The h Bar

The argument about general covariance is a bit silly. Yes any theory can be made generally covariant, but metric theories are so naturally covariant that they are the obvious approach.

0celo7

How can you make it generally covariant? What does that even mean

Slereah

6:16 AM

Are you arguing with Einstein and the evidence, @JohnRennie

John Rennie

:-)

@0celo7 that was Kretschmann's objection to Einstein.

0celo7

Yeah, well, you damn physicists need to tell me what it means

You will be happy to know that I managed to electrochemically polish tungsten ( also @Loong )

AND I AM ALIVE

I also did it to cerium

John Rennie

Cartan's theory is described in Penrose's Roads to Reality section 17.5.

However it's too long for me to easily reproduce here.

I'm sure there's a pdf version of RtR floating around the web somewhere though ...

Slereah

that would be illegal

🚨🚨🚨🚨🚨🚨🚨🚨🚨🚨🚨🚨🚨

0celo7

@Slereah amazon.com/…

we need this

@JohnRennie that sounds like something you would do

Slereah

6:24 AM

oh hey, Malament

Of Malament's theorem fame

That guy just loves foundational theorems

John Rennie

In the unlikely event you want a copy of RtR see:

0celo7

Please don't

John Rennie

You have 60s before I delete that link ...

0celo7

You're the room owner for pete's sake

that's illegal

Slereah

Anarchy!

0celo7

6:26 AM

and who downloads random .rar's from the internet

Slereah

yeah that's a bit of a risky gambit

John Rennie

I'm not going to defend book piracy, but if you want to read that one section of the book you'll find it there.

Slereah

BREAKING NEWS JOHN RENNIE DEFENDS BOOK PIRACY

0celo7

jesus

John Rennie

Alternative facts eh?

0celo7

6:28 AM

Bringing politics in?

@Slereah Too bad the book is $69, it looks very interesting

Oh wait, $42 used

John Rennie

Look dudes, I bought the book. I paid my own good money for the paperback version. That's how I knew it described Cartan's theory.

0celo7

@JohnRennie not penrose

I refuse to buy anything by that nutjob

John Rennie

@0celo7 Ah, I was a bit surprised you'd be interested in Penrose's book especially since it's basically popular science not a textbook.

Slereah

You bought his topology book

0celo7

That was before he went crazy

Slereah

6:33 AM

one day too you will be crazy

it is the fate of the scientist

0celo7

@JohnRennie I got some GR books for Christmas

and @Slereah got some too

Slereah

I got Hawking Israel

Which is nice

0celo7

O'Neill

Slereah

Yeah

I think for a good cross section of spacetime topology shenanigans, Hawking-Ellis, O'neill, Hawking Israel, Penrose and Sanchez is pretty good

That gathers most of the theorems

John Rennie

@0celo7: I'm sure the answer is no, but do you want to make a PDF of the bit of RtR that describes the Cartan formulation of non-relativistic mechanics. It's only a few pages so reproducing it is allowed by the fair use policy.

Slereah

6:36 AM

also since this is for research purpose, it is fair use

0celo7

I do not have it in my PDF folder

@JohnRennie do you want to know what a manifold is or not

John Rennie

@0celo7 in principle yes, but not right now.

I have to start work in a few minutes so I wouldn't be able to concentrate on it.

0celo7

I should probably go to sleep then

@Slereah Sanchez has a paper book?

Slereah

No

Just a big article online

I use it a fair bit though

John Rennie

The section on Cartan's theory is here if you want it

0celo7

6:41 AM

Hmm? I don't see equations

@JohnRennie I learned about this when I first learned GR

Nothing new

But I still don't know what "covariant" means

Slereah

mathwithbaddrawings.com/2017/01/25/…

user228700

7:00 AM

Hey, everyone :-) @0celo7: Oh, hello, u're back!

Sir Cumference

Howdy

John Rennie

@Kaumudi.H Morning :-)

I got my new laptop!

My new new laptop that is.

user228700

:-) Didn't see u yesterday. Were u busy with ur new laptop?

John Rennie

I was a bit busy yesterday - partly work and partly other annoying but necessary stuff. Oh well, it happens.

user228700

I see. How is it, the laptop?

user228700

7:07 AM

@JohnRennie x'D

John Rennie

That's my new laptop on the right and a laptop like yours on the left for comparison.

The new one is biiiiiiiiiiiiiiig!

user228700

Yep, it's big :-) Is that something that u wanted?

John Rennie

Yes. Every now and then I visit my mother and stay for a week or so. When I'm down there I need a laptop to work on and it has to be big because I need a big screen for work.

user228700

Ah, OK. How is it? (Other than "biiiiiiiiiiiiiiiig", that is :-)

John Rennie

It's ... well, to be honest it's just another laptop.

user228700

7:10 AM

:-P OK...

John Rennie

It's nice. The screen is nice and clear and it's fast. But it's no different to all my other laptops except for the size.

user228700

Right, OK.

John Rennie

But it is exactly what I need for working away from home. So it wasn't bought as a toy - it really will be useful.

user228700

Yep, I know. What went around literally came back around :-)

John Rennie

You should see the little laptop I bought a few days ago. It's just as fast as yours but it's so cute!

user228700

7:12 AM

Isn't that the one on the left?

John Rennie

No, the one on the left is like yours. The little one is even smaller.

user228700

Wait, why dyou have THREE new laptops?!

John Rennie

Maybe ... :-)

user228700

You bought two on E-bay?

John Rennie

I might have done ... :-)

But actually I do have uses for them all. It wasn't just a random purchase.

user228700

7:14 AM

Holy shit.

John Rennie

I joke about buying laptops but in real life I don't buy them unless I have a use for them.

user228700

Still, it is astonishing that u have use for so many laptops!

John Rennie

I bought one like yours and the little cute one. The one like yours has a few faults, but I'm going to repair it and set it up for my own use with Windows 10.

user228700

Show me what the "little cute one" looks like, now you've made me curious!

John Rennie

Hang on, I'll take a picture. This will take a few moments because it's in a cupboard at the moment ...

user228700

7:17 AM

I will wait...

0celo7

@JohnRennie I thought you had to work?

user228700

@JohnRennie BTW, dyou listen to music on your phone? If so, what music player app do you use? Neither Play Music (Google) nor VLC media player is any good...

John Rennie

@0celo7 I am working. Just ... not very hard :-)

I'm currently running a database reindex.

There. That's the baby laptop. Isn't it cute :-)

user228700

OMG! That is ridiculously small...and yes, very cute, I must admit :-)

John Rennie

:35227781 I prefer the Windows 7 classic mode desktop. I don't like the extra decoration that you get with Windows 10. But my new laptop has to run W10 because the 7th generation i7 CPUs aren't supported on W7.

So reluctantly I'm having to switch to Windows 10.

@Kaumudi.H I don't listen to music on the phone.

user228700

7:26 AM

OK...

John Rennie

Do you copy the music to the phone or do you stream it?

Slereah

I'm still using the windows 95 theme

user228700

@JohnRennie SD card. So yes, I copy it.

John Rennie

OK so you're playing it locally. VLC is the obvious choice. What don't you like about VLC?

Ramanujan

@Slereah XD

John Rennie

7:28 AM

@Slereah on what OS?

user228700

@JohnRennie It has a glitch when I close the app. It re-opens and I have to follow through with a few steps before it actually closes.

Slereah

Windows 7

windows classic theme

Although the start menu isn't quite the same

John Rennie

@Slereah ah yes, that's I'm using.

@Kaumudi.H BTW this was lunch yesterday:

user228700

Those look like mini-samosas.

user228700

What are they, really?

John Rennie

7:32 AM

They are samosas

Thirty samosas :-)

Ramanujan

In India we have some big samosas :)

user228700

Oh, really? That was lunch?! My mom would kick me if I asked to eat samosas for lunch.

user228700

Were they tasty?

John Rennie

They were OK. One of the supermarkets was selling them off cheap as a discontinued line so I bought them to see what they were like.

user228700

Oh, had u never tasted samosas before?

John Rennie

7:34 AM

They were nice but not amazingly nice. The samosas my mum makes are far better.

I didn't mean to see what samosas are like, I meant to see what these ready made samosas are like

user228700

Ah, OK. Only occasionally do I find great samosas. A few months ago, I found that a restaurant near my house sells excellent samosas.

John Rennie

This is the brand

user228700

...with Ketchup and some other dips, including chutney.

user228700

@JohnRennie I see. I don't like mini-samosas. They're a bit too oily and also crunchier than I like.

John Rennie

Ah, I like the crunchiness of the mini samosas.

user228700

7:39 AM

Samosas are ideally a bit crunchy on the outside, soft and tasty on the inside :-) Mini samosas sometimes have a different filling, making them crunchier.

John Rennie

I baked the samosas instead of frying them, so they weren't too oily.

user228700

Nice. What was the filling?

user228700

Ah, potato. OK, then they must've been soft on the inside as well.

John Rennie

Three different fillings: vegetable, chicken and minced beef.

They were nice and soft on the inside.

user228700

Ohh. The website only mentioned potatoes.

user228700

7:41 AM

The mini-samosas here are often filled with fried onion and tomato and the former adds to the crunchiness, which I don't like.

John Rennie

Chicken and beef

user228700

Ah, OK...

user228700

No dip?

John Rennie

Tomato ketchup :-)

user228700

Hmm. Pudina chutney would've been nice too.

John Rennie

7:43 AM

Mint?

user228700

Yep.

John Rennie

We eat mint with lamb. I'm not sure about mint with chicken ...

0celo7

@JohnRennie Ok, balls?

user228700

Oh, right, chicken. I'm not sure, then.

anonymous

@JohnRennie When you use "baby" and "cute" to describe a laptop, it is proof that you are crazy (for laptops) :'D I believe you will inspire many people to take up laptop breeding as an occupation :D

John Rennie

7:45 AM

@0celo7 I'm half working, half chatting. I certainly don't have enough brain cells left unused for point set topology :-)

In any case your conversation with Barry Carter is still on the chat if I wanted to go back and review it.

0celo7

@JohnRennie I'd probably want to redo it

And that conversation did not mention smooth manifolds

Just topological ones

John Rennie

amazon.co.uk/dp/B00D2WQ48A

I have this book (on paper not e-book) and I did have a go at learning about manifolds from that.

0celo7

Just get a math book, @JohnRennie

I have some math books

Slereah

The fun thing about GR causality theory is that it basically never writes down a metric

0celo7

Or field equations!

Slereah

7:50 AM

yeah

I mean, you sometimes get one

But usually only when you get to the higher levels of causality

Like the metric $-dt^2 + g$

0celo7

@JohnRennie If you really want a wild ride, check out "Quantum Theory for Mathematicians" by Hall

He has Hermitian operators $A$ and $B$ for which $A+B$ is not Hermitian

Slereah

Those are some bad operators

0celo7

Also, $X$ and $P$ cannot be defined on the whole Hilbert space

Slereah

Did you ever find out if derivatives of unbounded operators made sense

0celo7

ACM said it doesn't

And that one needs a whole formalism for the Heisenberg picture that is rigorous

Slereah

7:55 AM

Don't believe his lies

0celo7

But he didn't know details

He has no reason to lie!

Slereah

yes

that's what makes his lies so damning

Once you know QM

mb u should look into AQFT on curved spacetime

0celo7

What's the usual book for it?

Slereah

Haag is the big one

I think there's another more modern one but I forget the name

Plus you already have a book on AQFT

Wald

0celo7

That is true, I do have it

Is it any good?

Slereah

8:04 AM

Wald? I would say no

0celo7

I found it pretty incomprehensible two years ago

Slereah

Yeah I'm still having troubles understanding it

Haag is probably a better way to start since it's in flat space

0celo7

link?

Unfortunately I want to read most of Hall

Slereah

amazon.com/Local-Quantum-Physics-Theoretical-Mathematical/dp/…

0celo7

I am not reading all of the proofs of course

But I am getting a lot out of it

I will have to try hard not to correct my QM prof from now on

Slereah

8:06 AM

Uuuuh excuse me sir but that is not well defined

0celo7

if he integrates by parts I will get triggered

Slereah

Oh odds are good he probably won't even do that

Usually hermitian operators in QM classes are just defined as $A^* = A$

0celo7

Defining $A^*$ is nontrivial

Slereah

Yeah but such is the way

I'm guessing the math definition just throws the word "automorphism" around a lot

I first learned the real definition when I did my master thesis

Because I saw a paper saying that in curved space, $\hat p$ wasn't hermitian

And I was like, whaaat?

Seems that $\hat p = \hat p^*$ to me!

0celo7

@Slereah If $\mathscr H$ is a Hilbert space, and $\mathscr S\subset\mathscr H$ is a dense linear manifold, then $\mathscr S^\bot=\{0\}$.

True?

Slereah

8:18 AM

I don't knooow

0celo7

@Slereah Well, you want $\langle \psi,A\phi\rangle=\langle A^*\psi,\phi\rangle$

Slereah

Yeah

That is when I learned that definition

0celo7

But $A$ is usually only defined on $D(A)\subset\mathscr H$ (strict)

Slereah

Although i had not yet learned that integration by part is tricky

0celo7

So the question becomes, what is the domain of $A^*$?

And does such an operator even exist?

Is it unique?

The answer is yes

but you only have $D(A^*)\subset D(A)$ usually

To be self-adjoint you need equality

@Slereah it is true, but sadly it's an exercise in Conway

Most the book is left as an exercise.

Slereah

8:23 AM

I wish there were more books of exercizes with solutions for hard stuff

I have one

Supersymmetry exercize book

0celo7

What does $\dot +$ mean?

Slereah

Derivative of addition?

$$\lim_{\epsilon \to 0} \frac{(+(t+\epsilon)) - (+(t))}{\epsilon}$$

0celo7

It means $\oplus$ apparently

If $A$ is a symmetric op on $\mathscr H$, then $A$ is self-adjoint if and only if $$\mathrm{Ran}(A+i)=\mathrm{Ran}(A-i)=\mathscr H.$$

user228700

@JohnR: I'm off. Bye, have a nice day :-)

John Rennie

@Kaumudi.H Bye :-)

0celo7

8:28 AM

@Slereah will you read Wald with me when the time comes?

Slereah

I don't know, when is the time

I don't even like to look at it

0celo7

maybe two weeks

Slereah

it has very poor typesetting

i'm having a hard time seeing the difference between convergence and uniform convergence from the definitions

I've read what the difference is but it's hard to extract it from the definition

0celo7

In uniform convergence, $\epsilon$ does not depend on $x$.

Slereah

yeah, but

How do you see that

0celo7

8:33 AM

The difference is the order in which things are written

Slereah

$$\forall p \in D \forall \epsilon > 0 \exists \delta > 0 \forall x \in D, |x - p| < \delta \implies |f(x) - f(p) | < \epsilon$$

Versus

$$\forall \epsilon > 0 \exists \delta > 0 \forall p, x \in D, |x - p| < \delta \implies |f(x) - f(p) | < \epsilon$$

0celo7

@JohnRennie (you should be paying attention)

Slereah

Pretty subtle difference

0celo7

That's continuity

Not convergence

Slereah

Yeah, my bad

I meant continuity

John Rennie

8:36 AM

I'm currently checking the server backups have all completed successfully. The difference between that and physics is I get paid for checking the servers :-)

2

0celo7

PHYSICS

boi we out here analyzing

Slereah

Oh wait

I think I get it

The important part is

0celo7

That fact that in the first one, $p$ occurs first, means that every $\exists$ thing depends on $p$

and $\epsilon$ of course

In the second one, $p$ is not given anywhere