The h Bar

0celo7

14:00

@yuggib oh shut up

ACuriousMind

@0celo7 Yes. Everyone who uses that argument is flat out wrong.

yuggib

^

0celo7

So how do you get the uncertainty principle?

It's wrong I guess

yuggib

doing the Fourier transform as it has to be done for $L^2$ functions

0celo7

Ok, how do you show that $-\mathrm{i}\nabla$ is Hermitian on $L^2$?

yuggib

14:01

i.e. doing a suitable $\mathrm{l.i.m.}$

Hari Prasad

@0celo7 mathpages.com/home/kmath488/kmath488.htm read this

0celo7

Because I'm pretty sure you need the wave functions to vanish at infinity for that

John Duffield

@HariPrasad : nearly. The proton has a definite tripartite nature, but the partons idea leaves it at that, whilst the quark idea employs quark confinement to try to explain why you've never seen the "fundamental particles". Only it doesn't really work for pion production or low-energy proton-antiproton annihilation to gamma photons.

yuggib

@0celo7 it is not Hermitian, it is self-adjoint

ACuriousMind

@0celo7 Well, you can do that argument for compactly supported smooth functions, and they are dense in $L^2$, so you can get it by an approximation argument, I guess

0celo7

14:02

@yuggib literally the same thing

yuggib

@0celo7 no

0celo7

@yuggib yes

ACuriousMind

@0celo7 No

0celo7

@ACuriousMind yup

yuggib

a matrix is Hermitian, an operator is either symmetric or self-adjoint

0celo7

14:03

I'm reading a physics book

I don't care for your whacky terminology

yuggib

that's your fault

0celo7

@ACuriousMind do I want to know the proof of that

yuggib

@0celo7 no

ACuriousMind

@0celo7 For their density? No.

0celo7

@ACuriousMind why not

ACuriousMind

14:05

That's the part of functional analysis you do exactly once and want to never repeat

0celo7

I think it's in my analysis book

Hari Prasad

Why is there far more matter than antimatter in the observable universe?

ACuriousMind

@HariPrasad Tell Stockholm if you find out.

Hari Prasad

Why does the zero-point energy of the vacuum not cause a large cosmological constant? What cancels it out?

ACuriousMind

@HariPrasad Why should the zero-point energy of the vacuum be large?

All these "naturalness" arguments babbling about the Planck scale never convinced me

John Duffield

14:11

@HariPrasad : see things like this in your link: "Thus one expects a collision between hadrons at very high energy to be dominated by interactions among essentially free quarks or gluons". Gluons in ordinary hadrons are virtual. They only exist in the mathematics of the model. A quark-gluon "soup" is more like pea soup. And there are no actual peas in pea soup.

ACuriousMind

and I'm pretty sure that's @ChrisWhite's star :)

Hari Prasad

John Duffield

@HariPrasad : there isn't. Because positronium is an "exotic" atom, composed of both matter and antimatter. And it's like light hydrogen. Have a read of this.

The proton is more like the positron than the electron. It ought to be classed as antimatter. But it isn't because it's ore common than the antiproton.

Hari Prasad

@JohnDuffield lol that's a lot of downvotes :P

user54412

@ACuriousMind now it is

ACuriousMind

14:20

@ChrisWhite Heh, okay

user54412

If we lived in a $\Lambda = 0$ universe, I'm pretty sure no one would even think to ask why vacuum energy isn't driving the universe apart.

John Duffield

@HariPrasad : the strong force cancels it out. But not quite.

@HariPrasad : it sure is a lot of downvotes. But science is not a democracy. Evidence is what separates fact from fiction, not votes. It isn't a religion either. Or so I'm told.

Hari Prasad

@JohnDuffield lol

John Duffield

@HariPrasad : here's an answer comparing the bag model of quark confinement to the balloon analogy for the expanding universe. The important point is that for a balloon in vacuum, the energy-pressure within is balanced by the tensile strength of the skin. For the balloon to expand the energy-pressure has to increase, which is in breach of conservation of energy. But another way for the balloon to expand is if the tensile strength reduces.

0celo7

pea soup seems like a bad idea

@ACuriousMind where does the Yukawa PDE $\Delta\phi=m^2\phi$ actually show up

the PDE, not the integral for the solution

John Duffield

14:35

@HariPrasad : IMHO the $64,000 dollar question is where does the strong force go in proton-antiproton annihilation to gamma photons? And also IMHO, the answer has to be it doesn't go anywhere. Because it's the "elastic tension" present in space which means waves in space propagate at c.

OK, I gotta go. Bye for now.

yuggib

@0celo7 that does not look like the Yukawa potential

looks more like the eigenvalue equation of the Laplacian

ACuriousMind

Looks like Euclidean Klein-Gordon to me

0celo7

the Green's function for that equation is the Yukawa potential

ACuriousMind

That's the equation of motion for a (Euclidean/non-relativistic) scalar field.

0celo7

Yes, I know that

ACuriousMind

14:39

Then why do you ask me where it shows up!?

You keep doing that

0celo7

What would possess you to write it down

ACuriousMind

Asking a question, and then saying you knew the answer

yuggib

@ACuriousMind apart from the fact that it lacks time ;-P

ACuriousMind

@yuggib Mmmh, I've known people who write the $\partial_t^2$ into the $\Delta$ for the Euclidean theory

yuggib

@ACuriousMind that's just horrendous

0celo7

14:40

uh, $\Delta$ is the 3-dim Laplacian

ACuriousMind

I don't really disagree :D

0celo7

so where does it show up?

ACuriousMind

@0celo7 Well, then it's the vacuum Poisson equation for a massive instead of a massless mediating boson.

0celo7

You're gonna be mad

ACuriousMind

You knew that.

0celo7

14:41

:D

how about this

how does one get that equation from first principles?

I know the QFT calculation that gives the interaction energy

but that just gives an integral, not that PDE

ACuriousMind

Write down the Lagrangian for the massive scalar field. The time-independent solutions to the equation of motion obey that equation.

I.e. this is the field equation for the static case

Hari Prasad

Physics Physics chat session in 1 hour?

0celo7

hmm, does the KGE come only from the SE?

or is there a "classical" way of getting it

@HariPrasad allegedly

ACuriousMind

@0celo7 What? Klein-Gordon is the full equation of motion. The Yukawa/Poisson equation is the special case of it for static fields

0celo7

I know that

Hari Prasad

14:45

1

Q: Is there an established theory on statistical physics in curved spacetime?

I tried to check this in google scholar but didn't find a paper explicitly focused on this topic. Do anyone know of some references on this issue? I do not mean the thermodynamics in curved spacetime which is well covered by Tolman's book ``Relativity, Thermodynamics and Cosmology''.

0celo7

but how do you actually get the KGE?

ACuriousMind

@0celo7 Uh, write down the Lagrangian, compute the E-L equations?

0celo7

@ACuriousMind how do you get the Lagrangian

ACuriousMind

You guess it! You always guess it! (But in the case of the free scalar field, you can also get it as a continuum limit of a lattice of nearest-neighbour coupled harmonic oscillators. That is, in 1+1 D, it's the continuum Lagrangian for a vibrating string)

0celo7

lol

you should hate me

I...knew that

ACuriousMind

14:47

That what the heck was your question?

0celo7

but why should the field be a bunch of harmonic oscillators

ACuriousMind

Because everything's a harmonic oscillator! ;)

0celo7

how does this question have 200+ views but only +4 on the top answer and why is it not accepted

@ACuriousMind I hope you're not serious

Hari Prasad

@0celo7 views dosen't matter

i see your answer

ACuriousMind

I'm half-serious. The other answer is because it has been wildly effective as a (mostly toy) model.

user54412

14:50

@0celo7 You wrote a pure math answer to a much simpler physics question

0celo7

@ChrisWhite pure math beats physics any day

what the fuck is with physicists, anyway

just define stuff properly

Hari Prasad

@0celo7 JohnDuffield Did you even read my post? I explain everything very clearly.

0celo7

I get more confused by a line of physics babble than a block of math

@HariPrasad What?

@ChrisWhite how can you answer that question without math

ACuriousMind

@0celo7 You know, unless one already knows the math, it's not clear to a casual reader how you even answer the question.

0celo7

> Theorem. [...] $R_\Sigma=\text{const.}$

That's exactly what OP wanted.

ACuriousMind

14:53

It's always good to begin the answer with a short passage that answers the question in words, and then pull forth the heavy artillery

0celo7

Also, the OP on the Stokes theorem did not accept my answer -.-

ACuriousMind

@0celo7 Yes, it is. I didn't say it wasn't. I said to a casual reader it's not clear

Where casual might even include people who have taken a GR course :P

0celo7

He's lucky I didn't invoke some theorem on foliations!!

user54412

Neither in physics nor in pure math is complexity ever good in and of itself. Quite the opposite in fact.

0celo7

@ChrisWhite That answer is not complex, it's precise.

And my Stokes answer is, AFAIK, the only proof of that fact in existence.

@ACuriousMind He's really lucky I didn't invoke the Schur Lemma, I think there's another proof via that method.

ACuriousMind

14:58

@0celo7 No, you're lucky because that would have yielded even less upvotes :P

0celo7

@ACuriousMind Do people not know that lemma

I wonder if it's in do Carmo

It's in Jost

user54412

@0celo7 Maybe I'll write one later. The answer parallels the definition of $k$ -- it's not free to be just anything, since we scaled away any variation.

ACuriousMind

The only Schur lemma I know is the one about intertwiners of irreducible representations

0celo7

@ACuriousMind There's that one too

Basically, if the sectional curvature depends only on $p\in M$, then it's constant on $M$.

And $M$ is a space form

this might only work in dimensions 3 and up

(does sectional curvature even exist for a 2-dim space?)

@ChrisWhite what $k$?

a priori, we don't know that we can put the metric in that form

all we have is homogeneity and isotropy

user54412

@0celo7 the whole point is putting the metric into that form

0celo7

15:05

@ChrisWhite mb you calculate the Ricci curvature of a leaf, show it's $k$ and argue scalars constructed from a homogeneous metric are constant

is that what you want to do?

@ACuriousMind oooo, FLRW is a twisted product and there are theorems about the curvature of such spaces

there might be another proof lurking there...

user54412

You proved some thing was constant. Great. The question is why is this particular form of the metric fully general enough, where this particular k is not dependent on time.

0celo7

@ChrisWhite Hmm, interesting, I guess $k$ could still be a function of the foliation parameter.

@ChrisWhite hmm, I actually don't see a reason for it to be constant in time

Hari Prasad

@ACuriousMind who confirms the edits that i make to questions?

ACuriousMind

@HariPrasad Users with more than 2000 reputation who participate in the suggested edit review queue or the author sof the posts.

Hari Prasad

@ACuriousMind alright

0

Q: Feasiblity of a long spinning top using an electromagnet to pull on Earth's magnetic field

Would it be feasible to build a infinitely spinning top (ref. Inception) by including a battery powered electromagnet who's polarity flipped in sync with the top's rotation such that the pull against the Earth's magnetic field countered energy losses to air resistance, friction, etc. For scale,...

electromagnetism rotation drag

0celo7

15:17

@ACuriousMind why does $k$ have to be constant

@ACuriousMind is $\mathbb{R}^3$ homeomorphic to the 3-hyperboloid

Hari Prasad

@ACuriousMind I think there should be a live widget in a member's profile page that shows which question, the member is currently writing answer to.

ACuriousMind

I don't think so.

(Also, why does everyone @ me with general questions here?!

0celo7

You're the smart one

@ACuriousMind Is that a response to me or Hari?

Hari Prasad

@0celo7 yes

ACuriousMind

@0celo7 Hari

0celo7

15:21

why do I have so many damn GR books

ACuriousMind

cuz you're a nerd

0celo7

nooooooo

say it ain't so

I think this is missing a few steps

@JohnRennie so why is $k$ constant in time

John Rennie

@0celo7 which $k$?

0celo7

huh, the leaf of a Lorentzian warped product is totally geodesic

@JohnRennie the one in FLRW

constant in time, space is easy

ACuriousMind

@0celo7 You have to stop asking random people questions as if they should know what you're talking about :P

John Rennie

15:26

@0celo7 erm, because ACM said so?

0celo7

@ACuriousMind mb he read the transcript

@JohnRennie that's what I usually go with

but he didn't say anything about it this time

@DanielSank You know what's an asynchronous communication protocol? Snapchat.

I send stuff and get a response three hours later and have fuck all of a clue of what I originally sent.

John Rennie

@0celo7 I'd have to go away and think about it

0celo7

@JohnRennie It's not explained in Wald, Zee, Hawking-Ellis, Straumann or Weinberg.

Reading Beem et al. now.

John Rennie

I would guess it's related to a symmetry - mysterious constants usually are.

And it's probably so obvious none of the authors thought it worth explaining.

0celo7

Well now Beem et al. assume that the spatial topology doesn't change

Hmm, I wonder if you can adjust $a(t)$ by a time-varying factor to cancel the one in $k(t)$

John Rennie

15:39

Are there any metrics in GR that change topology? I didn't think there were.

0celo7

@JohnRennie No, but even then

The metric does not know about the topology, at least nontrivially

And it's certainly not "obvious"

and I'm not sure that $\mathbb{R}^3$ and $H^3$ aren't homeomorphic

they're not isometric with the standard metrics

ACuriousMind

What is $H^3$?

0celo7

hyperbolic space

ACuriousMind

A model for hyperbolic space is the open disk, and the open disk is homeomorphic to real space.

0celo7

@ACuriousMind If you have a foliation, do all leaves have the same topology?

ACuriousMind

15:42

Depends on how you defined your foliation :P

0celo7

@JohnRennie Ok, so it would seem that topologically the $k=0$ space could morph into the $k=-1$ space.

So it has to be (1) geometric (2) physical

(2) would be very unsatisfying

ACuriousMind

...said the person chatting in a Physics chat.

0celo7

@ACuriousMind my disdain for physics is known

Hari Prasad

@0celo7 you love mathematics.

0celo7

Oh I just realized you Fourier transform something in that one thing with neutrons

@ACuriousMind help, what is it

there's like a delta function potential

ACuriousMind

15:45

18 mins ago, by ACuriousMind

@0celo7 You have to stop asking random people questions as if they should know what you're talking about :P

That also holds for non-random people.

0celo7

@ACuriousMind neutron scattering

that thing, you know what I'm talking about, right?

ACuriousMind

I...know that neutrons can scatter. That's about it

0celo7

ah, the Born approximation

@ACuriousMind That is the one where the scattering amplitude is the Fourier transform of the potential, right?

Hari Prasad

what happens after 9 minutes?

0celo7

we feast

ACuriousMind

15:51

@0celo7 I don't know. Have you googled "Born approximation"?

0celo7

@ACuriousMind I think you know the answer

ACuriousMind

I fear I indeed do.

0celo7

I did, but the Wiki article was not what I was looking for.

dmckee

@0celo7 Which doesn't mean that he has an obligation to give it to you. And especially not that he has an obligation to drop anything and give it to you now.

John Rennie

@HariPrasad we have a scheduled physics chat hour once a fortnight, and it's about to start

Hari Prasad

15:52

@JohnRennie good

0celo7

@dmckee I know, but maybe you can help me?

ACuriousMind

@0celo7 Wait, did you mean that I know the answer to "Have you googled..." or were you saying I'm lying when I said I don't know?

0celo7

> The scattering amplitude is proportional to the Fourier transform of the potential energy.

Thanks Google

@ACuriousMind Depends on how paranoid you are.

ACuriousMind

@0celo7 No, it depends on what you meant and nothing else.

I understood one thing, dmckee apparently the other. Which one did you mean?

0celo7

Huh?

I actually did Google it

Before I asked you

ACuriousMind

15:55

That's not what I'm asking about

0celo7

And I didn't call you a liar

I misunderstood @dmckee misunderstanding

ACuriousMind

So...you were saying you thought I knew you had googled it before asking me?

0celo7

@ACuriousMind No, I was joking that you probably thought I didn't Google it

ACuriousMind

Okay, that's what I got. Except that I didn't think you were joking :P

vzn

← feel old! remember when 'google' was only a noun

Mike

15:57

@JohnRennie how is the scheduled physics chat any different from what happens the other 335 hours a fortnight?

vzn

@Mike it has special/ secret sauce added.

Mike

this is possibly the only SE chat room I'm ever in that's almost always on topic.

vzn

@Mike lol guess you are a newb then :P

John Rennie

@Mike in the old days the chat was very quiet, so a scheduled chat time was organised to drum up interest.

ACuriousMind

@Mike There are usually more and different people around during a chat session, but you're right, it's not particularly different these days

0celo7

15:58

@Mike hahahahahahahahah

John Rennie

These days the chat is a lot busier so the chat session does tend to merge with the general chatter

0celo7

We talk about physics maybe 15% of the time

Mike

@vzn ... well, I'm originally from Mos Eisley so perhaps my gauge of on topic is skewed.

0celo7

Mostly we talk about math

Hari Prasad

@0celo7 yes. Look a butterfly!

vzn

15:59

@Mike how is that room these days? tried it a bit in the past, saw rumors (in here) of a big/ epic conflagration, dont know details....

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