The h Bar

paracetamol

15:00

Which was pretty much what happened ._.

@JohnRennie Whup! What I meant was "The electron's got spin, yeah...but definitively allotting it an up or down spin is irrelevant" ._.

Slereah

The bonnor beam metric is also in $(+---)$

I am peeved

0celouvsky

Just multiply by -1?

Slereah

Does that work for all cases?

Hm, guess it would

John Rennie

@paracetamol I'm pretty certain @Emilio answered a question about this a few weeks ago. Unless you create the atom in a superposition of states, which is of course possible, then it does have a definite spin. Let me see if I can find Emilio's answer ...

paracetamol

Waits patiently

0celouvsky

15:06

@Slereah maybe? If you multiply a matrix by a constant you multiply all the eigenvalues by the same constant

I think!

And -+++ just means three positiveneigenvalues

Slereah

yeah sounds reasonable

Stephani's order is a bit weird

The spacetimes are classified by the number of Killing vectors

John Rennie

@paracetamol no sorry, I can't find it. Assuming of course that me memory isn't playing tricks on me and the post does actually exist.

Slereah

So stationary spacetimes aren't talked about until chapter 18

0celouvsky

@ACuriousMind There are too many sheaves.

There's no index of notation

What is $\mathcal E^\bullet (E)$ supposed to be

Something something $E$-valued differential forms?

paracetamol

@JohnR Well, then lets just directly jump to my question:

John Rennie

15:12

@paracetamol it's certainly true that you cannot measure the spin without interacting with the atom, which you can't do if the atom is isolated. And it's also true that the atom can be in a superposition of spin states in which case it doesn't have a definite spin.

@paracetamol go on ...

0celouvsky

$\mathcal E^{p,q}(E)=\mathcal E_X^{p,q}\otimes_{\mathcal E_X}\mathcal E(E)$

wtf is $\mathcal E_X^{p,q}$ now

I think that should be the sheaf associated to the bundle $\mathcal E^{p,q}(X)$

paracetamol

Came across these questions on ChemLibretexts:

Are those questions even correct?

They seem super broad/ambiguous ._.

0celouvsky

@ACuriousMind ok ignore those questions

Slereah

I'm so glad sci hub exists really

I remember the olden days

I had to bother people to get me a paper

0celouvsky

Scum

John Rennie

15:20

@paracetamol It seems odd that they distinguish between $+\tfrac{1}{2}$ and $-\tfrac{1}{2}$. That doesn't make sense to me. If there are unpaired electrons there will be a net spin and it will have some value and there will be an associated angular momentum.

Slereah

plz

Back then you were still playing with your playmobiles

back in the distant time of 2007

You were just a little rosy cheeked boy

John Rennie

But it doesn't make sense to label the spin $+\tfrac{1}{2}$ or $-\tfrac{1}{2}$ because that value is always relative to some axis and you haven't defined an axis.

paracetamol

@JohnRennie AHA! So the questions are faulty!

So I should just ignore those, right?

...or is there something else to it?

^ Unlikely

0celouvsky

I never had playmobile

That was too German for me.

Bernardo Meurer

Playmobile is the shitty version of lego

0celouvsky

15:24

Correct

I got lego

paracetamol

@0celouvsky How old are you? :3

0celouvsky

10

paracetamol

^ You're too old for this -_-

Bernardo Meurer

I am changing my profile picture here

Time for a new one

ACuriousMind

@0celouvsky Wait, the Simpsons' yellow color is suspect, but LEGO people are fine?

0celouvsky

15:26

@ACuriousMind I don't think their yellow color was the issue, just the fact that the show is all around disgusting and socially unacceptable.

Bernardo Meurer

There

ACuriousMind

Aug 6 '15 at 13:38, by 0celo7

@KyleKanos One of them. The other refused to even consider a show with stupid yellow people.

John Rennie

@paracetamol I must admit I don't understand what the question is getting at. Tungsten has 4 unpaired electron's so Hund's rules suggests the spins will align giving a total spin of 2.

ACuriousMind

Okay, I see you mentioning the social unacceptability also back then already :P

0celouvsky

Good to know I'm consistent over two years.

That proves I'm not lying, no?

Slereah

15:29

Killing vector : $K$ or $\xi$

0celouvsky

K

ACuriousMind

@0celouvsky Or that you're a consistent/good liar, but I can't fathom why you'd lie about this in the first place

Bernardo Meurer

@ACuriousMind What are you getting me for my birthday?

ACuriousMind

@Slereah $v_\text{Killing}$ :P

Bernardo Meurer

It's April 30th

Slereah

15:30

@ACuriousMind hush

ACuriousMind

@BernardoMeurer I...uh...it's gonna be a surprise :P

Bernardo Meurer

@ACuriousMind You better have something nice

@0celouvsky You too

John Rennie is the only person here who's free of doing something for my birthday. He has gifted me in advance for the next two years

0celouvsky

What do I get for mine?

John Rennie

@BernardoMeurer Oh. I'll return this Ferrari to the dealer then.

Bernardo Meurer

@0celouvsky Secret

0celouvsky

15:32

Give me the car @JohnRennie

Bernardo Meurer

@JohnRennie Good, I don't have a license :P

Slereah

paracetamol

@JohnRennie Great! So, I'll be ignoring those "questions", thank you :3

Slereah

the best present

John Rennie

@BernardoMeurer in any case you may find it hard to insure a Ferrari :-)

paracetamol

15:33

:O

0celouvsky

Wtf why does no one listen to me

Down Christopher

@0celouvsky shhhh

Bernardo Meurer

@JohnRennie True that :P

paracetamol

Anyone know what happened to @0celouvsky?

Bernardo Meurer

There, new picture, woohoo

ACuriousMind

15:36

@0celouvsky what reaction to "give me the car" did you expect? :P

0celouvsky

@ACuriousMind "Yes."

ACuriousMind

Hope and expectation are two different things.

paracetamol

1

Q: Are humans the only mammals that are known to display homosexuality?

REQUEST: In this post I don't refer to, nor do I encourage reference to, any ethical/moral/emotional aspects of homosexuality. So please don't start an pro/anti- LGBT campaign in the comments section. Are mammals (other than humans) known to engage in homosexual activity of any sort? From the...

Slereah

"Our final assumption (which always holds locally) is that $S$ may be given the structure of a differentiable 3-manifold such that $\psi$ is a smooth mapping. This assumption serves to eliminate certain global situations in which a trajectory of $\xi$ passes arbitrarily near itself in $M$."

Fuuuck

0celouvsky

@ACuriousMind so now that I know what a sheaf is, what are some things you've tried to tell me that I can now understand?

ACuriousMind

15:38

I...don't have a list of those.

Slereah

The splitting of the metric for stationary metrics might not work for non-strongly causal spacetimes

ACuriousMind

And I think it was mostly stuff like the deRham theorem, sheafy versions of things you can also see by other means

Slereah

Ahah

Bernardo Meurer

@0celouvsky What are you getting me for my birthday?

Slereah

One of the reference isn't in english

Bernardo Meurer

15:39

You gotta beat Nika

0celouvsky

@ACuriousMind I don't have a good conceptual understanding of the abstract de Rham theorem

Slereah

but lucky for me, it's in French

Bernardo Meurer

She got me a signed book by Zizek

Slereah

Before the 60's there was a bunch of french GR papers really

Bernardo Meurer

Two in fact

Physics Guy

15:39

@Bernardo Meurer Happy Birthday

0celouvsky

I can see the steps in the proof

Bernardo Meurer

@PhysicsGuy It's only April 30th :P

0celouvsky

But not why it's true

Bernardo Meurer

I'm saying ahead so people can plan their amazing gifts to me

Physics Guy

@BernardoMeurer Okay.

0celouvsky

15:40

Or why it's significant

John Rennie

@0celouvsky mail me your address and I'll post it:

0celouvsky

That's a better way to put it

John Rennie

Bernardo Meurer

@JohnRennie @0celouvsky He's not even kidding

0celouvsky

@JohnRennie you can get my address from Bernardo

I'm sure you two have some secret means of communication

Bernardo Meurer

15:41

@0celouvsky I don't think I have your address, text it to me, I can send it to John

ACuriousMind

@0celouvsky Well...I guess the "significance" is realizing that once you have the machinery of sheaf cohomology and resolutions, all the different "versions" of cohomology, like singlar/cellular/simplicial/deRham are just choosing different resolutions of the constant sheaf.

0celouvsky

Ah. So the significance of the theorem is really the corollary that different acyclic resolutions give isomorphic cohomologies?

Physics Guy

Hmm...

ACuriousMind

@0celouvsky At least to me, it is. It explains the "mysterious" accident of there being so many ways to compute cohomology, since acyclic resolutions are far from unique. It's a much more satisfactory explanation to me than the individual proofs that these computations agree.

0celouvsky

I see.

Right, nonuniqueness of acyclic resolutions. Good summary.

Emilio Pisanty

15:44

@paracetamol I would say that's pretty incorrect.

I strongly disagree with this comment.

CC @JohnRennie

The 2s electron in lithium, as far as spin is concerned, is equivalent to a free spin-1/2 particle

Slereah

Ironically that french GR paper isn't available online

Emilio Pisanty

the up and down states are indeed equivalent up to a rotation but that still means that they differ by a rotation.

Fawad

Hello everyone

ACuriousMind

@Slereah Why is that ironic?

Slereah

Because I am french

0celouvsky

15:47

@ACuriousMind Sheaves lie outside of my usual interests, but I'm now glad I have a very basic understanding of them.

Slereah

You'd think I would have an easier time finding a french paper

Physics Guy

@Slereah Bonjour

Emilio Pisanty

Saying "what is the spin of the 2s electron in lithium?" is equivalent to asking "what is the orbital angular momentum of the 2p electron in boron?". It depends on the situation. If you know that the atom is in a pure quantum mechanical state, then the spin will point in some direction $\langle \psi|\hat{\mathbf S}|\psi\rangle$, which can point anywhere. (Ditto for $\langle \psi|\hat{\mathbf L}|\psi\rangle$ of boron in a pure state.)

Fawad

Can we feel air due to production of sound wave in air? Sound waves are movement of particles which transfer energy. If frequency of wave is more,then our skin can feel it? (@JohnRennie)

Slereah

I'm trying to find a proof that for a spacetime with a timelike Killing field, there's a mapping $M \to \Sigma$ with $\Sigma$ some 3-manifold

0celouvsky

15:49

@ACuriousMind I'm now going to be totally obnoxious and throw in sheaves when doing other things :D

Slereah

But apparently that's not true!

Emilio Pisanty

However, you could still have things like a mixed state

bottom line: depends on the situation.

Slereah

You need to avoid weird imprisonned curves that fill the whole spacetime

Although I'm not sure those can exist for a timelike Killing field

0celouvsky

@Slereah normal coordinates exist for hermitian vector bundles

Bernardo Meurer

@0celouvsky I'll show you my vector bundle

Slereah

15:51

wot

John Rennie

@EmilioPisanty to be fair, the comment may mean that while the magnitude of the spin is 1/2 it doesn't make sense to label it +1/2 or -1/2 until you've chosen your reference axis.

0celouvsky

@BernardoMeurer ok

I'm sure it's pretty

Bernardo Meurer

@0celouvsky It's great

Fawad

Nice profile picture @BernardoMeurer

John Rennie

@Fawad as far as your skin is concerned a sound wave just creates an oscillating pressure on the skin. In most circumstances the change of pressure is too small to be felt, though if it's a large amplitude wave it is possible to feel it.

Bernardo Meurer

15:53

@Fawad Hm? Profile what?

Slereah

"Let $\mu'$ be a smooth scalar field"

What

0celouvsky

What's the issue?

Emilio Pisanty

@JohnRennie There is no guarantee that you can find an axis where it is +1/2 or -1/2.

Bernardo Meurer

@Fawad Ah, thanks man :)

Slereah

That's an odd symbol for a scalar field

Physics Guy

15:55

Pi ist irrational (Mathe-Song)

►

LOL

Fawad

Just curious:which sound has highest amplitude?

Slereah

So anyway apparently it may not be true that if you have a timelike (or spacelike) Killing vector, $ds^2 = \langle K, K\rangle dt^2 + h_{ab} dx^a dx^b$

you also need the absence of imprisoned curves

0celouvsky

@Fawad your mom burping

Physics Guy

HAH

Balarka Sen

lol

Emilio Pisanty

15:57

@PhysicsGuy presumably you've seen this one

Finite Simple Group (of Order Two)

►

Physics Guy

@EmilioPisanty That's actually good.

0celouvsky

Algebraists are the worst

Analysts are the jocks of the math world, not nerdy enough to do something that embarrassing

Physics Guy

@Ocelouvsky That's mathematical racism

Balarka Sen

yeah the finite simple group of order two is a classic

Fawad

@PhysicsGuy that's his view.

Balarka Sen

16:02

@0celouvsky Topologists are the best

Physics Guy

@BalarkaSen That's...somehow sad.

Balarka Sen

It's cult music.

Slereah

If a spacetime is maximally symmetric, are all vector fields Killing vectors?

0celouvsky

Should I enlist if we invade Best Korea?

ACuriousMind

@Slereah Given the space of vector fields is infinite-dimensional (over the reals) and the group of isometries finite-dimensional, I'm pretty sure the answer is no.

Slereah

16:07

Hm

0celouvsky

I agree with ACM

@BalarkaSen what's a heegard floer homology in simple terms

Physics Guy

@Ocelouvsky Boring.

;)

Slereah

I'm trying to think of a Killing vector field where that would matter

but it's not easy

The only examples I can think of are space filling curves on toruses

0celouvsky

He's so nervous

Slereah

but I doubt they are from Killing fields

0

Q: Projection formalism and Killing vector fields for imprisonned curves

The projection formalism that associates to spacetimes with a timelike or spacelike everywhere the mapping $\psi : M \to S$, where $S$ is the set of all trajectories with tangents being the Killing field, is the basis on which the decomposition of metrics for Killing fields is done, ie, for a sta...

general-relativity symmetry topology

Ben Niehoff

16:11

flat space is maximally symmetric

Slereah

It is.

Ben Niehoff

can you think of vector fields in flat space that are not Killing?

0celouvsky

Slereah

Well I guess I need to find $\partial_\mu K_\nu + \partial_\nu K_\mu \neq 0$

0celouvsky

@BenNiehoff Don't you love how one of the things is bolded and the other isn't?

Ben Niehoff

16:12

@Slereah It's easy to think of things that don't solve an equation!

Balarka Sen

@0celouvsky i dunno. it's blackmagic

0celouvsky

@BalarkaSen what does it do?

Balarka Sen

It's an invariant of spin 3-manifolds I think

Gives knot invariants, 4-manifold invariants.

That's about all I know

0celouvsky

Do you know any of the big theorems?

Physics Guy

I solved the Riemann Hypothesis.

0celouvsky

16:17

impressive

Physics Guy

Or I think that I solved it.

Years ago.

0celouvsky

I don't know why they don't just compute $\zeta^{-1}$

Physics Guy

Why should they? That doesn't proof anything.

ACuriousMind

Knowing $\zeta^{-1}(0)$ wouldn't prove anything? C'mon, a little more effort with the ridiculous claims, please :P

Slereah

Obviously it is $-1/12$

Physics Guy

16:22

@ACuriousMind You're joking, right?

0celouvsky

I'm confus

Isn't the Riemann hypothesis all about the zeros?

Balarka Sen

Reimanns Hypothesis says if $\zeta^{-1}(0) = 1/2$ is the real part of some complex function then the objective reality breaks apart

Of course knowing $\zeta^{-1}$ is the whole point!!

ACuriousMind

@BalarkaSen what is this "objective reality" you're talking about? :)

@PhysicsGuy Uh...not really, no.

Physics Guy

Oh, fuck. I mixed it up with $\zeta(-1)$

Balarka Sen

@ACuriousMind The interaction of prime twins with the collective consciousness

Refer to vixra/150678 for further reference

Slereah

16:27

Which value of $\zeta$ will help me find the pirate's gold

ACuriousMind

@BalarkaSen I will not search for that in fear it is an actual thing someone claims :P

Slereah

@ACuriousMind vixra.org/abs/1602.0010

if you want a fun paper

Jaime Gallego

Ah that one's good

For laughs

Slereah

16:38

arxiv.org/pdf/1004.1016.pdf

the hell is that book

It seems interesting

you can tell he's a classy guy because he uses $\mathscr M$

DanielSank

17:02

We need a bot that removes irrelevance from posts on the main site.

Whenever it sees "My question is why X?" it replaces with "Why X?".

Whenever it sees "Any help is appreciated", it deletes the line.

"Quantum Mechanics" --> "quantum mechanics"

Slereah

Any help will remain unappreciated

ACuriousMind

@DanielSank So go write it! ;)

(only half-joking)

DanielSank

@ACuriousMind How to do?

...and is that even ok with site policy?

I guess I could write a program that does this for new posts and run it in a test mode where it logs what it would have done.

Am I allowed to make auto-edits with my own credentials?

I'll become the greatest editor of all time!

ACuriousMind

@DanielSank There are no particular rules for bots - anything a user can do, you can write a bot to do with an account. The only limitation is that the account you're running the bot on is fully liable for anything the bot does, so running such a bot on your own account is...risky.

DanielSank

right

If I were to do this I'd have it buffer intended changes and wait for my approval.

Interesting...

I wonder if that's what QMechanic does...

'cuz ain't nobody got time for the number of edits he makes.

ACuriousMind

17:08

You're also allowed to set up an account only for that bot, then the only restriction is that that account must earn the reputation to do whatever you want to do legitimately, and in particular not through your own upvotes or bounties since that'd be the forbidden variant of sockpuppetry.

G. Bergeron

How you you go about coding up such a bot?

ACuriousMind

I don't know any specifics, but I'm told SE provides documentation for its API...somewhere

G. Bergeron

Beyond canned behaviours with pattern recognition, wouldn't you need to use machine learning

ACuriousMind

The most impactful bot I'm aware of that is currently running is SmokeDetector, that detects spam posts with 99.9% accuracy and is used by the Charcoal team to automatically cast three spam or rude/abusive flags with their accounts on any spam detected. For more info, see e.g. here

Slereah

Please

Nobody has detected that I was a spambot yet

Gerold Broser

17:14

Hi all

Slereah

It's all very subtle

ACuriousMind

@Slereah The 99.9% accuracy means that only 0.01% of the things it flags are false-positives, not that it catches 99.9% of all spam :P

The large brunt of spam blocking is done by SE's own filters, anyway

Gerold Broser

I'm confused. (Ok, that happens from time to time but I usually know why. ;)

Why is there "Last seen 15 mins ago" in a user's profile when he left a comment "5 min ago"?

G. Bergeron

@Slereah One made out of flesh

@GeroldBroser Crappy APIs

Jaime Gallego

I like spam with spam

ACuriousMind

17:17

18

Q: Timestamp on question is later than Profile's Seen, must be some time traveller or ninja

What kind of ninja skills allows for a user to post a question and have the timestamp appear later than when their profile says they were sighted? How did this user post a question without being "seen"? Shouldn't any of the main actions (posting, commenting) update the last seen field in thei...

bug status-bydesign profile-page last-activity

G. Bergeron

@JaimeGallego I'm surprised it still sells

Gerold Broser

@G.Bergeron Good point.

G. Bergeron

Cubic ham, come on

I only like luncheon meats when it comes with a Kaiser broodje

@ACuriousMind By the way, how are these called in Germany?

ACuriousMind

@G.Bergeron I was just about to comment that you spelled Kaiserbrötchen wrong ;)

G. Bergeron

@ACuriousMind I only lived in the Netherlands when in Europe :p

Actually, now for me any 'g' in a germanic language is pronounced with the guttural 'r' ...

@0celouvsky Still with the sheaves?

Emilio Pisanty

17:25

@ACuriousMind bejeesus

some design decisions made in early-SO history are really off the deep end

gotta back the commenters there

@JeffAtwood - You seem to have some confusion about the meaning of the word "last". — Martin Smith Oct 6 '13 at 8:16

ACuriousMind

It's a rather baffling feature, yeah :P

0celouvsky

@G.Bergeron no

Those are just forms, with a horrible choice of font

Emilio Pisanty

@DanielSank Unlikely. There's too little time between the questions getting asked and Qmechanic fixing the tags.

actually

that's a good query

G. Bergeron

@0celouvsky Well, couldn't you have the sheaf of real-valued linear functions?

Nope

0celouvsky

What?

G. Bergeron

17:34

So maybe linear functionals on the manifold

0celouvsky

What are you talking about

G. Bergeron

I'm trying to interpret forms as some kind of sheaf

0celouvsky

They're sections of a sheaf

Abuse of terminology

G. Bergeron

OK fine

0celouvsky

Any vector bundle is a sheaf, clearly

Forms are sections of a vector bundle, hence sections of the sheaf

G. Bergeron

17:37

Yes

I was thinking of making the connection not by just having the sheaf of p-forms, but rather in the direction of vector fields being dual to functions on the manifolds and forms being dual to vector fields.

Balarka Sen

Vector fields are sections of $\bigotimes^k TM$, whereas forms are sections of $\bigwedge^k T^*M$

That's the "duality" you want, I guess.

Emilio Pisanty

@DanielSank Upon closer inspection, Qmechanic isn't actually that fast

Fastest edits

Qmechanic's fastest is #66

fully three times slower than the record, at 45 seconds from post to edit

0celouvsky

I'm #9???

Emilio Pisanty

so it seems

and a body edit at that

admittedly an easy one though

$$I= \sum_{i=0}^n |i><i| $$

, really does look jarring, dunnit?

G. Bergeron

:( I don't have mathjax at work

0

Q: Can force change the mass of an object?

I have a difficulty in understanding this 'mass never changes'. Say, i punch/hit a ball until it deflates, or bursting a balloon with a needle - doesn't the mass of the ball/balloon change? the air already diffuses out from the ball. Please explain it to me. Thank you.

forces mass

How do you answer that?

Physics Meta

18:25

0

Q: Asking questions in another language than English

I will start by referring to a question on MSE (Math Stack Exchange) (this) and an answer on Physics Stack Exchange Meta (this). Let me cite the questioner on MSE: Imagine I want to ask an extremely precise question with a lot shades in one of all possible subjects on Stack Exchange but I am ...

feature-request questions language

AccidentalFourierTransform

chat ded

Emilio Pisanty

@AccidentalFourierTransform chat revive

AccidentalFourierTransform

yay

ACuriousMind

18:56

chat status critical

Loong

11 hours ago, by John Rennie

The backup on one of my servers failed last night with the error message "irgendwas grausames ist passiert".

Emilio Pisanty

19:09

Fun fact: there are children coding nowadays that were born after StackOverflow started

Mostafa

Have you guys ever encountered one-sided surfaces when calculating surface integrals?

How do you deal with that?

World Walker

hello everyone

Mostafa

2

Swapnil Das

Hi all.

Emilio Pisanty

@Mostafa in what context

if it's the flux across that surface, it doesn't really make much sense

Mostafa

19:22

@EmilioPisanty in genral, as the above text says.

(Arfken's mathematical methods for physicists)

Emilio Pisanty

@Mostafa see, that's the thing

why does the orientation matter?

if it's the integral of a scalar over the surface, it's not a problem

orientability is only a problem if you need to define a surface normal and that only happens if you care about $\int_S \mathbf f \cdot\mathrm d\mathbf S$

Swapnil Das

@Mostafa I'm curious to know, sir. Is your DP the pic of Neumann?

Emilio Pisanty

and that one will never come up because you cannot define $\mathrm d\mathbf S$ to begin with

Secret

Found art pushed to a whole new level

and no, I will NOT be interested to buy them, despite it makes me think

Mostafa

@EmilioPisanty yes but what if you want to just calculate one (vector integral) on a Mobius strip out of curiuosity?

@SwapnilDas Yeah :)

Emilio Pisanty

19:28

@Mostafa You can calculate whatever you can define.

Mostafa

OK thanks.

@EmilioPisanty Have you heard about photonic topological insulators?

@AccidentalFourierTransform I tried to bring it back to life but Emilio took that surface integral thing too seriously ;)

AccidentalFourierTransform

yeah, he tends to

¯\_(ツ)_/¯

0celouvsky

@BalarkaSen probably a stupid question, but are there any more complex manifolds of C dimension 1 than the line and the sphere?

@ACuriousMind

AccidentalFourierTransform

does a complex $S^1$ make any sense?

ACuriousMind

@0celouvsky What do you think a Riemann surface is?

Also, what kind of complex manifold is "the line"?

0celouvsky

19:39

@ACuriousMind never heard of it

@ACuriousMind C

@ACuriousMind so Riemann surfaces are complex manifolds?

How does one prove that

No answer?

On a level from 1 to 10, how stupid am I right now

AccidentalFourierTransform

$i$

Mostafa

@0celouvsky Prove what?

No answer?

0celouvsky

19:55

idk

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