1:32 AM
@Semiclassical If you happen to come around, please have a look at this question: physics.stackexchange.com/questions/380214/…

JAVA
coding . . . . . . JAVA. . . . . .

1 hour later…
2:49 AM
@Slereah I think, in eq. I.75, Scherk takes the $x^{\mu}$ from I.55 $x^{\mu}(\tau,\sigma) = q_0^{\mu} + 2 \alpha' p_0^{\mu} \tau + i \sqrt{2 \alpha'} \sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}[a_n^{\mu}(0)e^{-int} - a_n^{\mu *}(0)e^{int}] \cos(n \sigma)$ and then wants to factor out $2 \alpha' p_0^{\mu}$ so that $x^{\mu}$ becomes
$x^{\mu}(\tau,\sigma) = 2 \alpha' p_0^{\mu} [\frac{q_0^{\mu}}{2 \alpha' p_0^{\mu}} + \tau + i \sqrt{2 \alpha'} \sum_{n=1}^{\infty} \frac{1}{2 \alpha' p_0^{\mu}\sqrt{n}}[a_n^{\mu}(0)e^{-int} - a_n^{\mu *}(0)e^{int}] \cos(n \sigma) ] = 2 \alpha' p_0^{\mu} \tau'$ (which amounts to a change of variables possible by conformal invariance), but because this makes no sense (divided by a vector $p^{\mu}$) he forms a dot product with some vector $n^{\mu}$ to do this

@dmckee @JohnRennie Another one :)

Ahh, that's a vector, that explains why lightcone coordinates actually pop up, I.88
No wait, not dividing by a vector...
Seems like Scherk shows the fields $x^{\mu}$ in the NG action satisfy the wave equation, and then in section 6 (eq. I.66 on) shows the coordinates $\tau,\sigma$ also satisfy the same wave equation, so that we can set one of our $x^{\mu}$ fields equal to one of the $\tau,\sigma$ coordinates, say $\tau$, and so for some reason, maybe to guarantee we have a time-like coordinate, dot-products $x^{\mu}$ with a time-like vector so he can do the stuff I posted above, hmm
Something about the $n$ vector fixing the parametrization...

3 hours later…
5:49 AM
@JohnRennie isn’t here
I was going to tell him something
Oh well

1 hour later…
6:55 AM
I can't stop watching John Duffield being teleported into a CGI spaceship

It's warm outside and it still feels so cold indoors. I was forced to stop cold shower due to feeling over cold.

@BernardoMeurer are you sure it's CGI
He might have an actual spaceship

@Slereah Good question, now I don't know
Maybe that's why @0celo7 has been seeing manifolds in the sky

7:10 AM
I wonder if he'll come back
It's been a while since he dropped by

That is true
I miss him to be honest

Hmm, it turns out MSVC doesn't implement the getline function ...

@JohnRennie But that was standardized in POSIX-2008
*POSIX.1-2008

It implements std::getline

That's c++ mumbo-jumbo
get it away from me

7:21 AM
But not the straightforward C getline function
I must admit that surprises me

C++ doesn't implement all of the C standard
just most of it

@Slereah Well, to be fair, getline isn't in the C standard IMHO
It's not C99
And no one cares for C11
Also, it was a GNU extension before POSIX adopted

8:07 AM
Hello my dudes
where are the diff geo people
I am in need of the diff geo

go to math chat
really? I found it's like there are many math conversnt people in math chatroom. Or maybe compared to you, they are deficient.

Nah, I am just kidding

8:29 AM
1 message moved to trash
Silently the ninja room owner stalks his prey

boo

8:46 AM
"The background philosophy behind this paper is very simple: Finsler metrics are special pseudo-Riemannian metrics in a special vector bundle."
very simple indeed

9:18 AM
do spin networks represent real physical interactions, like the case of Feymann diagrams? Or are they just imagined graphs covering the spacetime manifold in order to describe the spacetime manifold, like coordinate patches?

From what I can remember, spin networks represent space at an instant
They evolve according to some dynamics

so are they real physical interactions or imagined graphs on that space?

what does "real" mean
It's the quantum state of the $3$-metric
you may decide how real it is

doesn't each Feymann diagram reprsent a real physical interaction, like an electron and a positron merge into two photons?
But if spin networks are just like coordinates covering a manifold, they are not real; they are the grids people carve on the manifold to describe the manifold.

hey physicists
why is symplectic geometry important to you? tell me
tell me all

9:29 AM
it can describe the dynamics of geometry

@BalarkaSen The Hamiltonian

tell me
tell me more

Did she put up a fight

@Slereah quantum state of the $3$-metric? So they are the real interactions? These edges in spin networks represent real particles with spins labeled by those edges.

9:35 AM
it's gives you the fancy version of the Legendre transform basically?
Well no, quantum states aren't interactions
You have to evolve spin networks to get the dynamic
Spin networks are eigenstates of an operator associated to the area of a region of space

really? it turns out spin networks really have an operator to give rise to. Last time I asked you this question, but you didn't reply me; probably you were sleeping.

yes, sometimes I do that
the human sleep

symplectic geometry can be performed canonical transformations.

yes
that way you can do that trick of turning Lagrange equations into first order equations
and do a nice split of time and space, if in spacetime
although of course you need the horrible polysymplectic geometry if you're using fields
Well summarized

9:51 AM
rip
rip in diagrams
also why is that diagram lopsided

the bundle is lopsided

so those edges in a spin network represent quantum states of 3-metric? then why does a vertice in a spin network represent?

No, the whole diagram is the state

a spin network represents a quantum state?

yes
you sum over spin networks to get the propagator

10:01 AM
so a vertice in a spin network represents tensor product (entanglement) between particles?

10:14 AM
the loops are apparently holonomies of the $3$-connection

how are loops related to spin networks?

the spin network is made of loops

[Random]
New thoughts on changing history:
(model independent(?))
Start at the present day, travel x hours back to the past
When the time traveler depart from the present as seen in the frame of the laboratory in the present day, and go back to the past, the worldline between x hours ago and the present as seen in this frame (and relativistically in other moving frames) will be updated instantly at all events along the worldline.
It's as if the hamiltonian that gives the evolution of all the events along the worldline changes into a new one at all events in this worldline the moment the time traveler arrived back in its past as seen from the laboratory frame.
Need to check later whether all of this makes sense...
(NB, this is not GR, as one cannot change spacetime topologies on the fly)

10:30 AM
@JohnRennie Last question? I am unable to figure out how these two molecules are mirror images...

@Abcd Here or in problem solving?

problem solving.

11:27 AM
Maybe I should read Cartan to get a good grasp on connections
He is the French

11:52 AM
"Let $\gamma : I \to M$ be a path with $\gamma(0) = p$ and $\gamma(1) = q$. For every $v \in T_pM$ there exists a unique horizontal lift $\tilde \gamma$ such that $\tilde \gamma(0) = v$ and $\tilde \gamma(1) \in T_q$"
What
I thought the geodesics weren't unique between two points for general manifolds
Or is it true
I'm not sure
I guess it might be with a specified tangent vector $v$?

12:17 PM
Oh wait
It was a RUSE THEOREM
The real theorem is the same but also requires the connection to be uniformly vertically bounded

12:48 PM
@ACuriousMind How does the connection work, like, formally speaking
I'm guessing you need to define a basis of the horizontal subspace of $TE$
Is this related to the connection form
Also since this is just $\Bbb R^n$ how does rotation of the basis work for a general connection
does it correspond to anything

So, about that nuke explosion question, I wonder if a 10 km long, 6 km spacecraft could realistically survive that.

1:03 PM
@Slereah the horizontal distribution is the kernel of the form

So the connection form is just the normal form to the connection?

Wot

Gentlemen?
In theory, could a carbon nanotube-tungsten alloy be possible?
Or is that not really doable?

@0celo7 If I have some vector $h \in H_e E$, and a connection form $\omega$, is $\omega_{abc...} h^a = 0$
Oh wait, I guess the connection form isn't rly a form

@Slereah? Question: is it possible that a carbon nanotube-tungsten alloy could work in real life?

1:17 PM
I dunno man

Mainly for vehicle and spacecraft armour?
@0celo7? Let me guess: carbon nanotube-tungsten alloy = unrealistic?
Or.....is current science able to allow that (in theory)?

Wot

He wants to know if he can make a Very Strong Tank

Or in this case, a very strong military spacecraft.
:P

I don't think any of us are really big in material science

1:25 PM