The h Bar

Galois in the Field

16:00

@ACuriousMind Wait maybe not, I know clebsch-gordan dimension formula lol

ACuriousMind

@GaloisintheField So, you just do the usual decomposition - you know the rep on the original space $\mathcal{F}_1$ and then you just decompose $\mathcal{F_1}\otimes\mathcal{F_1}$ into the direct sum of irrep. You'll get one three-dimensional rep (that's the antisymmetric part), one five-dimensional spin-2 part and one trivial part.

yuggib

or better, it is a representation of the Heisenberg group that is equivalent to $L^2$

Galois in the Field

@ACuriousMind Okay I will try to work out wtf that means haha thanks

ACuriousMind

In general decomposing tensor products into the sums of irreps is a bit of a hassle.

For $\mathrm{SO}(n)$, Young diagrams and such stuff can help

@yuggib I do not disagree

Slereah

Young diagrams can help to know which irreps to use

Not so much for the factors involved

ACuriousMind

16:03

Also useful to know is that $V\otimes V$ always decomposes into $\Lambda^2 V\oplus \text{Sym}^2 V$, i.e. the anti-symmetric and the symmetric part always carry subrepresentations.

Slereah

yeah but then there's a bunch of other ones to decompose again

Like the trace and whatnot

And I only know what happens up to SO(3)

Who the fuck knows what goes on with SO(4)

John Duffield

16:21

@0celo7 : in olden days there were people could not conceive of an Earth that was curved. They had a conviction that the Earth had an edge.

In modern times there are people who cannot conceive of a Universe that is not curved. They have a conviction that the Universe has no edge.

Danu

Hola bonitas

0celo7

@Danu Hola right back at you

@Slereah is SO(4) just two copies of SU(2)?

@JohnDuffield What do you mean by "not curved"? Spacetime or space or what?

Glen The Udderboat

I'm looking for good commentary on this:

nature.com/nature/journal/vaop/ncurrent/full/nature15759.html

0celo7

whatever happened to that paper claiming we needed a charged higgs?

Danu

Oct 18 at 16:55, by dmckee

> "Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km"

Here is a bit of talk about it

0celo7

16:36

@dmckee posted it a while back

ACuriousMind

@GlenTheUdderboat What kind of commentary? Like "Nobody should be in the least surprised about that"? :P

Danu

Follow the chat arrows from the message I linked

And you'll find what you lookin' for

Glen The Udderboat

@Danu Thanks. Looking...

Danu

Not anything long though I guess

0celo7

I guess my commentary is that we live in the matrix :D

@ACuriousMind what is "arithmetic geometry"

ACuriousMind

16:40

@0celo7 Do you know about this wonderful invention called "Google"? :P

0celo7

Yes, I'm asking the superior version :)

> My research interests are in the areas of commutative algebra, homological algebra, algebraic geometry, number theory, category theory and mathematics education.

Hmm, that last one is out of place!

How does anyone have 370 publications...

@ACuriousMind ever heard of "David Dobbs"?

ACuriousMind

@0celo7 Nope

Slereah

1.3 kilometers?

Good thing we have phones now!

Imagine otherwise

You have to walk all the way there to check!

0celo7

Lol

Slereah

16:56

send the intern to check the electron spin

0celo7

Poor intern

I had to walk 1.3 kilometers in the Capitol

That's actually a low estimate I think

The Capitol is a pretty damn big building

0celo7

17:49

@Slereah Are you gonna apply to PhD programs?

Slereah

Eh I dunno

i have that notion that I'd like to write a paper first

To show that I am still in shape to do physics

0celo7

Solve the three body problem

I hear that's a thing

Slereah

I can't even solve the zero body problem

0celo7

Yeah, solve the vacuum equations!

0celo7

19:16

@Slereah What's so hard about solving the Einstein equations. Just find the Greens function!

Robusto

In doing some translation practice I read this statement about a star that is destroying its planets: "The problem with white dwarves is not so much the temperature that they emit but rather their strong gravity." My question: How would a white dwarf, after collapse from a Sol-type star, have stronger gravity? Is this an error?

Slereah

Well you can't actually have the green function of a non-linear system, for a start

0celo7

@Slereah Then linearize that motherf*cker and find the Green's function for that!

@Slereah Are there any known solutions with no symmetry, isoptropy, homogeneity of anything?

Huy

19:39

@ACuriousMind: actually, what the student plotted was current (of the magnet) against intensity of the beam, which ended up looking somewhat like a scaled skew normal distribution

@ACuriousMind: i.imgur.com/f1MP9kl.png this is what the student plotted (and I just doublechecked with mathematica because he didn't provide any source code)

0celo7

@Huy I just talked with a math prof who shares my disdain of the linear algebra classes

ACuriousMind

@Huy Yeah, well, if the distribution of the energies in the beam that comes out was the aim, then that's good. But that has rather little to do with any "penetration length"

0celo7

He told me I need to read Hofman-Kunze because linear algebra doesn't teach me what I need to know

and he likes that book

Huy

@ACuriousMind I guess maybe these are some first measurements and then some more computations will follow

@ACuriousMind my help is really just needed because he and the physics teacher have no idea or whatsoever about statistics and his physics teacher claimed "it should look like a normal distribution"

@0celo7: so what are u gonna do

Danu

@Robusto If we are free to assume spherical symmetry, then the matter outside of the sphere "doesn't care" (can't distinguish) whether it's a black hole or a star that's attracting it.

0celo7

19:43

@Huy I now have winter break reading material

Slereah

@0celo7 Well you can make one up, I suppose

Danu

I'm pretty sure this holds much more generally, but the spherically symmetric case is easy to visualize and a classic example in e.g. electrodynamics.

Huy

@0celo7 that and functional analysis of course

Slereah

Just put random functions in the metric

0celo7

dude

Slereah

19:44

IIRC there's a specific word for spacetimes with no symmetries

0celo7

I literally know no math

2

Slereah

They are called

WILD SPACETIMES

0celo7

would you tell a German middle schooler to learn functional analysis?

Huy

ofc you do know maths

depends

come to MSE chat

there's many 14 years old doing way more than that

0celo7

I'm not one of them

Huy

19:45

but you act like one of them

0celo7

and it's stupid

Huy

:(

@ACuriousMind: so my question to you is: from the experiment setup and physical point of view, does it make sense that it is slightly skew? if so, why?

0celo7

@ACuriousMind Re that homotopy Cartan formula problem, I showed it to Freire and he had to pull out his 70s French edition to convince himself the hint wasn't inserted by the English translators. "Why is he trying to be so fancy"

ACuriousMind

@Huy I see no reason for the skewedness right now

Huy

is there some common measurement mistake or mistake in setting the devices up or something that might lead to that?

0celo7

19:48

@ACuriousMind You know that equation you said Arnold expected me to intuit? Freire got it in a few minutes, modulo a sign.

ACuriousMind

@Huy However, it could be that the current in the magnets does not exactly linearly relate to the field strength at the point where the protons fly through. Then the x-axis is not linear in energy, and the skew is in the plot, not the physics.

@0celo7 Why are you telling me that?

0celo7

@ACuriousMind Dunno, thought you'd find it interesting

Guess not

Huy

@ACuriousMind: if I'm understanding correctly, no the ticks on the x-axis are definitely all equally apart from each other

ACuriousMind

@Huy No, I mean: The x-axis is magnet current not energy

Huy

ah

"@ACuriousMind: actually, what the student plotted was current (of the magnet) against intensity of the beam, which ended up looking somewhat like a scaled skew normal distribution"

yes, it is magnet current indeed

aha

now I understand what you mean

if it was energy, it should be symmetric

ACuriousMind

19:52

Yeah, so if the magnet current is not linearly related to the proton energy, the distribution looks skewed although it isn't

Huy

ok that's a very good point

Slereah

@0celo7 : "Then we studied Szekeres-Szafron spacetime with no symmetries"

Huy

maybe the student understood something wrong and took the wrong set of data to plot

all this seems quite odd to me

0celo7

@Slereah hmm, I seem to recall that one can perturb a metric to obtain another solution. is that right?

Slereah

Well you can always add another symmetric tensor to the metric, sure

Huy

19:57

@ACuriousMind what do I get if I multiply current of the magnet and intensity of the beam? any reasonable thing?

Slereah

Szekeres-Szafron is this apparently

$ds^2 = dt^2 - e^{2\alpha(t,r,x,y)} dr^2 - e^{2\beta(t,r,x,y)} (dx^2 + dy^2)$

ACuriousMind

@Huy Uh, not that I would know.

Slereah

@0celo7 : link.springer.com/article/10.1007/BF01608547

ACuriousMind

@Huy: Hmmm, the student should look at how the magnets are arranged to select the protons of particular energy, and calculate if the energy is supposed to be linearly related to the magnet current in the first place

Slereah

"All solutions of Einstein's field equations representing irrotational dust"

"In this paper we abandon all a priori symmetry assumptions"

He's a madman

ACuriousMind

20:02

Because if this is a classic spectrometer setup where a magnetic field $B$ causes a particle of velocity $v$ to do a circle with radius $r = \frac{mv}{qB}$, then since $v\propto\sqrt{E}$, if $B\propto I_\text{magnet}$, we don't get a linear relation between $I$ and $E$

Huy

and that only causes skewness and not more distortion to such a graph?

ACuriousMind

@Huy Not sure, didn't plot it, and my imagination for such thing is weak

Huy

ok

thanks anyways, I'll let the student know and see what happens

vzn

20:28

@GlenTheUdderboat The universe really is weird, and a landmark quantum experiment proves it/ physorg

John Duffield

@0celo7 : either. Forget about the expanding universe for a minute, because that muddies the waters. On the largest scale there's no overall gravitational field, and so spacetime is flat. That means space is homogeneous, as per the FLRW presumption. Spatial curvature is something different, to do with electromagnetism. And there's no overall electromagnetic field either.

skull petrol

Do you believe in God? @JohnDuffield

John Duffield

20:45

@skullpetrol : no. When I have to go to church for family events, I'm sighing and saying how can anybody believe this stuff? Nor do I believe in fairies or unicorns. LOL, or Hawking radiation, or branes, or time travel, or the evil twin universe where time runs backwards, or the holographic universe, or many-worlds, or the fabulous multiverse.

skull petrol

I see.

Slereah

21:06

I know that I'm a physicist because when I hear Poliakov, I think of the string action instead of the vodka

2

ACuriousMind

There's Polyakov wodka?

I must have it.

0celo7

@ACuriousMind German detected.

ACuriousMind

@0celo7 Meaning to tell me that brand is common in other countries, but not here?

0celo7

@ACuriousMind hint: think of Moskau

@ACuriousMind The english word starts with a v, not a w.

ACuriousMind

@0celo7 Oh, you're just talking about wodka instead of vodka?

It's a transliteration from Cyrillic, anyway, so there isn't really a "correct" variant

0celo7

21:24

@ACuriousMind Certainly not the way 99% of people write it.

Slereah

but in a lot of countries w isn't pronounced like v :p

Danu

21:43

Lmao @ACuriousMind

when I wrote that G/G resource recommendation, I did not have this outcome in mind :P

ACuriousMind

@Danu Hehe...I'm doing that to all res. rec. question that I stumble upon. We have a policy for answers, and that policy was a condition for these questions to be on-topic, but in about 80% of cases no one seems to have given a damn and actually deleted non-conforming answers.

Danu

@ACuriousMind Sigh :P

Okay

But I can sympathize with strange pet peeves---I have recently been flagging comments all around.

I even tried spreading it to Mathematics but that didn't go down too well :P

ACuriousMind

@Danu ...how did you try to spread that?

did you just flag stuff and they declined the flags?

Danu

I went to chat, talked to a mod

Asked whether he'd appreciate it; his answer was yes.

Proceeded to flag, got them declined lol.

2/10

ACuriousMind

Uhhhhh

Danu

21:48

Not doing that again.

ACuriousMind

Sounds as if the mods over there should first sort out among themselves what they want to do with comments :P

I know that ours are very happy to oblige comment flags

Danu

105

A: Why does $1+2+3+\cdots = -\frac{1}{12}$?

there are many ways to see that your result is the right one. What does the right one mean? It means that whenever such a sum appears anywhere in physics - I explicitly emphasize that not just in string theory, also in experimentally doable measurements of the Casimir force (between parallel me...

My flag on comments under this got declined

I mean... come on

I think that, after I complained about it, at least a few comments still got deleted.

Nevertheless, screw that :P They should all be deleted, never mind how highly upvoted they are.

ACuriousMind

The most dissappointing thing is that no one there gives the rather insightful proof that the finite value of such divergent series is independent of regularization that Terry Tao gives in that blogpost about Euler-Maclaurin summation including this example.

They all just give different ways to calculate or not calculate the value

Shame on you, math.SE!

Danu

Link for the lazy ^

ACuriousMind

But, yeah, you're right, most of the comments below Lubos answer do not add anything of value.

Danu

21:57

In particular, I think they detract from the value of the discussions presented in the answers

ACuriousMind

It's also interesting that we migrated that version of that question over there, but kept several other variants of it here.

Inconsistency!!

Danu

Seeing these people bickering over such nonsense is just annoying IMO.

@ACuriousMind Humanity <3

ACuriousMind

@Danu Well, you don't have to read the comments ;)

Danu

Hypothesis: Hypocrisy is the unique identifying feature of the human species.

ACuriousMind

Data point 1:

21 hours ago, by 0celo7

I'm a hypocrite

Danu

21:58

lel

@ACuriousMind Even managing to scroll down to the next answer is a hassle in this case ;)

In other news, this week we had a question on History of Science and Mathematics which dwarfed our "viewed" numbers in all questions over the past few months all taken together.

Sometimes, I do like the Hot Network Questions list :D

ACuriousMind

@Danu Which question was it?

Danu

40

Q: What famous theorem or results were proven by female mathematicians?

We know that there are/were many famous female mathematicians who influenced the mathematics as we know it today, but their numbers are few compared to male mathematicians. While we have numerous famous results by many male mathematicians like Gauss, Euler and many others, what are famous results...

mathematicians

Bad answers :(

Also not an ideal type of question (list-based, pretty much)

ACuriousMind

@Danu Uh, textbook case of too broad, maybe? :P

Danu

But some contemplation on the success of it shows that this is something people really care about/are interested in.

The masculine image of the hard sciences and mathematics is something worth combating :D

Also, our site needs more attention :)

ACuriousMind

@Danu Grumpy old me says it's very good they care about this, but an SE site is not the place for curating such a list :P

Danu

22:03

@ACuriousMind You're getting too old.

ACuriousMind

@Danu You needn't tell me, I even said "grumpy old me" :D

I also find myself wanting to live in a house with a lawn.

Danu

Conifold is awesome :D

3

Q: Why is there no named unit for momentum?

Momentum and energy play very similar roles in mechanics, each being changed by the application of force over a interval. For energy the interval is in space and for momentum it is in time. Both have associated conservation laws. Yet, energy units are named in many systems and momentum units gen...

physics units nomenclature

How he could come up with such a detailed answer is absolutely beyond me

ACuriousMind

An unorthodox German series of physics educational material uses the "Huygens" as the unit for momentum.

Danu

@ACuriousMind lolwat

ACuriousMind

@Danu Yeah, the Karlsruher Physikkurs is quite weird.

Slereah

22:17

"The milliMom is also known informally as the "Mommy," and the kiloMom as the "big Mama." "

heheh

also there is totally momentum used in non mechanical contexts

HDE 226868

@Danu He scares the heck out of me sometimes.

How long will it take before he has more rep than everyone else on the site combined?

Danu

@HDE226868 :'(

I should try to write some answers 8)

ACuriousMind

So, he's the John Rennie of hsm?

HDE 226868

Yes, but with annoying quote formatting.

Using inline italics . . . ugh.

ACuriousMind

::checks JohnRennie's profile:: Holy shit, I remember when he passed 100k, and now he's past 150k already?!

Slereah

22:23

Obviously conifold is a topological space locally diffeomorphic to a cone

Danu

I think the average quality of his answers is much higher than John's.

Slereah

^conifold

Danu

And that really means something, because John's answers are typically pretty good.

ACuriousMind

@Slereah lol

Slereah

note the conical singularity

ACuriousMind

22:25

I'm still amazed you have such easy access to drugs in France.

Slereah

I mostly know conifolds because they are sometimes used in quantum gravity

for topologically dynamic theories

Danu

"I give the potential answerers the full right and privilege to patronise me." lol

-1

Q: Killing vectors in General Relativity?

I'm looking to derive the surface area of the event horizon of a Schwarzschild black hole. I was just wondering if it were possible for someone to explain to me this: $$ \sqrt{g_{\theta\theta}g_{\phi\phi}} $$ I don't know what it is, or how to compute it. I don't even know what it is called? Co...

general-relativity black-holes

ACuriousMind

@Danu Well, it's a nice change from the capslock-shouters that react violently to any attempt to tell them they're wrong/confused :P

Slereah

23:36

Apparently topologically a cone is defined as $(X \times I)/(X \times \{0\})$

Is a conifold a topological space with a mapping to $(R^n \times I)/(R^n \times \{0\})$?

Hm, I guess not

0celo7

23:49

@ACuriousMind Wow. That's gonna haunt me forever.

ACuriousMind

@Slereah That's a cylinder where one end has been collapsed into a point, not an unusual way to view the cone.

Slereah

Well I'm trying to find stuff on conifolds, but most physics papers do it as a surface in some higher dimension

How does a cone work out in arbitrarily many dimensions

Is it always $R^{n-1} \times I / R^(n-1) \times {0}$

Or can you have several identifications

ACuriousMind

@Slereah From reading the Wiki articles, the base $X$ is not required to be $\mathbb{R}^n$. The example on the conifold page itself gives a base for a singularity in complex projective space as $S^2\times S^3$.

Slereah

Although since it's a local map maybe that doesn't matter

Makes sense I guess

but wait

I'm talking about the atlas here

ACuriousMind

Since the manifold structure is absent at the singularity, I think the usual "locally $\mathbb{R}^n$" doesn't work, and you just have to examine the actual singularity to find $X$.

Slereah

23:56

That the base is $S^2$ or whatever doesn't matter too much, since those are locally whatever to $R^n$

@ACuriousMind : Well yes, but then it's not locally $R^n$

It is locally a cone

Similarly to manifolds with boundaries being locally $H^n$

ACuriousMind

@Slereah Exactly, but the base of the cone is not specified by anything.

It can be any $n-1$ dimensional manifold you like

Slereah

Well yes, but does it matter for an atlas, though?

Or does a conical singularity look different locally for different bases?

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