The h Bar

@IceLord : you don't need math to know that Maxwell unified electricity and magnetism. And that as Jackson said, "one should properly speak of the electromagnetic field Fμv rather than E or B separately".

Slereah

Not the first fellow to throw around using hyperreals to do renormalization but I don't think anybody ever really did much with it

ACuriousMind

8:22 PM

@Slereah Tell me when you've found the unsurmountable difficulty that's the reason why no one ever did much with it ;)

Slereah

Not so far!

I'm sure I will

It's always something

John Duffield

@IceLord : so what sort of field has the electron got?

Slereah

Hopefully the difficulty was just "It wasn't that interesting"

Physics Meta

3

Q: 2016 Moderator Election Q&A - Questionnaire

In connection with the moderator elections, we are holding a Q&A thread for the candidates. Questions collected from an earlier thread have been compiled into this one, which shall now serve as the space for the candidates to provide their answers. Not every question was compiled - as noted, we o...

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Q: 2016 Community Moderator Election

The 2016 Community Moderator Election is now underway! Community moderator elections have three phases: Nomination phase Primary phase Election phase Most elections take between two and three weeks, but this depends on how many candidates there are. Please visit the official election page a...

discussion moderators election

Slereah

If it was just useless I can still get a paper out of it

Sir Cumference

8:24 PM

Can anyone here answer an orbital mechanics question?

Slereah

There's plenty of theories that are perfectly fine but just not terribly useful concepts

Still good to write a paper

ACuriousMind

@SirCumference Just ask it, if someone wants to answer it, they will.

Sir Cumference

@ACuriousMind All righty then

In binary systems, under what conditions will $m_1a_1 = m_2a_2$?

Crap

ACuriousMind

Always define notation you're using.

Slereah

Sir Cumference

8:26 PM

What are you talking about?

Slereah

This is not very enlightening

ACuriousMind

@SirCumference I.e. tell people what the $a_i$ and $m_i$ are, even if they could guess.

user218912

@ACuriousMind do you take notes on a tablet?

ACuriousMind

@Slereah lol, wtf is that?

@IceLord yes

Sir Cumference

@ACuriousMind Crap, yes

Slereah

8:27 PM

Apparently it's a mapping of the order of p-adic numbers

Sir Cumference

a = semimajor axis of orbit, m = mass of star

user218912

@ACuriousMind can I ask what tablet you use?

user218912

and why you prefer it over paper.

Slereah

"Distribution of natural numbers by their 2-adic order, labeled with corresponding powers of two in decimal. Zero always has an infinite order"

ACuriousMind

@IceLord I use/have used various iterations of the Samsung tablets "with S pen".

John Duffield

8:28 PM

OK chaps, let's have your nominations please.

Slereah

Except it's not labeled or anything

Sir Cumference

Sigh, no one here knows orbital mechanics?

John Duffield

I don't.

user218912

@SirCumference use google or learn to read books.

Sir Cumference

@IceLord Google returns nothing, my textbook mentions nothing

user218912

8:29 PM

@SirCumference use books.google.com

user218912

and search the key words.

Sir Cumference

@IceLord First I need to find the right book

ACuriousMind

@IceLord I prefer it because I'm terrible at keeping any semblance of order once I have a lot of notes on paper, and because I often want to share my notes with someone, or access them when I'm not at home. It'd be a hassle to scan them all manually, but directly uploading them to my dropbox makes for easy, organized access.

user218912

@ACuriousMind cool, I may make the switch soon.

user218912

@SirCumference it will give you a list of books with those terms in it.

ACuriousMind

8:31 PM

One problem is that I got used to being able to erase mistakes very quickly. A bit ago, my tablet broke and I had to write on paper again for a while - and I kept trying to make the gesture for "erase" when I had written something wrong.

Sir Cumference

@IceLord Regardless, it's easier to clear things up if I can speak to an actual person about the question

user218912

@ACuriousMind lol xD

Slereah

Another graph for the p-adic norm, I think???

Why are none of them even labeled

Sir Cumference

Well, uh, anyone know about binaries?

Slereah

what is even the norm for hyperreal numbers

Hyperreal are a bit hard to research because there's a lot of plebs talking about them

Secret

8:41 PM

Last night dream is a time travel dream (nope, not CTCs not branching timelines) which interested folks are referred to the blog instead as it is quite long.

The non time travel theme in the dream revolves around ACM telling us to use small angle appproximation to the following Fourier series $$\sum_{n=1}^{\infty}-sin(n\theta)$$ therefore it becomes $$\sum_{n=1}^{\infty}-n\theta$$

HDE 226868

3

A: Semi-major axis and ellipticity of a binary system?

Why is Equation 1 true? Equation 1 stems from the definition of the reduced mass system. The reduced mass system is an accelerating frame of reference for a binary star system in which the heavier star is seen as having no acceleration. However, the physical orbital properties of the reduced...

Sir Cumference

@HDE226868 All right, that raises two more questions. In a binary, are the eccentricities of both orbits always the same?

Secret

I kinda have some idea on where the second bit came from. It is likely due to the the $r\sin \theta \sim r\theta$ remark of yesterday (which is quickly deleted as it is inapplicable for circular motion), which for some reason stuck in the mind without me explicitly awaring. One possibility is that I must be shocked enough as I probably might have seen a similar substitution in the past before when I did some phys\ics probelms, and wonder why I tend to forget these basic things

HDE 226868

@SirCumference Yes.

Sir Cumference

@HDE226868 So they have the same shape, but one is rotated 180° and is scaled?

HDE 226868

8:46 PM

@SirCumference Yes.

Sir Cumference

And lastly, will both stars always reach their apsides at the same time?

Slereah

Man Toka doesn't even include hyperreal at all

0celo7

I'll be apside yo momma

Slereah

Are hyperreal even used that much in math?

HDE 226868

@SirCumference Yes.

Secret

8:47 PM

@Slereah what is $u$, and how do we get a notion of distance betwen points based on the graph. (I am suspecting the limiting line looking thing of this fractal structure is the real number line?)

Sir Cumference

@HDE226868 All right, thanks

0celo7

@Slereah never heard of them.

Slereah

IIRC all extensions of R of the same cardinality are isomorphic, so I guess it doesn't matter too much what I use

0celo7

@Slereah never heard of them.

Slereah

Yeah they don't pop up too much

Mostly in non-standard analysis

0celo7

8:54 PM

Why does anyone need that?

Slereah

why does anyone need math

Non-standard analysis has a more difficult construction than standard analysis but it is easier to prove things in it

Secret

Dedekind cut?

0celo7

@Slereah tbh you sound like a crackpot nowadays

Slereah

Tough talk from someone who doesn't know physics

0celo7

you wanna fight?

Obliv

8:59 PM

If I were to reparametrize $\cos (t) i + \sin (t) j + tk$ with respect to its arc length from $(1,0,0)$ in the direction of increasing $t$, I would start by setting up: $s(t) = \int_0^t \sqrt{(\frac{d(\cos (t))}{dt})^2 + (\frac{d(\sin (t))}{dt})^2 + (\frac{d(t)}{dt})^2} dt$ then what

solve for t but how

Slereah

Big whoop wanna fight about it?

0celo7

@Obliv What class is this for?

Slereah

If it was a crackpot theory it would be a pretty boring one

Obliv

@0celo7 only math class i'm taking this semester. could ya guess

Slereah

It's just another run of the mill QFT axiomatization

No new theorem or anything

Just another renormalization scheme

Obliv

9:01 PM

oh i'm silly. I take the derivative w.r.t t

become $\frac{ds}{dt} = |-\sin (t)i + \cos (t)j + k|$

0celo7

good lord

Secret

6 mins ago, by Secret

0celo7

use proper vector notation

Secret

yuggib might knew the details of this since he has knowledge on p-adic and nonstandard analysis. I will postpone this for now as I dig through topology first

0celo7

I can never remember what $ijk$ means

@Obliv do the integral

Slereah

9:04 PM

Basis vectors

Sir Cumference

Howdy

Obliv

What would you use, $|-\sin (t)\vec{x} + \cos (t)\vec{y} + \vec{z}|$?@0celo7

0celo7

@Obliv a vector is $(x,y,z)$

ordered tuples

Slereah

$\vec e_x$ is my prefered way

0celo7

@Slereah $\partial_x$, you mean.

Slereah

9:04 PM

$\vec \partial x$ also works

Obliv

@slereah what is the e?

Slereah

Basis element

Obliv

also @0celo7 a lot of what I've seen suggest that it's angled brackets so not to confuse with points.

0celo7

@Obliv It's always clear from context

and points are vectors.

it's a vector space

to do arc length parametrization explicitly don't you have to compute the arc length?

Obliv

WAIT

0celo7

9:06 PM

lol

Obliv

no I remember $\vec{0}$

crap.

0celo7

@Obliv go home you're drunk

what you mean is that points are not tangent vectors

which is true

(maybe)

Slereah

In a vector space you can mostly ignore the space/tangent space distinction

0celo7

But $T_0\Bbb R^n\cong\Bbb R^n$ canonically, so that's not true either

@Slereah Proof?

Slereah

It's not a theorem, just

It is tolerable

Secret

9:08 PM

@Slereah Not for curved manifolds?

0celo7

No, it's true that $TV=V\times V$ canonically.

Slereah

Curved manifolds are not vector spaces

Only $R^n$ is

and similar spaces

0celo7

Similar spaces?

Slereah

$C^n$ and such

Secret

but if they are riemaninian manifolds, you can always find a tangent space to every point, this is different from the space itself?

Slereah

9:09 PM

yes

0celo7

@Slereah that's $\Bbb R^{2n}$

Slereah

Hence the "similar"

Also it is not $R^{2n}$

Only isomorphic to it

0celo7

@Secret Tangent space has nothing to do with Riemannian.

@Slereah Isomorphic $\cong$ equal.

Slereah

But $\cong \neq =$

0celo7

Proof?

What does $=$ mean?

Slereah

9:13 PM

$A = B \equiv \forall a \in A, a \in B \wedge \forall b \in B, b \in A$

Equality is a bit stronger than isomorphism in set theory

0celo7

PhD set theory is too advanced

Slereah

I wonder how equality is defined in category theory

Obliv

@0celo7 would $x(t) = x^2$ be considered a smooth curve? It has a point where $x'(t) = 0$ so I think no

on the interval $[-3,3]$

0celo7

What's your definition of smooth curve

what does $x(t)=x^2$ even mean

Slereah

$x = x^2$ is the constant function :p

Obliv

9:19 PM

does it matter what I put before the (t)

fine, $r(t) = x^2$

Slereah

But it's a function of $t$

Where is $t$

Obliv

it's just a parameter

this is in $\mathbb{R}^3$

Slereah

Well yes but it is supposed to be in the rhs

Obliv

wait..

yeah that's a mistake :D

$x(t) = t^2$

Secret

Found the original paper of that image, Looks like I do need topology to make sense of it. Better get back reading...

Physics Meta

9:21 PM

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Q: Can anyone run for moderator?

Ideally you want your leader to be the most educated and stable person in that field, but sometimes its popularity and campaigning. I want to be a moderator. What do I have to do?

discussion moderators election voting

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Is there a list of rules for people campaigning for moderator?

discussion support moderators election

0celo7

so what are y and z

Obliv

Okay.. let me rephrase. is $y(x) = x^2$ a smooth curve in $\mathbb{R}^3$

0celo7

undefined question

Obliv

on the interval $[-3,3]$

0celo7

what's the parametrization

Slereah

9:23 PM

yes

Obliv

$y(x)$

Slereah

of course

Obliv

is the parametrization

0celo7

@Slereah NO.

Slereah

All polynomials are smooth

0celo7

9:23 PM

@Obliv where is the $t$?

Obliv

U DONT NEED IT

0celo7

@Slereah Smooth function != smooth curve.

@Obliv What?

Slereah

What's a smooth curve that isn't a smooth function

0celo7

What's the damn definition?

Slereah

or vice versa

Obliv

9:24 PM

its parameter is one of its components

doesn't that work

0celo7

@Obliv That doesn't define the curve

@Slereah There are definitely $C^1$ curves that can be smoothly reparametrized.

Obliv

No wait that doesn't make sense. $r(t) = t^2\vec{e}_x + t\vec{e_y}$

0celo7

The "curve" refers to the map $c:[a,b]\to\Bbb R^3$, $t\mapsto c(t)$

Not the image of the curve.

Obliv

That makes sense, right?

0celo7

$y=x^2$ is the image of a curve.

But you cannot get the parametrization from the image.

Likewise, you can smoothly parametrize something like $|x|$, afaik.

Even though the image is not a smooth function.

I'd have to check that one though.

@Obliv Yes, that's a smooth curve.

But if you want $y=x^2$ I think you need $r(t)=(t^2,t,0)$.

Obliv

9:27 PM

@0celo7 $y(x) = x^2$ is a map afaik

0celo7

@Obliv Where's the parameter?

Obliv

it maps $x \in \mathbb{R}$ to $y \in \mathbb{R}$

0celo7

If $x$ is the parameter, then that works. But you never write a curve like that.

Obliv

Define parameter. I see a map as an object that takes input from some data in a set and modifies it then places it into another set

@0celo7 yeah I fixed it. It doesn't make sense in $\mathbb{R}^3$

but in 2D where $x$ is the parameter, i don't see any problems

Slereah

Ancient Aliens is pretty disappointing, really

They had enough material to do 3 seasons maybe and they stretched it into 11

0celo7

9:29 PM

@Obliv yes, that's fine

Slereah

They repeat a lot of shit

0celo7

But

You can have two 2D curves which are DIFFERENT but if you write them in terms of $x$, they are the same.

Do you want an example

Obliv

Back to the point: this text says it's not smooth if $r'(t) = 0$ at any point on the interval

0celo7

What a load of bull.

That means the curve is not regular at that point.

It's plenty smooth.

Slereah

ur mom is plenty smooth

0celo7

9:31 PM

@Slereah Yeah she knows how to shave, unlike yours.

Slereah

heyoooo

Obliv

@0celo7 what do u mean different

0celo7

@Obliv $r(t)$ and $r(t/2)$ are different curves, but have the same image

Obliv

how are the curves different?

0celo7

the maps $t\mapsto r(t)$ and $t\mapsto r(t/2)$ are different maps.

Obliv

9:35 PM

@0celo7 the domains are different but the maps are the same

er

0celo7

what?

The domains are both $\Bbb R$

Obliv

isn't there a bijective map $r(t/2) \to r(t)$

so they're like the same

0celo7

"""like""" the same?

@Obliv What?

Slereah

there is, yes

they are still different maps, though

Obliv

sigh I don't know.. they look like they'd produce the same 'curve' if you plotted it out

Slereah

9:37 PM

there's a bijection from $x$ to $x^3$ but they're not the same function

Obliv

Oh that's a good example thanks @slereah

Slereah

Take two circles, one with parametrization $r(t)$ and one with $r(t/2)$

Obliv

but this is more like arguing that $x^3$ and $(x/2)^3$ aren't the same maps

Slereah

The first one, $r(0) = r(2\pi)$

That's not true of the second one

Obliv

which I guess is true but if the domain is $\mathbb{R}$ does it really matter

0celo7

9:39 PM

@Slereah what does that even mean?

God, what is wrong with physicists?

Can we please be precise?

Obliv

Oh I think I'm confusing the image with the curve.

Slereah

It means exactly what it means

Obliv

I agree the curves are different, then. But the image is the same so doesn't it make sense to treat the image as the curve

0celo7

YES

YOU GOT IT

Obliv

like it's a smooth image from $[-3,3]$ instead of curve

0celo7

9:40 PM

@Obliv whut

Obliv

LOL

Slereah

Calm your tits, @0celo7

0celo7

I have very happy tits, sorry.

Obliv

i retract my previous statement

$k = |\frac{dT}{ds}| = |\frac{T'(t)}{r'(t)}|$ makes a lot more sense now, as the definition of curvature

$T$ is the unit tangent vector

user218912

yo

Obliv

9:47 PM

sup @icelord

user218912

doing my condensed matter homework WITHOUT looking up the solutions in the manual.

Slereah

digitalcommons.calpoly.edu/cgi/…

Good stuff

user218912

lol...

Bernard Meurer

@Slereah You comment on the election page made me laugh for a while. Props for that

Slereah

"The embedding $\Sigma_{D,\Omega}$ is constructed in the form $\Sigma_{D,\Omega} = Q_\Omega \circ D \star \Pi \bullet ^ \star$"

Kill me now

user218912

9:50 PM

@Slereah pretty symbols

Obliv

@bernard u mean the one on JD's nomination?

user218912

uhhh...

user218912

if only acm and jd are running

user218912

then jd will be elected by default

user218912

since there's 2 right?

ACuriousMind

9:52 PM

The nominations run for a week. Have patience.

Slereah

I'll run if necessary

0celo7

ACM is running?

Slereah

You know my platform

2

Obliv

@slereah free rep for everyone?

Bernard Meurer

@Obliv Yeah

Slereah

9:53 PM

Sure

Rep all around

A goose in every oven

Bernard Meurer

@Slereah Is the Vermin Supreme of PSE

ACuriousMind

@Slereah Not going for the vegetarian vote, I see

Obliv

A vote for slereah is a vote for geese in every oven and time travel. #slereah4prez

Slereah

Psh who needs 'em

Obliv

oh this is about the coming moderator election. got my elections mixed up.

Slereah

9:54 PM

I hope my Robinson book arrives soon because apparently it is some kind of secret club

Nobody ever mentions the construction of Robinson's field

They just defer back to the book

It's like Hawking Ellis

Maybe it is some kind of marketing technique

ACuriousMind

Interesting, the old nomination posts had comments that could be voted upon, but the current one doesn't allow that.

Slereah

Oh wait

Is it an election for a moderator for the whole site?

Rather than just the chat

ACuriousMind

Yes, there are no chat-only moderators.

Slereah

Hm

Although it still might

user218912

ACM is basically the face of PSE.

Slereah

9:59 PM

Perhaps something broader

"I will kick all their asses and teach them some manners"

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