The h Bar

0celo7

7:19 PM

@Blue circle of life.

Anonymous

@0celo7 huh?

Anonymous

Yeah, sort of

0celo7

@Blue it’s the circle of life

Anonymous

Just that it's not a perfect "circle" ;)

Anonymous

Just closed curves

Anonymous

7:21 PM

And we're at the moment stuck on why it is closed

Anonymous

And how to derive that from the equation

0celo7

@Blue it’s homotopic to one

Biology is really only up to homotopy

Anonymous

♦ $Mathematics$ the no-normie zone

no normies allowed

Anonymous

In case you can give any advice on how to proceed ^

0celo7

@Blue You blocked me on there. How rude.

What the hell have I ever done to you?

Anonymous

7:24 PM

What?

Anonymous

I never did that

Anonymous

Wait

Anonymous

I'm removing gallery mode

Balarka Sen

dont

let me add 0celo7 to access

if you remove gallery it's going to be spammed by other people

Anonymous

Okay

vzn

7:36 PM

Physicists design $100 handheld muon detector / MIT News

peterh

@vzn Wow! Another useful thing would be, a $100 muon generator.

Cows

hello . .

CooperCape

@vzn I'd make one but plastic scintillators are harder to get hold of than the inverse of a 50x50 matrix.

I tried looking but to no avail :c

0celo7

@ACuriousMind Schoen and Yau write O(n+1,1) for the coformal group of the sphere. Why n+1? Do I need to get BBS out from under my PC?

Phase

7:53 PM

@0celo7 @BalarkaSen did you ever play the Old Sonic games?

Sir Cumference

@RoryAlsop are you guys really like this or acting? how can you guys be so rude. I wish you be near death and something like this happens with your rescuer, only then will you understand cruel human. — Ram Keswani 2 hours ago

Jesus

Balarka Sen

@Phase Yep

0celo7

I did

I bet that guy is Indian

Phase

Do you guys remember these bonus stages

0celo7

@BalarkaSen what’s the domain of discontinuity of a group action?

Phase

7:55 PM

@0celo7 @BalarkaSen You may be interested to know [if you didn't already] that it's actually a Torus

CooperCape

@Phase coughs I think you mean a mug... coughs

Phase

@CooperCape you shut your mowf

Balarka Sen

No wonder; they're identifying opposite sides of the square

enumaris

square or rectangle

mmmm

deep

Balarka Sen

@0celo7 Not sure. Maybe it has something to do with discontinuous group actions

CooperCape

7:57 PM

@Phase Aww but how am I supposed to drink my tea from my torus if I have to shut my mowf... :c

Balarka Sen

$G$ acts properly discontinuously if the $G$-translates of $K$ hits $K$ back finitely many times

for any compact $K$

Phase

@BalarkaSen That's not maths and you can't convince me otherwise

I shall firmly place my hands on my ears and enjoy baby maths

0celo7

@BalarkaSen yeah because I’m interested in the quotient being a fold

But the statement just doesn’t make sense. Maybe the proof will explain

Phase

@SirCumference holy shit I wasn't surprised at all until I saw the user has 1k rep

Sir Cumference

@Phase He got all his rep from a single question.

Phase

8:04 PM

sidenote ever since I deleted my account I'm scared to ask questions or answers

I went from 500 rep to 100, and now I have 101. If I get downvoted, will I lose chat and meta privileges?

0celo7

Your account doesn’t exist

Wtf are you

Phase

Stuck between two realms

But nah it's just the chat link

My profile still exists

Sir Cumference

@Phase Why do you have two SE accounts?

Phase

I dont

brb

0celo7

Haha 106 on Christianity

Phase

8:10 PM

Ikr its my highest rep now

Sir Cumference

Wait so why doesn't the chat link work?

Phase

Because afaik it sort of establishes the link in the tile when you first join the chat, and doesn't change

when I deleted my account it probably changed the link in some way

perhaps the number before the name

Sir Cumference

You know, I have to wonder

Was this question on the hot network or something?

-28

Q: Do we need Maxwell's Equations since they fail to account for an experimental fact at least in one occasion?

This question is an outgrowth of What is the difference between electric potential, potential difference (PD), voltage and electromotive force (EMF)? , where @sb1 mentioned Faraday's law. However, Faraday's law as part of Maxwell's equations cannot account for the voltage measured between the rim...

If so the algorithm is worse than I thought

Phase

Maxwell isn't the fraud

Einstein is

gravity is electromagnetism $_{research\space flat\space earth}$

Mithrandir24601

8:25 PM

Kaluza–Klein theory

In physics, Kaluza–Klein theory (KK theory) is a unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time. It is considered to be an important precursor to string theory. The five-dimensional theory was developed in three steps. The original hypothesis came from Theodor Kaluza, who sent his results to Einstein in 1919, and published them in 1921. Kaluza's theory was a purely classical extension of general relativity to five dimensions. The five-dimensional metric has 15 components. Ten components are identified with...

Phase

@Mithrandir24601 I see you are also Woke

CooperCape

I've read about kaluza klein in like 2 popsci books and tbh all I remember is there's a guy called George or something and there's a dimension like a hosepipe

Phase

@CooperCape have you diagonalised two commuting matrices yet?

CooperCape

Can't say I have? Just staying casual

Phase

youve diagonalised one tho right?

CooperCape

8:29 PM

Though I did spend an hour trying to diagonalize a matrix today with 'generalized soemthing eigenvectors' that wolfram popped out only to realise that you can't

I've diagonalized a few matrices, yes... Mostly 2x2s cause 3x3s are soooo much effort omg

Mithrandir24601

@Phase I never said I agree with it ;) (How could I, having never even looked at it), but I have to admit, I've spent the last month wondering how CPT reversal symmetry makes fundamental sense - PT reversal is essentially a reversal of the metric, so how does charge fit into this??

Phase

@CooperCape 3x3's shouldn't be much harder than 2x2's

Get the characteristic equation and solve it and you've done all the real work

CooperCape

@Phase Yeah they're not but like bro inversing them is death

I swear to god I failed 7 times in a row...

Phase

just compute the eigenvectors

CooperCape

Uh huh...

Phase

8:33 PM

Ok say that you have an n x n matrix

It's only diagonalisable if it has n eigenvectors, not necessarily distinct. You can make a matrix $M$ such that it's nonsingular, out of the eigenvectors

CooperCape

I'm sure you do.

Phase

then sandwich the original matrix between the inverse of M and M

enumaris

yo

just use a linear algebra package to do it

CooperCape

Yeah... that's what I've been trying to do. Because I saw a q that said find

enumaris

like LAPACK on fortran or numpy on Python or Octave or w/e

CooperCape

8:35 PM

$$\begin{pmatrix}1&1&1\\0&1&1\\0&0&1\end{pmatrix}^n$$

So I was like "let's diagonalize this bad boi" but it only had 1 eigenvector

Phase

From first glance it seems nonsingular

oh

CooperCape

Then balarka started talking about Jordan norms earlier and I was like 'oh shit boi that's ma name' but those looked hard so I moved on.

Phase

You can have only 1 eigenvector

CooperCape

How can you have an eigenbasis from that though?

Phase

*1 eigenvalue

my brain wasn't thinking straight

good night

8:37 PM

@Phase it's alright this is a positive space

CooperCape

I mean I remember writing down $\lambda_{1,2,3}=1$ somewhere...

Anonymous

@CooperCape I linked a nice video on Jordan normal form few days back. Did you watch it?

Anonymous

With the super excited teacher :P

CooperCape

@Blue Whaaa for real? I can't say I did... :o Have you still got it or shall I go link hunting?

Mmmm I remember seeing that

Anonymous

Wait..checking

Phase

8:40 PM

Its just not diagonalisable

CooperCape

Just that I was like "way in too deep for me"

Anonymous

Jordan Canonical Form

►

Anonymous

lol

Phase

By any way I know at least, since a condition for diagonalising is that there are n independent eigenvectors

CooperCape

@Phase It was a sad conclusion I came to... :c Any ideas on finding it's nth term other than spotting a pattern in $A^2,A^3,A^4$ etc.

@Phase Yeah that makes sense now because to have a basis it's gotta have the same vectors as the dimension thingy

Anonymous

8:41 PM

@Phase Minimal polynomial having simple (non-repeated) roots is necessary and sufficient though

CooperCape

@Blue I'll give it a watch thanks :p

He does seem excited tho

Phase

I would love this guy as a lecturer

He's so enthusiastic

CooperCape

Well I just found my canonical form

take that suckers

ACuriousMind

@SirCumference Literally, a "collection of works", without further context I can't be more helpful

@0celo7 Well...the global onformal transformations in d dimensions are the Lorentz transformations in two dimensions more. Look at how ordinary Lorentz transformations map to Möbius transformations - the global conformal transformations in 2 dimensions - for motivation

Balarka Sen

9:04 PM

@ACuriousMind This is for you: youtube.com/watch?v=hopeFgwApCM

Phase

@0celo7 recommend a game

atm Im contemplating AC black flag purely because its like 5 quideronis

Balarka Sen

Please watch it. That man's a legend

Mohammad Areeb Siddiqui

why is this group named the h bar?

Phase

Because it's a pun

Mohammad Areeb Siddiqui

whats h

Phase

9:05 PM

$h$ is a fundamental constant, and often $\bar h$ is more useful as it's $\frac{h}{2\pi}$

Hm how do I write an h bar properly in latex.

Mohammad Areeb Siddiqui

latex works on chat? :O

its just syntax on my screen

Phase

Yeah, look at the top right

Install the Bookmarklet

ACuriousMind

@Phase \hbar:P

CooperCape

personally I've gone with chrome extension SE chat mathjax

Phase

@ACuriousMind ....

That's what I get for trying

Mohammad Areeb Siddiqui

9:09 PM

$\hbar\$

maybe need to refresh

CooperCape

@Phase Being a humble highschooler I've only ever really seen $\hbar$ in $E=\omega\hbar$ and Heisenbergs ting... what is it used for...

Phase

@BalarkaSen this is his best [trigger warning cus he talks about questionable content]

CooperCape

(Not that I know Heisenbergs ting other than the equation)

Mohammad Areeb Siddiqui

yay it works

Balarka Sen

yeah i have seen that

Phase

9:10 PM

@CooperCape $E = \hbar \omega$ and $T = \frac{p^2}{2m}$ with p being defined with the debroigle relation is all you need to.. 'derive' the Schrodinger equation

CooperCape

Yeah I derive the schrodinger equation like everyday tell me something new smh

Phase

I hesitate to say "derive" strictly, since it feels like cheating, and you start with a plane wave solution, but it's neat at least

Smh

CooperCape

(jk.. thanks tho... :p)

'cheating qm'

Phase

It feels like it

CooperCape

uh huh...

Right

Phase

9:12 PM

You start with $u(x,t) = e^{i(x - ct)}$

see if you can get the rest

CooperCape

Mmm u wot mate

Phase

Ok I'll give you a bit more

Mohammad Areeb Siddiqui

what's going on with the finding out the shape of orbit in this pdf: madscitech.org/tm/slns/l5e2.pdf

CooperCape

I'll leave it until like uni qm... yano

when I find out what stuff means

And I can do mafs

Phase

$x - ct = kx - \omega t$, by debroigle relation

It's all just simple differentiation

CooperCape

9:13 PM

Okay...

Right sure

Phase

Just see if you can think of ways to get the expressions i wrote above out of the formula

CooperCape

Doesn't schroeys have partial diffs?

Phase

Yeah but if it's 1 dimensional it's not something you really need to worry about

CooperCape

so what am I getting from where?

Phase

The expressions I wrote above for Energy [total] and T, the kinetic energy

CooperCape

9:14 PM

Okay

Phase

and then just sandwich a $Vu$ on the end when you're done : P since you need a potential as its Total = Kinetic + potential

CooperCape

Okay... be back in like 2 years

;p

Phase

It's really quite cheaty but I thought it was neat the first time I did it : p

You're overestimating the problem and underestimating yourself

CooperCape

Classic coopeycapey

Phase

Just see how you can differentiate $u(x,t)$ and get out constants you can plug in the planck and debroigle relation

CooperCape

9:16 PM

Okay right

Phase

tip, your definitions for the E and T will include a derivative of $u(x,t)$

CooperCape

Okay. Oh my goodness

Phase

and the equation is no higher than order 2 [$\frac{d^2}{d(some\space variable)^2}$]

CooperCape

okay

right

let's do this

Phase

Idk if you've seen it written that way before but $k = \frac{2\pi}{\lambda}$, so $p = \hbar k$

CooperCape

9:20 PM

yeah I had that down

Phase

Noice

CooperCape

Well not p=hk but k=2pi/lambda

I'm not sure where I'm going with this aha

vzn

@Phase sounds "not entirely off" to me. what is "tenuous" about it? whered you get the quote?

Phase

You'll need the debroigleboi

@vzn a creationist fb page

: P...

CooperCape

okay so we have p=h/lambad

Phase

9:22 PM

llambadda : P

Keep it as hbar k

vzn

@Phase lol ok you got me but frankly, top physicists have said similar things.

Phase

It's just easier here

CooperCape

Okay suure

Phase

@vzn anyone can be loopy, wasn't there a famous physicist who went around praising oranges and vitamin C as a cureall?

Balarka Sen

just because top physicists have said that doesn't make it any less corny

Phase

9:23 PM

@vzn it appears to be a chemist en.wikipedia.org/wiki/…

vzn

@Phase the basic ideas are not off. this reminds me of a zen koan about credibility.

Phase

How are you supposed to pronounce DeBroigle btw

"Dee-Broy"?

"Dee-Broh-lee-ay"?

CooperCape

de broy or seomthing

no le

Balarka Sen

debruh

Phase

de bruh look at the top of his diffraction pattern [wheeze]

ACuriousMind

9:27 PM

@BalarkaSen It's a silly situation where of course modern physics doesn't adhere to materialism in its naive infancy - to say physics is not materialist in the naive sense is both completely uncontroversial and completely true. Of course, that's not actually what people using such quotes want to argue for.

Phase

@ACuriousMind "consciousness affects matter and so we create the universe"

Is the usual argument

damn Neumann

vzn

@Phase googling the quote, couldnt find it, but did turn up this blogs.scientificamerican.com/cross-check/…

Phase

@vzn it was a creationist fb page : p

vzn

@Phase right. similar sentiments elsewhere from erudite philosopher(s) etc

Balarka Sen

@ACuriousMind I don't understand what it means to say "physics is not materialist". That people do not study physics out of the fundamental desire to understand matter and the desire to possess and consume it? Sure! The quote seems arguing that scientific (or, more specifically, physical?) progress is a massive argument against materialism. That's just pretentious garbage, IMO.

CooperCape

9:32 PM

Okay @Phase so..

$T$ goes into $T=\frac{\hbar^2k^2}{2m}$

right

Phase

@CooperCape You got somethin?

ACuriousMind

@BalarkaSen No, this is about materialism as an ontology - that all "things" are made of the same "fundamental stuff" (=material).

Balarka Sen

In no way does scientific progress affect the mass notion about material and the abstract interactions of material which is more or less the base of the human civillization in postmodern times

Phase

@CooperCape Yup!

CooperCape

and $u(x,t)$ can go into $u(x,t)=e^{\frac{iEt}{\hbar}$

Phase

9:34 PM

Yeah but thas ugly af

CooperCape

Which is $u(x,t)=e^{i\omega t}$

right?

Phase

wait what am I saying

CooperCape

idk

Phase

Your statements are wrong but not too badly

You're missing the x parts

ACuriousMind

@BalarkaSen I understand that your Soviet philosophy training leads you to think of materialism as an ideology, but it has a much older and traditional meaning as an ontological viewpoint :P

CooperCape

9:34 PM

okay...

so ummm

Phase

Define an operator $\hat T$ so that $\hat T u = T u$ like an eigenvalue equation

take that approach for all of em

CooperCape

Okay right...

Lemme get back to you on this

I gotta go now

Balarka Sen

@ACuriousMind Ah, I see, yes, I was indeed thinking about ideological materialism.

CooperCape

I'll think on it

Phase

But your $u(x,t)$ has both x dependent and t dependent

CooperCape

9:35 PM

: p

Phase

@CooperCape I'll write what to do

CooperCape

I promise

Phase

I feel like maybe I explained it poorly

Balarka Sen

I must say I do not have any intelligent comments to make on ontological materialism.

It's not something I think about

Phase

$\hat T u = \frac{-h^2}{2m} \frac{d^2}{dx^2}u$

Balarka Sen

9:36 PM

Sorry for the confusion.

Phase

as k^2 comes out of d2/dx2 u

and the minus sign cleans it up and keeps it positive

ACuriousMind

@BalarkaSen But indeed, the abuse of such quotes is of course intended to generate such confusion - the critic wants to equivocate the ontological claim with the ideological claim in order to "defeat" ideological materialism with the power of science :P

Balarka Sen

Hahaha, quite true

CooperCape

@Phase okay thanks... lemme get back to this in 30 mins ~~

Phase

For the total energy E, you want to use E = hbar w, so you differentiate w.r.t time and get $i\omega u$, and use that to write $\hat E u = i\hbar \frac{d}{dt}u$

Ok dude have fun

Balarka Sen

9:38 PM

That's why I was initially a little irritated at the quote.

CooperCape

Just having parent time cause haven't seen them since like 7 am yano

(Still living at home problems ;p)

Phase

Fair dude, enjoy it while you can

ACuriousMind

This is a recurring problem: There are two things denoted by the same name, and arguing for one meaning is completely uncontroversial, while the other is. So a common tactic is to establish the claim for the uncontroversial meaning, and then sneakily change the definition in order to establish the controversial claim you actually cannot defend

Phase

Parents may be annoying but its nice to live with people who [hopefully] have your best interests at heart

@ACuriousMind coughs feminism

Balarka Sen

@ACuriousMind Truly.

This kind of debate is mostly propagated by people who read actual thesis on neither of the things sharing the same terminology, and copy-paste quotes from other people to establish some silly argument

Unfortunately, the internet is populated by such people

ACuriousMind

9:42 PM

@Phase It occurs in most debates that involve the notions of equality and fairness, no need to single any particular use out :P

Phase

@ACuriousMind COUGH FEHMUHNISHUM

We are equal in the Cloud

ACuriousMind

@BalarkaSen Yeah, humans like to put neat little labels on things, and end up labeling wildly different things with the same label :P

Balarka Sen

Very true.

I still don't know what torsion of a Levi-Civita connection has to do with traditional meanings of torsion. Even the Frenet-Serret notion of torsion.

ACuriousMind

And it's often really hard to detect that that's happening - like you said "it's nonsense to say physics is/isn't materialist", and this wasn't even an emotionally charged debate. When it gets to the stuff people really care about, you'll sometimes not get the chance to clear up the confusion until it's too late.

enumaris

isn't the levi-civita connection defined as torsion free

ACuriousMind

9:48 PM

@BalarkaSen What are "traditional notions of torsions"?

Balarka Sen

@enumaris Thanks, I mean torsion of a connection.

ACuriousMind

Also, what @enumaris said :P

Balarka Sen

@ACuriousMind Yeah. Actually I myself am prone to such follies for certain notions that I believe in.

I try to work on it and listen to other people

Secret

> you'll sometimes not get the chance to clear up the confusion until it's too late.

Balarka Sen

@ACuriousMind Torsion as in mechanics, for example

enumaris

9:51 PM

hmm

Secret

Real life works better for these cases, since it gives no downtime for the person's own belief to become defensive and wall themselves off from other views

enumaris

I can't find rhyme or reason why torsion was brought up in this chat

lol

ACuriousMind

@BalarkaSen I actually have no idea what torsion in mechanics is :D

Secret

Both notions of torsions are distinct concepts. One describe the "act of making things rotate", the other is more about how many times you multiply something to get the identity

Balarka Sen

Oh, it's a thing which measures how much an object twists under application of a torque

I guess it's a bulk mechanics thing

You people hate bulk mechanics don't you

Secret

9:54 PM

oops I confused torque with torsion (mechanics)

ACuriousMind

@BalarkaSen Ah, I never cared for that, yeah

Secret

In that case, yes, as balarka said, torsion characterise the amount of twisting

ACuriousMind

Who am I to care about bulk mechanics, an engineer? :P

Balarka Sen

lol

good night

inb4 bulk mechanics

Balarka Sen

9:56 PM

But yeah I don't see a connection with torsion as in curve geometry, either. Torsion of a curve measures how far it is from being flat (contained in a plane in R^3)

Which is kinda ironic, because torsion of a module measures how far it is from being flat too ;)

I do believe that's a coincidence

Mithrandir24601

@DanielSank I do believe you might be interested in this:

FISRT TIME ON CAMERA: Octopus disguises itself in shell suit - Blue Planet II: Episode 5 - BBC One

►

Secret

So in summary, there are 4 notions of torsion:
1. Mechanics: The twist introduced when an object is under a torque
2. Algebra: Number of times an element multiply to itself to give the identity
3. Differential geometry: The deviation of a curve from a plane
4. General relativity and tensors: Measure how much a frame is being twisted.

Balarka Sen

I do believe that our simultaneous use of "I do believe" is a coincidence

good night

@Mithrandir24601 not available in my country

Secret

All of these, in an abstract sense, involves the idea of "deviating from something flat" and "wound around something"

0celo7

9:58 PM

That was pretty cool I have to admit. I’m not a big enough contrarian to hate on it

Balarka Sen

What was?

Mithrandir24601