arxiv.org/abs/1601.00785

best title

@Slereah don't various quantities in QFTCS depend on $1/\sigma(p,q)$

yes

It's the equivalent of $1/r$ after all

Hm

If I have a spacetime with a thin shell wormhole in it

That is, I remove two shapes out of the spacetime and I identify the inside of one with the outside of the other

To compute any differential equation, do I just check the equation on the original spacetime and force the solution to be identical around the identified parts?

That is, if $A,B$ is the area of the two mouthes, $f(A) = f(B)$

Or do I need a bit more

Ah, I think Friedmann discusses the problem

Ah, he requires both continuity of the solution and its derivatives

$\Phi(A) = \Phi(B)$ and $\vec{n}_A \cdot \vec \nabla \Phi(A) = -\vec{n}_B \cdot \vec \nabla \Phi(B) $

@Danu @ACuriousMind Whoever made this chart understands me

Mass has dimensions of mass, instead of dimensions of energy.

Hooray!

@DanielSank huh?

oh you hate natural units

why is that again?

@ChrisWhite oh?

what did they do

@ChrisWhite that's what they do in the government for people with TS clearance

clearly Princeton academics is sensitive fucking information

@ChrisWhite what happens if you do that

To actually get things to change on that front you would want to get the faculty and staff senates (or local equivalents) to weigh in on your side. You need to know how much this is annoying the department secretaries and other people with real power. And a few professors.

But the simple fact is that really tight data security is inconvenient.

Emeriti have no formal power in most places, but they often have a lot of swing even so.

@ACuriousMind Just read the proof of the Hairy Ball theorem, blew my mind

@ACuriousMind So how do we know that a noncompact manifold admits a nonzero vector field

@0celo7 o/

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ I have finally proved the Hairy Ball Theorem

@0celo7 cool

Wow, special speaker @Slereah !! I've always wanted to talk to him!!!

@MAFIA36790 Yes, anything special today? I've never seen 4 rows of names on the right hand pane!

So many people that I thought I entered a wrong room

I count 36 people :O

Hey, one question to some of the high reputation guys here. I have observed, that statements of high reps. which are essentially the answer of an asked question are sometimes given as comment, not as answer. But from all I could find on the meta site, this seems to be bad etiquette.

Especially due to the temporary nature of comments this seems to be a waste :-)

@user_na See Chris' answer. I won't write an answer unless I'm confident I can give a complete and accurate response to the question. There are times when I only think I know the answer or I only know part of the answer and then I'll leave a comment.

So, I see this as a chance for low rep'ed underlings like me to rise :-)

I agree that if you see a comment and it prompts you to extend that comment into a full answer then you should go for it. I've done this many times, though I usually credit the original comment in my answer. Part of my motivation for leaving a partial answer as a comment is the hope that someone more knowledgable will pick it up and run with it.

Good to know

We do have a few (mainly just one :-) members who specialise in answering in comments, but that's life - just ignore them and move on.

@ChrisWhite but how do you know know that you are moving to the front if you are logging off?

@ChrisWhite I see

@MAFIA36790 someone tricked me again

:D

My fav chat place is

Rest i can be found in agent of nothing, Hinduism chat room and occasionally in mos or maid cafe

@ChrisWhite I am experiencing the same.

It's just a bug.

It looks as if the icon does disappear if you click the leave link, but it doesn't disappear if you just close the browser.

speaking of bugs

Don't know if this is a bug or something else, but I seem to have lost the ability to access certain things on PSE. For example, I wanted to VTC a copy-paste homework question, but the "close" option was unresponsive. Same for all the other options as well as the downvote button. The only option that worked was the "edit" option. Trying to ask about this I wanted to come here, to the chat rooms, but the dropdown in the top left (the one with the SE logo) didn't drop down.

Instead, I was taken to the SE site. I was lucky there was a link here in de sidebar on the right hand side of the homepage. Any ideas? (I guess I should tag a mod or something, @Qmechanic)

@Wouter I've just been working through the review queues and everything seemed to be working normally. I wonder if it's some problem on your computer.

@JohnRennie Damn, I was hoping I wouldn't have to close my browser. I have the bad habit of keeping loads of tabs open. I'll give it a try and report back ;)

Okay, closing and opening the browser hasn't worked. But I've just noticed Matlab gave an error about low-level graphics.

That sometimes messes with other stuff as well, so let me close Matlab for a sec.

Still nothing.

Last resort: rebooting. See you in a few minutes.

It's still not working... :(

It worked perfectly fine until now. And atm I don't have any other tabs open. Not even any other software is running.

Weirdly though, it seems to be working on Chrome

I'm on Firefox :)

But I get the point. Firefox has been acting up more than it used to these past months.

Chrome it is :P

Thanks for the help ;)

@MAFIA36790 No, it's a bad sign in fact

A sign of desperation in the face of The Thesis

@ChrisWhite That's a great find

loving this one

Also this one

@MAFIA36790 boo, we've halved the room membership!

Too true, too true :-)

hi all

@JohnRennie Could I ask you a quick linear algebra question

@JohnDoe I'm one of the less mathematically accomplished members of the site so I may not be able to help. However you can certainly ask.

after that ill pose a question that is almost more philosophical

and hi there John

@user507974 Hi :-)

So this is a question that a 5 year old would ask but we as physicist dont really have the full answer: What is an electron?

@MAFIA36790 :

hey hey

With what we've confirmed, what is the most fundamental description of what exactly an electron is

Greetz, I think this question of atrts and crafts site is related to Physics. Please consider having a look and see if you can answer that w.r.t physics: crafts.stackexchange.com/questions/77/…

@JohnRennie Thanks. If you have a linear transformation given by say a 5x3 matrix and you want to find the image of the transformation. Then as I understand you can take any two columns of the matrix. Is this correct so far?

My attempt: The closest thing to a fundamental answer of the electron we have is that it is an excitation in a quantum field in a vacuum that observes a special family of symmetries in space and time, some of those heavily perturbed by their neighbors and others that are very difficult to change.

@JohnDoe Can you have a linear transformation that isn't a square matrix? I would have thought not, unless I'm misunderstanding what you mean.

what would you say @Slereah?

@JohnRennie did linear imply invertibility

@user507974 it isn't possible to say what an electron is because no-one knows. The best we can do is say how QFT describes an electron.

i thought that is why we have right inverse and left inverse, cuz you are still linear

@user507974 so I guess you're trying to come up with a succinct way to explain how QFT describes an electron.

An electron is a soliton in the associated bundle of the principal bundles of the standard model corresponding to the electron's charge

@JohnRennie QFT is our most fundamental definition we've confirmed (with string theory possibly more fundamental). But if we took QFT, GR, particle physics, and the rest of physics and tried to precisely define it what would that be

@user507974 I don't understand the question ...

I'd rather not use the particle definition commonly used because it doesn't work in interacting theories or in curved spacetime

So a well localized soliton is probably best

@JohnRennie i think @Slereah kinda got it all down

@Slereah can we defined according to the standard model a bit more

define*

Probably but I dunno

Like I don't know what soliton you could define as being "one electron"

you have spatial symmetries, lepton, rest mass

I guess it should have an energy of ~511 keV

@JohnRennie Yes you can, say $T: \mathbb{R^5} \to \matbb{R^4}$ given as $T(x) = Ax$

@Slereah but can we basically say that you have symmetries in spacetime [what are the symmetries other than that]

would mass be a spacetime symmetry too?

@JohnDoe OK, you've lost me now. You need to ask some who knows more about maths.

You don't need spacetime symmetries to define the electron

Well, you do, but only local symmetries

and yes mass is a Casimir operator of the translation group

@Slereah SU2 ?

@MAFIA36790 The response is not visible

SU(2) yes, kinda

(SL(2,C) technically)

@Slereah was that the difference between relativistic and not

Yes

(kinda)

@Slereah when you say kinda that only makes me more curious

You have SL(2,C) ~ SU(2) xSU(2)

what else besides relativity?

oh yea, it is locally SU(2)

is SL(2,C) still describing one electron btw

What do you mean by "describing"

The electron field isn't the rotation group

It's the associated vector field $\Bbb C^2 \times \Bbb C^2$

well, nonrelativistically we consider we treat the electron as having SU(2) symmetries right

yes

that's because SU(2) is the spin group of SO(3)

yea

@JohnDoe I think mafia367 simply meant you misstyped "\matbb{R^4}"

so for SL(2,C), what is the physics encoded by SU(2) x SU(2)

im probably wrong, but it looks to describe to me the behavior of those symmetries in relation to another identical symmetry

like electrons are correctly described by considering that another partner electron exists locally

(again though im probably wrong)

Wow! They fixed that chat avatar bug fast :O

did that wild guess make any sense @Slereah?

The two copies of $\Bbb C^2$ correspond to the left handed and right handed electrons

Somewhat "independant" particles

That are coupled by the mass term

"coupled"?

they interact

@MAFIA36790 no, I always stand at the back on these occasions

oh yea, back to the other part, @Slereah, so what about other particle flavours

here we got into this discussion because we were describing mass as having a spacetime dependence

Same, just different charges?

Homework?

they are also Casimir operators?

lepton number and etc

@MAFIA36790 well you could regard it as a conceptual question about how to mangle your graphs into a straight line. The best I could come up with is to graph $T^2h/2\pi$ against $h^3$ in which case you should get a line of gradient unity and $y$ intercept $2k/g$.

Aha, just when I feared the chat was getting quiet, and I'd have to do some real work, the delivery man has brought my new SSD. Now I can spend a couple of hours reinstalling Windows 10 instead of working :-)

I'm not a huge fan of W10 because I like a clean and uncluttered user interface. I normally use Windows 7 with the classic theme and turn off all the visual effects. However W10 has basically the same kernel as W7 and it's a perfectly good operating system.

@MAFIA36790 That sound as if the upgrade process went wrong. I would never upgrade an OS. I always back up all the data, install a nice clean OS then copy the data back.

Linux is fun to play with, but the reality is that I can work more productively on W7 than on Linux. For productively read money earning.

important note guys, if your computer starts automatically updating to windows 10 you can revert back by not agreeing to the terms that pop up after first boot up of windows 10

@user507974 I think I'm going to update

I can't handle the constant notifications and honestly 8.1 is shit

windows 7 is the tip of the power curve for me

I really dont like metro and their attempts to unify with phones

basically the worst part about 8 that still kind of exists less pronounced in 10

if all phones were touch screen compatible maybe

@user507974 they should have never made touch screen computers

worst idea ever

i think it can work ok

ive had to do something like 3 years of research on mac systems

id rank it better as windows 8 if thats any consoltation

@user507974 I use a Mac...

It's way better than windows

in every way

egh, they drop the ball in a few big ways i think

the only MAJOR advantage id give it over windows is terminal

for me: Windows 7>>Linux>>>Windows XP>OSX

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Win‌​dows 8

my lab has an XP laptop hidden away for the apocalypse

heh

they turn it on, automatically starts updating to 10

@user507974 not allowed to connect to the internet :P

@0celo7 There is no best OS. That's like asking what car is best. It's just a matter of what OS best suits you. I am a hardcore nerd - I've even done device driver development for Windows (back in the NT3.5 days) and I know my way around the Windows kernel. That's why Windows suits me best.

@JohnRennie Yea, thats what I think too.

@user507974 we keep it around for legacy programs

although someone got a program from a floppy disk onto a Win10 lab computer

ive had 7 since basically it came out, done 2-3 years of research on Macs, 6 months on Linux, and they kind of excel at their own things

pretty impressive

@0celo7 lol

@user507974 our X ray machine is from the 80s :D

OSX was based on the Mach microkernel so it's basically unix at heart. However in everyday use it puts too many barriers in the way of what I want to do. Doubtless I could work round these if I had the years of experience with it that I do with Windows, but life is too short.

What barriers?

Are you a nerd constantly typing stuff in the command line

@JohnRennie I remember my first time using it they put an open source compiler i needed behind a paywall (i could get around that but at the time i didnt know nearly as much about computers)

@0celo7 wait, you mean you dont do that?

@user507974 for work, yes

but when I'm watching pokemon videos, etc. why would i do that?

sudo python robot.py -bring tissues

oh iTunes works WAY better on OSX than Windows

@0celo7 dont use iTunes

so I haven't really missed that

@0celo7 which bit of I am a hardcore nerd did you not understand :-)

actually its been really funny to watch apple slowly add in features ive had on mediamonkey for years

@JohnRennie how do you poweruser with windows

id like to take notes

i can get by on unix systems but for me windows feels very closed off

@user507974 turn off user access control and stop being a pussy :-)

@JohnRennie well yea but after that what do you actually do

@user507974 Apple Music is a top 10 invention

of all time

you're missing out

ive done a few registry tweaks, context menu for overriding file owndership, image rescaling, open with Sublime Text 3, just basic things

oh and i added in a calculator to the start menu

or whatever its called when you pres the windows button

and a file previewer

for many other types of files (mostly text files)

@user507974 I don't understand what you're asking. Turning off UAC affectively gives all administrator accounts the same privileges as root. You do that then get on with doing what you want to do. Avoid any tweaks that aren't necessary.

@JohnRennie well yea, but what are you doing after turning UAC off

Why would you add calculator to the Start menu? Just press Windows-R and type calc.exe

@user507974 Nothing. I just get on and use my computer.

paranthesis and reorganizing the equation

dont really like calc.exe personally

a while back i use to have seconds on my clock

forgot how i did that though

In OSX I have a trackpad finger swipe command for the periodic table

pretty useful in a solid state physics lab

oh yea, usually i had a periodic table gadget on the desktop

forgot about that like 3 years ago

when i reinstalled

You know those people who buy a car then dangle a fluffy toy from the mirror and put a Garfield sticker in the back window? Well here's a hint - neither the fluffy toy nor the Garfield sticker will make your car any faster or more reliable.

@JohnRennie well mine is more like putting a little bubble mirror on the side view mirrors

they are little functionality improvements that just make the workflow faster

@JohnRennie I have my university parking pass on the mirror

so I don't get towed

mileage varies for the tweaks but they are nice when i need em

@Slereah So you basically use your nonzero vector field to construct a homotopy of the antipodal map of $S^n$ to the identity

and this is not possible in even dimensions

that sure is a solution

but a solution to what

oh, hairy balls?

@EmilioPisanty looks like the question was posted, then the answer was posted, then deleted, all on April 30, then on May 10 the question was automatically deleted, then on June 1 the answer was undeleted. I'm not sure why the answer currently shows up as deleted (independently of the question being deleted).

More importantly, what's the set of solutions for the wave equation in bipolar coordinates

Apparently might be something like $e^{i\omega t} U(\xi) V(u)\$

Where $U$ is hyperbolic functions and V is trig functions

Oh wait

Apparently the Laplace equation is not separable in bipolar coordinates

@Slereah what does that mean

That I'm gonna have to work out that equation

why would you use coordinates in which you can't separate one of the most basic PDE

how do you even solve a non-separable PDE

Because on the other hand, working out a wormhole in it is trivial

Well

Laplace is separable

But Helmholtz isn't

And by extension, the wave equation

no, bullshit

Laplacian is $\approx (\cosh(\xi) - \cos(u)) (\partial^2_\xi + \partial^2_u)$

what the fuck

are you talking about in bipolar coordinates?

yes