The h Bar

John Rennie

16:05

Should group names like SU(2) be mathjaxed? If so $SU(2)$ or $\mathrm{SU}(2)$ ?

AccidentalFourierTransform

IMO the latter looks best

Slereah

Hm

ACuriousMind

@JohnRennie I am of the opinion that they should be, in \mathrm

Slereah

I don't think the complete feather can be embedded in a manifold unless it's like $\Bbb R^\omega$, even if we identify the adjacent points

ACuriousMind

I find it jarring to have SU(2) in text just talking about the group and then $\mathrm{SU}(2)$ (or $SU(2)$, if you don't care about upright names) when you want to write down e.g. a map $f:\mathrm{SU}(2)\to X$.

Slereah

16:08

the basic feather would be embedded in $\Bbb R^2$ and look like the upper half space

Double feather in $\Bbb R^3$

etc etc

John Rennie

@ACuriousMind hmm, Qmechanic disagrees

AccidentalFourierTransform

$\mathrm{Qmechanic}$

ACuriousMind

@JohnRennie Many do. I'm on the extreme end of the scale when it comes to reserving not-mathrm'd letters only for variables.

Slereah

mathrm for groups I'd say, yes

and mathfrak for the algebra :p

I'm not sure what mathscr would be for

0celouvskyopoulo7

He disagrees?

With the upright thing?

Slereah

16:12

$\mathscr{SU}(2)$

gross

0celouvskyopoulo7

It's universally accepted that it should be upright

Just as -+++ is universally accepted

AccidentalFourierTransform

:: remains silent ::

Slereah

The only good way to do GR is with octonions, of course

I wonder what the metric looks like in that GR with octonion paper

let's see

uhoh

3

Q: Why doesn't thermal radio emission from a DSN "hot dish" completely swamp the benefits of a cold LNA?

The 70 meter DSN dishes are often used to receive the weakest signals, and so their receiver LNAs have cryogenic front-ends in an assembly that also contains a LHe refrigerator and vacuum system. If I understand correctly these are located in the "feed cones" pointed at the Cassegrain secondary r...

needs some physics attention?

Slereah

"ON FACTORIZATION OF EINSTEIN'S FORMALISM INTO A PAIR OF QUATERNION FIELD EQUATIONS"

oh it was quaternions

Naveen Balaji

16:18

Hey guys! Been stuck with this for a long time now, please do help

3

Q: On reducing complex ODE's to Bessel's form

I am trying to reduce the following ODE to Bessel's ODE form and solve it: $$x^{2}y''(x)+x(4x^{3}-3)y'(x)+(4x^{8}-5x^{2}+3)y(x)=0\tag{1} \, .$$ I tried to solve it via the standard method, i.e., by comparing it with a generalised ODE form and finding the solution from then on. The general form (...

differential-equations bessel-functions frobenius-method

Slereah

The quaternion metric is expressed as $$g^{\mu \nu} (x) = - \frac 14 \mathrm{Tr} (q^\mu \tilde q^\nu + q^\nu \tilde q^\mu)$$

where $q$ is a quaternion

it's the best metric

Though to be fair, I think this is basically thinly disguised GR with spinors

Since quaternions are $\approx \mathrm{SU}(2)$

Physics Guy

Quaternions are good.

Slereah

Basically the quaternion $q$ is just $\sigma^\mu e_\mu$

Where $\sigma$ is the Dirac matrix/imaginary units

So it's basically $q^\mu = e^\mu_t + e^\mu_x i + e^\mu_y j + e^\mu_z k$

Physics Guy

@Slereah Who are you talking to?

Slereah

The room

Feel free to respond at any time

Physics Guy

16:29

Okay.

DanielSank

Hi, everybody.

Slereah

Hello

Physics Guy

Hello

BAYMAX

Any help on this ? SAXS is preferred for nano material characterization then that of XRD

Slereah

nanomaterials are very small

I would use my tiniest hammer

BAYMAX

16:34

:)

any reference will help too! I searched but got none ><

Slereah

Whatever happened to quaternions

They were all the rage in physics and then everyone forgot about them

though we still use them a lot, we just call them Dirac matrices now

Physics Guy

Yeah, I was just about to say that.

Quaternions play a huge role in the physicists everyday life.

Slereah

it just has become unfashionable to call them quaternions

How does one represent spinors with quaternions, I wonder

AccidentalFourierTransform

using the spinor-quaternion lemma

Physics Guy

@AccidentalFourierTransform definition?

AccidentalFourierTransform

16:42

something about vector spaces

0celouvskyopoulo7

@ACuriousMind if you were to teach an intro QM class would you try to insert any Rigor?

Haha my phone autocorrected to a capital R

Slereah

considering the rigor needed for QM that might make for a long class

also you'd be mostly loss when reading QM books

Considering that for most physics books, the adjoint means "just replace $i$ by $-i$"

0celouvskyopoulo7

You have to do an incredible amount of work to show there's an eigenbasis

(In certain cases)

Slereah

also the eigenbasis isn't even an eigenbasis for most physics applications

is $\hat x$ even an observable, since you can't really have a particle in an $\vert x \rangle$ state

AccidentalFourierTransform

sure you can

Slereah

16:51

Can you

AccidentalFourierTransform

for example, let $\hat x=\sigma_z$ and $|x\rangle=|+\rangle$

Slereah

What

AccidentalFourierTransform

there you go

0celouvskyopoulo7

...

AccidentalFourierTransform

I just fixed QM

you thank me later

Slereah

16:52

What if I let $\mathrm{AccidentalFourierTransform} = \mathrm{A smelly man}$

0celouvskyopoulo7

Use \text ffs

Slereah

You're not my mom

AccidentalFourierTransform

ಠ╭╮ಠ

John Rennie

@BAYMAX the X-ray scattering angle is inversely proportional to the size of the object doing the scattering. Nano structures tend to be around a few nanometres in size, and the scattering angles for this size range are smaller than the angles easily measurable in XRD.

That's why we tend to use small angle scattering for nano sized structures.

Slereah

I should make a latex shortcut for ^{-1}

Koolman

17:00

Hii @JohnRennie

Slereah

I use it a lot

0celouvskyopoulo7

So is a spinor field just a section of a vector bundle?

Koolman

It is written ' Last seen 12 hours ago' . Does it mean he was online .

0celouvskyopoulo7

Maybe spinorial regularity isn't that hard

Oh wait spacetimes are noncompact

Koolman

physics.stackexchange.com/users/12350/kenshin?tab=profile

0celouvskyopoulo7

17:01

Ignore that

John Rennie

@Koolman Hi

Koolman

@JohnRennie see my above problem

BAYMAX

thank you@JohnRennie

John Rennie

@Koolman I can't see it. Have you got the link?

BAYMAX

so in XRD it cannot measure small angles!

Koolman

17:04

@JohnRennie You can't see what .

BAYMAX

like small in sense 0.1 to 10 degrees

@JohnRennie

John Rennie

@Koolman the above problem that you mentioned.

Koolman

3 mins ago, by Koolman

It is written ' Last seen 12 hours ago' . Does it mean he was online .

physics.stackexchange.com/users/12350/kenshin?tab=profile

John Rennie

@Koolman oh, I thought you mean you had a question about physics. I have no idea what the last seen date in profiles means.

@BAYMAX The diffraction angle is given by Bragg's Law $$2d\sin\theta = n\lambda$$ where $n=1$ for the first order scattering.

Koolman

Okay

John Rennie

17:08

So put $d = 1-10$ nm and $\lambda$ = whatever the X-ray wavelength is.

Koolman

@ACuriousMind hi

BAYMAX

then $\theta $ ?

ok

John Rennie

@BAYMAX I'm sure you can do the sums ...

BAYMAX

yes,ok.

Slereah

17:24

I looked up a post on spinors in quaternion representation, saw the math and then closed it

It's too late for so much algebra

Ben Niehoff

17:47

so what's new in the Land of Mathematical Rigor?

@0celouvskyopoulo7 Yes...a section of the spin bundle. So the manifold must be spin in order to have spinors on it

Some people might call it a Clifford bundle? I'm not sure

Some people call it the square root of the tangent bundle...yay!

Phase

Can anyone point me to a wiki page or source about actually calculating penetration of light with Lead as a function of energy?

Ben Niehoff

probably not

sounds more like engineering

AccidentalFourierTransform

Bethe formula

The Bethe formula describes the mean energy loss per distance travelled of swift charged particles (protons, alpha particles, atomic ions) traversing matter (or alternatively the stopping power of the material). For electrons the energy loss is slightly different due to their small mass (requiring relativistic corrections) and their indistinguishability, and since they suffer much larger losses by Bremsstrahlung, terms must be added to account for this. Fast charged particles moving through matter interact with the electrons of atoms in the material. The interaction excites or ionizes the atoms...

@Phase ^ perhaps?

Phase

I don't see why it wouldn't be a part of physics

Thanks!

0celouvskyopoulo7

@BenNiehoff those were self musings. I'm having think about spinorial PDE

I don't expect to find the answers I need here

It's just that elliptic PDE in vector bundles on closed manifolds is well understood

Open ones or with boundary, who knows

And on a Lorentz manifold everything is bad

Ben Niehoff

17:56

what do you mean by spinorial PDE?

you mean finding Killing spinors?

0celouvskyopoulo7

I'd have to look up what that is again, but I don't think so

Ben Niehoff

or maybe something with the spectrum of a Dirac operator?

those two examples basically exhaust my knowledge of actual occurences of spinorial PDEs

I recently submitted something to a journal that asked me to recommend reviewers

it was so bizarre

0celouvskyopoulo7

@BenNiehoff your topic was probably too obscure for them :D

Ben Niehoff

it was part of their standard submission procedure

0celouvskyopoulo7

@BenNiehoff I'm looking into (generalizations of) Witten's positive mass theorem.

One of the basic PDE's is...fuck how do I Feynman notation

Ben Niehoff

18:02

oh, cool! I had to learn that for a paper once

0celouvskyopoulo7

Been too long since I've physics'ed :D

Ben Niehoff

oh no, don't do that slash bullshit

0celouvskyopoulo7

@BenNiehoff Witten's original paper doesn't actually contain a proof that his equation $\sigma^a\nabla_a \psi=0$ has a solution for the boundary conditions

(which are asymptotic conditions)

And I have to work with a metric that's only in $C^{1,1}$ as well

Pretty terrible

Ben Niehoff

what is $C^{1,1}$?

0celouvskyopoulo7

$C^1$ with first derivatives locally Lipschitz

There are some papers on this by Tam and others but they're far more complex than what Witten did

Ben Niehoff

18:06

so, I don't remember the paper very well, is \psi a spinor?

0celouvskyopoulo7

And I have to investigate manifolds with ends

Currently massively stuck on a paper by Li and Tam

@BenNiehoff It's a spinor field, yeah

Ben Niehoff

but anyway, I'm not sure that Witten could be expected to prove something that isn't true

not every manifold has a spinor satisfying $\nabla_a \psi = 0$

in fact, very few do!

0celouvskyopoulo7

The goal of Witten's proof was to express the ADM mass as an integral of a certain positive spinor quantity

Ben Niehoff

yes

0celouvskyopoulo7

@BenNiehoff I think $\sigma^a\nabla_a\psi=0$ is weaker

Ben Niehoff

18:08

ah, ok

0celouvskyopoulo7

The condition is that it's "asymptotically constant"

and you need two linearly independent ones

Quite a hard problem!

On a compact manifold it should be easy. Although I'm not sure how many compact Lorentzian 4-manifolds are spin (maybe they all are lol)

Ben Niehoff

well, compact Lorentzian manifolds are not of any interest to physics anyway

0celouvskyopoulo7

My manifold is $\Bbb R^4$ anyway so topology is not an issue

I want to deal with the PDE without having to worry about some subtle algebraic topological issue

Ben Niehoff

there are certainly compact Lorentzian manifolds which are not orientable

0celouvskyopoulo7

The problem is: consider a compactly supported perfect fluid in $\Bbb R^4$. Suppose the spacetime is static. Then the spacetime is rotationally symmetric.

Ben Niehoff

18:11

so I would guess that it's reasonable to assume they could also fail to be spin

Slereah

Well IIRC you can't have a spin structure if it's not orientable

Ben Niehoff

that's the opposite of the Birkhoff theorem, right?

0celouvskyopoulo7

*Compactly supported on spatial sloces

@BenNiehoff it's a partial (?) converse

Ben Niehoff

@Slereah Indeed, so the interesting question is whether compact orientable Lorentzian manifolds can fail to be spin. In 4d

Slereah

Oh, I think I have a paper on that topic somewhere

I think it's from Geroch or some other guy

Ben Niehoff

18:13

but yeah, proving theorems in GR is hard

0celouvskyopoulo7

Yes Geroch has a paper on it

Ben Niehoff

because spacetime is generally non-compact

Slereah

Tell me about it

Geroch has a paper on everything

Ben Niehoff

and Lorentzian, etc.

peterh

-4

Q: Bose Condensate Computer

I designed a computer that is a spherical shell, with descending spherical shells one underneath another and stop at some distance from the center. In all the spherical shells beneath the outer surface, will be drilled holes in a 2d four sided symmetrical diamond pattern that's the same as the o...

quantum-mechanics newtonian-mechanics

Slereah

18:14

well if it's not Lorentzian it's not a very good spacetime

0celouvskyopoulo7

@BenNiehoff Well...the problem is on spatial slices. So it's actually a Riemannian problem.

But still noncompact

So Witten's theorem doesn't really apply

peterh

As I was young, I've thought about these people, that they are maniacs

0celouvskyopoulo7

there are some methods in 3D by Schoen and Yau

gtg

peterh

Now I think, they see something, what we can't.

Ben Niehoff

@peterh who?

peterh

18:15

@Ben physics.stackexchange.com/questions/329239/…

Ben Niehoff

oh, I often don't follow links, lol

peterh

@Ben Intrasite links in the case of the PSE have negligible security risk.

Ben Niehoff

it's not because of security risks, I'm just lazy

peterh

@Ben He has thought a lot on quantum computers, neural networks, robots. And wrote, essentially, an essay. And posted it as a question.

Ben Niehoff

sounds like the hottest new thing for crackpots to do!

peterh

18:19

@Ben My big fear that I will be the same as I will be old

Ben Niehoff

it's possible

Sir Cumference

I miss obe...

Everyone's leaving the chat these days

Slereah

Ben Niehoff

maybe the weather's getting nicer?

somewhere else?

certainly not here!

peterh

@Ben It depends on your continent. In EU, it is joking

Ben Niehoff

18:23

I'm in Belgium, weather currently sucks :(

AccidentalFourierTransform

goddammit inverting matrices is hard

I give up

Ben Niehoff

lol

I literally spent 2 weeks of my life inverting a matrix recently

how big of a matrix are you dealing with?

AccidentalFourierTransform

its like $A_{ab}^{cd}\sim c_{ab}\delta_a^{c+1}\delta_b^{d-1}+\cdots$

with Kronecker deltas

so it should be easy

but its infinite-dimensional so there's that

Ben Niehoff

sometimes that's easier

other times it's impossible

it could have a left inverse but not a right inverse, for example

AccidentalFourierTransform

I guess we'll never know

peterh

18:27

I need a native Greek speaker

Bye

AccidentalFourierTransform

who left?

Ben Niehoff

so I've been playing this computer game Hollow Knight

AccidentalFourierTransform

why

bolbteppa

qft is so mental, it's all so mental

Ben Niehoff

@AccidentalFourierTransform because it's fun?

AccidentalFourierTransform

18:42

no it isnt

Ben Niehoff

you don't like computer games?

or just that one?

AccidentalFourierTransform

I dont like you

Ben Niehoff

well, obviously

AccidentalFourierTransform

indeed.

Slereah

JUST

bolbteppa

18:46

Wow that makes a lot of sense

0celouvskyopoulo7

I was just in a PDE seminar where one prof assumed it was a presentation on an undergrad thesis but it was a PhD student talking

Ben Niehoff

and how did that work out?

0celouvskyopoulo7

He asked her advisor lol

Ben Niehoff

asked her advisor what?

0celouvskyopoulo7

If she was an undergrad

Ben Niehoff

18:48

ah, ok

0celouvskyopoulo7

It's sad because she got a grad fellowship the other day and he was at the ceremony

Ben Niehoff

lol

AccidentalFourierTransform

ouch

bolbteppa

cruz crew qft

Ben Niehoff

sounds vaguely like sexism

Emilio Pisanty

18:53

^ that

0celouvskyopoulo7

Nah

She was just presenting a small part of the overall (in progress) thesis

He misunderstood and thought it was the whole project

Ben Niehoff

ah

0celouvskyopoulo7

It's half analysis and half numerical, she only talked about the analytical bit

Something like that

Ben Niehoff

how do PhD programs work in math, anyway? My vague understanding is that mathematicians write much fewer papers than physicists

0celouvskyopoulo7

Idk, I'm a sophomore

Ben Niehoff

18:58

oh, well you seem to know a lot

0celouvskyopoulo7

I'm not even sure how I'm supposed to write my undergrad thesis

I looked at what people do and they look like things I could crank out in a weekend

(slight exaggeration)

AccidentalFourierTransform

as long as you do it in word

Ben Niehoff

I published 5 papers during my PhD (and I felt like that wasn't really enough)...my thesis was basically the papers stapled together, with some extra chapters at the beginning for background material

AccidentalFourierTransform

(half the people in my class did their undergrad thesis in word)

0celouvskyopoulo7

Sick

Ben Niehoff

19:00

be a true hipster and do it on an antique typewriter

leaving space to handwrite equations

bolbteppa

In combinatorics you can get one out very quickly if you are lucky, and a few more

Ben Niehoff

in fountain pen

AccidentalFourierTransform

19:12

> I'm not exactly great at formulas and stuff like that

Jaime Gallego

19:27

@ACuriousMind Can you move this message to the trash? I think it is not correct.

AccidentalFourierTransform

dude who cares lol

$E=mc^3$

see, its fine

Jaime Gallego

This is more subtle

Slereah

well yes, because $c=1$

AccidentalFourierTransform

$E=cm^2$

Slereah

I'm not sure the notion of mass really makes sense

Mass isn't the fundamental concept, it's more $m^2$

As in $p^2 = -m^2$

AccidentalFourierTransform

19:33

$\sqrt\cdot$ is smooth though

Slereah

Things get dicier if you have spacelike momentum, though

AccidentalFourierTransform

(👁 ͜ʖ👁)

Slereah

--🤠
💪🏻👕👍🏻
--👖
-👢👢

AccidentalFourierTransform

you should delete the first line and use my face

Slereah

Sorry I don't have a butt emoji

AccidentalFourierTransform

19:39

oh no

rekt

Slereah

Walked right into that one

AccidentalFourierTransform

Slereah

👨🏻‍🔬👨🏻‍🔬👨🏻‍🔬👨🏻‍🔬👨🏻‍🔬👨🏻‍🔬👨🏻‍🔬👨🏻‍🔬👨🏻‍🔬

Let's make some science baby

It's kind of weird that generally, physicists are the foremost scientists in the popular conception of what a scientist is, but for some reason the image of the scientist is always a chemist or biologist

I guess because physicists don't wear a uniform

Can't just show a bearded guy in an ugly sweater

AccidentalFourierTransform

scuse me

all my sweaters are beautiful

Slereah

Well you have to post a photo now

I warn you

There is only one beautiful sweater

AccidentalFourierTransform

19:51

wow

I want that one

ebay.co.uk/itm/…

Jaime Gallego

Oh god

Why?!?!

eBay descriptions are the Yahoo Answers of typesetting

0celouvskyopoulo7

20:41

@Danu it was indeed easy :)

Slereah

spacewarpdynamicsllc.com

lol

"Our idea to develop artificial inducement of local space warp was based on naturally occurring phenomena and heretofore unexplained cases in aviation. After researching some reports of pilots that had flown through thunderstorms, several cases indicated that these pilots experienced a linear displacement in terrestrial space.[7][9]
The total linear displacement varied from 100 to 300 miles. Forensic weather studies for these cases were created and analyzed. It was found that very large thunderstorms produce copious amounts of energy and antimatter which might explain pilot reports. "

the only actual scientist on that team is a meteorologist

judging from that sentence, not a very good one

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