The h Bar

ACuriousMind

00:00

However, also if this is a resonance and because resonances are B-W peaks, I don't see a reason why this process should continue far above the allowed energy, either.

So if I understand you correctly, I would share your scepticism about this being a lower bound for the process, and not the peak energy which the process happens around.

Maybe a true particle physicist like @dmckee could say something more definite, though

GPhys

hmm

Semiclassical

there's probably some discussion of this in the context of the GZK limit in the literature as well

GPhys

00:20

*writes $\partial^\mu(\phi_1)\partial_\mu(-i\phi_2)+\partial^\mu i\phi_2\partial_\mu\phi_1$ *

0ßelö7

what about it

GPhys

preeeety sure this is zero 🤔

0ßelö7

proof?

GPhys

no :3

0ßelö7

then it's false

false unless proved correct with a Bourbaki proof

GPhys

00:24

don't worry I will find a way to avoid learning how to manipulate it with the partials again like I did the last 40 times

0ßelö7

unless those are operator-valued, what is the issue?

@ACuriousMind This is a torus

the black curve is homotopic to the blue one, right?

GPhys

@0ßelö7 dunno think it's just magic, unless I can just flip an up/down index anywhere anytime

0ßelö7

@GPhys please state that carefully and I will agree/disagree

I think I agree but best be careful here

GPhys

@0ßelö7 if I write say $g_{\mu\nu}$ and $g^{\mu\nu}$ twice, can the g float out of the partials? In this problem it's really eta though

0ßelö7

eta is constant

GPhys

00:32

since it's lorentz invariant, I guess so :P

but does it work with g?

0ßelö7

@GPhys this has nothing to do with Lorentz invariance

@GPhys yes

GPhys

@0ßelö7 what is lorentz invariance?

0ßelö7

is that a rheorical question?

GPhys

no I think you have some different definition than what I have in my notes somewhere (?)

Semiclassical

the metric tensor is a list of numbers.

0ßelö7

00:35

Lorentz invariant means it is invariant under Lorentz transformations

what on Earth could it mean beside that?

GPhys

is eta not ?

0ßelö7

that depends wholly on what you mean by "eta"

GPhys

@0ßelö7 why can I write in the g_\mu\nu and the like here and move them out, but not everything else? What is the property?

0ßelö7

maybe @Semiclassical can help, because I'm afraid i don't know what you're talking about

maybe if you write some equations

GPhys

$\partial^\mu(\phi_1)\partial_\mu(-i\phi_2)+\partial^\mu i\phi_2\partial_\mu\phi_1$

0ßelö7

00:40

I mean $a_\mu b^\mu=a^\mu b_\mu$

Semiclassical

If you write down any instance of $g_{\mu\nu}$, is there any spatial or time dependence?

0ßelö7

everyone knows that

what is the issue with $g$ there?

Semiclassical

@0ßelö7 for a certain definition of 'everyone'

GPhys

$\partial_\nu(g^{\mu\nu}\phi_1)\partial^\nu(-ig_{\mu\nu}\phi_2)+\partial^\mu i\phi_2\partial_\mu\phi_1$

$g^{\mu\nu}g_{\mu\nu}\partial_\nu(\phi_1)\partial^\nu(-i\phi_2)+\partial^\mu i\phi_2\partial_\mu\phi_1$

Semiclassical

conservation of indices...

0ßelö7

00:42

@Semiclassical if a 10 eV electron hits a 5eV barrier of width 100f, do you expect the transition probability to be 1 to within calculator erorr?

GPhys

@0ßelö7 the operator $\partial$ doesn't care about the $g$, what is the property a tensor has to have to do this

0ßelö7

3 mins ago, by 0ßelö7

I mean $a_\mu b^\mu=a^\mu b_\mu$

Semiclassical

@0ßelö7 ugh, i'd have to think about that and I don't have the energy for that.

(I know it's not actually hard---just figure out the momentum and compute the tunneling action---but eh)

0ßelö7

@Semiclassical I have the formulas, but I'm wondering if the guy wants me to show that it's not 1 at like the 10th decimal place or what

it's 0.99999999995

1-5E-11

Semiclassical

bleh

0ßelö7

00:46

works for me

Semiclassical

yeah.

0ßelö7

I wonder what the precision on trig tables in the calculator is

Semiclassical

well, you're going to plug uthe tunneling action into $e^{-\Gamma/\hbar}$ (or whatever it is)

GPhys

or is g just the only thing I will ever write down that can do this?

0ßelö7

@GPhys can you prove what I wrote or not?

Semiclassical

00:48

if you write down any element of $g_{\mu\nu}$, what can it be?

0ßelö7

Semiclassical

ah, that thing

GPhys

@0ßelö7 sure, the index switching with g works fine

0ßelö7

it just seemed like it was exactly 1, had to trick the calculator into giving more decimals

Semiclassical

What does $k_2a$ work out to in this case?

0ßelö7

00:49

@GPhys so those derivatives are just vectors

the same identity applies

@Semiclassical wolframalpha.com/input/?i=(2*mass+of+electron%2Fhbar%5E2+*5eV)%5E(1%2‌F2)*100+fermi

damn you link

here

Semiclassical

ah, the joy of WA links being stoopid

a handy factoid for doing this by hand is that $\hbar c$=1240 nm-eV =1.24 fm-keV

0ßelö7

...how does $c$ enter?

Semiclassical

mass of an electron = 511 keV/c^2

0ßelö7

ah, ok

Semiclassical

I should check if I have that product right, mind

I know 1240 nm-eV is right

GPhys

00:52

@0ßelö7 is there a tensor other than the metric that works to float outside the partial like that though?

Semiclassical

but I'm juggling the powers of 10 in my head to get fm and keV

0ßelö7

@GPhys I honestly don't know why you're fixated on the partial derivatives.

The metric is not being differentiated

Semiclassical

@GPhys to be clear: Is the metric tensor here just the usual SR case?

0ßelö7

@Semiclassical It doesn't matter!

There are no derivatives on any metric :/

GPhys

I'm fixated because it was the only thing I was trying to ask about, I have known this thing is zero the entire time

0ßelö7

00:55

...is it an issue that the thing is zero?

GPhys

no, I genuinely just want to figure the conditions for the things that don't have derivatives, so I am free to rearrange them

0ßelö7

@GPhys idk if I'm being dense but that sentence does not parse. Please write a specific equation and a specific question

Semiclassical

@0ßelö7 oh derp

hc=1240 nm-eV

0ßelö7

h or hbar?

Semiclassical

$\hbar c$ = 197 nm-eV

GPhys

01:00

@0ßelö7 I did earlier, but you responded with a different equation :3

0ßelö7

@GPhys link?

Semiclassical

I tend to remember the hc version for reasons I don't remember.

GPhys

around 20:40 gave an example of a property g had that in general tensors do not have

0ßelö7

@GPhys this?

GPhys

and have been asking when a tensor has that property

0ßelö7

01:01

Because I genuinely do not know what that is supposed to mean

GPhys

I honestly can't tell if you're serious

Semiclassical

What you're asking about seems to be this. Under what conditions does $\partial_\rho(g^{\mu \nu}A)=g^{\mu \nu}\partial_\rho(A)$ for a tensor $g$?

0ßelö7

that's a bad question

the answer is "in coordinates when $g$ is constant in those coordinates"

Semiclassical

which is why I was asking what his metric tensor was....

0ßelö7

I guess in SR there's an implicit assumption that everything is happening in cartesian coordinates

because already in polar coordinates that isn't true

GPhys

01:24

oh god do I have to vary phi and phi dagger independently

:o

Semiclassical

have fun with that

0ßelö7

::laughs at peasant physicist doing calculation::

::continues deriving inequalities::

@Semiclassical in other news, I found a formal statement for Lagrange multipliers for a variational problem on an infinite dimensional space

turns out everyone has been cheating, there's a PITA hypothesis

there's an issue with the constraint map being singular at the minimum point

GPhys

@0ßelö7 a what

0ßelö7

@GPhys pain in the ass hypothesis

you need to check that the derivative of the constraint map $E\to \Bbb R^k$ is surjective at the minimum point

that's usually a complete pain

...especially when the constraints are nonlinear integral operators

Secret

03:46

So. Heat wave incoming in Australia. Is it possible to harvest its energy thus lowering its temperature?

0ßelö7

@BalarkaSen I have a doozey for you

Balarka Sen

hm?

0ßelö7

@BalarkaSen Do there exist complete $n$-manifolds $(M,g)$ with $\mathrm{sec}\ge 0$ such that the sum of Betti numbers is arbitrarily large?

Balarka Sen

What about CP^n?

Or are you fixing dimension

0ßelö7

I mean $n$ fixed

Balarka Sen

03:49

Got it

cute question

0ßelö7

@BalarkaSen if you come up with the right answer we will call you gromov

Balarka Sen

lool

John Rennie

@Secret Antarctica is next door. Just put the cold end of your heat engine in Antarctica.

0ßelö7

holy shit @JohnRennie is a genius

why can't we build a heat engine from the Sahara to Antarctica

0

Q: How to interpret 1 second equals to approximately 300,000km in general relativity?

I am reading how massive object can cause other object to shrink in 4D (haven't touch the math yet), just want to know why time must becomes spatial dimension in order for relativity to work?

general-relativity

wot

Balarka Sen

So I am guessing large betti numbers somehow imply that the manifold can't admit nonnegative sectional curvature

That'd be pretty interesting though

I have no idea why something like that should hold

0ßelö7

04:01

@BalarkaSen I have no idea how his proof works

Balarka Sen

Can you link me ze paper

0ßelö7

He showed that for those hypotheses, $\sum b_i$ is bounded by $C(n)$ and also that the number of generators of $\pi_1(M)$ is bounded

Balarka Sen

Woah. (What's $C(n)$?)

0ßelö7

a constant depending on n

Balarka Sen

ohk

0ßelö7

04:02

@BalarkaSen looking

@BalarkaSen jstor.org/stable/2161381?seq=1#page_scan_tab_contents and references therein

Gromov's 1981 paper should reference a 1978 one with the fundamental group result

Balarka Sen

ok thanks

0ßelö7

@BalarkaSen it would be interesting to see if anyone has calculated some of the $C(n)$s!

Balarka Sen

yeah

0ßelö7

@BalarkaSen Mike might know about that. I don't know anyone that deep into Gromov-type geometry.

user308168

Why is there only one ad in the right sidebar of the main site?

0ßelö7

04:13

I dunno, are you a narc?

what kind of question is that

Balarka Sen

@JohnRennie Who is this mystical Captain Beefheart

0ßelö7

@BalarkaSen I have a topological doubt

Balarka Sen

cringe go ahead

0ßelö7

ok I'm not that bad at topology

no need to cringe

just need to make sure before I tell a prof he's wrong

Balarka Sen

:P

0ßelö7

04:16

this is a torus. The blue and black curves are homotopic

dmckee

@JohnRennie I don't but them for that purpose, but it is a big part of why apple can sell them so dearly.

Balarka Sen

OK

0ßelö7

@BalarkaSen I claim that there is no other curve in their homotopy class disjoint from both

user308168

I want to know whether there exists a limitation on the number of ads on the main site.

John Rennie

@BalarkaSen It's a long and psychosis ridden story involving Frank Zappa and some other very strange people.

dmckee

04:16

They are generally well built and durable, but a comparably well build windows laptop is generally 20ish% less expensive.

I do think that Apple puts some thought into the engineering tradeoffs, but again, you can find windows laptops that exhibit very similar choices and they cost less.

0ßelö7

@dmckee I think you're making a mistake by comparing OSX and Windows machines

John Rennie

@dmckee my (somewhat bitchy :-) comment applies to pretty much every consumer product. Cars for example. Humans are like that :-)

dmckee

I buy them because (a) unix (b) on day one with (c) all the peripherals working.

Balarka Sen

@0ßelö7 That doesn't look true (by homotopy class you don't mean to fix endpoints, do you?).

Oh, I see, no, you should be correct.

0ßelö7

yeah no one cares about endpoints

I want it to be disjoint anyway

Balarka Sen

04:20

If you project the cylinder as $S^1 \times I \to S^1$, the black curve maps to the full $S^1$ being the point

You constructed it that way

0ßelö7

yeah and it intersects the middle line which you can't cross

so if you start on either side of the blue line you eventually run into the black one

Balarka Sen

Yeah, that works.

0ßelö7

@BalarkaSen Now to put this in tikz...

help

Balarka Sen

@0ßelö7 Wait. What if you perturb the blue curve slightly to the left so that it becomes disjoint from the black curve?

0ßelö7

What about it?

Balarka Sen

04:25

Ah, I keep forgetting it's a closed cylinder. You'd still need to make it disjoint from the original blue curve at the endpoints; that's impossibruh

0ßelö7

yep

Balarka Sen

ok ok ok you're good

0ßelö7

I'm pretty happy with this

two profs said it shouldn't be possible

it makes the fluid mechanics homework 10x harder though :P

now it's a geometric measure theory problem

Balarka Sen

Good counterexample, proud of you for drawing that picture :P

0ßelö7

I draw lots of pictures

@BalarkaSen I think this is also a good counterexample for the problem. What's a $\Sigma$ such that $\partial\Sigma$ is a union of those curves?

it really doesn't work because the black one is on both sides of the blue one

Balarka Sen

04:30

well they intersect each other

0ßelö7

@BalarkaSen yeah? Never said the union has to be disjoint

Disjoint mod sets of measure zero or some shit

Balarka Sen

No I mean that implies there's no such $\Sigma$ right?

0ßelö7

?

Balarka Sen

That's very not a surface; what is $\Sigma$?

0ßelö7

a Lipschitz manifold

Balarka Sen

04:33

lol

alright then that should do the trick

0ßelö7

@BalarkaSen But not in the case I drew because of the torus shenanigans

the curve wraps around and intersects on the wrong side!

Balarka Sen

Right, there's no way to consistently fill the regions bounded by the black curves.

0ßelö7

that's actually a doubly wonderful counterexample then

can't apply Stokes theorem in any obvious way

Balarka Sen

I mean you can't apply Stokes on any surface that's sandwiched between the curves, but they are homotopic so there's a map $H : [0, 1]^2 \to S^1 \times I$ sending two sides of the squares to the curves you drew and pullback whatever form $\omega$ you have along $H$, then apply Stokes to $H^* \omega$ on $[0, 1]^2$.

0ßelö7

but remember, $\omega$ is not closed

I have a vector field $u$ (velocity) such that $\nabla\times u$ (vorticity) is tangent to the surface

Balarka Sen

04:41

Frick ok yeah

0ßelö7

@JohnRennie any bets on what a benchmark will show?

John Rennie

@0ßelö7 that you have too much free time?

0ßelö7

@JohnRennie random speeds keep going down

John Rennie

@0ßelö7 meanwhile my neuron count keeps going down and my cholesterol level keeps going up. Shrug.

0ßelö7

stop drinking so much then

John Rennie

04:54

If I stop drinking it won't mean I'll live longer, it will just feel that way

0ßelö7

@JohnRennie you need brain cells to do math

John Rennie

@0ßelö7 now you know why all the great maths is done by people under the age of forty :-)

0ßelö7

They either drink themselves to death or go insane?

Gnight

vzn

06:12

← get the led out was awesome, 3rd times a charm =D

Leaky Nun

Sand liquefied

►

@JohnRennie

John Rennie

That's pretty standard colloid science :-)

It's also the reason why ground liquifaction occurs in earthquakes

Although that's due to water fluidising the earth rather than air

Incidentally that technique is known as a fluidised bed

Leaky Nun

@JohnRennie is physics.SE down?

John Rennie

06:31

It's fine here ...

Slereah

07:25

Hey hey

Sid

08:33

@JohnRennie yeah, stop drinking and do yoga and stuff. You will be healthier

And try eating healthy stuff too..

Slereah

08:54

3

Balarka Sen

beautiful

Slereah

Balarka Sen

40 keks to you

Slereah

Hurray

So differential geometry question

If I have a (punctured) Clifford torus with coordinates $(x,y)$, is it a good idea to switch to polar coordinates

Balarka Sen

Depends on what you want to do

Slereah

08:57

$r^2 = x^2 + y^2$ and such

Well I need to have a coordinate system centered around the puncture so I can send it off to infinity

But I'm not 100% sure that this coordinate system makes sense on a torus

Ben Niehoff

It seems like this kind of thing is natural if you're describing your torus as a Riemann surface

so, a complex plane with two branch cuts

but I'm not sure how one does differential geometry this way

ah, I'm beginning to see it

a torus is just two copies of the Riemann sphere, glued together along the cuts

Slereah

09:19

The issue is the range of those coordinates mostly I suppose

Slereah

09:30

I guess I could just do one coordinate patch of this that's a disk

and then try to match them

lılostafa

@LeakyNun interesting. didn't know this

The first two comments were funny though :)

John Rennie

10:14

@Kaumudi.H: ping me when you're out of the exams

Qmechanic

10:38

@0ßelö7 : Ceci est une pipe!

Mithrandir24601

@Slereah Noooo!!!! I thought I'd finished with diff geom over a year ago, only to come here and find alas! It will always be there, ready to pounce when I least expect it

ACuriousMind

@Mithrandir24601 As long as this chat has ocelot at Slereah visiting it, you'll always ahve a chance to stumble over random geometry here ;P

Mithrandir24601

@ACuriousMind maybe that'll sink in some day. Perhaps I'm just in denial?

Slereah

10:59

@Mithrandir24601 Bad channel to come to if you don't like diff geo!

GPhys

@ACuriousMind I have a problem

keeping track of my signs in my QFT homework 😩

ACuriousMind

@GPhys May Feynman have mercy on your soul. Signs are the worst.

John Rennie

@Mithrandir24601 Unlikely if you're in Bristol. More likely you're in de Avon.

Balarka Sen

why do you hate geometry

thats so rude of you

user228700

11:30

@JohnRennie Ping! :-)

John Rennie

Aha. Exams over! Have a look on Hangouts ...

user228700

Wokay.

Mithrandir24601

12:15

@JohnRennie Well... I'm actually in Crete at the moment :) Aside from a couple of annoying things, I don't actually mind diff geometry - I was just being slightly dramatic :P

0ßelö7

12:45

@BalarkaSen The class of R folds with $vol\ge v,$ $diam\le D$, and $sec\ge -k$ has finitely many homotopy types

Leaky Nun

13:09

@JohnRennie would be a pity if something sunk, lol

Balarka Sen

@0ßelö7 what is an R-fold

you mean complete riemannian manifolds?

0ßelö7

Just Riemannian manifold

Balarka Sen

okizay

that's a pretty neat result

0ßelö7

I'm not sure if one needs completeness

Needless to say the proof is impossible

Balarka Sen

is this also by the G-dawg?

0ßelö7

13:16

Nope

Grove and Petersen

Balarka Sen

ah ok

Slereah

Who is

the G-dawg

0ßelö7

It requires one to look at the "space" of all Riemannian manifolds with the Gromov-Hausdorff distance

Balarka Sen

@Slereah the baboon man

gromov

@0ßelö7 Ah yes that's a thing

Leaky Nun

The gyroscope continuously amaze me.

0ßelö7

13:19

@BalarkaSen you basically "cover" this "space" with "balls" in which things are homotopy equivalent, and then use a "compactness" result

The actual proof doesn't look that bad.

@BalarkaSen Gromov's theorem requires two-index exact sequences and filtrations, which give me Bott and Tu PTSD flashbacks

Balarka Sen

uh oh lol

0ßelö7

Actually the fundamental group bound looks elementary

Anyway I think you should compute the gromov constants for your PhD @BalarkaSen

I imagine that's a seriously difficult task

Physics Meta

0

Q: Why was I blocked from asking a question despite recently having only positive answer and question reactions?

In my early days of using Physics Stack Exchange, I had no idea how the website worked and admittedly didn't do my research. And I'm talking about one question. I've asked only 6 questions - two with a total of 3 downvotes asked a while ago, one without any positive or negative votes, and three ...

support suspensions

0ßelö7

14:59

@EmilioPisanty TeXGod, I need to use a .cls file and tex.stackexchange.com/questions/1137/… is very inconsistent with how that's actually supposed to work

@EmilioPisanty I can't find this /texmf file

there's a hidden file /texmf-var

Emilio Pisanty

15:15

@0ßelö7 what sacrifice did you use?

anything less than a lamb and two chickens is unlikely to work with that one

0ßelö7

@EmilioPisanty I have two young nephews

Emilio Pisanty

@0ßelö7 about one and a half, then

seriously, though, how desperately do you need this to be installed centrally?

0ßelö7

@EmilioPisanty I want to turn my notes into something a little more organized and want to use the springer monograph template

including the usual Springer math fonts, etc. which I really like

Emilio Pisanty

that wasn't the question ;-)

0ßelö7

I don't know the answer to your question

I am telling you what I want to do

Emilio Pisanty

15:19

you know you can just put the .cls file on the same folder as your .tex, right?

0ßelö7

maybe you can figure out what my answer should be then

@EmilioPisanty and it will run?

Emilio Pisanty

the question you linked is for when you want to avoid doing that

@0ßelö7 yes

0ßelö7

@EmilioPisanty why would one want to avoid that?

Emilio Pisanty

this is me doing just that right this minute

@0ßelö7 'cause you use the same cls file over and over and you don't want the hassle

or similar situations

0ßelö7

I have over 100 tex in the same folder

so if I just keep doing that and put the .cls in there I'm good?

Emilio Pisanty

15:25

@0ßelö7 sure

whatever compiles that you're happy with

I'm not one to criticize others for their coding practices

Leaky Nun

I'll criticize others' coding practices every day.

0ßelö7

@EmilioPisanty I've tried to clean it up but it's too much of a hassle

Slereah

Woo hoo

the week end

Anonymous

15:41

@LeakyNun You might be interested in this, this and this.

Leaky Nun

thanks lol

0ßelö7

@Slereah still got an exam

Slereah

what are you examining

Anonymous

@LeakyNun The papers are good though. The tension explanation we used yesterday was hand-wavy. Also, I tried out the experiment today (mentioned it in my question). BTW, I see nothing to be lol-ing about.

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