The h Bar

Wrichik Basu

13:01

@JohnRennie got it. Thank you!

0ßelö7

@ACuriousMind I think in $n=3$ I want $p=6$, actually

ACuriousMind

@0ßelö7 Well, $\phi^n$ theories are rather common - but the non-integer theory produces weird units for the coupling constant and I imagine all sorts of other things breaking, especially if you tried to quantize it. I'll admit that my statement that it's not physical is more "I've never seen that" than "I can point precisely to where it fails".

0ßelö7

@ACuriousMind wait, can you actually imagine me quantizing something?

@ACuriousMind I'm doing classical field theory -- stability of the field equations under perturbation of an interaction term

ACuriousMind

Well...as a classical field theory model it might not actually have pathologies, but I'm still hesitant to call it "physical"

The non-integer powers of units worry me

0ßelö7

@ACuriousMind units are all $1$

ACuriousMind

13:07

@0ßelö7 No, they are not if you are doing physics :P

0ßelö7

@ACuriousMind I'm a mathematical physicist, does that excuse me?

ACuriousMind

Not from at least considering some watered down version like mass-dimension

heather

IBM uses 7 qubit quantum computer to calculate the ground state of the largest molecule ( BeH_2 )that can be solved exactly by perturbative Hamiltonians and a classical computer.

2

ACuriousMind

"solved exactly by perturbative Hamiltonian" ::raises eyebrow::

0ßelö7

@ACuriousMind in my QM class there was at least one perturbation problem that gave the exact answer

ACuriousMind

13:09

@0ßelö7 Well, but how did you know it was the exact answer?

0ßelö7

solved it exactly by hand

the irony is not lost on me

ACuriousMind

So you understand why I find this claim...strange, at the very least

0ßelö7

yes

@ACuriousMind the lone algebra book looks so lonely i.gyazo.com/731fbc26f3d629b2a6227b1009e97162.jpg

Balarka Sen

"Eigenvalues in Riemannian geometry" looks real nice

is that spectral theory

0ßelö7

yes

Balarka Sen

13:19

kewl

0ßelö7

It has some fantastic math if you're into analysis

if you don't care about the first eigenvalue of a manifold you might find it fantastically boring though

Balarka Sen

I am an open minded guy

i have been accused of being open minded to the point that my brains fall off the skull

3

0ßelö7

Chapter 3, $\lambda_1$ and curvature, is generally pretty damn cool

Balarka Sen

maybe someday i'll read this stuff

0ßelö7

@BalarkaSen Do you know Bonnet-Meyers yet?

Balarka Sen

13:23

no

0ßelö7

@BalarkaSen It's the one that says uniformly positive Ricci implies compact

lemme know when you learn it, there's some very neat related theorems

Balarka Sen

I should try to progress a little bit more on Riemannian geometry perhaps

Right now studying Riemann surfaces

0ßelö7

too algebraic

Balarka Sen

Forster is totally analytical

0ßelö7

does it involve sheaves?

Balarka Sen

13:26

yep

i thought you analysts love that shit

0ßelö7

then it's algebra

@BalarkaSen no. It's a convenient terminology, but people tend to forget what it means because we use it so little

Balarka Sen

i see

ACuriousMind

@0ßelö7 Nah, complex geometry involves sheaves because it's close to algebraic geometry thanks to GAGA, but it has an analytical part :P

0ßelö7

complex analysts will always use it

ACuriousMind

So...the conclusion is "some analysts love that shit"

0ßelö7

13:28

that's what I just said

I'm definitely not a complex analyst

Balarka Sen

i'm pretty hyped up to learn sheaf cohomology

0ßelö7

I've tried to learn complex geometry and I barely got through Wells' book and that's pretty analytical. I find it pretty boring.

I have no reason to care about complex manifolds.

@ACuriousMind Let's put it this way: if I went to the analysis seminar and started talking about sheaves, the only people who would understand me are Denzler (he knows everything), Richter and Lind (complex analysts) and that's it

No one else has a reason to care about them

@BalarkaSen Bonnet-Meyers is in Chapter 9 of do Carmo. The proof is very clever

Jasper

@ACuriousMind Joseph Taylor's Several Complex Variables is the only book I know of that treats the GAGA theorems in detail.

Balarka Sen

@0ßelö7 I'll check it out

rob

Good morning, hbar

ACuriousMind

13:42

Good afternoon, rob

0ßelö7

@ACuriousMind Is the thing that makes a finitely generated module a free module the uniqueness of the expansions?

Jasper

@BalarkaSen Forster's Lectures on Riemann Surfaces is more algebraic compared to say Napier and Ramachandran's Introduction to Riemann Surfaces which is more analytic. The latter uses the so called L2 methods.

0ßelö7

ctrl F Sobolev

no hits in Forster, can't be that analytic :P

Jasper

@0ßelö7 Wells's Differential Analysis on Complex Manifolds is more analytic than say Huybrecht's Complex Geometry which is more algebraic, but both have lots of theorems not proven. Consider Griffiths and Harris's Principles of Algebraic Geometry for complex manifolds too.

0ßelö7

I said I have no desire to learn anything about complex manifolds.

Balarka Sen

13:51

how about lipschitz manifolds you geometric measure theorist

the stuff nobody cares about

(False, I know)

0ßelö7

Lipschitz? Oh that's high regularity :P

Balarka Sen

lool

0ßelö7

Sets of finite perimeter is where it's at

Distributional boundary, etc.

@BalarkaSen A set of finite perimeter is one where the characteristic function is a function of bounded variation (distributional derivative is a signed measure with finite variation)

Balarka Sen

k

0ßelö7

Equivalently, there exists some "surface measure" such that the Gauss-Green theorem holds. They're pretty nasty

Balarka Sen

13:55

oh that's interesting

0ßelö7

@BalarkaSen They're a natural choice for geometric problems because integration of that surface measure gives a reasonable definition of perimeter (area of the boundary)

@ACuriousMind Need help with module theory

If I have a unital ring $A$ and a finitely generated $A$-module $V$, why isn't $V$ automatically semisimple? It's the sum of finitely many simple submodules, no? Then by module theory we can make that a direct sum.

The book says one needs to assume $_AA$ is semisimple as well, but I don't see how that applies

0ßelö7

14:15

@ACuriousMind I don't know what I'm doing wrong

$V=\langle v_1,\dotsc, v_n\rangle=\sum \langle v_j\rangle\implies V=\bigoplus \langle v_{j_k}\rangle$, no?

Is the issue that $\langle v_j\rangle$ needn't be simple? How the heck does that work

How could it have a nontrivial submodule

I guess the existence of zero divisors in the ring could do it

ZeroTheHero

@heather I have not forgotten. I'm still waiting on additional answers from colleagues. I will be off for a couple of weeks but will get back to you. Latest I have is "Great question. I can’t think of any reference of the top of my head, but let me think about it and get back to you…it might be straightforward."

ACuriousMind

14:33

@0ßelö7 What is $_AA$?

Slereah

archive.fo/oH1n3#selection-1440.0-1440.3

So tell me

How much has peeing helped you understand physics

ACuriousMind

@0ßelö7 finitely generated modules are not, in general, free

DanielSank

@ACuriousMind Meh.

;-)

ACuriousMind

@0ßelö7 That's not what "finitely generated" means. Finitely generated means there is a surjection $A^n \to V$ where each $v_i$ is the image of the 1 in one copy of $A$, but it does not mean the module decomposes as the direct sum of cyclic submodules. The latter, i.e. $V = \oplus_i \langle v_i\rangle$ is only true over PIDs.

0ßelö7

@ACuriousMind the regular representation of $A$

@ACuriousMind Finitely generated means $V=\langle v_1,\dotsc, v_n\rangle$

ACuriousMind

14:42

@0ßelö7 Yes, that's equivalent to what I said, and to $\sum_i \langle v_i\rangle$, but not to $\oplus_i \langle v_i\rangle$.

0ßelö7

And is that because $\langle v_j\rangle$ needn't be simple?

ACuriousMind

@0ßelö7 No, because the sum is not direct

0ßelö7

I can't come up with an example but that's where my argument has to fail

ACuriousMind

The $\langle v_i\rangle$ overlap

0ßelö7

@ACuriousMind Ignore what you said

please answer what I am asking...

is $\langle v_j\rangle$ simple?

ACuriousMind

14:44

@0ßelö7 No, not necessarily.

Physics Meta

1

Q: A decrease in reputation from 931 to 919 - what's the reason?

A few days back, my reputation was 931. However, each day I found it going down by 2, and now it stands at 919. Can anyone account for this loss? It seems no one has downvoted my answer or question as it doesn't cross up in the achievements.

0ßelö7

@ACuriousMind example?

apt45

Hello, guys. I have a question for you. In arxiv.org/pdf/0912.4258.pdf, above eq.3.4 the authors state "The strong coupling scale associated with this term in the amplitude is...". What do they mean by strong coupling scale in this case? How can you determine at which energy the coupling becomes strong just by looking at the amplitude computed at tree-level with the Effective theory? It might be the UV completion to be weakly coupled as well at those energies, doesn't?

ACuriousMind

@0ßelö7 The ring itself is rarely simple over itself. Consider that $\mathbb{Z}$ as a $\mathbb{Z}$-module has plenty of submodules, i.e. $n\mathbb{Z}$ for every $n\in\mathbb{Z}$.

apt45

Do they mean "the scale at which the perturbative expansion breaks down?"

0ßelö7

14:46

Ah ok. So the statement is that not all cyclic modules are simple?

When phrased that way I understand. Thanks

ACuriousMind

@0ßelö7 Ah, yes, cyclicity and simplicity are not directly related

Still, your claim fails much earlier - it is not true that, "by module theory", the module is a direct sum of the cyclic modules generated by its generators.

0ßelö7

@ACuriousMind If the cyclic modules are simple it's true

"$V=$ sum of simple modules" is equivalent to "$V=$ direct sum of simple modules"

ACuriousMind

@0ßelö7 Ah, I misunderstood what your argument was supposed to be

Carry on, then

vzn

← lately pondering/ trying to understand an apparent connection between linear algebra and "multidimensional derivatives", maybe/ apparently similar to "operators" in QM, hunting for applicable theory, suspect it arises in various physics contexts... vzn1.wordpress.com/2017/09/07/…

vzn

15:19

Matrix difference equation

A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. The order of the equation is the maximum time gap between any two indicated values of the variable vector. For example, x t = A x t − 1 + B x ...

↑ sigh, where are all the math ~~fiends~~ friends when you need em :| o_O

ACuriousMind

@Slereah Wasn't it you who said you had many insights on the toilet?

Ah, yes:

Feb 18 at 19:07, by Slereah

I learned many things on the toilet

11 stars on it, even

Sid

You get inspiration in toilets

vzn

@Slereah did my best to resist commenting on that but others didnt refrain either... that is one of the most bizarre science articles have seen in quite awhile. it seems like an april fools prank, but apparently the authors are totally serious. dare somebody to post it to reddit physics section and let the internet masses take it from there. (cant bear to do it myself...)

Slereah

reading on the toilet

Sitting down

My pee doesn't arc up then

vzn

15:37

reminds me of "biopsychosocial" model, (mis?)applied to STEM/ gender differences en.wikipedia.org/wiki/Biopsychosocial_model

Slereah

Do you think Isaac Newton came up with classical mechanics while peeing

3

on an apple tree

vzn

wondering about the authors. 2 female authors, same last name, sisters? lol a very strange case of mature en.wikipedia.org/wiki/Penis_envy ?

0ßelö7

16:09

@Slereah methinks it wasn't the apple falling that made him think about gravity

Fawad

If I was Newton I would eat that apple :D

0ßelö7

@Fawad I was hinting at a turd

Slereah

16:34

very subtly

Jasper

17:08

@PhysicsMeta If nobody downvoted you it probably means that some post you edited was deleted, because that edit gives you two points.

0ßelö7

@Jasper why are you talking to a bot?

Jasper

@0ßelö7 Oh I see, lol. Well, partly because nobody talks to me, and I am also sick.

Sir Cumference

18:09

Wikipedia lists the Universe's diameter as "At least 156–554 billion light-years"

Universe

The Universe is all of space and time (spacetime) and its contents, which includes planets, moons, minor planets, stars, galaxies, the contents of intergalactic space and all matter and energy. The size of the entire Universe is still unknown. The earliest scientific models of the Universe were developed by ancient Greek and Indian philosophers and were geocentric, placing Earth at the centre of the Universe. Over the centuries, more precise astronomical observations led Nicolaus Copernicus to develop the heliocentric model with the Sun at the centre of the Solar System. In developing the law of...

How could someone possibly determine that?

Welp, found the paper

arxiv.org/abs/astro-ph/0310233

0ßelö7

@SirCumference googling

Anonymous

@SirCumference The method is described here...web.archive.org/web/20080822013053/http://www.space.com/…

Sir Cumference

@Blue Secondary sources can be misleading

Anonymous

They are just considering the visible universe

Anonymous

@SirCumference space.com is legit though

Sir Cumference

18:20

Like how the title claims the Universe is 156 gly wide, but the paper says "at least" that amount

Anonymous

@SirCumference Read the article

Anonymous

They mention that it is "at least"

Sir Cumference

@Blue I'm better off just looking at the paper

@Blue Not in the title :P

Anonymous

@SirCumference Sure

Sir Cumference

Though I actually want to know what other cosmologists seem to think about it

It's from 2003

In a meh journal

Anonymous

18:25

This is relatively recent paper: arxiv.org/abs/1304.1811

Anonymous

I wish I knew topology

Sir Cumference

@Blue Same... ;-;

@Blue It's in the same meh journal though

Anonymous

ocw.mit.edu/courses/mathematics/…

Anonymous

"The prerequisite for the course is a first course in Analysis, at the level of Rudin's "Principles of Mathematical Analysis" (18.100B here at MIT.) This background is essential both for the knowledge of the subject matter and for the experience in formulating proofs."

Anonymous

Yay...I can take up that course next year then :) :P

Anonymous

18:29

@SirCumference Heh...search on arXiv a bit

Anonymous

You'll get more papers

0ßelö7

19:12

@SirCumference when you judge journals like that then you're accruing very bad academic karma

0ßelö7

19:52

@ACuriousMind do the Germans use sp for tr?

Nvm

heather

20:45

2

Q: Last chance to study theoretical physics

I have had a lifelong interest in physics and mathematics but life events have prevented me from pursuing the subjects I'm fascinated by. I'm most interested in theoretical physics (cosmology, astrophysics, quantum mechanics, relativity) and in the past pure mathematics was the subject I found my...

particle-physics cosmology mathematical-physics astrophysics mathematics

^does this maybe belong more on academia...?

ZeroTheHero

@heather Definitely academia.

heather

flagged to suggest migration.

Sir Cumference

21:21

@0ßelö7 I probably am...

ZeroTheHero

21:32

Would anyone know of a book of counter examples in physics in the style of the math books on the same theme, as for example this one: store.doverpublications.com/0486428753.html

The closest thing I know is this ca.wiley.com/WileyCDA/WileyTitle/… but it's not about counterexamples.

dmckee

22:15

@ZeroTheHero I keep meaning to buy that. But I don't know of anything similar in physics. Partly because of the general lack of emphasis on "proof" and partly because experienced people recognize that almost all 'firm' statements in physics come with preconditions and as such can be broken by finding a way to evade those preconditions.

Phase

22:33

Could someone please help explain Quotient spaces to me?

Im just not clicking with this books explanation

If a coset of $x \in X$ with respect to $E$, a proper subset of $X$, is it really just a set composed of ${x} \cup (\cup _i (E_i))$

GPhys

I have a dumb particle physics question

Phase

If you're worried about your questions being dumb rest assured I've set the bar low

GPhys

in something like $\gamma +p\to \Delta^+$, can this still occur if the photon and proton have more energy than the rest mass of the $\Delta^+$ in the center of mass reference frame?

Phase

22:50

Well are there any lorentz transformations you can apply to get it to match?

GPhys

if they have more energy than this then the interaction I wrote wouldn't conserve energy, my question is can it happen anyway e.g. if the $\Delta^+$ is then immediately decaying

Phase

I haven't really studied particle physics but coming from a general physics thing, why couldn't it just create a particle with kinetic energy?

GPhys

@Phase because then it would have momentum; there's a reference frame where the gamma and proton are moving toward each other with the same momentum

so they can't produce a system of particles with momentum that doesn't add to zero, and it's only producing one particle so it can't be moving

Emilio Pisanty

@ZeroTheHero Yeah, I tend to agree with @dmckee there. That is a nice book, though.

not that the mechanism doesn't have its place in physics

you could think of the CHSH game as a counterexample to the claim "nature is real and local"

ditto for, say, the PBR theorem

but I'm not sure there's enough of those to fill a book

0ßelö7

23:10

@GPhys did you get more GR homework?

GPhys

yes but I haven't started it yet

Phase

Also could someone warn me if this is shit so I can delete it

0ßelö7

@GPhys my fluids homework is only words, no equations or parameters. No idea what to do

DanielSank

Y'all need to learn your wave physics.

CYMATICS: Science Vs. Music - Nigel Stanford

►

Bam.

@heather

heather

23:35

i'll have to watch that.

Balarka Sen

@DanielSank I was hoping he would play Darude Sandstorm in the beginning

I'm pretty sure the equipment would break from dankness overload if that happened

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