@0celo7 The basics. And I haven't done anything with it for months now.

@HDE226868 I thought "ah the Canadian!"

And then I thought "ah, convex normal neighborhoods!"

And I wrote down the proof, of which I fear @ACuriousMind is not convinced...

@0celo7 (Sigh) I hope I get into the University of St. Andrews (Scotland), just to confuse you even more.

@ACuriousMind p. 253

@HDE226868 My sister was an exchange student there

@HDE226868 I would say "convex normal neighborhoods" is pretty basic, but I don't think Hartle/Schutz/Zee talk about them.

Which is probably the level you mean.

@0celo7 Yeah, about Zee's level.

Well, that's respectable.

I didn't get my first "real" GR book until December of my senior year.

And you certainly know more other stuff than I do.

And even then, I'm pretty crappy at this stuff

What would you call "other stuff"?

Classical mechanics, thermo, astro

Very basic thermo, and mostly self-study astro, in part for Science Olympiad, but yeah.

I'm always surprised that you're not too familiar with some parts of classical mechanics.

I got a 5 on physics C

Doesn't mean shit, though.

After reading Arnold I understand a lot of it better. But "better" in a way that is completely irrelevant :D

And I'm still not sure what nonconservative forces are about.

@0celo7 Okay, I could not resist looking at it before I go to bed. Note that those aren't paths in configuration space, but in configuration space together with time. Also, note that the statement that the mapping is non-degenerate is stronger than "they don't cross" (which is local injectivity), since non-degeneracy means the mapping is locally invertible.

@0celo7 ?

I have no idea right now whether or not that affects your proof

G'night, everyone.

@ACuriousMind Tomorrow?

Night.

Good night.

@HDE226868 What

I'm unclear on the precise formulation of what they are

I want a Lagrangian formulation with them, but apparently that's not possible.

@ACuriousMind Ok, I see what you mean.

Well, off to the holy book of GR!

@HDE226868 you should get Hawking-Ellis

it's a good book for random theorems about curves on manifolds

@0celo7 Sounds interesting.

+ singularity theorems and cauchy problem in GR

@0celo7 You aren't satisfied with Lagrange equations of the first kind?

@ACuriousMind Well, the convex normal nbd theorem uses the exponential map, which is nondegenerate, I think.

@HDE226868 What?

@0celo7 You include a term for forces that don't arise from a potential.

How does that happen in the Lagrangian formulation

I looked at a paper that had to use fractional calculus to incorporate it

@0celo7 See for instance Section 6.5 here.

@0celo7 A friend of mine likes fractional calculus.

Can somebody answer that question?

@TanMath I've never heard of it, although it sounds interesting.

@HDE226868 that person is weird

@0celo7 Welcome to my entire school.

@HDE226868 No!

I want an action that you can vary to get the nonconservative stuff

@0celo7 Ah. That's trickier.

They're cheating and adding stuff in by hand

@HDE226868 I know

I'm reading a "graduate texts in mathematics" book that leaves that out because it gets too messy :)

@HDE226868 huh?

@0celo7 I go to a special STEM high school. The nerd percentage is higher than normal.

@HDE226868 am I a nerd

@0celo7 Hell yes.

@ACuriousMind Pretty sure the exponential map is injective and surjective

@HDE226868 wtf

You're nerdier than me by a long shot

Stars are nerdy as fuuuuuck

@0celo7 Yeah, but you're still a nerd.

@HDE226868 That's like the pot calling the grey paint black

faint gray

off-white

@0celo7 Still. . .

white - $\epsilon$

see, I don't like any strange things

fractional calculus is just weird

@HDE226868 what does that even mean

why not just "yes"

what have I done to deserve this

@0celo7 Emphasis.

@HDE226868 I'm asking why

@0celo7 Because you're nerdier than you think.

@HDE226868 noooo

I'm not good at math or physics

how can I be nerdy

@0celo7 I beg to differ:

Presumably, you understand that sentence.

Uh, that should be second-countable.

I uh, see the point.

But

But just because I know what that means, doesn't mean I'm any good at it

Define "good at it".

be able to prove things

@HDE226868 the other day I couldn't prove all n-dimensional vector spaces with norm are isomorphic

the proof is so simple but I couldn't come up with it

@ACuriousMind Hmm, they never cross in $(q,t)$ space...but I don't see where by proof fails to show that they don't cross in $q$ space by itself D:

@ACuriousMind Hmm, harmonic oscillator on a line. I think that is a counterexample.

Well, really any system on the line.

I give up

see, @HDE226868

I'm terrible at math

@0celo7 The other day, I finished a complicated gradient problem, only to find out that I screwed up adding $2+2+1$, or something, at the very end.

@ChrisWhite Do you have any ideas?

Anyway, gotta go. 'Night.

@HDE226868 I almost ran out of time on my linear algebra test because I stared at $14\times 10=144$ for 25 minutes

night

@ChrisWhite the claim on page 253 of arnold

you have it handy?

right under the picture

I got you

Recent preprint analyzing various reports of beta-decay lifetime variability and looks at some proposed mechanisms:

arxiv.org/abs/1510.05996

WORD

what's he like

I want to meet ACM

but I don't think the dates are gonna work out

also, I could drop by @dmckee's office

10 and a half hour drive

I'm not in Canada very often, so I probably won't see @HDE226868

never been to Jersey

@ChrisWhite please prove that assertion above

Isn't Jim in Toronto?

extremal satisfies $\delta S=0$

yes, that's what I wanted to do

but it's in (q,t) space or something

and the Maupertuis principle is in q space

hmm

I will attempt to discuss this with the ayy lmao tomorrow.

@ChrisWhite No

Why do you think I/it did?

ah, I see where the issue lies

Does that clear things up?

huh?

@dmckee What is his problem?

You're not even that old.

What are you, 24?

26?

I think my 40 year old sister is hipper than you.

You're just a curmudgeon

@ACuriousMind yes, the exponential map is invertible

@ACuriousMind but I don't know how time factors in!

@ACuriousMind but what I don't understand is how my Maupertuis argument can hold when e.g. on a line extremals have to intersect for any t

@ChrisWhite There have been occasional papers alleging time variations on several different time scales. Many (most?) people think it is nonsense, but the persistence of such reports leave some wondering or at least unwilling to categorically rule it out.

@0celo7 Penetrated my secrete identity, huh? Well, if you did drop by we could go see the tallest waterfall in Missouri which is near by.

All of 18 feet when the stream is in full flow.

But it is scenic. Alas that the height of our tourist stuff in town. After that it is just bars and the occasional mediocre rock show.

@0celo7 He is a kind, wise, upstanding gentleman.

@0celo7 a religious avatar?

@ChrisWhite It was my pleasure to meet you and for you to survive the encounter.

@ChrisWhite What does that mean?

I feel like I should find this cool.

@ChrisWhite Wow.

Thanks.

I wonder why the example color thingies aren't straight.

Oh, I think I get it.

The horizontal axis is the numerical value of the data.

Jeez, they should label their damned axes.

>.<

Heh, so "jet" Is super-duper non monotonic. That's funny.

@ChrisWhite not even a single one, although I would love to.

@bolbteppa : I'm not. I'm just telling you about physics you don't know about. Follow up on my references and do your own research. I'm not making this stuff up. I haven't defined inertial mass at all, nor am I mixing up concepts. A photon causes gravity just like any other concentration of energy, and it can change direction when it loses energy. You know acceleration isn't just a change of speed. And you should know that I haven't defined inertial mass.

@bolbteppa : E=mc² is not nonsense. However string theory is. It's been around for fifty years, and there is not one shred of supporting evidence. Because it isn't physics, it's pseudoscience. And I'm not making that up either.

@0celo7 : parallel universe, antiverse, parallel antiverse, new universe, new parallel antiverse... This isn't physics, it's woo. Sorry.

@bolbteppa : What did I sayyyy

@ACuriousMind : Those theorems are here because otherwise, there really isn't any limitation

Some initial slices can have non unique developments

Also non-globally hyperbolic spacetimes are not very well behaved

I don't know if naked singularities are nice enough but CTCs don't play well with quantum fields

dl.dropboxusercontent.com/u/19940612/CTCs.ods

I need more CTCs :V

Oh wait I remember

Singularities violate unitarity in QFT

@Slereah Note quite. It is a sort of diminutive form which, I was told in Russian class many moons ago, carries a sort of mischievous connotation.

@DavidZ @Qmechanic ehh.. what do? physics.stackexchange.com/review/suggested-edits/104543

Singularities basically permit particles to disappear

Or appear

So time evolution can be non unitary

To be fair though

Physics being deterministic with unique time evolution is kind of wishful thinking

Could be the case, but people are quick to assume it true no matter what

It would certainly be convenient

Reading about Norton's Dome

I like to imagine that he found that solution randomly

and when he realized what it was

He got a grinchy grin on his face

@JohnDuffield There's no point, I can't respond to these strawmen / avoidance's-of-my-arguments / incorrect-statements in good conscience anymore if this is all you can say after I spent a whole day trying to help you with the basics, good luck, hopefully a good book will challenge your pre-conceptions one day.

@bolbteppa : Re "there's no point, I can't respond to these strawmen..." Those references to Einstein etc are not my pre-conceptions. Again see material like

this.

Sir @JohnDuffield could you explain to me how many times 0 goes into 0?

@skillpatrol : no, it's undefined. Look it up. Anything divided by zero is undefined, even zero divided by zero.

I don't want to "look it up" Sir @JohnDuffield I want you to explain it to me please :)

I've told you enough times. Division is how many of x are there in y? That's fine when you divide 6 by 2. But when you divide 6 by 0 there is no answer. It does not compute. The result is not infinity, it is undefined. In similar vein when you divide 0 by 0, the result is not 1, it is undefined.

Why?

@StanShunpike Uh, he's a Roman emperor who looks high as hell. Nothing religious about it

*Byzantine/East Roman

@skillpatrol : why? Go look it up: "division by zero is the operation of taking the quotient of any number and 0, i.e., . The uniqueness of division breaks down when dividing by zero, since the product is the same for any , so cannot be recovered by inverting the process of multiplication".

@JohnDuffield For crap's sake, I said right after that it doesn't represent reality.

By telling me that "the result is undefined" means there "is" a result, correct?

It is the textbook example of an unhyperbolic spacetime, though.

@0celo7 : the point is that you were dismissing Einstein and bandying around Penrose diagrams, like you did in that question I was going to answer. They're just junk 0celo, and when you pay attention to Einstein and the evidence you'll understand why.

@ACuriousMind Isn't the "global topological consideration" you were talking of just the fact that hyperbolic spacetimes split as RxΣ

@JohnDuffield I probably am a punk. Just put me on ignore and do us all a favor.

@0celo7 Actually, he is a Greek who claimed to be the legitimate heir for the byzantine empire

but he was never emperor (in addition, the empire did not actually exist anymore)

@yuggib he knows

:P

@0celo7 : I'd rather do you a favour by telling you about things like E=mc² and what Einstein said about gravitational fields. If you want to ignore that because you think you know better that's up to you.

At the event horizon of a black hole the "coordinate" speed of light is zero. A gravitational field is a place where optical clocks go slower when they're lower. And they can't go slower than stopped.

Sir @JohnDuffield if you could ask Einstein one question what would it be?

@skillpatrol : I'd ask him if I could have all his post-1920 documents. There's not much online.

Have you visited his home in Princeton?

@skillpatrol : no. Why should I? He's been dead for fifty years. My point is that when you read the Einstein digital papers you appreciate that what you were told about say the speed of light is a load of old cobblers.

When you understand that light can't go slower than stopped, you appreciate the Kruskal-Szekeres coordinates and Penrose diagrams are just... junk.

So, I take it you understand Kruskal-Szekeres coordinates and Penrose diagrams enough to pass judgement upon them as "junk."

@Danu nothing to do, I think. It seems to have resolved itself.

@DavidZ about 2 hours til chat time :D

yep, I've noticed

hopefully I can be around for this chat session

yup, me too

@skillpatrol : yes. Because I understand gravity. Because I've read the Einstein digital papers, and things like "the curvature of light rays occurs only in spaces where the speed of light is spatially variable". The speed of light at the event horizon is zero, so your optical clock doesn't tick, and switching to KS coordinates isn't going to change that.

Yes, Sir @JohnDuffield we have talked about your definition of time...

...it is as unsatisfying as your explanation of division by 0.

It's not my definition. See A World without Time: The Forgotten Legacy of Godel and Einstein. I didn't define it, or the division by zero.

You know, there's a recurrent theme here whereby people who don't know something dismiss it instead of following up the references and finding out about it.

I know you didn't define it Sir and I mean no disrespect .

:)

@skillpatrol : then follow the link to the things I tell you about, and do your own research.

I am Sir.

It's not easy.

Good stuff. It gets easier with practice.

Now please excuse me, work calls. Ciao for now.

I hope so :)

Ciao

So... why are derivatives of chiral primary fields said to have conformal dimension $h+1$? Plugging stuff in seems to suggest $h-1$ instead...

@JohnDuffield if a child came to you and told you they wanted to study supersymmetry, what would you tell them?

@Danu because of $\partial \phi = \partial_x \phi dx$ adding a $dx$ right?

adding a dx

wat

@bolbteppa Meh

it turns out it's a stupid matter of notation

sometimes the conformal weights are defined as $-h$

sometimes as $+h$

In either case, you end up subtracting $1$. Of course, only the former then yields $-(h+1)$

@bolbteppa Also this makes very little sense to me

@0celo7 No

@ChrisWhite Neat. Where am I at?

@Danu If you define a primary field by $\phi(w)dw^h = \phi(z)dz^h$, then I think it's something like $\phi = \partial \psi$ goes into $\partial \psi (w)dw^{h} = \partial \psi(z) dz^{h}$ going into $\partial_w \psi (w)dw^{h+1} = \partial_z \psi(z) dz^{h+1}$, might need to clean that up

@bolbteppa What is $\mathrm{d}w^h$ supposed to mean?

@bolbteppa That definition is not standard

It's pretty unclear what your $\partial$'s and $d$'s mean.

Sorry should be $(dw)^h$, see page 65 Blumenhagen String theory

In any case, I'm not confused anymore

@bolbteppa There are no $d$'s there :P

Well then I've succeeded ;)

No, it was cleared up before you responded. If anything, you've confused me more :P

@Danu Oh, he's taking the "transform as tensors" too literally and thinks the $\phi(z,\bar z)$ with weight $h,\bar h$ is the coefficients of $\phi(z,\bar z)(\mathrm{d}z)^h\otimes(\mathrm{d}\bar z)^{\bar h}$.

Which doesn't work because $h$ is not required to be integer to begin with

@ACuriousMind Ah... :P

If you write it as $\phi(w) (dw)^h = \phi(z) (dz)^h$ then clearly it's derivative $\frac{d \phi}{d w}$ transforms as $\partial_w \phi(w) (dw)^{h+1}= \partial_z \phi(z) (dz)^{h+1}$, again from page 65 "Primary fields transform as tensors under conformal transformations. All other fields are called secondary fields"

See ACM's comment

@bolbteppa It's a nice mnemonic for remembering what transformation behaviour is associated with the weights, but it doesn't work rigorously because what does a weight like $\frac{1}{12}$ signify?

I think I've identified myself on @ChrisWhite's plot

Sticking to a 1cm wide vertical strip around ACM, I'm the third guy below him (i.e. fourth in the strip in terms of # of downvotes)

(and 7th overall)

Me too :P

I kinda think the log plot makes this look way more crowded in the upper regions of votes than it actually is

@ACuriousMind Then what was it?

You said something about topology

@ACuriousMind $1/12=-(1+2+3+4+\cdots)$

lol

lmao

Checkmate, atheists

Well, I just got fisted in ODE.

@0celo7 I think I need to sit down and properly write out what I exactly mean because I've kinda got the feeling no-one really understood what I was talking about

@ACuriousMind Maybe!

@0celo7 Ah, the college experimental phase

You had some strange gauge theory analogy

@ACuriousMind Link?

@ACuriousMind Yes, freaking partial fractions on quartic polynomials and multiple integration by parts with fractions and multi-level step functions

And now the internet is broken

Partial fractions ain't so bad, is it? :P

Good point, if you're working with common fields like the EM tensor or derivatives of some string field or something they are integer weights

That was probably the hardest test I've ever taken. Maybe I haven't taken hard tests before.

It would have been a joke with my calculator ;_;

@Danu Starts here

What the hell does $(dz)^{1/12}$ mean?

@bolbteppa Nothing, that's why you shouldn't think in terms of $(dz)$

$(\mathrm{d}z)^{1/12}:=\mathrm{d}z^{-(\sum_{i}i)}=\otimes_{i}\mathrm{d}z^{-\otim‌​es i}$

@ACuriousMind Pretty sure there is nothing like this

In fact, some of the more subtle points of QFT in curved spacetime crucially depend on this type of stuff

and nobody knows what to do

I'm still gonna think that way to remember it and try to hopefully find some excuse to justify it in 5 years time :p

In some sense, it's natural to take the full manifold

but in another sense, it's natural to take only what we observe

My thesis on QFT in dS spacetime also ran into this issue: Global coordinates or a Poincaré patch?

Nobody knows, and everybody assumes whatever seems most convenient for their conclusions section in the paper :D

@Danu Yes, that is exactly what I was worrying about

@ACuriousMind I'm pretty sure HE has a (at least a) partial answer of your question. The theme of the book is global properties of spacetime. But I haven't read the chapter on the Cauchy problem, which I think is what you want.

@0celo7 I'm not interested in what global properties spacetime manifolds miight or might not have. I want to know how to select the physically correct manifold.

You uniquely construct it from the initial data.

@0celo7 No.

@Danu Yes.

We only have measurements

Ain't no unique constructing going on.

@Danu ...I'm also not talking about how to determine the correct manifold from experiment

Not yet, at least

Alright then, how do you interpret theorem 10.2.2 in Wald?

I want to know first how the dynamical theory selects the correct manifold

@ACuriousMind But it seems very unreasonable to require GR to uniquely tell you some manifold... From what?

How will it distinguish a submanifold from the global one?

Given an initial set of data one can construct a unique globally hyperbolic manifold.

@Danu Exactly, at a first look a local theory can't do that

@0celo7 Initial set of data = non-existent here.

@Danu Why, because we can't have perfect measurements?

Among other things, yeah

We're not talking about the same thing, then.

@ACuriousMind Hmm

@Danu However, some other aspects of the theory depend crucially on the global structure, e.g. the types of instantons that appear are related to the possible principal bundles structures over the manifold, and those possible structure depend on the global structure.

@ACuriousMind I think I understand your question now.

This is another face of this issue, the typical Yang-Mills Lagrangian assumes a fixed bundle, but the fact that we treat the instanton number not as constant means there should be somethign dynamical determining the bundle.

See now this book says $\psi(w) (dw)^h = \psi(z)(dz)^h$ is valid even on bundles books.google.ie/… :\

@ACuriousMind Note: there is a principle along the lines of "all physical spacetimes are globally hyperbolic"

So the above theorem answers your question. (If you accept that principle.)

@0celo7 No, it reduces the question from "What determines the global structure of the manifold" to "What determines the global structure of a spatial slice" in that case.

@ACuriousMind Well

Hmm

I see.

@bolbteppa I think the "like" there is crucial, and I seem to remember that, classically, no fractional weights occur

Hm, they're quantum there, though

@ACuriousMind You know, that's actually a very good question.

You should write a question.

Completely unrelated: Is it me, or do we get this type of answer regularly? I seem to recall reading the same thing (up to minor variations in the phrasing) a few times now.