The h Bar

Danu

2:00 PM

@ACuriousMind any chance that you can read french?

ACuriousMind

@Danu Not a word

0celo7

@ACuriousMind if you want to do some useful math, please explain why $G(x,y(x))=\mathrm{const.}$ if $y(x)$ is the solution of the ODE $f(y',y,x)=0$.

ACuriousMind

@0celo7 1. What is $G$? 2. I won't do your homework :P

0celo7

Freire tried to give a rigorous justification using vector fields, but he didn't write anything down

@ACuriousMind 1. $G$ is some relation

2. I got a perfect score on the homework, I'm trying to understand the concept

Slereah

@ACuriousMind : Is it the thing with contractible curves

Danu

2:02 PM

@ACuriousMind You're really missing out then, by not being able to read Grothendieck's memoir: He talks a lot about cohomology in the first ~50 pages (which is where I'm currently at)

Slereah

Or am I confusing with another homo- thing

Danu

In a very poetic, beautiful way.

0celo7

homotopy

Slereah

Ah yes

ACuriousMind

@Slereah It's got to do with it, but you may also be thinking of homotopy

Slereah

2:02 PM

Too many homos in math

0celo7

must...not...star

Slereah

Homotopy, homology, homothety, homomorphism

ACuriousMind

@Danu I'd love to read Grothendieck

0celo7

homothety?

Slereah

Hm

That may be a french word

0celo7

2:03 PM

what does it mean

Slereah

Homothetic transformation

In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio, which sends in other words it fixes S, and sends any M to another point N such that the segment SN is on the same line as SM, but scaled by a factor λ. In Euclidean geometry homotheties are the similarities that fix a point and either preserve (if λ > 0) or reverse (if λ < 0) the direction of all vectors. Together with the translations, all homotheties of an affine (or Euclidean) space form a group, the group...

Danu

@ACuriousMind It's so nice

Slereah

Apparently not

I should read about Wilson loops

0celo7

@ACuriousMind So you're really starting BBS?

Slereah

It seems nice

0celo7

2:05 PM

You doing the exercises?

ACuriousMind

@0celo7 Yes

Slereah

Gauge theory from homotopy

ACuriousMind

@0celo7 Perhaps. Probably not those in th early chapters.

Slereah

or whatevs

0celo7

@ACuriousMind Do you want a partial solution guide?

ACuriousMind

2:05 PM

@Slereah That's holonomy

Aaaaarghn

haha

I was had again!

string theory has that too

Slereah

Next I will confuse it with holography

Or the Holocene

Or whatever happened in 1942

ACuriousMind

2:07 PM

@0celo7 Perhaps later, but if I have such things, my willpower to work through the things myself drop significantly, so not yet

@Slereah lol, a few thousand years off

Slereah

I wasn't talking about the holocene there :p

Two eras you don't want to confuse

0celo7

TIL what holocene is

Slereah

though I suppose

ACuriousMind

This chat is sometimes educational while goofing around :)

Slereah

A lot of people died during both events

ACuriousMind

2:09 PM

"SE is about questions and answers, not about people" awwwww, but dorking around in the chat room is so much fun. — DanielSank 10 hours ago

Shing

@ACuriousMind According to wiki "When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.[" Does that not imply that ball will stay right top of the dome never move unless by a small kick?

Slereah

It will, if it's in equlibrium

ACuriousMind

@Shing You have to analyse the solution carefully - there is no moment in which the ball as non-zero acceleration in which not also a force is acting on it.

@Slereah This is Norton's dome

0celo7

@ACuriousMind lol, I can't even begin to solve half of the exercises

Slereah

Emperor Norton?

ACuriousMind

2:11 PM

20

Q: Norton's dome and its equation

Norton's dome is the curve $$h(r) = -\frac{2}{3g} r ^{3/2}.$$ Where $h$ is the height and $r$ is radial arc distance along the dome. The top of the dome is at $h = 0$. Via Norton's web. If we put a point mass on top of the dome and let it slide down from the force of gravity (assume no frict...

I think it's John Norton, not Emperor Norton, though

Slereah

Please be kind to the only monarch of the US

0celo7

@ACuriousMind lemme know when you've done 3.16 please

Shing

@ACuriousMind I know, that's why I said "non-accelerating" & "at rest" makes a difference. I agree with it is the case for "non-accelerating". But for "being at rest", it is really demanding "stay right there".

ACuriousMind

@Shing Yes, it stays there as long as no force is acting on it. I know where your intuition is saying this can't work, but please point at the part of the solution that contradicts "objects don't move unless a force acts on them".

Slereah

It's the same with me

I can't think of any time period between dinosaurs and humans

It is the eras that nobody cares about :(

ACuriousMind

2:20 PM

@yuggib: Your ability to read French a secret or what? :D

Slereah

Aaaah

yuggib

@ACuriousMind No...just quite of context :-D

Slereah

Maybe it is a good thing that it is forgotten!

Begone Eocene

yuggib

thought he was asking for a translation

ACuriousMind

@Slereah Awwwww, cute

yuggib

2:21 PM

then read the following

0celo7

what on Earth has this chat turned into

mathematician circle jerk was preferable

Slereah

Oligocene

Maybe we should talk about GR instead then :V

0celo7

how about ACM does exercise 3.16

and then explains it to the masses

ACuriousMind

@0celo7 What, you don't like "Slereah's tour through the ages"?

0celo7

@ACuriousMind I'm just cranky

ACuriousMind

2:23 PM

@yuggib Nah, he just wanted to show off :P

Slereah

The masses are the peaks of the spectral representation of a quantum state

0celo7

you won't help me with ODE concepts

you hate me :'(

and I have to do more homework

and I want to play Deus Ex

ACuriousMind

@0celo7 I have no frigging clue about ODEs, to be honest

yuggib

@ACuriousMind :-D

0celo7

@yuggib do you know anything about introductory ODE stuff (implicit solutions)

yuggib

2:24 PM

@0celo7 ODEs are useless...the only thing that matters is Gronwall's lemma

0celo7

jesus people

Danu

hahaha

yuggib

@0celo7 Not so much...

0celo7

@yuggib I used that once in...HE?

you need it to show the "matter can't violate causality" theorem

Slereah

from what I hear the one mathematicians love is Zorn's lemma

yuggib

2:25 PM

Maybe...if you do estimates with evolution involved you probably use it

ACuriousMind

@Slereah Zorn's lemma is awesome. Prove existence of something, but still have no idea how it looks.

0celo7

@yuggib yeah you have to show that matter can't evolve outside of it's light cone, essentially

Slereah

yuggib

@Slereah The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma

ACuriousMind

^good one :)

(but a bit overused :P)

yuggib

2:27 PM

By Jerry Bona

Slereah

Can't have your cake and eat it!

yuggib

@0celo7 see...I could tell even without knowing a thing about HE :-D

Slereah

You know

One thing I wonder is

If the metric tensor has a non-metric connection

Can matter evolve outside the lightcone

yuggib

@ACuriousMind Yeah...Hahn-Banach theorem is probably a less obvoius restatement of the full axiom of choice

0celo7

oh my god the mathematicians have taken over again

Slereah

2:29 PM

Because then the mass is like $g_{ab} p^a p^b$, but $\nabla g_{ab} \neq 0$

ACuriousMind

@yuggib Hm...Wiki says choice implies HB, but not the other way around, so it's not a restatement, right?

Slereah

I forget the exact details but IIRC I think that maybe mass could change with time in such conditions?

ACuriousMind

@Slereah Why would you look at a non-metric connection?

0celo7

@Slereah why would you not be able to get a non-metric connection

ACuriousMind

@0celo7 You have to decide, it's either this or @Slereah posting random pictures :P

yuggib

2:31 PM

@ACuriousMind HB implies almost any weaker version of the axiom of choice that I know...but it has not been proved to be equivalent that's true

0celo7

it the manifold is pseudo-Riemannian there is always a Levi-Civita connection, no?

@ACuriousMind I want to do my damn homework

Slereah

There is, but you don't have to

0celo7

so if the chat could die that would be nice

Slereah

It's the same way people look at spacetimes with torsion

0celo7

are there any good books on that

not that I'll ever read them

my reading list has gotten out of hand

Slereah

2:32 PM

The oldest trick in the book to write a theoretical physics paper is "unreasonable generalization"

ACuriousMind

@yuggib Still interesting though. This explains why my course began talking about Zorn's lemma shortly before showing HB :D

0celo7

haha

Slereah

"What happens if I remove every fucking restriction"

ACuriousMind

@0celo7 Uh...just log out if you really want to do it :P

0celo7

"what happens if QFT particles are points"

Slereah

2:33 PM

IIRC Poplawski talks about the non-metricity tensor a bit?

0celo7

@ACuriousMind no self control

Slereah

Also the non-metricity tensor is fun because if you do the EOM for a spacetime with it

It is linked to a quantity called the HYPERMOMENTUM

space noise

0celo7

are there any good books on spacetimes with torsion

Slereah

Ahahah

I was way into that at some point

The answer is no

The closest there is is Poplawski's proto-book

"Spacetime and fields"

arxiv.org/abs/0911.0334

it's quite nice

there's also a PDF floating around that is like

Inserts to put in your Wald that deals with torsion

slimy.com/~steuard/teaching/tutorials/GRtorsion.pdf

Put this in your Wald

For extra Wald

The thing about torsion is that it's not totally necessary from a GR point of view

0celo7

is there any physics there or just math

ACuriousMind

2:37 PM

"Put this in your Wald"...I was briefly wondering why one should plant it in a forest.

0celo7

German jokes are not funny

ACuriousMind

Then I remembered this is English

Slereah

Because in the end, torsion interactions end up being just 4-fermion interactions

0celo7

@Slereah

Slereah

Because the torsion is ~ the axial current

0celo7

2:38 PM

you need to help me

I need help (screw you star person) [I see you saw the error of your ways]

my reading list is just too big

Slereah

Burn the books

ACuriousMind

Damn, I need to wait for the edit grace period to star such stuff :P

0celo7

IT WAS YOU

but...you're not an astronomer

it was all a lie

Danu

Serious question: Do you guys think (uncountable) choice is really relevant in physics?

ACuriousMind

@0celo7 What? That I starred this doesn't mean I starred everything else

Danu

2:40 PM

I'm catching up on the transcript---you guys were talking about the axiom of choice.

0celo7

@ACuriousMind you can't fool me

I'm on to you now

yuggib

@Danu Yes, I do. There are people who think it is not, and that we could do physics in e.g. the Solovay model where all subsets of reals are measurable

0celo7

@Slereah seriously i need help with my reading list

Slereah

Well I can't read them for you

Books are not like worms

0celo7

I think my priorities should be Weinberg and Nielsen-Chuang

Slereah

2:42 PM

I can't regurgitate them to you

yuggib

but I think than when you deal with duality, distributions and so on you need Hahn-Banch and therefore uncountable choice

Slereah

Weinberg's a pretty important one

ACuriousMind

@Danu I don't know enough about which things depend on it. Do we get the spectral theorem and enough functional analysis without it?

0celo7

yes, I really need to learn renormalization

ACuriousMind

The HB thingy seems to say no.

Slereah

2:43 PM

You know what else has renormalization?

Birrell.

Except it's for GR

0celo7

like...from scratch?

Slereah

So it is much better

0celo7

@Slereah what about book worms

yuggib

@Danu And probably the most important motivation (in my opinion): the Weyl algebra of CCR is non-separable when constructed on any non-zero vector space

Slereah

Renormalization is basically like

"Oh fuck this is divergent"

yuggib

2:44 PM

so you cannot work on the CCR algebra choosing only in countable sets

ACuriousMind

@Slereah nononono

Slereah

"Let's expand the terms and hide the divergence under the rug"

ACuriousMind

That's more what regularization does. Renormalization can be explained without saying "we need to hide this".

Slereah

Do tell

I am curious

0celo7

I will once I make my way through Weinberg again

Slereah

2:45 PM

Weinberg is nice but maybe not the best to learn QFT

ACuriousMind

@Slereah I've linked this before: "Renormalization without infinities" by Neumaier.

Slereah

thanks

0celo7

@Slereah I always have ACM handy ;)

ACuriousMind

It's...just a reparametrization, essentially, and the divergences are there because the naive parameters you chose to describe your theory are crap :P

Slereah

@ACuriousMind Isn't there still problems with like

Landau poles and such

yuggib

2:47 PM

@ACuriousMind I am afraid that ZF+HB is not a very used model; it is easier to stick to the full ZFC (that implies HB) at that point...

Slereah

What is HB

yuggib

@Slereah Hahn-Banach theorem

0celo7

Hawking Bellis

Slereah

(the first set theory I learned is the one from the Principia Mathematica)

ACuriousMind

@Slereah Laudau poles are just an indication that you shouldn't do perturbation theory :P

Slereah

2:48 PM

It's a bit awkward

ACuriousMind

(Or that some theories might be inconsistent)

Slereah

@ACuriousMind : Are they a sign of quantum triviality?

I was wondering

0celo7

(Or maybe quantum mechanics is wrong)

ACuriousMind

@Slereah I think they are kinda the opposite (since triviality is when everything gets renormalized to zero, I think), but I'm not sure

Slereah

Well like

You have to renormalize it to 0 because otherwise you get poles

ACuriousMind

2:50 PM

Ah...maybe

Fortunately, non-Abelian gauge theories don't exhibit Landau poles if you don't add too many fermions, so all is well, iirc

Slereah

What is "too many"

0celo7

more than a few

ACuriousMind

Depends on the $n$ in the $\mathrm{SU}(n)$, but there's an explicit formula for the running of the coupling in terms of the number of fermions and that $n$...it's like you mustn't exceed $12n$ or something like that.

yuggib

@Slereah A little bit outdated by now :-P

Slereah

12n is quite large I suppose, yes

Although, do left handed and right handed fermions count as 2

ACuriousMind

2:52 PM

Because then something switches sign and you get a Landau pole instead of asymptotic safety (or whatever the correct term is)

0celo7