@0celo7 Yes. That's exactly what it means. Divergence-free fields are curls unless there is a topological obstruction (i.e. the cohomology in that degree is non-zero).

@ACuriousMind so something like R^n without the origin?

@0celo7 Yep, that's homotopic to $S^n$.

@ACuriousMind I...I'm confused

@0celo7 You should also ignore any frictional torque at the pulleys and as Glen said the weight of the rope.

don't know what is confusing me :O

@dmckee perfect rope := massless, stretchless, frictionless rope

I know how to do it with torque

As so often, perfection doesn't exist.

but I had to check my sanity because there the tension is not the same, right?

am I insane or is the tension different when we take torque into account

not insane confirmed

sanity as a whole still questionable

but

If the rope is massless

Shouldn't it go the speed of light

you...

broke physics

you literally broke intro physics

or intro physics broke relativity?

what about a tachyonic rope

@0celo7 Isn't that theee

Helmoltz theorem

Or whatever

All nice vector fields can be decomposed into a scalar and vector potential

Altho... Maybe it is related to the thing

All 1-forms are such that $\alpha = df$

If simply connected etc

mb it is related

I dunno

@ACuriousMind, tell us math

exact form, that's the term

oh wait I mangled the theorem

I don't know

@Slereah You're probably thinking about Helmholtz decomposition, which is a special case of Hodge decomposition

indeed

Everything is a sum of an exact, a coexact and a harmonic form.

Helmholtz is: Every vector field is a gradient plus a curl.

coexact is d*, yes?

$\delta = (-1)^{n(k-1) + 1}s\, {\star \mathrm{d}\star} = (-1)^{k}\,{\star^{-1}\mathrm{d}\star} $ apparently

CLOSE ENOUGH

Which sounds like a curl thing indeed

Do you guys have a good geometric intuition of $dF=0$ and $d\star F=0$?

-sigh- it seems to me like there should be some way in which special relativity makes maxwell's equations obvious, and it seems like that's it, but I don't have any geometric intuition of differential forms...

@NeuroFuzzy It's a 2-form in 4D space. I don't think you should expect all too much intuition about that

Our "intuition" is very bad at dealing with 4D things.

...annnnd another failed attempt to reach the Mun. I hate/love this game.

@ACuriousMind knew that

@NeuroFuzzy I think MTW has a way of "drawing" forms

might check in there

@Slereah don't you just love the plusses and minuses in forms

@ACuriousMind what is it (the game) about? is it good?

what's a "kerbal"

@0celo7 Well...it's about the Kerbal's space program

The Kerbals are the inhabitants of Kerbin, a planet. You get some parts to build rockets with.

If you build the rocket wrong, it doesn't take off, does flips in the air, goes up but comes down again, or other things.

hey this is a pretty good looking game ::presses P button:: what the...

why is there a button to lower visual fidelity!?!?!

@ACuriousMind "get some parts"

where do these parts come from

@0celo7 That depends which mode you play. In sandbox, you just get everything from the start to play with, in "Science mode" you have to explore and take samples and stuff to research better parts, and in "Career mode" you have to additionally pay for everything (but also get some sources of income)

@ACuriousMind I bet you play science mode

commie

lol

indeed

called it

seriously, why does the game have a button assignment that shits on the graphics

I don't think I could finance the rate at which I have to hire new Kerbonauts.

stop killing your dudes :O

Well...it's not my fault if they can't keep a rocket on course :P

Actually, it is...

You're a physicist, not an engineer

Of course you can't not kill people

@ACuriousMind It's got you!!! yess

I built a rocket train that got into a retrograde kerbin orbit

and hit the surface at 24 odd kilometers per second

("Rocket train" meaning I had five or six pods of fuel that I docked in orbit, used up, and then undocked one by one. Really really really difficult to turn)

@0celo7 I'll check there. Thanks

Did @ACuriousMind miss his calling as an aerospace engineer?

@FenderLesPaul I can do a GR talk tonight

did he find his skype?

no clue

do the problem set!

damn today in class I didn't understand some parts.

like in scalar field theory why is there a $\phi^2$ term?

mass term

or...potential energy?

lol, gl

how did the lecturer do it? starting from the KG equation?

here look

the Lagrangian is $(\partial\phi)^2-m^2\phi^2$ because that's what gives you the Klein Gordon equation

2.61

and 2.64

with a 1/2 out front for shiggles

why is there a del.

and why is the field squared

so you don't get the $b\phi^2$ term?

yeah

am i being dumb

what's hard about "the simplest thing we can write down"