The h Bar

12:34 AM

@Danu: THE GRAVITY OF THE SITUATION

3

I actually sort of like this one.

@KyleKanos Perhaps there is an integral performed that ends up with the volume of a sphere of radius R minus the volume of a sphere of radius (R-dr)?

Bernard Meurer

2:20 AM

@DanielSank That might be one of the best titles here so far

0celo7

3:40 AM

@Slereah : physics.stackexchange.com/questions/248365/…

Danu

7:28 AM

@DanielSank It's always pun-time!

Shing

8:14 AM

Would anyone explain to me how a complete set of commute operators can completely describe a quantum system?

kevin Tah N.

8:57 AM

Hey dudes

Slereah

hey

kevin Tah N.

9:13 AM

I could not sleep so i figured i would hang out here😀

:D

I finally understood the definitions of open and closed balls after drawing venn diagrams :p

Slereah

10:08 AM

why would you need a diagram for that

Danu

10:55 AM

@Slereah, @0celo7 any good sources for mathematical perspectives on the equivalence principle?

I know there is a small discussion in Sachs & Wu, but anything more would be appreciated as well.

Slereah

Errrr Rovelli?

He muses a bit on GR philosophy and math

Danu

Does he stick to pure GR?

Slereah

The first chapters yes

Danu

Which book?

Slereah

He discusses the hole argument and all

Quantum Gravity

It's available for free online

Danu

10:58 AM

I was shocked to find out that Hawking & Ellis not so much as mention the equivalence principle...

Danu

11:09 AM

By the way, that's not really what I'd call a mathematical perspective @Slereah.

Slereah

Well isn't it just diffeomorphism invariance really

Equivalence principle is basically just the existence of a Riemann normal coordinate system

Slereah

11:40 AM

heh

In my old files I have a solution for the first 9 chapters of Feynman's path integral book

If you're interested : dl.dropboxusercontent.com/u/19940612/Correction%20Feynmann.pdf

The forced oscillator took me a while

skill patrol

12:16 PM

@Slereah nice, thanx for sharing

Slereah

it's a bit in french

most of it is just equations, tho

skill patrol

@Danu as far as the laws of mathematics are certain, they do not refer to reality :P

reality being the equivalence principle :-)

innisfree

12:46 PM

Has anyone seen any calculations/discussions about checking that fermion and vectors don't obtain VEVs? I've seen calculations of tadpoles, but I mean something similar to a background field method for the Higgs

Slereah

don't you need a weirdo vacuum topology to get a VEV

Danu

@skillpatrol I think you misinterpret the quote

innisfree

1:07 PM

I don't know. How do I check that a vev doesn't develop in the SM fermions or vectors?

skill patrol

@Danu how would you interpret it?

Slereah

check if the vacuum value corresponds to the 0 of the field?

innisfree

1:22 PM

If so, presumably it's been done in textbooks?

I find the minima of some effective potential? Just like for a scalar?

0celo7

1:59 PM

@Danu Try Straumann?

I'm not sure exactly what a "mathematical" perspective is.

@Danu I mean, I think the "mathematical" part is that since $m_\text{inertial}=m_\text{grav}$, the only data you need to solve the EoM of a free falling particle is its position and velocity, and that't exactly what you need to solve the geodesic equation.

So Einstein postulated that the paths taken by free particles are inherent to spacetime.

@Slereah Yay Kobayashi-Nomizu 1 has shipped.

user116211

@0celo7: Currently I have 57 pages open apart from it in Opera!

user116211

And it's still working well....

user116211

@BernardMeurer hmmm..... check this:

user116211

> Exorcism of Maxwell's Demon

user116211

It is one of the titles I like the most.

skill patrol

3:05 PM

how do you @ACuriousMind interpet this

ACuriousMind

@skillpatrol Interpret what?

skill patrol

as far as the laws of mathematics are certain, they do not refer to reality :P
reality being the equivalence principle :-)

ACuriousMind

It refers to mathematical theorems being undoubtedly true. They are proven. No "law of physics" can ever be considered proven, in the sense that it could always turn out to be false tomorrow.

skill patrol

thank you

Slereah

Why are all software jobs web shit nowadays

skill patrol

3:11 PM

market saturation?

ACuriousMind

Because the web is the shit ;)

Slereah

The web is great but I don't think every bloody company needs that much of a WEB PRESENCE

Also too many fucking apps

ACuriousMind

You should get a lawn, so you can tell the kids to stay off it

skill patrol

lol

0celo7

why so old

Slereah

3:27 PM

The Simpsons - Grandpa Simpsons "I had an onion on my belt"

►

possibly me

0celo7

@Danu Huh, you're right, it doesn't.

But it's not an intro book.

Slereah

HE is really a book that is like

Focused on a few specific topics

Mostly the Cauchy problem and the singularity theorem

and cosmology

0celo7

4:38 PM

@Slereah dude why isn't Petersen out yet

Danu

@0celo7 No, I'm talking about other stuff, but never mind, I'll do some research on my own.

0celo7

@Danu What other stuff?

Maybe I could help if you told me what you want

barrycarter

He is the best of the many, I summon here Mr... @JohnRennie

Danu

4:59 PM

@0celo7 More about the connection to how it's used in physics to justify simply doing SRT on small scales

Maye what I'm looking for simply does not exist. I'm looking for something to connect to what I heard in that mini-course on GR I went to a few days ago.

The relevant part in Sachs & Wu is closest, probably.

0celo7

@Danu Ah.

It's because you can set up Riemann normal coordinates at each point of spacetime.

And the curvature effects are of second order in "distance" around that point.

barrycarter

@0celo7 Could you help me with a constant acceleration relativity problem using the invariant?

0celo7

@Danu Basically, as you know, you can transform the metric to the flat one at any point in spacetime. There are coordinates where the "corrections" are "small" within a "small" neighborhood of that point.

The relevant calculations are in e.g. Straumann IIRC.

barrycarter

Can anyone help me with a constant acceleration relativity problem using the Lorentz(?) invariant?

Danu

@0celo7 Yeah, I know this of course, but I'm looking for a mathematical discussion.

@barrycarter What is the Lorentz invariant?

0celo7

5:08 PM

@Danu Straumann!

Danu

@0celo7 Aight!

barrycarter

@Danu I think that's what it's called. The invariance of ds^2 with respect to different observers.

0celo7

I don't have it memorized so I don't know if it's really in there, but I would check.

If you asked nicely I can get up and grab it and look.

Danu

@barrycarter That's called the line element/metric

barrycarter

@Danu Got it, thanks.

Danu

5:11 PM

@0celo7 I've got my own, don't worry.

0celo7

@Danu Your ebook is not as nice as my hard copy. Which is almost destroyed for some reason.

Springer cheaped out on the binding.

Danu

Ctrl+F is life

0celo7

@Danu I do that on my ebook and then read the relevant section in the hard copy.

I'm weird like that.

@Danu Have you ever seen the notation for $\Phi$ as a group in algebraic topology?

There's a random $\Phi$ in this exact sequence and I have no clue what it is.

Danu

@0celo7 Nope

$\Phi$ would typically be a map

0celo7

@Danu What about $\Pi_1(M)$? I don't think it's the fundamental group.

(Because he says $\Pi_1(M)$ is infinite when $M$ has a Euclidean factor, and the fundamental group of Euclidean space is trivial.)

Slereah

5:19 PM

Are there any realistic cosmological models where the metric isn't homogeneous

Or do people go straight to numerical models for those

0celo7

Why on Earth would you use $\chi(M)$ for the set of vector fields?

Danu

@0celo7 Are you sure it's not $\mathfrak X(M)$? Because that's pretty standard...

0celo7

@Danu I can tell the difference between X and chi, thank you very much.

John Duffield

5:37 PM

@barrycarter : those are collector-item silly-money prices. I'm sure I could find a spare copy lying around if you'd like one. I could even sign it.

0celo7

Lol

@Danu For once I don't think you were being derogatory.

Danu

@0celo7 Even we have to agree sometimes... right? ;)

0celo7

@Danu If agreeing with you means disagreeing with JD...yes.

Wow!

I wonder who deleted all of those messages!

Danu

That was me.

0celo7

You don't say.

Danu

5:48 PM

(that message is for others reading the transcript later)

0celo7

Ok comrade.

@Danu Do you have a reference for Chern-Weil theory?

Is Kobayashi-Nomizu V. 2 the standard one?

Danu

No idea.

0celo7

You took a course on it!

Slereah

Hurray I proved the Hamiltonian

0celo7

What?

Slereah

5:54 PM

Still doing Peskin

0celo7

Why did my mega GR reference list get only 2 upvotes?

I put a lot of effort into it.

Slereah

you answered a question that was satisfyingly answered a long time ago

not a very good way to get internet points

0celo7

What?

There's a billion more GR books to read than David Z put

Slereah

Danu

@0celo7 Were you trying to imitate me? ;D

0celo7

5:58 PM

@Danu No, I had it planned for a while.

And I can actually vouch for most of the books on the list.

Danu

Maybe that's what's wrong with it ;)

0celo7

I would tell you to shove it but (a) you're a mod (b) you don't have feelings

@ACuriousMind Lol, new record. Cheeger & Ebin prove the Hopf-Rinow theorem on page 9.

Slereah

No time to slack!

0celo7

What?

@Slereah Can I see your Proof?

Slereah

It is on paper

I can take a pic

0celo7

6:04 PM

Do eet.

Slereah

0celo7

why do you do math in English

Also you need to work on closing parentheses

Have any of you watched Archer?

barrycarter

6:24 PM

@JohnDuffield Thanks! I was just going to ask for an e-version, but sure. Do you have my email address or other method I can provide my addr?

Slereah

Most of the books are in english

barrycarter

Can anyone here help me work out a relativity problem involving constant acceleration, using the line interval? @JohnRennie I summon thee, though I suspect it is too late.

dmckee

I've deleted some posts here in chat.

Slereah

Down with the Man

0celo7

Uh-oh.

Bans incoming?

dmckee

6:29 PM

This facility is not here for users to try to turn disagreements into public spats, and continuing to attempt this will get our attention.

0celo7

@Slereah It was nice knowing you.

Slereah

Welp onto proving the bloody momentum operator

dmckee

@0celo7 No. Just a warning that I'm miffed because people are making me work.

barrycarter

Can you name the offenders or at least the subject of the miff-causing messages?

I accuse ... (pointing finger)

dmckee

A user wanted to turn a on-site disagreement into an argument in the h bar. That's not kosher.

barrycarter

6:32 PM

But you won't tell us who the user was or what the disagreement was about? Can all of us currently in this room safely assume it wasn't us?

The murderer is in this very room. It is... (turning slowly)

0celo7

@dmckee Ah, that user.

Am I in trouble?

Slereah

You're always in trouble

dmckee

That would be too much work. I have grading to do.

barrycarter

Someone please confess before I build up too much angular momentum

Slereah

Not I!

barrycarter

6:37 PM

Technically, that's an anti-confession.

Loong

@barrycarter Professor Plum

barrycarter

@Loong (too dizzy, falls down). I knew that!

With the keyboard in the h bar?

dmckee

@barrycarter The butler who is in reality a long-lost heir masquerading as a con man.

barrycarter

I've always wanted it to be the detective himself.

Bernard Meurer

@dmckee May I ask you a somewhat subjective question?

barrycarter

6:39 PM

What's the objective of your subjective question?

Bernard Meurer

@barrycarter You'll see when I ask it.

dmckee

I don't know. Are you going to write the key for the isochrone problem I have to grade?

barrycarter

I tingle with anticipation.

Bernard Meurer

@dmckee What do you think of UCSD?

0celo7

@dmckee Sure.

dmckee

6:41 PM

I don't know much about the program there. It's a serious university, but it's not prestige tier.

Bernard Meurer

Yeah that's what I thought too. Meh, hope Waterloo takes my ass

0celo7

Why would you ever want to go to Canada.

Bernard Meurer

@0celo7 It's further away from you

On a serious note Waterloo has: Chanele, IQC, Canadians and maple syrup

Slereah

Hm

Danu

@barrycarter Just stop asking about stuff :P

Slereah

6:52 PM

If I do $p \rightarrow -p$

Should I do $d^n p \rightarrow -d^n p$ if n is odd

And not if it's even???

Danu

@BernardMeurer Don't worry too much about prestige now; grad school is more importnat when it comes to that kinda stuff, I think.

Slereah

Looking at a solution somewhere the sign of $dp$ doesn't seem to change

0celo7

@BernardMeurer Chanele?

@Slereah Yes.

Bernard Meurer

@Danu yeah I've been told so by other people as well. I just don't feel all that into UCSD

0celo7

@Slereah Yes.

Bernard Meurer

6:54 PM

@0celo7 Don't play fool

0celo7

@Slereah Roughly, $d^np=\wedge_{i=1}^p dp\to \wedge_{i=1}^n d(-p)= \wedge_{i=1}^n -dp=(-1)^n \wedge_{i=1}^n dp$

Slereah

Because one of the proofs relies on $\int d^3 p\ \vec p a_p a_{-p} \rightarrow -\int d^3 p\ \vec p a_{-p} a_{p}$

But the minus of the measure should compensate the one of $\vec p$

0celo7

@BernardMeurer She's 25 dude, you have no chance.

@Slereah Hmm.

Bernard Meurer

@0celo7 Not my point. It's cool that she exists in the area

Like living next to a famous person or something like that

0celo7

She's not famous.

Bernard Meurer

6:57 PM

In my heart she is

0celo7

@Slereah Well

Don't you also have to flip the region of integration

Which gives another minus

Like in $\int_{-\infty}^\infty f(x)dx$

Slereah

My answer is 100% "eeeeh"

Could be?

0celo7

if you do $x\to -x$, then you get $\int_{-\infty}^\infty f(x)dx\to \int_{\infty}^{-\infty} f(-x)d(-x)=\int_{-\infty}^\infty f(-x)dx$

Slereah

Sounds about right

So... the actual rule will be - for even dimensions, + for odd

0celo7

I'd ask @ACuriousMind or @Danu to be sure.

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