The h Bar

ACuriousMind

17:00

@0celo7 Well, in combination with an absymal lecturer

John Rennie

@0celo7 Schutz isn't really a book for people who want to be rigorous about GR

Danu

@JohnRennie Also of course his treatment of "group theory" is garbage.

John Rennie

Is there any group theory in Schutz's GR book?

Danu

(this is about Schwartz)

About Schutz---I also dislike it. It's too elementary

0celo7

Is that the one that doesn't even derive the geodesic equation?

Danu

17:02

I feel like, if you need Schutz' book to teach you GR (and are unable to understand it from e.g. Carroll), you probably shouldn't be doing GR yet.

Similar story with e.g. Zwiebach's string theory book.

0celo7

@Danu tbh none of the ST books are good

Danu

As most people here know, I'm very much opposed to rushing into advanced topics without basic understanding of the prerequisites.

ACuriousMind

@Danu Honestly though, ST books are all kinda bad

0celo7

@ACuriousMind :)

Danu

I haven't really read any yet: Did you try Lüst's book?

His lecture, which I am currently attending, is based on it.

It's non-rigorous, I realize that.

so ACM won't like it

but @0celo7, did you read it?

0celo7

17:04

@Danu BLT?

The one I have, on my shelf?

It's very dry. Partition function after partition function.

Maybe that's what string theory is.

John Duffield

@0celo7 : I know. But there is other stuff out there on things like Dirac's belt and spinors.

John Rennie

Incoming!!!!!!!!!!!!!!!!!!!!

0celo7

?

Danu

@JohnRennie MY BODY IS READY

0celo7

wtf

@JohnDuffield What does the Dirac belt have to do with anything, again?

ACuriousMind

17:08

@Danu I think that's the one I'll try after I'm no longer furious at BBS for being garbage :P

Danu

@ACuriousMind I think it's the closest to rigorous

John Duffield

@0celo7 : spin ½ particles. Follow the links, do your own research: "an object must be translated around the loop twice in order to be restored to its original position and chirality. In this sense a Mobius strip is reminiscent of spin-1/2 particles in quantum mechanics..."

0celo7

smh

ACuriousMind

@Danu I think I know its first half already

user54412

@Danu What then should those people do? I've always been of the opinion that GR has no prereqs beyond some linear algebra and calculus, so I can't imagine what else you could take to prepare for it.

ACuriousMind

17:11

The guy who wrote the notes my ST course was following was one of Lüst's PhD students and closely followed BLT in writing the notes

Danu

@JohnDuffield John, I think you would do really well to just read a book on Lie algebras. Especially one for physicists, where they explain how $SU(2)$ and $SO(3)$ are related. You're getting sidetracked into some crazy stuff by this, in principle, not too complicated little fact.

ACuriousMind

Can we please not fill this chat room with another iteration of a discussion with JohnDuffield that does not accomplish anything?

Danu

@ChrisWhite Some ideas about Lagrangians

Multilinear algebra

(so tensors)

bolbteppa

@JohnDuffield how is supersymmetry due to a lack of understanding of electrons if it applies to all particles?

Danu

@ACuriousMind That was going to be my only message, I swear!

user54412

17:14

@Danu Lagrangians. So it has come to this.

0celo7

Sigh. I know why my ODE test was so hard. The integral of $1/x^2$ isn't $-1/(3x^3)$. I'm pretty much mentally retarded.

Danu

@ChrisWhite Not Lagrangians per se---I mean "theoretical mechanics"

@0celo7 Reset to Calc. 1?

0celo7

I did the power rule wrong on the whole test.

bolbteppa

:o

0celo7

@Danu I guess...

Danu

17:16

@0celo7 That's a pretty serious mistake :P

0celo7

@Danu No fucking shit

I even went back and changed the correct stuff.

Danu

@ChrisWhite Also what's so bad about mentioning Lagrangians

John Duffield

@Danu : no I'm not getting sidetracked into crazy stuff. Dirac's belt and spinors is not crazy stuff, and nor is electron diffraction and the wave nature of matter. Thinking that E8 is some theory of everything is getting sidetracked.

bolbteppa

That's the kind of mistake that should force one to shift emphasis onto Thomas/Stewart/Piskunov calculus to master the basics, no shame in taking one's time

0celo7

I've never made that mistake before.

And today, on a freaking test, I do it on the whole thing?

bolbteppa

17:19

@JohnDuffield do you understand how supersymmetry arose?

Or any of the things people think justify it's existence?

Danu

@0celo7 It's your call whether this "means" anything or not, but I'd give it some serious thought

0celo7

@Danu And do what?

I got a near perfect score in calculus.

user54412

@Danu I'm not against Lagrangians -- everyone should know them. But I've always felt GR is over-inflated in terms of requirements, being treated like only the most advanced undergrads can handle it. It may be hard, but you don't need to know field theory or E&M or thermodynamics to do the fundamentals of GR.

0celo7

I only missed one question on the AP test.

My homework to this point has been flawless.

Danu

@ChrisWhite Depends what you mean by the fundamentals

0celo7

17:20

I did 3 tests to prepare for this.

All perfect.

Danu

@0celo7 your call, as I said

0celo7

Then this shit?

John Duffield

@bolbteppa : supersymmetry proposes a selectron without understanding what an electron is, or how gamma-gamma pair production actually works to convert two bosons into two fermions, or what the difference between a boson and a fermion really is.

Danu

No need to convince me

0celo7

What is there to call?

Terry Bollinger

17:21

@0celo7 have you tried talking to the prof, explaining? You never know unless you try...

ACuriousMind

@ChrisWhite What are "the fundamentals"? Solving geodesic equations for given metrics?

0celo7

@TerryBollinger Explain what?

That I'm stupid?

ACuriousMind

That'd be about as insightful as the "electromagnetism is solving PDEs with boundary conditions"-approach most EM classes devolve into

Danu

@ChrisWhite I have this (fairly radical) point of view that it's better to wait until you're ready to really understand the general ideas. It's not about calculating, but about some kind of hard-to-define "maturity" that does, in my experience, come from really doing all the more simple stuff first.

Terry Bollinger

@0celo7 You're not stupid, you made one cascade error. Flaw of grading methods in that it amplifies that one error.

Danu

17:22

Of course, one can handle GR as in pass a class in it quite simply

user54412

@ACuriousMind I'd say intuitively "getting" spacetime as a manifold.

Danu

That doesn't mean that you really know what's going on

0celo7

@TerryBollinger So what is @Danu talking about?

Danu

@ChrisWhite So you'd have to know basic differential geometry, too?

0celo7

What is there to think about?

I messed up the product rule for inverse powers.

John Duffield

17:23

@bolbteppa : of course I understand how supersymmetry arose, and why people try to justify it. But do you understand that there's no point proposing a selectron if you don't know what an electron is?

ACuriousMind

@ChrisWhite I'm not sure the coordinate-laden approach that is necessary when you only know calculus is good for understand what exactly a manifold is.

0celo7

Obviously I must have some massive deficit if it warrants a serious thinking.

user54412

@Danu Sure, but I don't know what simple stuff there is. I mean, you can do QFT or thermo on a curved manifold, but that's not fundamental GR. And someone who isn't ready for Carroll won't become ready by studying them.

Danu

@0celo7 Can you stop being so dramatic?

0celo7

@Danu No!

bolbteppa

17:24

@JohnDuffield would you say the same thing to Dirac about anti-particles?

ACuriousMind

The whole confusion about "singularities" and whether they're "real" or "coordinate" singularities basically comes from people not knowing the difference between a chart and the manifold.

Terry Bollinger

@0celo7 Dunno, I just don't think point errors that spread through a test should be graded as multiple errors at every point they touch.

0celo7

@TerryBollinger It's the same error on multiple questions.

user54412

@ACuriousMind Maybe my opinion is colored by the fact that I learned differential geometry from GR, whereas my math department failed at teaching it.

0celo7

Not one error throughout a long question.

Danu

17:25

@ChrisWhite Of course I don't think people should be able to do (without guidance, that is) QFT in curved spacetimes right after a course on GR (although Carroll DOES do it).

I mean classical field theory

user54412

@Danu And maybe I think you should be able to do magnetohydrodynamics in curved spacetimes right after a course in GR :p

Danu

@ChrisWhite and maybe I am

(jk)

Oh...

Terry Bollinger

@0celo7 Ouch, yet still: Sometimes, communicating what happened to the person doing the grading might help in some unexpected way. Often not... but I've absolutely seen cases where it helped.

Danu

Hah. I forgot a "don't" in that previous message

[editing]

John Duffield

@bolbteppa : I not sure what you mean. But if I could talk to Dirac maybe I'd make Moebius strips with two different chiralities, then talk about Dirac's belt and spinors, and the Dirac equation and the Dirac spinor.

Terry Bollinger

17:31

@JohnDuffield are you a troll or are you for real? You are pasting identical text...

Danu

Regina Belle - If I Could

►

0celo7

Can @Danu explain what he means by "give serious thought"

Read a calc 1 book?

Danu

@TerryBollinger (DO NOT ENGAGE, DO NOT ENGAGE)

0celo7

I know what I did wrong, it was a stupid mistake

So why does it require serious thought

Danu

@0celo7 Maybe reread the sentence?

Terry Bollinger

17:32

@Danu Thanks, questions answered, will comply!

Danu

@0celo7 whether this "means" something

It appears you have already decided it does not

John Duffield

@ACuriousMind : no, the whole confusion about real or coordinate singularities basically comes from people who don't understand GR, and who have never read Einstein's material.

Danu

good for you, now carry on with your life

0celo7

@Danu Ah

I was just...not stressed...excited? I was just nervous.

I think.

Terry Bollinger

@yuggib back on your discussion of trace classes and von Neumann algebras, did you have any good refs or papers on any of that?

user54412

17:35

Raise your hand if you're done with college and remember any grades you got on particular tests.

user54412

::looks around::

ACuriousMind

I'm still in college and I tend to forget which grades I had on exams that were more than a few months ago

Danu

@ChrisWhite ::begrugingly raises hand::

0celo7

@TerryBollinger I was planning to talk to him later about the extremal problem. I'll try to bring it up.

Danu

Also, as I've said before, here MSc. degrees still have grades, and they do matter.

ACuriousMind

17:37

@Danu ...you're done with college? oO

Danu

@ACuriousMind College = bachelor's

user54412

@Danu You don't count.

ACuriousMind

Oh

Danu

Also it's easy to remember cause they were all #perfect

(just kidding)

0celo7

@ACuriousMind We've established that we're completely different.

John Duffield

17:37

@TerryBollinger : am I a troll? Huh? No. And what are you on about saying I'm pasting identical text? I'm giving references for people to follow up. You know, to demonstrate that I'm not making it up?

0celo7

@Danu I don't think you are.

bolbteppa

@JohnDuffield my point is, Dirac predicted anti-particles before they were discovered and your argument against supersymmetry could be levelled at Dirac, can you address that point?

Danu

@0celo7 I can prove that they weren't all perfect :P

Terry Bollinger

@0celo7 thanks, I see he's gone now, but some of that was fascinating (to the degree i was following it, which was alas minimal)

ACuriousMind

@Danu I'll never understand how the American university system translates into the European one I think

Danu

17:38

I'm not sure I've gotten a 100% score on any test

maybe once

0celo7

@TerryBollinger What?

Danu

@ACuriousMind It's the German one that's really weird ;)

0celo7

Who's gone now?

What is fascinating?

@ACuriousMind Shorter hair is a big part.

ACuriousMind

@Danu Probably :D

Terry Bollinger

@0celo7 I conflated threads, sorry!! I thought you were replying to my last question on a different topic.

Slereah

17:39

Guys

bolbteppa

@JohnDuffield has your understanding of the definition of energy changed since yesterday?

Danu

@bolbteppa could you just stop it? Do you really enjoy this discussion you're having?

bolbteppa

Okay lets just do the energy thing then I will

Slereah

If I have a PDE of the form $f_{rr}(r,t) + A(r) f_{tt} = 0$

Can I still do separation of variables

Or did I fuck up

Danu

@bolbteppa It's pointless, remember? :P

bolbteppa

17:41

@Danu I have hope since he ignored me pointing this out twice telling me he has recognized it, fingers crossed :D

Terry Bollinger

@0celo7 and I'm glad you are bringing it up, good luck.

bolbteppa

You would think someone in search of the truth would recognize something like this anyway :)

Danu

@bolbteppa Sigh...

Disney's Frozen "Let It Go" Sequence Performed by Idina Menzel

►

John Duffield

@bolbteppa : Dirac predicted antiparticles in 1931 and they were discovered a year later by Anderson. Supersymmetry has been around for fifty years and hasn't been vindicated at all. Spot the difference. The reason is that it isn't founded on understanding.

Slereah

@bolbteppa please stop

There is no point

ACuriousMind

17:43

@Slereah What happens if you try?

(Taking the physicist's approach :D)

bolbteppa

@JohnDuffield that's not a fair assessment at all, but nevermind that I guess, has your understanding of the definition of energy changed since yesterday?

Slereah

@ACuriousMind : Well I did try :p

bolbteppa

@Slereah please, uno momento

Slereah

But I didn't check manually if I could

Hm

Let's see

$f(r,t) = R(r) T(t)$

Hm

I guess I can't

Dang it

So now I actually have to solve an unseparable 3 variable PDE D:

Oh bother

All that solving for nothing

bolbteppa

@Slereah did you reduce the PDE to canonical form in the separate domains? I think you can do separation?

John Duffield

17:46

@bolbteppa : no, my understanding of the definition of energy has not changed since yesterday. Why should it? Noether's theorem doesn't tell you what energy is.

Slereah

@bolbteppa I will as soon as I read up on what that is!

bolbteppa

@JohnDuffield and finally, are you going to continue to repeat that physicists define energy in a circular fashion?

Slereah

As it is the separated big PDE is $\coth(r) f_{r} + f_{rr} + 2 \cosh(r) f_{\phi t} - f_{tt} - f_{\phi\phi} = k$

0celo7

@ACuriousMind What is there to not understand about how the US system works

Slereah

I thought I could separate $r$ and $\phi t$

bolbteppa

17:49

@Slereah on pages 2 & 3 the Tricomi equation is given as an example math.psu.edu/wysocki/M412/Notes412_5.pdf you'll sadly probably have a similar situation with your one

Slereah

But then I remembered the $\cosh$

"sadly"?

I don't like this

I don't like this one bit!

bolbteppa

Neither do I

ACuriousMind

@Slereah Ew.

Slereah

Yeah

It looked okay when I thought I could get the $r$ out

But now I'm not so sure

John Duffield

@bolbteppa : yes, I will repeat that physicists define energy in a circular fashion. Would you like me to give you some references for that? Why don't you say what energy is? And then when you struggle, ask Slereah and Danu to say what energy is. When they can't and instead say it's pointless you'll maybe learn something.

Danu

17:51

It's pointless :)

bolbteppa

@Slereah But the first thing you have to do is reduce your pde to canonical form before anything else, and since you'll probably have to solve it as though it's a wave equation in one region, a hyperbolic in another, and an elliptic in another, which I've never even seen done before, and I have no idea about matching up solutions at boundaries and stuff, but my feeling it your problem is very mechanical assuming all this stuff magically doesn't cause problems

ACuriousMind

@Danu You're pointless :D

bolbteppa

Also it's inhomogeneous, giving more fun, but still, this exercise will probably teach you everything there is to know about pde's haha

Danu

@ACuriousMind You're less than a point!

Slereah

@bolbteppa : I highly suspect things will be problematic

Since this space has no achronal spacelike foliation

bolbteppa

17:53

I would love to throw away a week on this

Slereah

Dang

ACuriousMind

@Danu I'm the empty manifold?

Slereah

I'm not sure I can find a topologically trivial spacetime with a simpler metric for CTCs

bolbteppa

@JohnDuffield Okay I see I've wasted my time

Danu

@ACuriousMind You're the empty intersection...

Slereah

17:54

Don't answer you fool

Danu

YOU'RE MY EVERYTHING!

bolbteppa

Lesson learnt

Slereah

Just stop

Danu

see what I did there? :D

0celo7

@ACuriousMind do curves created by the exponential map which differ only by the magnitude of the initial velocity define the same geodesic?

Slereah

17:55

@0celo7 : Well I'm pretty sure a curve of a different velocity will give a different geodesic :p

John Duffield

There is nothing more important than understanding energy. Energy is fundamental. Matter is made of it. The mass of a body is a measure of its energy content. But you will not gain any understanding from answers like these.

Danu

hi @Tycho

0celo7

Same direction in the tangent space, only different magnitude

ACuriousMind

@0celo7 Yes.

@Danu You are greeting an user who can't chat yet :P

Danu

Nobody saw what I did there? :'(

Slereah

17:56

Is the usual foliation of Minkowski space also a foliation for $(T^2, \eta)$?

Danu

@ACuriousMind Ha-ha-ha. But I know the guy, so it's cool

ACuriousMind

@Danu Actually, no, I don't :/

Danu

@ACuriousMind The empty intersection is the full space

do you even power set?

user3183724

@Danu Just stop it

ACuriousMind

@Danu Ohhhhhhhhhh. I thought: Empty intersection: $A\cap B = \emptyset$, not $\cap_\emptyset$.

Danu

17:58

@ACuriousMind :-)

@user3183724 No u

0celo7

What is cap_emptyset

Danu

The empty intersection

You intersect nothing

Note: That is not an intersection of empty sets

0celo7

What

ACuriousMind

@0celo7 An intersection $\bigcap_{i\in I} A_i$ for $I=\emptyset$.

John Duffield

@bolbteppa : no you haven't wasted your time. You're just doing a runner because you can't define energy, and nor can you defend supersymmetric pseudoscience.

Slereah

17:59

Hm

John Duffield

OK, time for tea. Bye for now.

Terry Bollinger

Does the set of all sets include itself? If so, isn't that another set that must also include itself?... :)

Slereah

I think you can totally define a foliation for $T^2$

ACuriousMind

@TerryBollinger There is no set of all sets

0celo7

@ACuriousMind what??

Danu

18:00

Universe (mathematics)

In mathematics, and particularly in set theory and the foundations of mathematics, a universe is a class that contains (as elements) all the entities one wishes to consider in a given situation. There are several versions of this general idea, described in the following sections. == In a specific context == Perhaps the simplest version is that any set can be a universe, so long as the object of study is confined to that particular set. If the object of study is formed by the real numbers, then the real line R, which is the real number set, could be the universe under consideration. Implicitly,...

ACuriousMind

At least not in standard ZFC axiomatization of set theory

Danu

relevant

Slereah

Same leaves as Minkowski space, except on the restriction $[0,1]$, and then a map $[0,1] \rightarrow \mathbb{R}$

Though now I wonder if you can foliate a topologically trivial acausal spacetime

0celo7

@ACuriousMind Damn. My Maupertuis approach is deeply flawed.

ACuriousMind

@Slereah The relevant question is if you can fornicate with it.

::hides::

bolbteppa

18:02

@Slereah I would love to see how you manage this problem, I think the Tikhonov problem book would be helpful

0celo7

I wonder if there's some general calculus of variations principle hiding around.

bolbteppa

...

Slereah

@bolbteppa I'll give it a whirl, though I suspect it's gonna be a tad beyond me!

bolbteppa

@Slereah all you need to do is find a problem that looks similar in the book, already in chapter 1 there are examples which will help you classify it properly, one even has a $\sin$ function in it, I'm sure later on in the book they solve similar problems too!

Terry Bollinger

Question: If one were to assume that causality resolution "takes place" within a single foliation that is treated as a single, unified, dynamic state space (vs worldlines), is it mathematically possible to show that all other foliations also remain self-consistent in terms of their interpretations of causality? I think so, but that's far from a proof...

Slereah

18:06

Although I think the equation will always be hyperbolic really

No worrying about it being different things in different regions

0celo7

@ACuriousMind Did you ever ask @ChrisWhite your topology question?

bolbteppa

@Slereah did you look at the Tricomi example math.psu.edu/wysocki/M412/Notes412_5.pdf your cross terms are a function of $\tan$ it will almost certainly be different in different regions

Slereah

Not $\tan$, $\coth$

And it's a physical equation, so I doubt it will be not hyperbolic

Terry Bollinger

(BTW, I don't seriously expect anyone to answer that, just thinking out loud again...)

Slereah

@TerryBollinger : Sounds like a question for Hawking Ellis

Hm

what's the canonical form like for 3 variables

bolbteppa

18:12

You only have two variables in the pde though?

Slereah

The eq. is $f_{rr} - f_{tt} - f_{\phi\phi} + 2 \cosh(r)f_{\phi t} + \coth(r) f_{r} + k = 0$

'fraid not

$rt\phi$

Terry Bollinger

@Slereah heh, I have no idea who Hawking Ellis is, Googling now...

0celo7

Hmm. The velocity vector's magnitude is constant along a geodesic, right?

Slereah

Hm

Seems to be the number of real roots of the principal part

What's a good document on PDEs that is not terribly slow

And general

Terry Bollinger

Heh, Hawking and Ellis, I just created a new composite physicist!

Slereah

18:18

I don't want to have to go through all the slog of reading the linear homogeneous wave equation 2D case every time

Every PDE book seemingly does that

Terry Bollinger

I don't think Hawking ever really addressed that type of question, though.

Later all...

Slereah

$L u =\sum_{i=1}^n\sum_{j=1}^n a_{i,j} \frac{\partial^2 u}{\partial x_i \partial x_j} \quad $

Thank you wikipedia

Hm, let's see

What's the determinant for cubic equations

Or I could just put the matrix in Wolfram Alpha really

-1, -1 and 1

Indeed hyperbolic

No worries

I don't think you can really get non-hyperbolic equations from Klein Gordon

Even in a weird metric

Slereah

18:37

grumble grumble

What to do

maybe method of characteristics, I guess

user54412

@0celo7 It just occurred to me I'm right next to his office right now. Should I convey the review? :p

Slereah

Oh wait

Method of characteristics is first order

grumble grumble

Danu

@ChrisWhite I do wonder why he chose to be so handwavey in his book

If you can somehow inconspicuously find out I'd be interested :P

Slereah

Hm

I do know a paper about solving Klein Gordon in the Godel metric

Maybe that is worth a looksie

projecteuclid.org/download/pdf_1/euclid.cmp/1158328656

Sort of unrelated but also neat

Apparently a lot of symmetry is involved

Hm, the metric is pretty similar

"we shall employ the separation ansatz reflecting the translational symmetry in t
and x3 directions:
(2.4) $\Psi(t, x, \phi, x_3) = e^{−i\omega t} e^{ik_3x_3} \psi(x, \phi)$"

Don't mind if I steal that ansatz, Piotr Marecki

I guess I can separate out time, maybe

I dunno

I guess that's what ansatz are for

Let's try it and see what happens

The old "Whatever" method of PDE analysis

0celo7

18:58

@Slereah What makes you think it can be solved?

Slereah

Why not

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