The h Bar

HDE 226868

00:00

Maybe ask me again in quite a few years.

I get some of it, but not all.

Danu

:(

@HDE226868 Close enough! Hint: It ends in vector notation ;D

user54412

Does electromagnetism make a sound as it goes over your head?

HDE 226868

@Danu I saw that when I first skimmed it.

Danu

@ChrisWhite Only if you're not bald ;)

user54412

$Z^0_{000000}$!??????

Danu

00:03

@ChrisWhite Hey, I defined a new symbol as soon as I could!

In fact, I'll just get rid of those anyways.

They're unnecessary

Thanks for pointing it out ;D

user54412

I just wanted to see ACM's reaction to all those indices

Danu

@ChrisWhite Hush now :P

HDE 226868

@ChrisWhite By the way, I've decided to stop putting it off and use orbital resonances as the base of an answer on Worldbuilding. I don't expect it to get much attention, but hopefully some folks will see it.

Danu

I hope the night brings some upvotes ;D

HDE 226868

Regrettably, my best source is an obscure thesis from 1968, but still, that's better than the minimal amount of other stuff I've dug up.

@Danu Isn't it already (late-ish) night for you?

Danu

00:13

in Mathematics, 2 mins ago, by Danu

It's 1 AM now and I've got a string theory lecture at 8 :(

HDE 226868

Ouch.

dmckee

@EmilioPisanty Id be interested in know what procedure led to the selection of the films to list as candidates for their "scientific content".

In addition to the one I have selected I liked several loathed at least one and haven't seen a couple, but about half of them would never have made my list of films whose "science content" was mattered or was at all interesting.

Danu

@dmckee "Science" in movies is a funky thing...

dmckee

Indeed, I am having a very hard time choosing a favorite film based on "science content", and almost as much trouble choosing a favorite at all (it's easier with certain classes or genere's, but even then...).

Danu

Jeez, yeah this is hard!

dmckee

00:19

Even on plain favorite I am waffling between Leon: The Professional, Das Leben Der Anderen, Ghost Dog, and Secondhand Lions. Argh!

Danu

I've seen two of those

Leon was not that impressive to me.

What'd you think of There Will Be Blood?

I can't pick a favorite movie either overall or by scientific content (I cannot actually think of any movie that was good in this respect)

Calling @ACuriousMind (note the asker!)

1

Q: What, to a physicist, are instantons and the Donaldson invariants?

I study gauge theory from a mathematical perspective. To me, one of the most fundamental ideas is the notion of an instanton on a 4-manifold. To be precise, I have a Riemannian 4-manifold and a principal $G$-bundle $E$ over it (usually $G=SU(2)$, $U(2)$, or $SO(3)$). Given a connection on this ...

dmckee

@Danu Haven't seen it. I don't actually get to the cinema much these days.

Danu

Do you know something about instantons? I don't know if you do @ACuriousMind

dmckee

Any way, I've put Dr Strangelove down as my favorite on "Science content" even though it hasn't much because the question is making my feel crotchety and cranky.

@Danu I took a summer school at JLAB once, and one of the speaker defined a instanton as "a topological soliton", at which point I knew I wasn't going to get much out of that unit...

Danu

@dmckee hehehe :D

user54412

00:28

@Danu someone you know?

Danu

@ChrisWhite No, just a guy who I admire :P

kevin Tah N.

Can anyone tell me what Andrei Belitsky physics.asu.edu/people/faculty/andrei-belitsky at ASU really does ? What are the principal focuses of his research arxiv.org/find/all/1/all:+AND+Belitsky+AND+A+V/0/1/0/all/0/1 ?

His papers look hardcore

dmckee

@kevinTahN. You don't find "phenomenological and formal aspects of gauge and string theories." enlightening?

user54412

better than hypothetical and casual aspects I suppose

kevin Tah N.

@dmckee I always thought "formal" meant some type of super math abstractions

hehe

dmckee

00:32

@kevinTahN. I suspect it does mean something like that in this case.

Danu

Gotta go sleep now. Cya!

kevin Tah N.

@Danu nigt night . . cya 2moro

@dmckee just open any of his papers lol, then let me know if you choose to revise that statement lol

dmckee

And phenomenology means a certain amount of just trying out different schemes for binning or organizing facts things to see if you learn something from them.

HDE 226868

@Danu Have fun with tomorrow's lecture!

kevin Tah N.

yeah, I have always wondered what pheno people really do. On wikipedia it mentions something about bridging theory with experiments and computing things with certain corrections

like this arxiv.org/pdf/1512.00555.pdf or this arxiv.org/pdf/1407.2853.pdf

kevin Tah N.

00:51

In one of the papers there are pictures of "Hexagon Wilson loop decomposition into pentagon transitions." wtf does this guy study lol

ACuriousMind

03:09

@Danu Right up my alley indeed - I will attempt an answer tomorrow

dmckee

04:29

Question for the undergrads haunting this place. Actually a couple of them.

(A) How would you feel if the professor wanted to randomly assign you group work partners every week or so (this is for in-class peer-learning activities where you are graded on participation)?

(B) If he said "Wheel of group-work turn turn turn, tell us with whom we should learn" in a high and sing-song voice would you be familiar with the reference?

Mike Miller

04:55

@ACuriousMind: Thanks, I appreciate it! I should warn that I only had a vague sense of what your comment means (though I haven't read your link yet - will do so later) so the more insultingly low-level you could write it, the better.

dmckee

05:43

Looking for help from the peanut gallery.

I need a small collection of problems suitable for students who have finished the introductory sequence (in this case out of Halliday and Resnick), but they need to require a some decision making rather than being plug-n-chugs.

So far I have adapted

2

Q: Which formula is correct to find the terminal velocity of a sphere falling through a liquid?

Consider a sphere of radius $R$ & density $\rho_s$, falling through a liquid having density $\rho_l$, attains a constant terminal velocity $V_t$ then in this case the net force acting on the sphere is zero. Neglecting effect of buoyancy (see in the picture below), $$F_{\text{net}}=F_{d}-F_{\text{...

drag viscosity

to my needs. I used the data for a ping-pong ball falling in air to force them to try both ways.

I could use two more questions at a similar level of difficulty and decision making.

Any ideas?

DanielSank

Ahem

Please do not spoil Star Wars in this chat over the next couple weeks.

10

We all like to come here to talk physics etc. It would be nice to be able to continue doing that without fear of having the latest installment of such a beloved sci-fi spoiled.

@dmckee I'm not sure I understand.

You give them data for a ping pong ball with the idea that they plug into both formulae and see if the numbers match the data?

dmckee

@DanielSank Yeah. They don't apriori know the Reynolds number, so they have to try both and see which one gives internally consistent results.

From a back-of-the-envelope calculation it seems that ping-pong balls reach terminal velocity of about 1.5 m/s at a Reynolds number a bit over 2000 (to one sigfig in each case).

By data I mean the density and viscosity of air and the mass and diameter of the ball.

DanielSank

06:38

@dmckee Do they drop the balls themselves?

kevin Tah N.

06:52

ola

dmckee

@DanielSank Not until after they've calculated. The point of the exercise isn't actually the problems, but one about communication in physics.

These students habitually turn in homework sets devoid of written reasoning, and asking them to work on problems of this order is planned to set them up for learning what a bad idea that is the hard way.

But that means that I need problems they can do after some thinking, but can't comprehend in one go.

skill patrol

No comments on my susskind quote about Feynman's scientific style? @dmckee :-)

dmckee

@skillpatrol Not really. I'm a greasy handed kinda guy who's slightly stoned on solder fumes. What do I know of the machination of the big-brained blackboard boffins?

skill patrol

Nothing really.

Thanks for replying.

0celo7

09:40

@DanielSank y

@dmckee lead based solder?

@dmckee Is that for Freshmen?

Huy

sup @0celo7

0celo7

Just slept a LOT, had to overcome a 36 hour day

Huy

nice

0celo7

@dmckee I would have known everything except for $F_d=6\pi \eta r V_t$.

Fermi paradox

10:34

To flag as spam, or not to flag as spam: http://physics.stackexchange.com/a/128991/71860 ?

Terrible answer (posted 6 months after the other answers, providing nothing new, sloppy repetition of things already said) and a link to a commercial website.

yuggib

@Huy gâteaux $\neq$ cake

0celo7

@yuggib wrong

yuggib

tarte = cake

0celo7

what would a yugoslavian know about cake

yuggib

@0celo7 that is not called gâteaux in french

0celo7

10:45

@yuggib since when do you speak French

yuggib

@0celo7 since when I lived for two years there...

I have a modest level, but I can survive

and order cakes :-P

0celo7

@yuggib why would you live there for 2 years

yuggib

@0celo7 to work?

0celo7

why

there are better places to work

such as places with running water and air conditioning...

this "natural operations" book seems pretty advanced...springer.com/gp/book/9783540562351

yuggib

in Brittany you don't need air conditioning...

0celo7

10:48

diff geo with functors is interesting

Fermi paradox

@dmckee Could we speak in private?

yuggib

@0celo7 probably...

but I would need another twenty years to have time for that (and have learned the prerequisites)

0celo7

@yuggib so: I'll get the AMS book which does introductory stuff with cat theory

I'm also taking algebra and analysis next semester...

then I might be ready for the natural operations book

@yuggib I wonder how much category theory you actually need for this...or if they just call maps "functors" for the hell of it

yuggib

I am downloading the book

I will take a quick look

@0celo7 It doesn't seem you would need much analysis for it

but definitely algebra

and I also don't think that they use functors just for the sake (hell) of it

however since you would like to do PDEs, and you have already a knowledge of diff geo and relativity, you should look at the people working at the intersection of the two:

dpmms.cam.ac.uk/~md384

web.math.princeton.edu/~seri/homepage

people.math.ethz.ch/~dchristo

imho it is far more interesting than categorical diff geo ;-P

web.math.princeton.edu/~seri/homepage/grap/index.htm

yuggib

11:16

@Huy but it seems that in Switzerland gâteau is strictly a synoym of tarte, so you may also be right...

@Slereah Would you translate gâteau by cake? I would say more 'pastry'

Danu

12:11

@ACuriousMind as usual... references?

Pliz not the usual answer!

Fermi paradox

@Danu Hello, could we speak in private?

0celo7

@Danu hmm, @ACuriousMind, why the $\pi$ there?

@yuggib what makes you say that

@yuggib 403 error

Fermi paradox

@Danu Oops. Ignore my comment, i thought you are a mod on physics.

yuggib

@0celo7 strange

Demetrios Christodoulou

Demetrios Christodoulou (Greek: Δημήτριος Χριστοδούλου; born October 19, 1951) is a Greek mathematician and physicist, who first became well known for his proof, together with Sergiu Klainerman, of the nonlinear stability of the Minkowski spacetime of special relativity in the framework of general relativity. Christodoulou was born in Athens and received his doctorate in physics from Princeton University in 1971 under the direction of John Archibald Wheeler. After temporary positions at Caltech, CERN, and the Max Planck Institute for Physics, he became Professor of Mathematics, first at Syracuse...

he has a wikipedia page anyways

0celo7

@yuggib I'm on Czech internet...censored?

yuggib

12:23

@0celo7 I don't see why the ETH of Zurich should be censored

@0celo7 because surely in the context of Weil's and Grothendieck's work the categories are important; and it seems that they review Weil's theory of something

but I do not know much about that

0celo7

@yuggib have you heard of amazon.com/… ? Straumann (GR book I really like) recommends it for an intro to the Cauchy problem in GR

@yuggib is that diff geo book no kidding PhD level

@yuggib i.e. AoC, ZFC level

yuggib

I have heard about it...she is surely a very well-known mathematician

but I don't know the book

@0celo7 :-D

0celo7

yuggib

I can't rate the level of that book, for I am too far from the subject

well, that definition does not seem so incomprehensible

0celo7

12:39

@yuggib maybe for you!

You're a PhD

I'm a German middle schooler!

yuggib

@0celo7 well, it's descriptive

(even if I have no idea what it describes)

0celo7

@yuggib I'm in the same boat

now that is 400 pages in...

so I'm sure they explain some of the symbols

yuggib

and my level on geometry/algebra is that of an undergrad :-D

0celo7

why do you say I need a lot of algebra for this?

to appreciate the categorical framework?

yuggib

yeah, I think so

I once started to read this book:

katmat.math.uni-bremen.de/acc/acc.pdf

it seems pretty accessible even for someone who knows nothing of algebra like me ;-)

but I went no further than the middle of the third chapter

0celo7

12:43

there's a book "category theory for scientists"

it's for biologists working in DNA stuff

yuggib

@_@

maybe there is something on categories for cellular automata

0celo7

if a biologist can understand it

I certainly can...

yuggib

probably not

0celo7

:(

yuggib

better said: I think that no biologist wants to understand it

0celo7

12:45

o

amazon.com/Category-Theory-Sciences-David-Spivak/dp/0262028131

yuggib

I have some doubts of its real usefulness...

but maybe you will use categories in nuclear engineering

if will ever you do that, post the paper here :-D

0celo7

will do

what if I'm working for a company and it falls under my NDA

I could not tell you that cat theory is actually useful :o

yuggib

well...I seriously doubt that

but in case you could at least tell me that you know it can be used

David Z

@Fermiparadox in general it doesn't hurt to flag, if you're not sure. But we do want to be a little more careful with spam flags since they carry severe consequences if 6 people flag the same post as spam. I'd say go ahead and do it, but if you really aren't sure, you can use a custom flag for mod attention. (That's for spam flags. For other, more mundane flags, we'd really rather people use the standard flag, when there is one, instead of flagging with a custom reason.)

Fermi paradox

@DavidZ Could we speak in a private chat about this issue (and another related issue)?

Slereah

12:53

@yuggib Gateau is cake, yes

pastry is more "viennoiserie"

David Z

@Fermiparadox something that concerns another user?

0celo7

@yuggib rekt by the frenchman

Fermi paradox

@DavidZ Yep

yuggib

@0celo7 I asked him...

David Z

ok, just a moment

Slereah

12:54

Oh no

0celo7

>video games

Slereah

A bunch of nobles were working in my cistern and someone pulled the lever to fill it

Now they won't be able to complain and send my dwarves to prison

quite a tragedy

0celo7

@yuggib is anyone looking at categorical PDE

yuggib

@0celo7 Ahahah luckily no

0celo7

@yuggib does algebraic geometry have any PDE applications

yuggib

12:56

there is not an easy way to categorize PDEs

even with the non-mathematical meaning of the word

@0celo7 I really doubt so

0celo7

what is algebraic geometry good for?

ACM doesn't want to tell me

yuggib

there are some "geometric" PDEs, but I doubt there they use results from algebraic geometry

0celo7

32

Q: Which nonlinear PDEs are of interest to algebraic geometers and why?

Motivation I have recently started thinking about the interrelations among algebraic geometry and nonlinear PDEs. It is well known that the methods and ideas of algebraic geometry have lead to a number of important achievements in the study of PDEs, suffice it to mention the construction of...

ag.algebraic-geometry ap.analysis-of-pdes reference-request complex-geometry

yuggib

my friend uses algebraic geometry to do number theory

0celo7

your friend sounds like a nerd

yuggib

12:59

not really

@0celo7 that's the opposite direction

algebraic geometry applications of PDEs

0celo7

@ACuriousMind Geometry book that talks about a dozen different bundles and functors and more bundles also uses indices.

Secret

Ok, I have analysed that book, I should start with this question before the group theory ones:
https://en.wikipedia.org/wiki/Internal_conversion

0celo7

@yuggib huh, that natural operators book was written by profs in the town I'm visiting

yuggib

you could pay them a visit then

Secret

Relevant excerpt of the book

0celo7

13:13

@yuggib and do what

@yuggib that book is 1991, I can't even imagine what they've come up with in the last 24 years

yuggib

that is up to you

ams.org/mathscinet/search/…

this is just one of them

0celo7

need a password

and username

yuggib

damn

you have not enable the remote access

0celo7

not a grad student

Secret

Q1. The author said the internal conversion (laballed IC in that energy level diagram) is isoenergetic, which means there is no energy change in that transition

a. If we use what we have discussed earlier (with Acuriousmind, 0celo7, Slereah) that a state can be changed by a measurement (i.e. a suitable operator acting on the state which changes it), and energy does not necessary change in the process

how does the molecule knows it has to transit to a lower electronic state (but vibrationally excited) as after the absorption of the photon, the molecule is not interacting with anything else

0celo7

13:16

I don't have my own account yet

yuggib

you don't need the account

it is sufficient to be connected to you institution's network to enable it for 90 days

0celo7

I do if I want to access stuff outside of civilization!

yuggib

maybe with zbmath it's open:

zbmath.org/?q=ai:kolar.ivan

0celo7

@yuggib how do I do that

yuggib

@0celo7 when you access the mathscinet webpage (or the page of a journal of the AMS) from your institution

there is a link to "remote access"

and there you can pair your device with the subscription for 90 days

also APS does that for physics journals

but you have only 14 days of remote access

then it has to be renewed

0celo7

13:26

Well I didn't do that...

Secret

@yuggib @0celo7 @ACuriousMind
Q2.

Is my understanding of the following about group theory correct?

1. Groups are sets with a binary operatation such that associativity, existence of inverse and identity and closure under the operation are obeyed

2. For a given group, the representation of the group means you express the group elements (e.g. a symmetry operation) under a basis (such as x,y,z) and find the corresponding object in that basis (e.g. matrix for x,y,z basis vectors) that does the same outcome on some elements spanned by that basis as the group element itself

yuggib

1 is ok

2: a representation of the group $G$ is a couple $(X,\pi)$ where $X$ is some vector space (maybe with some additional structure), and $\pi: G\to L(X)$ (where $L(X)$ is the set of linear maps) is such that it preserves the law of the group, i.e. $\pi(g_1)\pi(g_2)=\pi(g_1\circ g_2)$

3+4: An irreducible representation is one that has no invariant subspaces that are not trivial (i.e. $\{0\}$ and $X$). An invariant subspace $Y\subset X$ is a space such that for any $g\in G$ and for any $y\in Y$, $\pi(g)y\in Y$.

5: A representation is a different object from a (infinitesimal) generator of a (Lie) group.

Secret

13:46

Ah I see.
I particularly want to make sure I understood irreducible representations right, because they are the crucial component of a character table in point groups

which brought me to the next question:

yuggib

To sum up, a representation of a group is an instantiation of the group (i.e. of the group law) by means of linear transformations on some vector space. For example the unitary evolution group of QM is a representation of the abelian group $(\mathbb{R},+)$ by means of unitary (linear) operators.

Irreducibility means that you cannot restrict to a subspace of your vector space and still have a representation of the group.

It is useful because non-degenerate representation can always be written as the direct sum of irreducible representations.

Secret

Q2a:

1. It was said that a reducible representation can always be uniquely decomposed into a linear combination of irreducible representations. (which is why a reducible representation of a point group can be expressed as direct sums of irreducible representations (thus why characters in a row of a character tale can add together and these will equal to the characters of the required reducible representation. In such a case, does the irreducible representation form a basis in the subset of reducible representations $A \subset L(X)$ (because $L(X)$ also form a vector space)?

Slereah

14:02

I am doing the science in cinema form thing

and then the question is

yuggib

1: I am not sure I understand completely. In particular, you want to consider the set of all possible (non-degenerate) representations on $X$, as a subset of what? Each representation $\pi$ is, roughly speaking, a set $\pi(G)\subset L(X)$ and it is not so meaningful to consider the set $\{l\in L(X),\exists \pi, l\in\pi(G)\}$ because you are mixing up things

Slereah

"Which of the following films appeals to you most in terms of scientific content?"

But all the choices are bad

yuggib

2: I don't know the subject so I can't tell

Slereah

The closest thing to a movie that is somewhat serious about science that I know of is the Andromeda Strain

yuggib

well, is it not the day after tomorrow a perfectly accurate scientific representation of a (possible) reality? And very appealing on scientific grounds?

:-P

Slereah

14:05

Andromeda Strain isn't a particularly realistic movie (it's about some alien virus), but it spends like 30 minutes just preparing for lab work

Secret

@yuggib
1. Ok it's more like this. Because of how any reducible representation can always be uniquely decomposed into a direct sum of irreducible representations. Does the set $A$ of irreducible representations form a basis for the vector space $\pi(G)$, or is it not very useful to think of it this way?

Physics Meta

0

Q: How do theoretical physicists work?

How do they spend their day? Looking out the window trying to think up something new? Learning new maths? Reading other people's papers? And how is their productivity measured beyond churning out papers?

discussion

Secret

@Slereah
Q1. The author said the internal conversion (laballed IC in that energy level diagram) is isoenergetic, which means there is no energy change in that transition

a. If we use what we have discussed earlier (with Acuriousmind, 0celo7, you) that a state can be changed by a measurement (i.e. a suitable operator acting on the state which changes it), and energy does not necessary change in the process

how does the molecule knows it has to transit to a lower electronic state (but vibrationally excited) as after the absorption of the photon, the molecule is not interacting with anything…

yuggib

Well...any reducible representation can be thought of as a direct sum of irrep, i.e. you can decompose the space in a direct sum of subspaces, and on each subspace you have an irrep. If I understand correctly what you are meaning, I suppose (not sure) that yes, you could see each reducible $\pi(g)$ as a direct sum of operators on each irreducible subspace: $\pi(g)=\bigoplus_{j\in J} \pi_j(g)$

where for any $j\in J$, $\pi_j$ is an irrep on the subspace $X_j$ such that $X=\bigoplus_{j\in J}X_j$

however bear in mind that if $X$ is infinite dimensional, then the index set $J$ can be infinite, or even continuously infinite (i.e. you have to take direct integrals)...but for finite dimensional representations everything should be quite clear

Secret

It looks similar to the equation for a vector space element expanded in a certain basis, but with $\oplus$ instead of +, which is why terminologywise, I am worried I might get it wrong that we don't call the above direct sum thingy (the $\pi_j$) as a basis, but I am not really sure, which is why the question

Slereah

14:18

Kinda.

yuggib

I would say that for finite dimensional spaces you should have no problems, and indeed you can choose as a basis for $X$ the basis elements of each $X_j$

Secret

makes sense. I 'll keep in mind about the infinite part subtlety

yuggib

probably it is true also for many infinite vector spaces, for example it is true for Hilbert spaces

with the basis in the Hilbert space sense (i.e. you can allow infinite combinations)

but I would not be confident to make it a general statement

Secret

I see

Secret

One reason I want to understand character tables well is because I noticed when deriving the symmetry of orbitals and normal vibration modes, there's a lot of parallels between that and the standard model stuff shown here (e.g. we also do direct product of irreducible representations when computing the selection rules)

thus I felt lik if I can fully understand the character table, it might help me to get a better grasp on stand model and othe particle physics maths (minus QFT integrals)

both involve a lot of group theory

dmckee

15:56

@Fermiparadox Should I assume that your chat with David Z met your needs, or is your request for a private conference still live?

David Z

@dmckee I think we covered it. I'll ping you in.

oh wait I see you found it

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