@JohnDuffield You're not telling it to some 17-year-old kid. You're telling it to everyone who disagrees with your utterly wrong statements. And an ad hominem like that is not going to make anyone want to give you the benefit of the doubt and listen to what you have to say.

Again, you've completely dodged Daniel's point of a sizable number of competent people disagreeing with you, and decided to attack a strawman instead.

@BernardMeurer Not helpful :)

It's funny because I'm not 17

@JohnDuffield Interesting. Are you familiar with the term "appeal to authority"?

He is

Ok. ::clicks ignore again and moves on with life::

If you search the chat history for "appeal to authority" is difficult to find a message that's not a reply to him.

@DanielSank : there's no such thing as magnetic charge. Maxwell unified electricity and magnetism a hundred and fifty years ago. They're electromagnetic waves, not electric waves. An electron has an electromagnetic field, not an electric field. So electric charge is a misnomer. It ought to be electromagnetic charge. That leaves magnetic charge out in the cold. It can't exist anyway because there are no freely-rotating discontinuous regions of space. Because space isn't like that.

@DanielSank True, my bad

And reading that chat history from more than half a year ago you can see that these debates really go nowhere.

@DanielSank : of course I am. But that's no reason to dismiss Einstein when we're talking about gravity/relativity/etc.

@ACuriousMind : it's not an ad-hominem. When we started having these conversations 0celo7 was 17, and he still dismisses Einstein even now he's had ample chance to go and read the references I've given. He simply won't read them because he thinks he knows better. Amazing.

@JohnDuffield You know what, I'll bite.

Why is my argument wrong?

@ACuriousMind : I haven't dodged anything. But DanielSank has dodged what I said about no magnetic monopoles.

There is no possible way to express the sigh I just let out in words.

Hey, @BernardMeurer, why are you searching for a Python ninja? Weren't you reading...some book about QM? (I forgot which)

@0celo7 : which one? The constant curvature? We talked about that. A gravitational field is a place where space is inhomogeneous space. When space is homogeneous there is no curvature and light goes straight.

Ah, ok. What is inhomogeneous space?

@ACuriousMind : you won't discuss physics with me because you're afraid I'll show that you're wrong.

@ACuriousMind I just got a job as an intern, so during the day I code Python and Java and at night I study QM :)

Sounds like me at the Senate

Except it was GR at night

@ACuriousMind I'm reading Griffiths normally and Shankar and @0celo7 is on skype to save me on-the-go

@JohnDuffield I think all of our problems are because you don't understand the standard definitions of math and physics.

So let's clear them up.

What is inhomogeneous space?

@0celo7 : space that is not the same at various locations. The important thing to understand is that space is not nothing. It's like this ghostly gin-clear elastic thing. You can do things to it, you can curve it, you can subject it to pressure.

But I'm getting pretty lost anyway, still having trouble to really get the definition of vector independency and stuff

"space that is not the same at various locations" Please be more precise.

@BernardMeurer Ah, well, if you didn't do much linear algebra before this it's perfectly fine to get lost I'd say

@ACuriousMind I didn have Linear Algebra at all in school\

@ACuriousMind This.

(Someone tell me when 0celo7 is finished debating with Duffield so I can unignore him)

I was perfectly comfortable with vector calculus when I read Shankar.

We had a two classes about vectors, and they were just pretty arrows not this ket magic

@BernardMeurer I see how that might be rough, then

@JohnDuffield I don't see what this has to do with spacetime itself.

When I learned QM, I knew both linear algebra and Hamiltonian mechanics, which is both really helpful

@0celo7 : see above. The stress–energy tensor "describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics". There is stress is space. Stress is directional pressure. It reduces with distance from the gravitating body. You need to zoom in when you depict it to avoid getting confused by the curvature of the Earth. Something like this:

@ACuriousMind Yeah I'm hoping to put up an effort to pick things up on the way, but I stayed up all night yesterday solving the first problem set of Griffiths

which is supposed to be trivial

@JohnDuffield Ah, ok. Looks like we've found a problem.

I felt like a chimpanze

What happens when $T_{\mu\nu}=0$, like in a vacuum?

Spacetime can still be curved.

@BernardMeurer Well, aren't you interning as a "code monkey"? ;)

@ACuriousMind Yeah but I'm interning to get money for a computer

I'm leaning QM because I'm a masochist

QM really isn't hard.

And Shankar is excellent.

(except for that one thing ACM helped me with the other day, which even he didn't get)

@0celo7 Our perceptions of hard are very different

I find low-level C code for ARM architectures pretty easy, you might find that the materialization of devil

I find QM pretty devilish, you find it alright

@0celo7 : spacetime is curved in that space is expanding. Set that aside for now and instead think about "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". Mentally blot out the planet, and just think about the inhomogeneous space. The energy density is not uniform. So this region of inhomogeneous vacuum causes a gravitational field, hence the non-linearity. Then ask your self why we should assume that space is homogeneous.

@ChrisWhite Huh? It's not the energy-momentum tensor in the second case?

Oh, and see this: arxiv.org/abs/1209.0563.

@JohnDuffield What is the energy of spacetime?

@ChrisWhite That sounds like the spin-2 analogue of the Proca action having an ill-defined massless limit, while the un-gauge-fixed version, the Stückelberg action, has the correct one.

@JohnDuffield Space should be homogeneous because that's what cosmologists tell us.

Also you're confusing the short-range Schwarzschild geometry with the long-range FLRW geometry.

I'm not saying that the universe is perfectly homogeneous.

But over long distances it's a good approximation.

@ChrisWhite "Or something."

Physics in a nutshell.

@ChrisWhite By chance, would you happen to have the calculation for the deflection of light in Brans-Dicke theory on hand?

Or know where to find it?

Duffield is not interested in a debate, someone please tell ACM to unblock me.

@ACuriousMind You can unblock @0celo7 now

Thank you.

@0celo7 : the energy of spacetime is spacetime. Space is like this gin-clear ghostly elastic "jelly", and when you create a gravitational field by introducing a photon, you are introduced what is in essence a pressure pulse, the spatial and time derivatives of which are the sinusoidal E and B waveforms. It's like injecting more jelly into the middle of the jelly, creating a pressure gradient in the surrounding jelly. Space is jelly, energy is jelly. You can't distinguish them.

@JohnDuffield Sorry, you're not making any sense. We can't have a proper debate if you're not going to say anything quantitative.

> It's like injecting more jelly into the middle of the jelly, creating a pressure gradient in the surrounding jelly. Space is jelly, energy is jelly.

@0celo7 : the cosmologists who tell you that have never read Einstein saying a gravitational field is inhomogeneous space.

@JohnDuffield That statement is meaningless because you never said what inhomogeneous space is.

@BernardMeurer Tell me when they are really done :P

@ACuriousMind Nooooo

@ACuriousMind I swear they were done a second ago

@0celo7 : I can't explain things like gravity and energy with quantitative statements. You've had the quantitative statements in Wald etc. They didn't explain why a concentration of energy results in the thing we call a gravitational field. And nor did they explain why light curves and why your pencil falls down. For that you need to read the Einstein digital papers.

@0celo7 : I told you what inhomogeneous space is, and since you're pretending I didn't, I guess we're done.

Bernard tell ACM we're done.

@ACuriousMind @JohnDuffield Duffield said that now they're done

I'll go back to work now, even NullPointerExceptions are better than this

and that's saying something

Yay, my Stokes proof got accepted.

@BernardMeurer : alternatively you could google Einstein elastic space instead of sniping from the sidelines.

@BernardMeurer Just put JD on ignore.

@0celo7 Congrats

@0celo7 Nice one

I'm still not convinced that's the only way to do it

I'm sure Wald/Carroll/Hawking have a one-line proof scribbled somewhere.

@ACuriousMind Suppose we have some smooth embedded codim 1 submanifold $S$ in a Lorentzian manifold. Suppose $S$ has spacelike and timelike parts. Does $S$ also necessarily have a null part?

If it's smooth, the normal vector varies smoothly. (Theorem in Lee)

I would say yes because the metric changes smoothly, doesn't it?

But you cannot go smoothly from spacelike to timelike without being null.

@ACuriousMind Yeah, I think so.

I'm just thinking about how to extend my result to general hypersurfaces which have hybrid pullback metrics.

@ACuriousMind Huh, I just had an interesting thought. The pullback metric on a null hypersurface is degenerate. Which means the Hodge star is not defined. Does that mean integration is not defined either?

The integration of forms doesn't depend on that

But the integration of vector fields...yeah, seems like that is going to be tricky

@ACuriousMind Oh right, should have made that clear.

@ACuriousMind Or 0-forms/functions.

@0celo7 :O

Ugh. A theorem in Straumann states that the orthogonal tangent space is 2-dimensional. So the normal vectors span a 2-dimensional vector space. There goes the whole theory of normal vectors out the window.

@ACuriousMind What's that face for?

The integral of a function is $\int\star f$.

Astonishment

But $\star$ is not defined.

Yes, I agree

Hmm, is it not possible to integrate over a general hypersurface in GR?

I smell another week of pain and torture

Go for it.

@JohnDuffield Maybe you have the answer for me?

@ACuriousMind Hmm, isn't the Bondi mass or something taken as an integral over null infinity or something? Investigating...

@0celo7 lol, you keep forgetting I don't really do GR at that level

@ACuriousMind I don't either.

I need to get Stewart's book.

Also I need Beem et al.

And that thing on asymptotic methods.

@0celo7 Yeah, but you know about "Bondi mass" or something. If it's not geometrical and might appear in other contexts, it's pretty unlikely I've heard of it

@yuggib I'm going home over spring break but will be needing my Springer account. How do I do that?

eh, without shibboleth or athens, the only way is a university proxy service

Those services don't work in the US.

@0celo7 : No I don't. But I do think you should focus all your energies on 2-dimensional orthogonal tangent space along with general hypersurfaces and hybrid pullback metrics and that smooth embedded codim 1 submanifold S in a Lorentzian manifold. Just think of all the upvotes you'll get from your chatroom friends!

@JohnDuffield Hmm, that doesn't really make sense the way you put it.

@0celo7 your university may have a proxy service

@0celo7 : ditto.

@JohnDuffield Well you just jumbled a bunch of words together.

@JohnDuffield Ok, let's take an easy example

Let spacetime be Minkowski space, and $S$ be the boundary of the light cone of some point

@0celo7 Stop the presses!

How would you integrate a function $f$ on the light cone

@Danu Would you happen to know how to integrate a scalar field over a null hypersurface of a Lorentzian manifold?

@0celo7 : Let spacetime be Minkowski space is an abstract statement. Spacetime is the block universe, it's static, and the real world isn't. Instead it's a world of space and motion. Einstein gave us the equations of motion. When you say Minkowski space what you mean is "spacetime is flat", and the reality that underlies that is that space is inhomogeneous. This means light goes straight. Light from an energetic event propagates outwards in all directions, the light cone is really a sphere.

@Danu Suppose $\iota:\Sigma\to \mathcal{M}$ is the inclusion. Then $\iota^* g$ is degenerate, so $\star_\Sigma$ is not defined.

So $\int_\Sigma\star_\Sigma f$ is not defined.

But maybe there's some canonical fix for this.

@JohnDuffield An abstract statement for an abstract math problem.

I don't see the issue.

@0celo7 : there's no issue if you want to spend all your time on an abstract maths problem instead of physics. After all, you aren't doing a physics degree.

@JohnDuffield If I do pure math do I have to deal with Einstein and the Evidence?

@0celo7 : nope. You can ignore all that silly stuff like the scientific method and falsifiability. After all who needs hard scientific evidence when you're going to be building nuclear power stations for a living? Heck you don't need me to tell you that the best place for those emergency generators is down in the basement.

The pure math will tell you that!

OK enough of that. Who wants to talk physics?

@JohnDuffield Not me!

Physics is too hard.

@dmckee : would you like to talk about neutrinos?

@JohnDuffield Nothing follows the scientific method more strictly than mathematics (every mathematics statement is falsifiable). You should not disrespect something only because of your ignorance. But this does not surprise me, and frankly tells a lot about you.

@yuggib : er, mathematics does not follow the scientific method. Now, what were you saying about ignorance?

@JohnDuffield you clearly don't know a thing about mathematics

apart from the data gathering (mathematics has better ways to test assertions), it is exactly what mathematics does

and, as I said, nothing is more clearly falsifiable than mathematical statements

@yuggib it's pointless

he doesn't want to learn

and now I'm stuck doing crappy geometry

@0celo7 I know, but I don't like when people disrespect my field

@yuggib I'll disrespect functional analysis all day

@yuggib : I know plenty about mathematics. And plenty about science. So I know that mathematics does not follow the scientific method. You don't propose a theory then make predictions then look for hard scientific evidence to disprove or support that theory. It's that simple. And telling it like it is is not disrespecting your field.

lol

@0celo7 That's a weird way to say "I'm spending a lot of time doing stuff with PDEs and Fourier transforms :P

@yuggib : and if you don't like that, you'd better talk to the Faculty of Mathematics at the DAMTP in Cambridge: "The undergraduate course, called the Mathematical Tripos, is a three-year or a four-year course. If you graduate after three years, you receive the BA degree. If you graduate after four years, you receive the BA and MMath degrees. In both cases, you automatically qualify, after a further three years, for the MA degree."

@JohnDuffield Shut up, please; you're embarrassing yourself. When I develop a mathematical theory (e.g. the theory of operators in Hilbert spaces) and then prove results about that (e.g. the spectral theorem) I am clearly doing something completely different from what you just said.

That's BA as in Bachelor of Arts.

@JohnDuffield I couldn't care the less about what terminology Cambridge university uses...

@yuggib Saying embarassingly wrong things has never stopped him before, why start now? You won't accomplish anything here except getting yourself angry.

@yuggib Just like Danu doesn't care what your university considers as mathematical physics

:)

@ACuriousMind I know, but don't worry I will stop very soon :-D

@yuggib not nice

@0celo7 nah, the truth is always nice ;-P

@yuggib : your theory is not a scientific theory that is supported or invalidated by observations or measurements of real-world phenomena. Its a mathematical hypothesis, and your "proof" is a mathematical proof. In physics you cannot prove a theory. Again, you do not follow the scientific method.

@yuggib not really

@JohnDuffield For your knowledge, this is a quote of Popper, that knew something about scientific method and falsifiability: "most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently"

rd.springer.com/book/10.1007/b11550259

What is this?

@yuggib Not an Einstein quote, hence useless as an argument ;P

@ACuriousMind : only I haven't been saying embarrassingly wrong things. Which is why you can't explain why anything I've said is wrong at all. All you can do is make snarky comments, such as this on on my time dilation answer. Tsk.

But nice quote, I'll keep that one in mind.

@ACuriousMind can you explain why I can remember random theorems from Riemannian geometry and GR but can't remember conversations we've had in this chat

@0celo7 I have no idea how my own memory works, let alone yours

> book on variational techniques with applications in GR (maybe)

> sheaves

wtf

Interesting name for a conference

@0celo7 It's fun that the Spanish relativity meeting is held in Portugal

lol

@yuggib that too

rd.springer.com/book/10.1007/978-3-642-21452-3

Why is this a thing

is this the holy grail

> 2 citations

ok probably not

Physical Applications of Homogeneous Balls

hahahhahaa

@yuggib : that's an appeal to authority, and an opinion too. The facts remain: a scientist proposes a theory with predictions to test against real world phenomena to invalidate or support that theory. Mathematicians do not. Of course, some would like to discard the scientific method and falsifiability like Sean Carroll, who has advanced a "theory" about the evil twin universe where time runs backwards. Fortunately that hasn't happened yet, and isn't going to happen any time soon.

@Slereah rd.springer.com/book/10.1007/3-540-07540-2

@ACuriousMind NO

Functional analysis is running next semester

no measure theory can't take it ;(

It's the operator algebra guy too, who applies the whole thing to QM

I don't know measure theory either, only what we did as "recap" in functional analysis. It was not terribly relevant for anything except defining the Lebesgue integral, and you can just put that in a black box and forget about it

It might get relevant if you talk about spectral measures and stuff, though...which we didn't :(

@ACuriousMind My guy who's teaching it is my advisor and said I'd get rekt without the grad-level analysis course

I'm still angry at that prof for choosing to do shit in Sobolev spaces over operator theory.

@ACuriousMind it's a two semester thing here

the second semester is nothing but QM

@JohnDuffield Yours are facts, and the others' are only opinions, funny. I don't need to appeal to any authority, I just gave you an interesting quote. Anyways, I see that you already started shifting goalposts (as usual). This also denotes the point when I will stop this conversation. As usual it was useless (at least ACM got a nice quote).

looks like they're running all the math courses except for Riemannian geometry

but Dydak is running two courses on geometric topology, whatever the hell that means

@ACuriousMind he did the useless Sobolev shit

Sobolev can be useful and interesting

They're running two different analysis courses next semester

three

FOUR

five if you include functional...

@Anthony Well, re-reading it now, I'd say I could have worded that better.

@yuggib Ok, I'm taking the next level of analysis and a course on probability next semester

I've got room for one more math class

you choose

I don't have the bandwidth to think about it right now though.

Suggest an edit!

@0celo7 probability as in measure theory, or probability as in probability distributions?

@yuggib second

damn

the graduate probability has measure theory has a prereq

and you need SOME probability to graduate

I see

I don't want to take this course, but I have to

so you have one math course to choose

:o

the timing works out for topology

I was about to say that

@yuggib ok, I have to talk to my advisor

He said I could just take topology at the grad level

@yuggib : I haven't shifted the goalposts. And they're not my opinions. They're facts, and you can check them out for yourself. End of conversation.

and then measure theory

and skip the "advanced undergraduate" analysis

since any stuff on Banach spaces they do there will be reviewed in PDE or FA

or measure theory

@0celo7 Don't know; I think some general topology is important also at the undergrad level

but it's just my opinion, and I don't know the programs well

@yuggib the grad course here is probably undergrad where you're at

and I have permission to take it next semester

but can you take the grad topology next semester?

yes

my advisor cleared me for Riemannian geometry and topology as two grad courses I can take

I see

it seems a good option

I can't Riemannian geometry because, well, it's not running

I think you would benefit more from topology anyways

@yuggib Yes

I'm not sure how much I would learn in Riemannian geometry, I've read the book (and understood a lot of it)

now if he ran a course on Lorentzian geometry I would take it

and a lot of stuff in topology would come in handy in functional analysis and co.

uh

that's only 16 credit hours

I can take another class...

Right now my schedule is: Intro to Nuclear Engineering, MATLAB, Probability, Analysis, Topology, E&M

E&M?

$\mathrm{U}(1)$ gauge theory

for dummies

ah ok

I can't send you the course list because you need to log in...

so you have room for another one

some more advanced algebra?

yes, but I'll have to talk to my advisor

4 math classes + 1 physics + 2 engineering seems a little...crazy

is my math right on that?

it seems so (assuming matlab is engineering)

4*3+2*2+1*3=?

19

yeah, and that's the max number

Ok, next semester might be my hardest.

it seems so

if I take another math class.

Let's see what there is...

> Seminar on applied math

I think that's the computational QM course.

Oh shit I wanted to take QM

haha the grad QM course is taught by Dr. Batista

dunno if you could do grad QM without functional analysis and measure theory

@yuggib in the physics department

also in physics, you need to know something about $L^2$ and distributions etc

lol

you're so European

Well, if there was a "graduate level" QM course here, that would definitely be the mathematical one. But there typically is no grad level QM.

The QM class uses Sakurai and Cohen-Tannoudji

Which is standard for graduate QM in America

cohen-tannoudji is nice

but I used it in undergrad QM ;-)

along with landau and messiah

@yuggib ok, and I'll use it as a sophomore

...what is a sophomore again?

second year

yeah, if you follow cohen-tannoudji, you can do without functional analysis

@yuggib I already said that there is a functional analysis QM course

but that's in the math department

@DanielSank You don't have the bandwidth? lol

and taught next semester

@0celo7 My grad course used Cohen-Tannoudji and Dr. Ram's encyclopedic knowledge of the subject.

yeah but you can do it later, and now do introductory QM

@yuggib I doubt I'll have time to take functional analysis

maybe senior year

in my third year I'm only taking engineering and physics courses

I'll have to squeeze in measure theory and complex analysis somehow

if I can intern at ORNL next summer I can get some more stuff out of the way

yeah, and then funct anal

@ACuriousMind No, he's dead wrong.

you can't graduate in math without FA

@ACuriousMind my gf wants to know what topology is, what the hell is it

@yuggib bullshit

@0celo7 you shouldn't graduate in math without FA

it's not even required for PhD students

@yuggib FA is a "PhD" course, I'm not allowed to take it as an undergraduate

I won't get a grade for it

@0celo7 the examination of spaces that have a vague notion of "closeness" or "neighbourhood", but no way to quantify distances or any other structure

@DanielSank Anyway, I don't have an edit to suggest- I was just confused.

@ACuriousMind Seems alright to me

I would have said "the study of sets which have a topology"

:P

@yuggib Ok, I'll talk to Dr. Batista and see if he thinks I'm ready for his course.

@DanielSank In fact, I'm not sure there is any problem with it. If you find yourself with time to think, I'd appreciate a ping! I guess my understand of tension just isn't well suited to things that aren't strings.

@HDE226868 I thought you would say that, but apparently not everyone on Worldbuilding shares your idea that science-based should, well, be based on science :P

holy crap the topology lecturer is "Morwen B Thistlethwaite"

sounds like a LoTR character

@ACuriousMind Take a look at our meta discussions on the hard-science tag. That was the attempt of me and a couple other users to solve the issue. The science-based tag was originally supposed to do the same thing, but - and I alluded to it in my comment - it's grown laxer and laxer.

@0celo7 That's an epic name if I ever heard one :D

wonder what the B stands for

You managed to get into a discussion on the #1 thing that pisses me off on Worldbuilding.

Is "Morwen" a male or a female name?

It sounds Elvish either way

@0celo7 Looks like Balin.

He just needs more hair.

Balin?

@0celo7 Oddly enough, that is pretty much how I imagined someone with the name "Thistlethwaite"

The string theorist?

@0celo7 The dwarf.

@HDE226868 oh :P

I don't think the dwarves studied string theory, but I could be wrong.

knot theorist

@ACuriousMind Damn, what will a knot theorist do in a topology course

He'll probably do nice topology

what does that mean

That I don't think him being a knot theorist will lead to an unorthodox lecture or something

@ACuriousMind is there "fucked up" topology?

Damn, Morwen is Elvish, you're right

@0celo7 Oooooh yes. People who spend their time with spaces that don't fulfill nice separation axioms get pretty nuts

@ACuriousMind Is surgery nasty?

Oh no

@0celo7 Well, there's often a lot of blood involved

I forgot the lab for physics

@ACuriousMind you know what I mean

@0celo7 Yes, but I don't actually know what exactly is done there except gluing spaces together, and gluing is not nasty, it's a pretty fundamental operation

@ChrisWhite Heh. I'm afraid I couldn't read it

I wonder whether Morwen embraces his name or hates his parents for it. I could see it go either way.

random fact: I forgot the physics lab and I'm going to have to drop a math course

@DanielSank Oh duh- the tension is imposed by whatever's holding the wood, 'eh?

@ChrisWhite Uhhhh...what did they do to get in there?

Cool, he has an unknot named after him.

How do you guys remember the formula for the divergence of a cross product: $\nabla \cdot (A \times B) = (\nabla \times A) \cdot B - A \cdot \nabla \times B$

@bolbteppa I don't.

@ACuriousMind huh?

@bolbteppa Write it as the wedge it is and use the product rule for the exterior derivaitve: $\mathrm{d}(A\wedge B) = \mathrm{d}A \wedge B + (-1)^{1}A\wedge\mathrm{d}B$

@ACuriousMind huh

All you need to remember there is the product rule and that the second term has a minus for forms of odd degree.

ok, I'll have to have lab from 4PM-6PM

but then everything works

Oh wow, wtf I'm so stupid that's awesome

@ACuriousMind what about an unknot?

@0celo7 Look in the lower right corner: The "Thistlethwaite unknot".

where

oh

> He has made important contributions to both knot theory and Rubik's Cube group theory.

Haha

@Anthony Well, you can say that but in reality the guitar face is not stretched out before it's glued down, so there isn't really an tension in the same sense as the string.

I should reword that part of the post.