@ChrisWhite yeah.

I figured that if you're in something thicker/heavier then shouldn't you be able to impose the equal transmit time hypothesis?

I understand that

I was just wondering if it would hold in other media- I remember in high school my teacher tried to justify it by giving the analogy of a plane flying through jello

saying the jello would kind of close back on itself as soon as the plane flew through. It makes sense to me that it shouldn't hold for air, and I know it has been shown it doesn't, but thought maybe in things that were more like gelatin, or something like this, that it may exhibit equal transit time

And so what's the difference? Is it just because air doesn't "hold together" very well?

Oh cool. I'll look at that.

close misses?

@ChrisWhite I see. Well, thanks. I should really learn more about fluids...

@ChrisWhite What is the fundamental equation, or idea governing fluid stuff? Like what is the insight that starts the approach? Mathematically, what does a fluid look like?

Should I be looking at navier stokes?

arxiv.org/pdf/astro-ph/0510825v2.pdf

According to this paper $e^2/(4\pi\epsilon_0\hbar c)$ is a function of time.

Great, all of standard QFT is wrong. How did this happen?

@ChrisWhite Cool. Thanks!

@0celo7 Same mistake as always when you are tempted to shout "standard QFT is wrong" - the situation described in there is not a situation that lies within the framework of standard QFT.

@ACuriousMind Are you telling me Duffield would not read a paper before posting it

I don't believe it!

What is this talk of hyperbolic and parabolic?

@ChrisWhite are spacetimes with domain walls mainstream?

whatever a domain wall is...

@ChrisWhite I'm about to finish my undergrad in physics and math, I should be able to understand

@ChrisWhite what

The wiki says elliptic operators generalize the laplace operator, but why are they called elliptic?

@ChrisWhite What about that annoying Abraham-Lorentz force?

@ChrisWhite what about the string corrected Einstein equations

@ACuriousMind huh?

@0celo7 Huh.

@ACuriousMind Huh!

@ACuriousMind I don't see how it's nonlinear in second order

oh it's third order!

@0celo7 It is not linearity that fails :P

Ah, you saw it.

@ACuriousMind what do you know about domain walls

@ACuriousMind well my example was better because it fails linearity in the second derivative :)

@ChrisWhite When you say quasi linear, do you mean because of the nonlinearity in first derivative?

sanic is elliptic

@0celo7 Nothing

What is the definition of a parabolic equation though?

@ChrisWhite Oh, I see. Any idea why they're called parabolic?

oh

lol

Alright, thanks @ChrisWhite.

high school math too advanced D:

freaking conics

@ACuriousMind wait when have I said that before

@0celo7 Generic "you".

Apparently I need to stop using that when talking to you in particular :P

just say man

You might have noticed one can't do that in English :P

Same mistake as always when man is tempted to shout "standard QFT is wrong"

sounds fine to me

@ACuriousMind I don't see the issue ;)

@0celo7 : it isn't all wrong. What's wrong is the cargo-cult fairy-tale that virtual particles pop into existence. They don't. Like anna said, they only exist in the mathematics of the model. Virtual particles are field quanta. Like you divide a field up into abstract chunks. When alpha changes it isn't because electrons are spitting out photons spitting out electrons, it's because the field changes, because space changes. Now where's my upvote?

@JohnDuffield Can't upvote since you didn't edit.

@ACuriousMind @ChrisWhite What is the technical name for a "wave-like" solution of PDE such as the Maxwell eqns?

Your wish is my command.

@0celo7 I think such a solution is called "a wave" :P

(I don't really know what you're asking)

@ACuriousMind a...wave

@ACuriousMind just some solution that would pass for a light wave

@ACuriousMind how do I write $\nabla^b\nabla_b A^a=R^a{}_bA^b$ using forms?

@0celo7 : I read the paper. It contained what you asked for. Somebody else saying e²/(4πϵ₀ħc) is not constant. I don't just make this stuff up you know. I'm not some my-theory guy.

@JohnDuffield Jesus Christ, that paper has nothing to do with the running coupling of QFT.

Just ask @DavidZ .

@0celo7 $\ast \nabla \ast \nabla A = \iota_A R$, I think.

@ACuriousMind $*$?

Hodge star

No, that's $\star$ :P

$\star$ has that ugly spacing

And it's the Moyal star, not the Hodge star :P

Oh, but you figured out how to fix that

@ACuriousMind Wait what

no QM pls

@0celo7 Moyal product.

@ACuriousMind I know what is it

Then why ask?

Because I didn't know if you were serious!

@0celo7 : Jesus Christ, just accept the fact that the fine structure constant ain't constant.

@JohnDuffield I don't accept falsehood.

@ACuriousMind Hmm, what is $\nabla$ there?

@0celo7 Exterior covariant derivative.

@ACuriousMind Oh crap not that thing

Huh? It's just $\mathrm{d}+\Gamma$.

@ACuriousMind Ok, thanks...what's $R$

@ACuriousMind I know

@0celo7 Uh...whatever the ${R_a}^b$ components you wrote there belong to

doesn't mean I have to like it

@ACuriousMind Ricci tensor

...so what's the question?

can't turn that into a form :P

well you can...

but not in a way that $\iota_A R$ makes sense

@0celo7 sigh...yeah, do $\iota_A R^{\sharp_1}$ when ${\sharp_1}$ means raising one index.

@ACuriousMind wtf

Your problem was that $R$ itself eats vectors, not covectors, right?

Holy...

@ACuriousMind ok, what is $R$ in your first attempt

my answer for the astronomy site got 50 upvotes...

I don't even...

@0celo7 The Ricci tensor? I just didn't consider that it can't eat $A$ before raising an index.

@ACuriousMind oh I thought it was $R_{ab}\theta^a\wedge\theta^b$

Can stuff in fluid mechanics be used to talk about sand?

@0celo7 : you have accepted falsehood, and you're clinging to it. You won't follow up the references I give you or do your own research. The fine structure constant is a running constant. So it isn't constant. Get used to it.

ahhh, Straumann has a standard notation for that: $R(X):=R_{ab}X^a\theta^b$

@0celo7 If $\theta^a = \mathrm{d}x^a$, then yes. I don't get what the problem is

@ACuriousMind uh yeah that's not notation Straumann uses

no problem...

@ACuriousMind uh no

that's zero :P

@0celo7 wat

In Riemannian geometry the Ricci tensor is symmetric...

The basis of the cotangent space is surely not zero

Ahhh

You been doing Kahler geometry behind my back :P

Well, why is there a wedge there then, and wtf is $\theta$?

@ACuriousMind section of $T^*M$

Straumann's notation

@ACuriousMind So he just writes $R(X):=R_{ab}X^a\,\mathrm{d}x^b$

thus, in good notation, $\star D\star D A=R(A)$

@ACuriousMind how do I fix the spacing? (or is it kerning?)

@JohnDuffield And you have completely misunderstood what a running coupling constant is.

@0celo7 I don't remember off-hand

and the TeX god left

@ACuriousMind is it like \newoperatorsymbol or something

I think you have to declare a new math operator and set its class to not be a binary operator like \star, but unary, and I don't remember how exactly that worked

hmm I thought you figured out how to do it in one line

Maybe, but I don't remember because I never actually used it after that :P

@ACuriousMind $\mathord{\star}\mathrm{d}\mathord{\star}$

:)

you're welcome~~

hello bar mates

it was Chris White that figured it out, thanks @ChrisWhite

So yesterday I finally understood orbifolds , today, there are two things I want to understand. They are things I struggle with. As most of you know I can barely understand addition lol

what is an orbifold?

It is more or less an orbital manifold, I guess it is something like M/G where G is some group actions acting on M or something like that lol

M is some manifold

hmm, did I tell you that

hehehe

sounds like something I would say

but it doesn't mean much to me ;)

yup hehe

actually there is an exercise in my geometry book to find the condition for an orbifold to be Hausdorff

don't want to do it :(

Which book is this?

do Carmo Riemannian Geometry

I have heard good things about this book

so, maxwell's equations are $\mathord{\star}\mathrm{D}\mathord{\star}\mathrm{D}A=R(A)$

@0celo7 : Au contraire, I completely understand what a running coupling constant is. You don't: "of course α is constant". Duh, no it isn't. And don't you remember me telling you how Einstein described a gravitational field as inhomogeneous space? If α was constant, your pencil wouldn't fall down. When this experiment gets done, remember what I said. Until then, you really aren't listening, so, let's end this conversation, OK?

@JohnDuffield Our conversation ended months ago.

My first struggle is with convincing myself I understand what symmetry breaking really is in phi^4 .

heh

@Ghost Hey

@0celo7 That should be like one half of them, since that's the generalization of $\mathrm{d}\ast F = J$. You have to have a version of the Bianchi identity $\mathrm{d}F = 0$.

@kevinTahN. What's that got to do with orbifolds?

@ACuriousMind The one that matters for my PSE post!

I know the other half :V

not much, I think , it is just something else I am trying to understand lol

@ACuriousMind but $\mathrm{d}F=0$ should also hold in curved spacetime, no?

because that's just $\mathrm{d}^2A=0$

@0celo7 hello

@0celo7 Yep.

@ACuriousMind so why did you mention it?

I am weary of you

Suspicious!

Because you said "so Maxwell's equations are:" and then only wrote half :P

are *for my purposes

F= -*F

I need the dynamical half for my stuff

@kevinTahN. you doing solitons now?

hehehe

anti self dual stuff? you say soliton lol

neh

@Ghost Why are you here? I thought you left us

@0celo7 That's not a soliton, that's just what Maxwell's equations reduce to in vacuum on some manifolds.

@0celo7 haunting

@ACuriousMind wtf

I've never heard of this

@0celo7 I see you didn't read my instanton answer, since the first part is "instantons as classical solutions" :P

@ACuriousMind wait

lol I knew that

from Nakahara, Weinberg, BBS and Jost

It can happen that there are more solutions than the (anti-)self-dual ones, but all anti-self-dual configurations are minima of the Euclidean action

just ignore me...

@0celo7 k

@ACuriousMind bye

:(

@ACuriousMind also, I did read it

Just instantly forgot it, apparently...

I am just trying to understand how spontaneous symmetry breaking happens in phi^4, my other question is about how large N approximation really works with may be a simple matrix theory and some hints on how planar diagrams work, and why string theorists get to "guess" the relevant string theory from this. But for now I just want to understand symmetry breaking algorithm step by step in phi^4 lol

@kevinTahN. What do you mean "symmetry breaking in $\phi^4$"? What symmetry do you want to break there?

@ACuriousMind is (anti)self duality possible in Minkowski spacetime

we once talked about this in 10 dimensions

say this for example en.wikipedia.org/wiki/Quartic_interaction

actually may be that was not the best simple case to consider? which one would you recommend? I would be super excited if I can convince myself I have an intuitive and mathematical understanding of how it works. I mean I have deceived myself in the past to understanding it but I think i don't really do lol

I am just reading the site - have a few questions, seeking answers that are already present...

@kevinTahN. do you know what $\star^2$ is off the top of your head

@0celo7 not really lol

what is it?

not fun

hehehe

$\star^2=\mathrm{sign}(g)(-1)^{p(n-p)}$

@0celo7 Why don't you just look it up? Practice your weak google fu :P

@ACuriousMind or I can access my near infinite library of books

Either way, asking random people in this chat seems like the least efficient method.

well

you're not wrong

so $\star^2(\eta, F)=(-1)(-1)^{2^2}=-1$

thus, (anti-)self-dual thingies are not possible in Minkowski spacetime

any FRET guys?

don't fret, it'll be okay...

what is FRET?

Forster Resonance Energy Transfer

wow

anyone want to teach me symmetry breaking in a very simple theory? How about large N and planar diagrams . . . I want to know these things :D

@kevinTahN. Large N and planar diagrams are not "very simple". Do you know usual perturbative QFT, i.e. LSZ formula and Feynman diagrams?

Well, I have some acquaintance, but not expert competence

I have played with a few QFT's

made some feynman rules and diagrams , computed G^2 . . . wick contracted etc. . . but at baby level though. I have not done any epic calculations lol

Okay, so you said you wanted to understand symmetry breaking in $\phi^4$. The original Lagrangian is invariant under the symmetry $\phi\mapsto -\phi$. The specific solutions of the classical equations of motion are not (because any $\phi$ invariant under $\phi\mapsto -\phi$ would be identically zero). What do you want to "understand" about that?

give me a few more seconds let me process something

I though the general idea was that some potential rendered things in such a way that under some variation, the object <0|something|0> shifted

I have a feeling I have said something completely wrong lol

ah yes I see what you said

@kevinTahN. Ehh...no. Spontaneous symmetry breaking occurs when a solution to the equations of motion does not exhibit all of the symmetries in the Lagrangian.

yes yes yes

you are very correct

ok one down

you just check the solutions to see if they obey the same symmetry and that's it ?

This often leads to a non-zero VEV of some overall field, because if $V(\phi)$ is the potential, then $\langle \phi \rangle = \phi_0$ where $\phi_0$ is the minimum of the effective potential. To first order, this means that the VEV is just the minimum of the classical potential.

Now, the LSZ formula needs to have $\langle \phi \rangle = 0$ for its fields, and so we need to write $\phi(x) = \phi_0 + \sigma(x)$ where $\sigma$ is now our dynamical field with $\langle \sigma \rangle = 0$.

@kevinTahN. Yes, you just look at the solutions and observe they are exchanged under the broken symmetry (one minimum becomes the other under $\phi\mapsto -\phi$ in the $\phi^4$ example.

I see, this is quite illuminating. I think I get it now

the symmetries are always there , but hidden :D

I have a rich friend who is applying for financial assistance for university.

<_>

what a loser.

lol

@ACuriousMind just went over your explanation and the wiki on Phi^4 can honestly say I understand it now

so who wants to talk large N approximation?

come on people teach me. . .

pls lol