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user54412
5:21 AM
remember the Oort cloud is rather hypothetical
 
user54412
it's treated as a definitive, well-known thing in popular science books for some reason, but it's existence is only inferred
 
Of course, but I want to know why theorists believe that there is such a large space between it and the heliopause
 
user54412
so I wouldn't lose too much sleep over its inner edge
 
Surely there's a reason, right?
Otherwise it wouldn't be a single region, but instead a bunch of planetesimals simply past the heliopause
It would be laughable if we had no reason.
 
user54412
it's not clear to what extent they really do believe that
 
5:25 AM
I guess enough to define the Oort cloud as a region
Instead of just calling it "all the planetesimals beyond heliopause, randomly dispersed"
They then wouldn't believe it had an inner-edge thousands of AU away
 
user54412
also, keep in mind that diagrams of the Oort cloud are just like diagrams of satellites around Earth -- they are extremely misrepresentative of the density of objects, since each one is expanded to one pixel, which is millions or billions of times its actual size
 
Of course
But you can clearly see how packed the Oort cloud is relative to the "gap" I was talking about
 
One of the comments under the question indicates that there are more known non-periodic comets with major axes beyond 1000 AU than those with axes between 100 and 1000. But the volume element may contribute.
There certainly seems to be a puapacy (sp?) of hard data.
 
user54412
that diagram is also just a cartoon
 
And? It's a diagram.
It's supposed to represent something.
 
user54412
5:29 AM
a thing that might not even exist ;)
 
I know, haha
But still wondering why the Oort cloud is thought to be in a region, rather than spread about all beyond the heliopause
 
@Chris Any notion why the Kuiper belt is assigned a 100ish AU outer limit? I mean, that's a largely hypothetical structure too (though we can at least see a few objects in that region), but surely the outer edge is even more hypothetical.
 
It shouldn't be random guesswork. It's a model.
 
user54412
I would trace the wiki citation about the inner edge, but alas it's a book, not an article
 
user54412
astronomy citations to anything other than freely available online articles ought to be banned
 
5:31 AM
@SirCumference "Model" can means as little as "wild ass guess" if the data is sparse.
 
user54412
@dmckee No idea.
 
Yeah, true, but it would be laughable if it were
 
user54412
perhaps because much further and it would start interfering with the Oort cloud :p
 
Nobody laughs at the Oort cloud like they do string theory
 
@SirCumference Word to the wise: all science reporting and primary or secondary texts should be assumed laughable until proven otherwise.
 
5:32 AM
Hmm...you make a good point
But I assume there's some reason why it isn't a joke by now
 
@SirCumference The Oort cloud people don't claim to be the smartest people in the room in front of TV cameras. That makes a difference.
 
I'm too lazy to see what the data is actually like
But it may be pretty logical. If so, there's surely a reason for the gap
Astronomers must have ruled out the possibility of tons of objects being there, right?
 
user54412
One thing to note is that comet-hunting used to be at least 50% of astronomy (back a couple hundred years ago). Now there might not be 50 people in the world who research comets.
 
Haha
True
 
user54412
If comets were as exciting as exoplanets these days, you can be there'd be a dozen competing theories as to where comets come from.
 
5:38 AM
Ah! The edges of the Kuiper belt are assigned by putting a little wiggle room around the 3:2 and 1:2 resonance orbits outside of Neptune.
 
I'm sorry?
 
But to this utter ignoramous that doesn't seem like a strong argument that there is nothing further out. Just that it should be lower density.
 
We're talking about the 900-4900 AU space cleared up
Er, no need to insult anyone...
We're just discussing space
 
@SirCumference You might be. I'm still puzzling over the edges assigned to the Kuiper belt.
 
5:40 AM
Heyo
 
That's a puzzle that (a) has some data and (b) is about my speed.
 
Dammit, ya got me at (a)
 
Can someone here give me any direction on how I'd approximate the change in entropy from dropping my pencil on the floor?
 
@SirCumference Because they seemed arbitrary.
 
user54412
@dmckee cute
 
5:41 AM
@Anthony The gravitational energy get turned (eventually) into heat. Check your thermometer and apply the thermodynamic definition of entropy?
 
Oh. That's easy, isn't it.
 
So we still haven't figured out why there's so much space. And yes, that doesn't seem like a strong argument that there is nothing further out
Call me an ignoramus
 
@Anthony If it's right. I'm guessing.
 
I mean that makes sense.
 
Wait a minute
in about a billion years, the Sun will get too hot for life on Earth...
wait, nvm, my question is stupid
 
Ooh ... more. Extra solar observing has revealed Kuiper belt like structures around a few stars other and some of them have sharp cut-offs. Interesting. Plus we see a drop outside the 1:2 resonance.
 
@dmckee Doesn't that formula depend on something like a reversible process, or something?
Quasi equilibrium? Something? The entropy one that is.
 
Yeah. Sets a lower limit.
 
tl;dr
What's his reasoning for the lower limit?
 
user54412
5:54 AM
Followup paper: "we shall show that the abrupt apparent termination of the Oort cloud at a critical inner semi-major axis $a = a_c \sim 2\times10^4$ AU is due to observational selection."
 
Huh, okay
 
Hm. Volume element or what?
 
Thanks @dmckee.
 
user54412
"We show that about one percent of the comets initially present in such an inner comet cloud, where the comets have $a$ semimajor axes on the order of $3\times10^3$ AU, would have been ejected by the perturbations of Jupiter and Saturn [...] Self-consistency then requires that the present-day mass of the inner-comet cloud be about two orders of magnitude greater than that of the Oort cloud."
 
::boggle::
 
user54412
5:57 AM
Much more recently: "The detached object Sedna is likely at the inner edge of the Oort cloud [...] all objects with perihelion distance q > 45 au and semimajor axis a > 250 au belong to the IOC."
 
user54412
I'll leave you with this gem from my literature search. No Death Star--For Now: "A star passing within ~$10^4$ AU of the Sun would trigger a comet shower that would reach the inner solar system about 0.18 Myr later. We calculate an a priori probability of ~0.4% that a star has passed this close to the Sun but that the comet shower has not yet reached the Earth."
 
10:20 AM
How am I supposed to learn anything when most of my memory is just ad jingles from the 90's
3
 
11:04 AM
Small terminology question: Is the conformal gauge (in string theory) the one where $h_{\alpha\beta}=\Omega^2 \eta_{\alpha\beta}$ or is the name reserved for $\Omega\equiv 1$?
I guess it's the case $\Omega^2\equiv 1$, based on Wikipedia and Lüst's book, but I find that a but of a misnomer!
 
 
2 hours later…
12:54 PM
@Danu If it's just a notational thing how can it be a misnomer
 
1:18 PM
@0celo7 Because the $\Omega^2\neq 1$ situation is also conformal(ly Minkowski).
 
1:45 PM
@Danu Ah, well according to BBS...well, they don't say it explicitly. Instead they refer to the "conformal gauge" in the exercises.
So I can only imagine it's the case when $\Omega^2\equiv 1$.
I don't see why you would pick a gauge in which it isn't unity...but maybe I'm still misunderstanding your question.
 
Well it wouldn't be a full gauge fixing to keep $\Omega^2$ free
It'd just parametrize a family of conformal gauges
But I guess the convention is to say that there is only one
I'd call it the flat gauge if I'd get to choose.
 
@Danu Once you're Witten-tier I'm sure you can let everyone know what the "best" terminology is ;)
 
@0celo7 No, that'd be Grothendieck-tier.
 
Hmm, are you capable of that?
(And I was going for the string theory analogy of course.)
 
I know :) It's just that Grothendieck is (1) a huge boss (2) renowned for coming up with very good names for things
 
1:56 PM
Isn't he one of the big category theory guy
 
He sadly died a while back.
But yes, he did work on category theory, among other things.
He described himself mostly as a cohomologist though
whatever that may entail...
 
@Danu I think it means whatever the person using it says it means :P
 
@ACuriousMind Welp, the book doesn't say it explicitly.
Which is why I asked
 
@Danu Oh. Well, that sucks
 
@Danu : He was the dual of a homologist, I suppose
 
2:29 PM
Morning folks
 
hey
 
3:00 PM
"Tarski's axiom also implies the axioms of infinity, choice, and power set."
Damn that's a fancy axiom
Very fancy indeed
 
I have no idea what I'm reading
 
⊢ ∃y(x ∈ y ∧ ∀z ∈ y (∀w(w ⊆ z → w ∈ y) ∧ ∃w ∈ y ∀v(v ⊆ z → v ∈ w)) ∧ ∀z(z ⊆ y → (z ≈ y ∨ z ∈ y)))
Is this better
 
Ehm
Not really hahaha
the hell's that?
 
It is math
 
Axiomatics seem so uninteresting, somehow
 
3:03 PM
@Slereah Oh gosh, another 0celo7
 
Nah we have enough @0celo7
2
 
Well, about as oblivious tho hahaha
 
Maths is of course shorthand for "mathematical anti-telharsic harfatum septomin"
 
Sigh, I'll go back to coding
 
For all x there exists y ??? x is in y and for all z that is in y ??? for all w ??? if w is a subset of z then w is in y ??? and there exists w in y for all v ??? if v is a subset of z then v is in w ??? ??? and for all z ??? if z is a subset of y then ??? z approximately??? y or z in y ??? ???

How many nested 'things' are here?
 
3:09 PM
Just a double nesting, I think.
yeah
For every x there exists some y such that (three properties)
The second and third one have a bit of nesting
 
whats '???' ?
 
I don;t know how to translate the brackets because I am used to see "such that" as :
 
For every set x, there exists a set y whose members include:
- x itself;
- every subset of every member of y;
- the power set of every member of y;
- every subset of y of cardinality less than that of y.
 
@Slereah See how much nicer that is than that abominable formula?
 
attempt to venn diagram failed...
 
3:14 PM
What's cardinality?
 
I'm not quite sure what that translates to, though
 
@BernardMeurer Size, basically
 
If y contains every power set of every member of itself
 
@ACuriousMind gotcha
 
Does it have infinite members
 
3:16 PM
@Slereah Yes
 
Hm
I wonder what an example of such a set looks like
Wait
Is that $N$ for the empty set
 
@Slereah Yes
 
Oooh neat
I guess it's easy to see how the axiom of infinity arises
 
Haha
 
3:23 PM
@BernardMeurer wtf
 
I suspect OP doesn't know what Fourier series are.
 
I suspect OP should not do quantum mechanics, then :P
 
wtf
 
Meh, I disagree.
 
you people have ridiculous prereqs for QM
 
3:24 PM
Yeah break my heart @ACuriousMind
 
You can definitely do basic QM without Fourier series
 
it is best to know 'em tho
 
@Danu Yes. But not the kind of QM they are apparently doing
 
You can do a gentle first semester course (up to, say, chapter 4 of Griffiths) no problem
 
3:24 PM
If you're gonna do physics you need Fourier series m8
 
@Slereah Of course
But no need to feel bad (at that point)
 
Yes, feel bad
Your science is bad and you should feel bad
 
Hi there :)
 
Phonon? Did you change your pic?
 
ye, a while ago
 
3:27 PM
If there are phonons and photons for sound and light, where are the smellons
Riddle me this Batman
 
how are you doing? you still pay your occasional visits to chess.com? @Danu
 
All the time!
Over the past week I managed to get back to ~1550 in blitz
 
oh haha way to go!
 
which is about my all-time high
I had been 1300-ish for a few months
 
ye I remember, well done! we should play sometime
 
3:29 PM
I need to learn how to play chess well
I know the rules and movements but that's pretty much it
 
I just started
No need to do training or whatever
I started playing about 3 years ago now
Just plyaing a lot gets you quite far.
 
Being 17 3 years ago is a significant portion of my life
hahaha
 
I'm not that much older.
I was ~1300 within 9 months
But I played about 2 hours per day :P
@Phonon Do you still play enough?
 
@Danu unfortunately not as much as I d like to, every now and then a friend challenges me and I end up playing some
@Danu but I still do tune in on the competitive scene
 
@ACuriousMind I don't see the difference
 
3:38 PM
@Phonon Carlsen was good last tourney :(
 
@Phonon what
 
Caruana good too though---he's still my favorite player.
 
@Danu oh ye, he's in top shape indeed! Did you see his games against Michael Adams and Eljanov? just wow...
 
does not liking chess indicate stupidity
 
@Phonon I didn't really get to follow anything in detail :(
@0celo7 No, but liking chess does correlate with intelligence.
 
3:42 PM
I used to play, was pretty terrible
 
These are the exam weeks for me, so I can't really invest hours to follow matches in detail :(
 
I guess that's to be expected.
 
@Danu :(, gl with your exams
 
3:58 PM
@0celo7 wow rude
 
4:12 PM
@FenderLesPaul ?
 
If you've been focusing on the tactics of chess (as a beginner must), then just reading a book or two on strategy and then practicing for a while will change your play for the better. And the effects last.
 
@0celo7 I said hi earlier and you didn't say anything
:(
 
My nephew has started beating my brother often enough to get a swelled head about it. So Kevin sat him in front of me and I beat him four games running even though I haven't played in years.
All because I approached each game with a broad plan as well as watching the consequences of individual moves.
I never was a competitive player, but I've had IMs ask me back to play again. Because even though they beat me consistently I was strong enough to be entertaining.
 
4:31 PM
@FenderLesPaul you never answer me
 
5:10 PM
@0celo7 I do :3
I just did
 
5:35 PM
Ok almost never
 
5:51 PM
Anyone out here?
 
Nope
 
Mind if I ask a very short question?
 
Why does everyone always ask that? Just ask your question - if someone wants to answer, they will.
6
And if someone minds you asking a question, they will certainly also mind you asking if they mind asking a question.
 
Oh, alright.
 
@ACuriousMind most people are not rude
 
5:55 PM
Just wanted to make sure, potential energy among uncharged gas particles is generally negative right?
 
@0celo7 ...so?
@busukxuan Signs for energies are always convention, since you are free to put the zero energy where-ever you please.
 
@ACuriousMind barging in and just asking a question is seen by most as rude.
Nevermind the room culture.
 
@ACuriousMind If I say kinetic energy is positive for a moving particle and zero for a stationary one, then would that make potential energy among uncharged gas particles negative?
 
@0celo7 I don't see asking a question in a chat where currently no one is chatting as "barging in", but whatever
 
@0celo7 not here
 
6:02 PM
@busukxuan No, no, no, you have to set the zero of potential energy. What kind of potential energy do uncharges gas particle have among them, anyway?
The kinetic energy of a stationary particle is always zero, you're not free to set that
 
@DavidZ "Nevermind room culture"
 
@ACuriousMind gravitational, perhaps. But I mean internally, no external gravitational effects. I guess I'll set 0 when they are infinitely far apart.
 
@busukxuan Then it's negative, but that has to do with the zero at infinity and the attractiveness of the gravitational force, nothing with the gas particles.
 
@ACuriousMind I know gravitational potential energy is generally negative by convention, but I'm not sure if I'm missing anything in a gas case.
@ACuriousMind is gravitation really all there is?
 
I don't know, you were the one who started talking about potential energy between gas particles. I'd say that there isn't any potential energy between them in the case of an ideal gas.
 
6:07 PM
@ACuriousMind Oh my bad, I'm talking about a non-ideal gas.
like atmospheric gas
 
Non-ideal gasses are cancer
 
@busukxuan Well, then it depends on whether your interaction is purely attractive or not. Typically, it is not, they will repel at short distances, for example by the London dispersion force (see the nice graph right there to see the energy isn't always negative)
 
6:19 PM
@ACuriousMind The caption said the "long-range" section is due to London dispersion force, but what does "long-range section" specifically refer to? Also what about the "short-range"?
Well I always thought London dispersion could only be attractive...
 
Ah, sorry, the picture is what I wanted, but it's indeed not the dispersion force that's repulsive
The short-range repulsion is due to electromagnetic repulsion and Pauli exclusion when the electron orbitals of two close particles overlap significantly.
You can't really model that force from first principles, a common "hack" is the Lennard-Jones potential
 
Why not
 
Hm... Same question here. Is it just a metaphor because it will take a lot of effort, and might not be applicable to every atom/molecule out there?
 
@busukxuan With "you can't really model" I mean you cannot derive an expression in terms of a potential as a function of molecular distance from the quantum-mechanical description because there is no tractable approximation - the exact behaviour depends highly on the shape and binding structure of your gas particles.
 
@ACuriousMind that means a more accurate model for a molecule needs to be built ad hoc and even then it will be pretty unpredictable?
 
6:33 PM
@busukxuan You only need a more accurate model if you have need for the precision. What are you trying to do?
The reason the L-J potential has its own name and is so common even if the twelfth power in there has no physical basis is that it suffices for many applications.
For modelling gases, it's usually fine
 
@ACuriousMind I am not really trying to do actual stuff, it's just that when I learn I need to look deeper into the picture, though it is a little deeper in it actually helps me grasp the more basic concepts.
So in a usual, STP gas, without weird polar interactions, potential energy is generally negative?
Or is repulsion actually important under that condition?
 
Important for what?
 
As in having enough influence to probably make the potential energy positive.
 
The potential energy will always get positive at short distances.
That's what makes things solid.
That's what makes gas molecules rebound from container walls and from each other
 
I understand that, what I mean is would it make a whole gas system's potential energy positive.
 
6:46 PM
Sometimes. Why are you so concerned about the sign of the energy?
 
IIRC at STP molar volume is about 0.0224 m^3 mol^-1
 
I had to do a calculation with moles earlier
It was terrible
 
@ACuriousMind Wanted to get a better picture in a situation when liquid turns into gas
@0celo7 Why was it terrible?
 
@busukxuan confirmed my suspicion of severe mental degradation
due to something
 
@0celo7 Wow the first sentence was pretty hyperbolic
 
6:54 PM
@busukxuan it's really not
ask @ACuriousMind
 
@busukxuan For that, you can indeed forget about the repulsive short-range force. Just model it with attractive forces and think of the particles classically as little billiard balls that can bounce off each other, instead of modelling the "bounce off" with the quantum mechanical repulsive force
 
@ACuriousMind Oh yeah, now that I think of it I might as well say billiard balls have quantum mechanical repulsive forces that stop them from running into (literally) each other.
I guess I understand the thing now, thanks a lot!
 
@Danu Btw Polchinski seems to call "conformal gauge" the case when $\Omega^2$ is general :)
 
7:38 PM
@ACuriousMind What's SU(3)?
 
@BernardMeurer The special unitary group in three dimensions
 
That's what I told him!
 
What's a Hamiltonian?
 
@BernardMeurer Often the energy function in terms of position and momentum. More generally the thing that determines the motion in Hamiltonian mechanics.
Where are you stumbling across these words?
 
Oh oh last question now; promise
@ACuriousMind How can we say an electron has an 'up' or 'down' spin?
In relation to what is it up and down
 
7:50 PM
In relation to some fixed axis
 
@ACuriousMind He stumbled across me.
 
@ACuriousMind 0celo7 likes to throw them at me on skype
and since you won't join I have to ask here
 
I told him that the up and down spin is caused by the SU(3) of the Hamiltonian.
 
@0celo7 Stop trolling.
 
You did not!
He told me a quark was something something SU(3)
 
8:00 PM
That's better
 
@ACuriousMind Who knows what I'm telling @BernardMeurer on Skype without your watchful eye
I could be telling him the mysteries of Dirac belt standing wave spinors.
 
8:27 PM
An airplane is flying at an altitude of 7000 ft and velocity of 100 ft/s. At a point on the wing, the velocity is 120 ft/s. Calculate the pressure at that point assuming incompressible flow.
I can get pressure and density at 7000 ft from Standard atmosphere, but how does this help calculate the pressure at the wing
 
9:15 PM
@Danu Everything is ready for my talk tomorrow
they told me to make it Ph.D.-student level
so it would be perfect for you :-P
 
user116211
Can anyone tell me why thermal equilibrium is added to the ergodic hypothesis?
 
user116211
In an isolated system, in thermal equilibrium, all microstates are equally likely- can anyone tell me why thermal equilibrium is added here?
 
I honestly do not know, but it does sound right
 
user116211
@BernardMeurer: Okay let me elaborate a bit.....
 
@user36790 Why do you say "added"? Do you think that "In an isolated system, all microstates are equally likely" is something that can be true?
 
user116211
9:28 PM
@ACuriousMind: 'Included'??
 
@user36790 I'm not understanding what you are trying to ask. The ergodic hypothesis is that macrostates in thermal equilibrium have equiprobable microstates.
What's the question about that?
 
@ACuriousMind Is my favorite source of fancy words
 
user116211
@ACuriousMind: What is bothering me is: doesn't equilibrium mean only one macrostate which has the greatest multiplicities? You can't say that the macrostate corresponding to all particles confined in the corner of a container, represents thermal equilibrium.
 
@ACuriousMind How is the Fourier series really defined?
 
@user36790 A macrostate is a probability distribution on the microstates, which are the "actual" states of a system. You seem confused about how thermodynamics works, in genera.
 
9:36 PM
@ACuriousMind What's the exact mechanism for the coupling of standing waves to inhomogeneous spacetime?
 
user116211
@ACuriousMind: A macrostate is a probability distribution on the microstates- I didn't know a macrostate is a probability distribution; could you elaborate on how macrostate is a probability distribution or give me some links?
 
@user36790 No, I don't really do thermodynamics, so I don't know references, but I am at a loss how else you might have defined a macrostate. What is your definition of it, and what is your definition of equilibrium?
@BernardMeurer wat
@0celo7 wat
 
@ACuriousMind Is there something deeper besides "it's the expansion of $f(x)$ using the eigenfunctions $1,\cos(n\pi x/L),\sin(n\pi x/L)$"?
 
@0celo7 Yes, it is the simplest manifestation of Poyntryagin duality, in this case between $\mathbb{Z}$ and $S^1$.
 
wtf
 
user116211
9:42 PM
@ACuriousMind: To me, a macrostate is just a configuration of energy, number of particles, volume and temperature. I didn't know macrostate is probability distribution ...
 
@user36790 And how does a given macrostate relate to a microstate in that framework?
What's temperature, for that matter? Statistical mechanics usually defines temperature through the derivative of the entropy, for which you need the notion of a probability distribution.
 
@ACuriousMind blame @0celo7
 
Why am I being blamed
 
For you are the root of evil
 
@BernardMeurer that's a bit of an exaggeration, don't you think :/
 
user116211
9:48 PM
@ACuriousMind: Micorstate is a specific possible way for the system to achieve that particular macroscopic configuration. and yes, temp. is defined on entropy. I got this from thermodynamics, not from Statistical mechanics.
 
@user36790 I'll write an answer to your question clarifying the terminology. Your entire confusion is really due to you not having precise definitions of the words you are using.
 
@ACuriousMind "not having precise definitions of the words you are using." Did you call me?
 
user116211
@ACuriousMind: thanks; I'll be modifying my question: physics.stackexchange.com/questions/217970/… in order to clear up my argument.
 
10:14 PM
@ACuriousMind how do I deal with stalkers
@ACuriousMind Is $\partial\alpha/\partial s$ the same as the tangent to $s\mapsto \alpha(s,t_0)$ for fixed $t_0$?
 
10:35 PM
@0celo7 That's more or less the definition of the partial derivative.
@0celo7 wat
 
@ACuriousMind no no in the context of HE/do Carmo
 
@0celo7 My answer remains the same.
 
@ACuriousMind sigh I still don't get it
 
10:47 PM
@ACuriousMind Bernard is stalking me
 
AM NOT!
 
you went to my sister's company's staff page and started naming all the women
 
@ACuriousMind wtf how is this funny to you
 

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