far apart unfortunately
I'll confirm that the day I find a proper functioning society
Aim to be a proper functioning society*
hell even that is a pretty high bar for most countries
Modern day politicians prefer to go with austerity than funding
It's things that prevent scientific development to its greatest realistic extend that make me a firm believer that the best governing way is Scientism
18:46
I mean historically that too had pretty mixed results :p
@Slereah politicians are like Icemans, they shouldn't exist anymore
Although it gave us some bitching designs
Project Cybersyn was a Chilean project from 1971 to 1973 during the presidency of Salvador Allende aimed at constructing a distributed decision support system to aid in the management of the national economy. The project consisted of four modules: an economic simulator, custom software to check factory performance, an operations room, and a national network of telex machines that were linked to one mainframe computer. Project Cybersyn was based on viable system model theory approach to organizational design and featured innovative technology for its time. It included a network of telex machines...
@Slereah I don't think it was ever tried. Well actually governing systems are not tried, they are enforced in one way or another
Nah there was plenty of attempts at technocratic style government in the early 20th century
it was a somewhat popular idea
where was it tried?
18:48
partly why people soured on the notion in modern times
various places, for instance ie the soviet union with central planning
Like obviously, Scientism like the rest, is flawed. But it is way less flawed compared to anything else, I so believe
Well the hard part is 1) what are the goals you set for your scientism 2) do you have good models 3) do you have adequate means to get data 4) do you have the way to actually implement things
@Slereah Soviet union wouldn't be the best example, considering that it was communism.
Why wouldn't it
I can tell you that actually doing it was a nightmare certainly
like this was before computers
They had to try to plan the entire economy with pens and papers
But where the people planning, proficient and experts of the respective fields?
Like, you have politicians, talking about energy etc
18:51
I mean they had experts, sure
and they have a degree in Law
But there are problems even beyond that
Like realistically they couldn't model everything, especially before computers
You couldn't ask them to try to model the production of every item in the economy, likely millions of them
I mean, that is a technicality regarding how one would implement Scientism. That is a whole and extremely long discussion
So typically the model was flattened to about 10,000 of them which were assumed to be representative
@Slereah and how were they selected ?
18:53
But if you try to ie represent every type and diameter of steel pipe with a single "steel pipe" variable, what is gonna happen
What usually happened is that factories just made the cheapest version of these
and people who needed specific pipes were usually left without any
so there were long ass waiting periods for items
Isn't that a production issue?
I mean what would you do instead :p
If you want to run your state with Science it's the type of thing you have to figure out
I am not saying that scientism is the perfect way to govern. Far from it. BUT it is the best possible one. Starting from the premises that only people EXPERT in a certain area are the one who take decisions.
Ironically it might be more doable these days with big data
@imbAF I mean I don't necessarily disagree but it is a little funny that you assume that, ie against the scientific method
What do you mean against it ?
18:57
well to prove that this is the best way to run things you'd have to try it and encounter success!
Exactly
You should try it
And I doubt
They have yet to allow me to run the country 😔
there is a situation where someone who has a law degree and is the minister of finance or agriculture or w/e will be a better fit than an economist or idk botanist or something like that. You get the idea
of what I mean
but then how do you decide who is the best fit for such a thing
through nation wide competition
18:59
But what is the competition
@imbAF Impossibly naive. Politics is mostly not about solving textbook problems with a single correct answer, but making decisions on the basis of unclear data while dozens of different interest groups try to convince you their solution is the best.
Also, what if the "experts" decide you should starve as a result of the most efficient allocation of resources?
Like typically you don't need one expertise to run a whole department
It is the confluence of many
"let's be ruled by experts" is just oligarchy by another name
00:00 - 19:0019:00 - 00:00

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