The h Bar - 2018-10-17 (page 3 of 3)

« first day (2904 days earlier) ← previous day next day → last day (2019 days later) »

Anonymous

8:00 PM

@enumaris Well, maybe I'm just overthinking this

I take your Kerr GR and raise you to an M2 super-GR

In theoretical physics, an M2-brane, is a spatially extended mathematical object (brane) that appears in string theory and in related theories (e.g. M-theory, F-theory). In particular, it is a solution of eleven-dimensional supergravity which possesses a three-dimensional world volume. == Description == The M2-brane solution can be found by requiring ( P o i n c a r e ) 3 × S O ( 8 ) ...

${\displaystyle {\begin{aligned}ds_{M2}^{2}&=\left(1+{\frac {q}{r^{6}}}\right)^{-{\frac {2}{3}}}dx^{\mu }dx^{\nu }\eta _{\mu \nu }+\left(1+{\frac {q}{r^{6}}}\right)^{\frac {1}{3}}dx^{i}dx^{j}\delta _{ij}\\F_{i\mu _{1}\mu _{2}\mu _{3}}&=\epsilon _{\mu _{1}\mu _{2}\mu _{3}}\partial _{i}\left(1+{\frac {q}{r^{6}}}\right)^{-1},\quad \mu =1,\ldots ,3\quad i=4,\ldots ,11,\end{aligned}}}$

lol

that's not too bdad

god-does-not-play-dice.net/Geroch_1968.pdf

I don't even want to post the equations it solves :p

The spacetime I mentionned, btw

8:13 PM

"The general covariance of relativity theory creates serious dit%cuIties in formulating
a suitable definition of a singularity in this theory. We review and, by means of an
example, add to these difficulties. We examine the arguments which lead from one’s
intuitive picture of a singularity as “some quantity’s becoming infinite” to the notion of geodesic completeness. Even within the framework of geodesic completeness there is still a great variety of definitions to choose from. It is claimed that none of these

I see where he goin with this

gonna be painful lol

oh that's part of his thesis, interesting

Anonymous

Where does classical field theory fit in, in the physics pedagogy? Is it usually before taught before QFT?

classical field theory like...E&M?

Anonymous

@enumaris This is a sample syllabus for example - nptel.ac.in/syllabus/115106058

Anonymous

Doesn't fully look like E&M to me

Generally one learns E&M after the traditional "classical mechanics" course

but framing things as a "field theory" probably doesn't occur much outside of QFT classes...in that case a "classical field theory" is like just a stepping stone towards the QFT

Anonymous

8:26 PM

@enumaris I see

So, I suppose one is "exposed" to "classical field theories" as early as first year of College in E&M course, but it's just not presented as such.

Anonymous

So that course seems like a prerequisite to QFT

Anonymous

@enumaris Gotcha

well I guess even in classical mechanics, gravitation can be thought of as a "field theory" in terms of the gravitational field

It's pretty rare for people to do non-EM non-QFT field theory

Except in GR

and SR

That's where you usually get classical field theory

8:29 PM

It really depends on what you mean exactly by a "field theory"...like any theory that involve "fields" in some way? Then you start to use that real early on. But generally they also mean some Lagrangian or Hamiltonian methods used that's somehow analogous to QFT through "second quantization"...so...that stuff you don't get into right away.

I remember some article about finding out if black holes emitted a neutrino field

Since back then neutrinos were thought to be massless

Anonymous

Makes sense. BTW are gauge theories taught in E&M or no?

and black holes do have an EM field

@Blue To some degrere

But not a lot

Anonymous

Ah

Usually EM gauge is always Coulomb or Lorenz gauge

You don't really see a lot of the general gauge thing

8:31 PM

It's not taught as a "gauge theory" so to speak

but the fact that there is gauge freedom in E&M is taught

Well it's taught somewhat

Like you learn about the invariance under $\phi \to \phi + \partial_t f$

and whatever

yeah

but nothing fancier

but at least in my experience, that was more presented as "an interesting facet of E&M" rather than something that would lead to some deeper concepts

it usually goes $\vec{E}$ and $\vec{B}$ are the "physical fields" and so potentials $\phi$ and $\vec{A}$ are only determined up to their ability to define the $\vec{E},\vec{B}$ fields.

This view leads, imo, to a painful realization one has to make when dealing with the Aharonov Bohm effect......but meh, I dunno if there's a better way to teach it

going straight into gauge theories seems like overkill

it seems Wald took inspiration for some of his discussion on singularities from this paper by Geroch...

Anonymous

Unrelated: I'm getting a bit confused with $C^{\omega}$ manifolds. I understand that they arise from additional restrictions on $C^{\infty}$ manifolds to allow for Taylor-expandability, but I don't know which exact restrictions they're talking about (and it's not Google-able since I don't know the keyword(s) I'm looking for :P)

8:42 PM

Why are you using mathbb font for the C

it's not the complex set there is it...

Anonymous

Oops...sorry..bad habit XD

Anonymous

I feel like putting in a Bbb whenever I see a capital C

Do you understand what the $C^\infty$ definition means?

$\mathcal{C}^{\infty}$!

Anonymous

$C^k$ means k-times continuously differentiable

8:44 PM

but do you know what is being called "differentiable" there?

as it pertains to manifolds

Anonymous

The map $\Bbb R^d \to \Bbb R^d$?

Right

so if that map is analytic

then you get $C^\omega$

Anonymous

@bolbteppa Ah, I'll go with mathcal :D

if that map is only smooth, you get $C^\infty$

It's really nothing more than that

Anonymous

@enumaris What's the definition of analytic in this context?

8:46 PM

The same definition as from regular multi-variate calculus

Nobody uses $C^\omega$ manifolds in GR really

No need to worry too much about it

Anonymous

user image

Anonymous

This ^ @enumaris

Anonymous

?

Anonymous

user image

Anonymous

8:48 PM

@Slereah Good for me then :P

Right, except that's for a single variable mapped to a single variable, you just need n variables mapped to n variables...tbh I can't recall that one lol

Anonymous

Here, $D = \Bbb R^D$ ?

I think D in that image is some subset of $\mathbb{R}$

Anonymous

I meant in the multivariable case

Anonymous

@enumaris Yup, here it's single variable

8:51 PM

there's a small blurb on analytic functions of several variables

Anonymous

But if we are talking about $\Bbb C^{\omega}(\Bbb R^d \to \Bbb R^d)$

Anonymous

I guess we need pointwise convergence on whole of $\Bbb R^d$ (?)

Interestingly I've always just glossed over this statement by Wald: (Since we are dealing here with maps of $\mathbb{R}^n$ into $\mathbb{R}^n$, the
advanced calculus notion of $C^\infty$ functions applies . )

danielunderwood

Isn't there some constraint on a $C^\omega$ function having an analytic continuation or something?

It's easy for $\mathbb{R}^n\rightarrow \mathbb{R}$ but I don't recall the definition when it's mapped into $\mathbb{R}^n$ lol

since then it's not a function so to speak

but merely a mapping

danielunderwood

8:54 PM

Every website that decides to make links not work like links makes me hurt

Most spacetime manifolds are analytic I think

I don't think you ever really get manifolds weird enough to be non-analytic

but it's usually not necessary for proofs

Anonymous

I guess I need some reading material about $C^{\omega}$ :/...I'm still confused about the domain of convergence of the Taylor series for $C^{\omega}(\Bbb R^d \to \Bbb R^d)$

@Slereah I think we are currently stuck at, what it means for a map $\mathbb{R}^n\rightarrow\mathbb{R}^n$ to be differentiable/analytic

Anonymous

Yeah ^...save us :P

I suppose it wouldn't be too bad to construct the definition

but I'm not sure if it's the standard one

8:56 PM

@enumaris The usual?

Derivatives defined up to bla bla bla

I suppose it would be

think of the map $\mathbb{R}^n\rightarrow\mathbb{R}^n$ as instead $n$ maps from $\mathbb{R}^n\rightarrow\mathbb{R}$

if each of those $n$ maps are $C^\omega$ then the map itself is $C^\omega$

yeah...that should work

Anonymous

@enumaris So smoothness and pointwise convergence on all of $\Bbb R^n$ are sufficient I suppose?

So then if you have a function $f(x_1,x_2,...,x_n)$ and you are given an initial point $(a,b,c,...,n)$ you can look at the taylor expansion $$f(x_1,x_2,...,x_n)=\Sigma_{k_1} ...\Sigma_{k_n} \frac{\partial^{k_1} f}{\partial^{k_1} x_1}(x_1-a)...\frac{\partial^{k_n} f}{\partial^{k_n} x_n}(x_n-n)$$ I think...

Something like that??

But yeah, smoothness and pointwise convergence to the taylor series expansion

dang, I can't edit to include the big Sum symbols anymore

but you get the idea...

Anonymous

Or we could use the compact notation with Jacobians, Hessians and all that

I'm also missing the exponents in the (x_1-a) and (x_n-n)...

Anonymous

9:10 PM

I don't remember the exact forms tho

Anyways, I think once you view $\mathbb{R}^n\rightarrow\mathbb{R}^n$ as actually $n$ maps of $\mathbb{R}^n\rightarrow\mathbb{R}$ the definition isn't hard to get from there

Anonymous

@enumaris Right, right

Anonymous

Got it now

Anonymous

Thanks!

np :D

Anonymous

9:12 PM

user image

Anonymous

This notation is nice :)

Anonymous

There's a generalized form of that too

Anonymous

But I can't find it now

ah...use vectors

seems legit

anyways, the point is, there's a multi-variate calculus method of defining $C^\omega$ so the "manifold" related definition is really just down to the multi-variable calculus way on the maps that describe the intersections of different coordinate charts

Anonymous

Oh, a complex differentiable manifold is even more restrictive than $C^{\omega}$

Anonymous

9:16 PM

They (the chart maps) need to pairwise satisfy the CR equations

Anonymous

Lemme see how that makes sense now

Anonymous

Complex manifold

In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex manifold), and an almost complex manifold. == Implications of complex structure == Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than...

well the complex plane has a lot of extra "restrictions" on it than simply $\mathbb{R}^2$ so I guess that's expected...

but I don't deal with complex manifolds lol

Anonymous

I heard Calabi Yau is a thing in physics

Calabi Yau manifolds are used in string theory I think

Anonymous

9:19 PM

Anyhow, my memory of complex analysis is getting rusty

but that's about all I know about it :D

Anonymous

Hmm, this is a nice theorem: Topological manifolds which have a $C^k$ ($k \geq 1$) atlas, necessarily have a $C^{\infty}$ sub-atlas

hmmm

indeed interesting

@Blue string theory

Anonymous

Whitney embedding theorem

In mathematics, particularly in differential topology, there are two Whitney embedding theorems, named after Hassler Whitney: The strong Whitney embedding theorem states that any smooth real m-dimensional manifold (required also to be Hausdorff and second-countable) can be smoothly embedded in the real 2m-space (R2m), if m > 0. This is the best linear bound on the smallest-dimensional Euclidean space that all m-dimensional manifolds embed in, as the real projective spaces of dimension m cannot be embedded into real (2m − 1)-space if m is a power of two (as can be seen from a characteristic class...

Anonymous

9:34 PM

@Avantgarde Yup :)

I've had to deal with the Whitney embedding theorem only once

in a Differential Geometry for Physics class taught by a mathematician

Anonymous

The proof doesn't look simple :P

just use it

Anonymous

lol

just like the Jordan curve theorem

danielunderwood

9:39 PM

This is physics; we don't need proofs!

Anonymous

Imagine the mathematicians revealing to us one day that half of the theorems we use in physics are nonsense and were meant to prank us...

Anonymous

Better not trust them blindly!

danielunderwood

That's what the mathematical physicists are for, right?

Anonymous

@danielunderwood Traitors are everywhere :P They might have teamed up with the math guys

If the Jordan Curve Theorem is wrong I'm gonna have a hissy fit

danielunderwood

9:43 PM

Though I will admit that I wish we learned more of the mathematical side of physics in our courses. I could just do without going through detailed proofs

Someone should make a "tree of mathematics" where dependent definitions are linked together

Anonymous

@danielunderwood Reminds me: any progress on applying to the grad school front? Or will you continue with the data science job?

danielunderwood

Not really. Most places seem to require 3 recommendations and I only have one solid academic one. I figure my best bet is to move somewhere that I can build academic connections and volunteer for stuff

The recommendation I do have is quite solid, but I feel many places may just not look at my application if I only send in one

Anonymous

3 is a lot :/ The US has some strange rules

Anonymous

Shifting to the European side is an option?

You won't be able to submit your application without filling in the details of 3 referees.

Unless, maybe, if you're like John Nash and your solid letter is like "he is a mathematical genius"

Anonymous

9:51 PM

@Avantgarde Yeah, and that might be a disadvantage for some

Well, it's the "law"

danielunderwood

Yeah that's about what I figured. I know a good many people that kind of sucked up to professors they had a class with and asked them, but I don't feel that that's really a genuine thing to do. European side could be a possibility, but I haven't really looked into it much

You can ask profs whose classes you took, but just think about what they could write about you anyway if you haven't interacted with them much.

Europe needs 2-3 letters.

danielunderwood

Yeah I don't really think that's a great way to go, but it's what a number of classmates did

But this is all for physics grad school. I presume that's what you're also talking about.

danielunderwood

9:55 PM

Yeah mainly. I could get a professional recommendation, but I feel that's going to be fairly weak for academic purposes

Anonymous

In my country, you just have to appear for some exams and you're done :P No recommendation letters involved. And from I what I heard it's not very competitive

danielunderwood

Too bad I can't go redo undergrad now that I know better how to approach it lol

@danielunderwood That I'm not sure of. Maybe, maybe not.

@Blue The good schools and some fields are competitive.

Anonymous

@Avantgarde Yeah, I mean the top places like TIFR, etc would be competitive

Anonymous

Or the top IITs

9:58 PM

I'll write you a recommendation

"He chats with me sometimes on PSE chat, accept him, thx. - Dr. Enumaris"

#Make Dan great again

danielunderwood

Best bet so far lol

Anonymous

Most of our mods have PhDs. They could write for you too XD

Anonymous

And JR

danielunderwood

Better yet, you guys go become professors and get enough influence to pick grad students :D

Anonymous

10:04 PM

"Hi, I'm a chemist, soap scientist and a GR expert from Cambridge, and I have more rep than what you can ever achieve in your lifetime on PSE. I command you, puny intellect folks, to accept Daniel." - Dr. J. Tech Support. R.

lol

danielunderwood

Woah JR's a soap scientist?

Was. At Unilever

Anonymous

@danielunderwood [jokes on him having worked at Unilever] ;)

danielunderwood

I'll just assume he's responsible for half the soaps in my house

Anonymous

10:18 PM

@Avantgarde Hmm, they might write something similar for me at gunpoint

Anonymous

I just need to get hold of a gun now

danielunderwood

I think I need to learn how to sit and read. I sat at a desk reading most of the day yesterday and today my neck and shoulders are having quite a time

Anonymous

Getting a cushiony chair with back rest helps

good chairs are important

danielunderwood

But do you not lean forward to read the book?

Anonymous

10:23 PM

....I don't read books

Anonymous

Or physical books....as such

danielunderwood

I probably wouldn't really if I didn't spend pretty much all my time staring at a computer screen

Anonymous

Most of what I read are from my own notes which I make from a collection of books (I usually have a soft copy for most of them)

Anonymous

And my notes are written in small and thin copies...so I can just lay back on my chair and read

danielunderwood

I've always made the mistake of not going over my notes after reading/class

I've looked at some of my old notes and wondered what I could ever have meant by what I wrote

Or things that are just plain wrong after I've learned more

Anonymous

10:26 PM

Good notes help, yeah. Either you write it yourself or get it xeroxed from the sincere guy in class having a decent handwriting :P

Anonymous

It's almost impossible to revise from books before exams

danielunderwood

Also I kind of just didn't go to class for the first half of college, so I don't have those notes at all

Anonymous

@danielunderwood Oh, why?

danielunderwood

Well I never really had to pay attention to classes in high school to do well, so I figured college would be the same. It actually was for the first bit, but I couldn't really do that once I started getting into the serious physics courses. I still didn't know how to study after that though

There were a couple courses that I found interesting enough to go, but those were a bit rare

Anonymous

@danielunderwood Ah, I can sort of relate to that

10:31 PM

I've only been to a handful of lectures in my... numerous years of college

Anonymous

Going to class sort of helps to keep in touch with what is going on, even if you don't get to grasp the lectures completely

12

Q: What caused this site to be excluded from Hot Network Questions?

Recently, the Stack Exchange team made the decision to exclude this site from the Hot Network questions on the right sidebar of questions across the network and on the stackexchange.com homepage. Why was this decision made? Were question titles on this site too inappropriate? Can we please get f...

discussion support hot-network-questions

I just learn better from reading

**********ing finally

praise be!

danielunderwood

And I didn't go to professors when I found things confusing until my last semester or so. I suppose that's a large part of my recommendation issue

oh no duct tape and regex

I've worked on software built like that

10:46 PM

@danielunderwood the HNQcalypse is here

danielunderwood

If my experience is anything, "duct tape and regex" becomes rewrite from the ground up and end up with a bunch of unexpected results

Anonymous

11:10 PM

Stack Exchange keeps amazing me. I never expected someone would read the two papers for me and answer my queries within a few hours: quantumcomputing.stackexchange.com/questions/4426/…. :)

Anonymous

I'm really happy with the progress QCSE made in the last few months (and it would be impossible without the enthusiastic participants who managed to make it a success despite the fact that the site was put in private beta at just half-threshold)!

danielunderwood

I may learn something if I put that much effort into answering a question

Also

229

Q: What is dynamic programming?

What is dynamic programming? How's it different from recursion, memoization, etc? I've read the wikipedia article on it, but I still don't really understand it.

algorithm dynamic-programming

@EmilioPisanty @enumaris here's the short version:

70

A: Why can't Northern Ireland just have a stay/leave referendum?

If you don't understand Irish history then you can't understand anything about Northern Ireland. Briefly, the whole of Ireland used to be part of the British Empire. This was due to some uncommonly bloody history since the Tudor era (roughly 1550 to 1600) in which the Protestant UK invaded Irela...

user280247

11:42 PM

Does inclination of rotation axis for the earth has to do with sun's magnetic field?

@santimirandarp No.

Hint: different planets have different axial tilts.

user280247

@EmilioPisanty hmm I'll think about it...but is magnetic interaction between sun and earth strong?

user280247

It might be not, but I don't know really...

@santimirandarp what type of interaction, and what do you mean by "strong"?

user280247

as to explain it's orbit, at least part of it...

11:49 PM

Strong enough to kill a human? Strong enough to exert an astronomical amount of torque?

@santimirandarp No.

magnetic effects have negligible impact on orbit parameters

user280247

Nice...

« first day (2904 days earlier) ← previous day next day → last day (2019 days later) »

Transcript for

Oct '1817

The h Bar

General chat for Physics SE (physics.stackexchange.com). For M...

join this room
about this room

00:00

06:00

12:00

18:00

all times are UTC

site design / logo © 2024 Stack Exchange Inc; legal

mobile