The h Bar - 2016-08-15 (page 3 of 5)

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4:08 PM

@JohnRennie really like the idea but there is not much time for questions in the chat, dont really know if youd be getting your moneys worth, you might consider a private session instead if youre funding it, unless you have low expectations for the public session

@JohnRennie would like to see more diversity myself but went for the "low hanging fruit" to begin with, despite all the expressed enthusiasm for the prj over months now, nobody else is helping round up guests (aka "cat-herding"). intending to write a meta post on that soon (maybe tonite), hope it doesnt get downvoted (too much) o_O

@vzn it isn't really an idea in the sense that I've given it any real thought. I was just wondering if there was any enthusiasm for it. No-one seems to be jumping up and down with glee at the idea.

@JohnRennie really like the idea myself. what more do you want? starred it, repeated it in the other chat room DS set up etc. ... it seems like the whole guest speaker thing is basically a success but not nec gaining any momentum (which is sizeable nonetheless)...

@ACuriousMind thx for your interest! youve been requested as/ encouraged to be a guest by multiple ppl. plz consider it. dont think it would take any extra time for you outside what you already contribute to the site/ chat.

@JohnRennie true, but we're also not coming at you with torches and pitchforks for suggesting it

Actually, I am kinda wondering whether the reason that acuriousmind and many others found my questions confusing is actually describable with a string at all...

perhaps it is one of those things like the experience of seeing red that no paragraph can describe it

And tbh, text communcation can only convey 20% of the information from me. The rest, 80% are gestures, body language and a whole lot of dark matter

(joke) and we don't even have idea what dark matter is

@Secret I'm sorry, I only understood 20% of what you just said

4:19 PM

lol

@jim: this is the sort of thing I've been flagging as unclear:

-2

Q: What happens when you put carbon under a high pressure vacuum?

I'm trying to do some research, and was wondering what happens on the lower level if you put carbon under a higher pressure vacuum.

@Secret In physics, text communication is the most efficient communication there is. You can't convey a precise physical idea through "body language". The reason I often don't understand what you're saying is simply that you tend to create very long posts that have erratic line breaks and don't seem to possess a clear thread of reasoning holding them together.

Because I can't work out what is actually being asked.

@Secret please pay attention to what @ACuriousMind just said.

@JohnRennie Yeah, that one makes sense

Also, am I now the Clarity Czar?

4:23 PM

@Jim Not unless you're wearing a pointy hat.

Are you wearing a pointy hat?

..... no comment

I think next time when I ask a question, I should just state my question and omit that block of "background on explaining why I am asking the question". I kinda suspect that's where all the confusion is generated from.

I'll try my best to keep my questions more precise, hopefully that will resolve the confusion problem

:Jim quietly takes off his pointy hat and hides it:

@Secret Precision is good.

@Jim You don't want to be the clarity czar?

Do Czars wear pointy hats?

4:25 PM

^ my question

@JohnRennie The Clarity Czar does.

[citation needed]

@Jim Citation?

In other news, there used to be a Q4 prepared for acuriousmind, but coincidentally, Q4 was addressed by the quantum move nature article, thus it no longer exists

Imperial Crown of Russia

The Imperial Crown of Russia, also known as the Great Imperial Crown, was used by the Emperors of Russia until the monarchy's abolition in 1917. The Great Imperial Crown was first used in a coronation by Catherine II, and was last used at the coronation of Nicholas II. It survived the subsequent revolution and is currently on display in the Moscow Kremlin Armoury State Diamond Fund. == Background == By 1613, when Michael Romanov, the first Tsar of the Romanov Dynasty was crowned, the Russian regalia included a pectoral cross, a golden chain, a barmas (wide ceremonial collar), the Crown of Monomakh...

^only kind of pointy

4:26 PM

@ACuriousMind Not Clarity Czar. Your argument is invalid.

@DanielSank Maybe you just need to have the superior insight of the Clarity Czar to see how it applies here

::Clarity Czar's guards come to to take @ACuriousMind to the gulag::

Noooooooooooooo!

You know too much.

To be clear (and as the Clarity Czar, I have the right), we need to officially establish whether there is precedent of a Clarity Czar similar position wearing a pointy hat

4:29 PM

Proof!!

user image

That settles it! The Clarity Czar must always wear a pointy hat

:Jim slowly replaces his pointy hat:

I'm calling you out as a fraud. The true Clarity Czar wouldn't have removed their hat in the first place.

Your actions have muddled the situation. True Czar of Clarity, you are not!

I had to make it clear whether or not the Clarity Czar was required to wear it

You stole the hat!

@DanielSank That point is unclear

4:33 PM

No, it's clearly pointy.

Nothing unclear about it.

If I did, the rules clearly state that the Czar must always wear a pointy hat. Whomever I supposedly stole it from, therefore, can no longer be the Clarity Czar

@Jim In my case, although I don't vtc much at all, I vtc stuff as unclear if it's unclear. I think there's no correlation with question length.

@Jim You're technically correct.

The best kind of correct.

@DanielSank Most of the crowns weren't used everyday, they were sacred things and they were used only on specific occasions. In the thoughts of the medieval people, the kings weren't like the dictators in our era, but they were appointed by some sacral/spiritual power. The crown symbolized this contact between the king and the higher powers (f.e. God in the christian kingdoms in the medieval Europe), it had been blasphemy to use it everyday.

I have already ruled!

At the risk of contaminating the chat with physics, see this question:

0

Q: Do many body systems fall apart eventually?

Imagine an n-body problem with lots of particles of identical mass (billions of them). I saw several simulations on the internet, where the particles first form small clumps then bigger clumps, then finally one huge globular cluster like clump around the center of mass. Is this clump a stable f...

classical-mechanics many-body

4:35 PM

@JohnRennie What about it?

It's a crappy post.

I think the answer is yes because any three body system is unstable and an n-body system is just a load of three body systems.

But has this been formalised? Is there a relevant theorem?

so.... Earth should eventually fall apart?

@JohnRennie Wut?

I'm somewhat sure the answer depends on the particulars of the system.

@DanielSank didn't Poincare prove any three body system will eventually eject one of the bodies? Assuming no special symmetries.

@JohnRennie I don't know! Interesting.

I find that rather difficult to believe though.

4:38 PM

not if they form a clump

Ah.

as in the question

@JohnRennie Froze a glove in LN2

@Jim: the argument applies to bodies moving in a central force. Interatomic forces in molecules aren't central.

Maybe the idea is that a three body system is somehow ergodic and so you're guaranteed to eventually visit a state wherein all of the energy is in a particular one of the bodies.

@0celo7 Fun timez in teh physicis labz?

4:39 PM

@DanielSank Sounds reasonable, though I know too little of this area to tell.

@0celo7 Always good to see taxpayers money being put to good use :-)

@JohnRennie I'd like to point you to a Black Hole. Was an n-body system. Did the opposite of fall apart

@JohnRennie Well ok but suppose I put three massive bodies all next to one another with zero relative motion.

There's no way those are flying apart.

@JohnRennie That's a good point.

Back to work! @0celo7

@JohnRennie it was a big deal in math long ago to prove the 3 body system eqns for gravity are unsolvable/ and/ or chaotic, but dont know the details. its nearly an open question in math...

@vzn The three body problem doesn't admit analytic solution. That doesn't preclude knowing whether or not the system becomes unbound in some way though.

@DanielSank that's a bit of a special case. If you consider point masses then any two can get arbitrarily close and therefore liberate an arbitrarily large amount of KE for the third mass to escape.

4:42 PM

@DanielSank afaik determining its eventual bounds ls nearly the same as requiring analytic eqns

Real masses obviously aren't pointlike, but for galaxies I think pointlike masses are a pretty good approximation.

If an n-body system ejects a body, it reduces the average energy of the remaining system, which makes it less likely to eject another body. Nevertheless, galaxies are great proof that an n-body system won't just dissolve away

@Jim except that I've seen it claim that galaxies will evaporate, though you're looking at absurdly long timescales.

what kind of scale?

@Jim The dark matter plays there a significant role as well, to stabilize them

4:44 PM

@JohnRennie instability is different than "lack of analytic eqns" ie one does not nec imply the other. there are probably lots of stable 3-body orbits but finding them systematically is open problem...

@Jim the escape velocity from the galaxies are around 500km/s, while the mean speed of the stars is around 160km/s

> The results of N-body simulations have shown that the stars can follow unusual paths through the cluster, often forming loops and often falling more directly toward the core than would a single star orbiting a central mass.
In addition, due to interactions with other stars that result in an increase in velocity, some of the stars gain sufficient energy to escape the cluster. Over long periods of time this will result in a dissipation of the cluster, a process termed evaporation.[81] The typical time scale for the evaporation of a globular cluster is 1010 years.[60] In 2010 it became possi…

@peterh details, details

@Jim Kyle Kanos was the expert of this topic :-(

From:

Globular cluster

A globular cluster is a spherical collection of stars that orbits a galactic core as a satellite. Globular clusters are very tightly bound by gravity, which gives them their spherical shapes and relatively high stellar densities toward their centers. The name of this category of star cluster is derived from the Latin globulus—a small sphere. A globular cluster is sometimes known more simply as a globular. Globular clusters, which are found in the halo of a galaxy, contain considerably more stars and are much older than the less dense galactic, or open clusters, which are found in the disk. Globular...

4:46 PM

@JohnRennie I was waiting for the spectrometer to get cooled down!

@JohnRennie this is starting remind me of the discussion of "rogue/ super waves" awhile back in here. suspect very similar concept/ phenomenon applies to n-body problems

@DanielSank Yeah, but why are you spelling like that?

all this says that you might certainly eject a few bodies from the system, but nothing shows yet definitively that things like galaxies or galactic clusters will dissolve or fall apart. Or planets and stars too, for that matter

@JohnRennie I think what one can show in general is that the three-body motion is chaotic, however, chaoticity does not necessarily imply that the system is unstable in the sense that it will eject a body. E.g. the solar system is seen to be not ejecting bodies in most simulations.

> the solar system is seen to be not ejecting bodies in most simulations

Is that true?

4:48 PM

Actually, the Sun-planets system is remarkably stable

I was under the impression that if you ran the simulation long enough planets did get ejected.

@JohnRennie It's a dim memory from what I've been told, but I think it is true

No, the Sun explodes first

@Jim details, details, bloody experimentalists!

but that's cheating

4:49 PM

@JohnRennie this is another open problem, there is some connection to chaotic dynamics. findings in area are something like orbits that are "stable" for billions of years may still lead to eventual instabilities (somewhat similar to butterfly effect)

OK, OK, we're agreed it's an open problem then. So the question can't be answered.

@JohnRennie think it is answerable with the ideas sketched out & good refs :)

@vzn The point is exactly that the system being "chaotic" doesn't tell you much about it's stability. Chaos and stability are two completely disjoint notions.

@JohnRennie sure it can. It asks if it falls apart or dissolves away. The answer is no. In no reasonable amount of time will the whole system dissolve away or fall apart. It may lose some or most of it, but the system will remain for any reasonable timescale

Although being chaotic does mean that it will be harder to get any kind of certain statement about stability in the absence of analytic solutions

4:51 PM

@ACuriousMind it might seem that way but not exactly... they interconnect

See: relativity.livingreviews.org/…

@vzn How do they interconnect?

Globular clusters evaporate!!

Hey guys !

@ACuriousMind ok admittedly am just trying to paraphrase/ summarize a popsci book once read on subj, but it was citing sci research, will have to try to dig it up again. there was a lot of interest in these types of questions in the ~1990s... it might have been by ian stewart who covers similar areas...

4:52 PM

@JohnRennie is that true for globular clusters not around other galaxies, or only the result of interacting with another n-body system?

In this case a GC is just a conveniently sized spherically symmetric object. The (average) spherical symmetry means you can assume random stellar velocities and I guess they assume the system is ergodic.

Obviously in a spiral galaxy the situation is less clear cut as the stellar velocities are highly correlated.

@ACuriousMind let me try to think of an example. the earth climate system is basically a chaotic system but is generally pretty stable. another example would be jupiters red spot. but we dont know if the spot will disappear someday, or longterm directions in earth climate because of so many "moving parts". ie in a sense, locally temporally stable, but unpredictable beyond that. another neat example, rings of saturn (which actually are quite chaotic in a local sense, but not globally). etc

Is this a thermodynamics or chaos theory discussion ?

So it's not certain that n-body systems dissolve. And given that galaxies have existed for what, 10Gy(?), that's pretty solid evidence that some n-body systems won't dissolve. That's about the upper limit on reasonable timescales. Longer than that and it really doesn't matter

@vzn But Saturn's rings are a transient feature

@Jim theyve been around billions of years & probably will be for billions more. so "transient vs stable" almost has a "relativistic" aspect/ pov to it...

4:58 PM

@vzn the rings are only on the order of millions of years old

@vzn So...you just gave a few examples that show that stability and chaos are not really interconnected?

@Jim If no particle can get the escape energy, like the particles of the Earth, then it won't dissolve. In the case of the Earth, there is a strong stabilization mechanism what doesn't exist in the case of a galaxy

the result of moons or large rocky objects disintegrating at the roche limit

I.e. there are stable chaotic systems and unstable non-chaotic systems.

Not sure how that is supposed to support your point about them being interconnected

@peterh exactly, so the answer to the OP question is no, not all n-body systems eventually dissolve

5:00 PM

@Jim [question that/ sounds too young to me/ citation needed] ... looking at wikipedias long article, strangely it seems not to estimate age en.wikipedia.org/wiki/Rings_of_Saturn

Ok, I'm going now... Bye

Wow, Physics Guy just evaporated :-)

This chat room must be ergodic.

@ACuriousMind stability and chaos are not black-and-white concepts but exist on a continuum, somewhat like simultaneity in a universe etc

@vzn cv.nrao.edu/~rdickman/notesa121/saturn.html

100 million, my mistake

still transient

@Jim thats the remaining estimated age

> ...suggesting that they were only recently formed.

5:03 PM

same with the rings around all the gas giants

Anyhow, I'll leave you lot to argue it out. I have to go fold my washing (not a euphemism).

"recently formed" is not any numerical estimate of age.

they are continuously replenished because saturn has so many satellites and every so often one drops below the roche limit

@vzn it doesn't include billions of years ago

@Jim admittedly was guessing ("swag") but you havent refuted the idea yet :P

@ACuriousMind Does the five lemma work in any category?

5:06 PM

@vzn I showed they are transient, which means impermanent

@Jim Somebody has proven, that the at least 3-body systems are chaotic. -> the question is, is their energy distribution limited. If not, for example,the Boltzman-distribution isn't, then this + chaotic means they will eventually evaporate

@Jim our sun/ solar system/ galaxy/ universe are impermanent also, but some )( credit for actually citing something :P

@jim Once I've asked a question, do the stars in a galaxy have a thermal distribution

@vzn What do you mean by that? Both "stable" and "chaotic" have clear cut definitions that either apply or do not apply to any given system (of course, determining whether they apply is a different matter)

@0celo7 It holds in any abelian category, but there are also specific non-abelian categories where it applies.

nasa.gov/mission_pages/cassini/media/cassini20071212.html

5:14 PM

Re: the above discussion about globular clusters, etc., any purely gravitational N-body system eventually dissolves, until only 2 particles remain. Writing up a referenced answer if you're curious, check in a few.

2

nice, an actual expert! :D

There, Saturn's rings persist, but they are similar to the sea bed. Oceans are always around, but the sea bed is only a few hundred million years old, compared to the continental crust, which is a few billion

@KyleOman I'd again like to point to a black hole

@Jim and I'll point to Hawking radiation.

@Jim From where they get a re-supply?

@KyleOman sure, but that's no longer a purely gravitational n-body system now

5:17 PM

@Jim Maybe the galilean moons help them to catch asteroids?

and it's evaporating, not dissolving

@Jim neither is the BH!

Well, the technical term for the dissolution of e.g. a globular cluster is evaporation

@KyleOman details, meaningless details

@KyleOman Schwarzschild black hole? How is it not purely gravitational?

A BH is 1-body... the theorem I'm referring to deals with collisionless systems of N bodies.

So it will break down if you allow collisions to combine things into BHs

ah, but it was n-body just before the hole formed

5:19 PM

collisionless

just because thos n bodies merged into one...

I have a solid solution under particular assumptions (which are in some cases pretty darned good), which afaik is pretty typical in physics ;)

@KyleOman yes, if you have an unlucky set of dark matter that falls inward and forms a clump dense enough to be a black hole, that's what you get. Let's see even dark matter get out of that one

@ACuriousMind they are very tricky to define strictly/ mathematically etc, dont know what defns you are referring to... there are some rough ideas that have been subject to recent scientific revision in the 1990s and later due to study of "chaotic dynamics" field etc

No realistic dark matter system I know of will directly collapse into a BH. Heck, you can barely feed a SMBH with DM.

Also, that's a collision, so of course what I'm talking about won't apply.

5:22 PM

what's a collision?

@Danu done!

@Jim ?!? the article you just cited says (as my estimate) saturn rings probably as old as age of solar system and you then compare them to the sea bed, a few hundred million years old? huh?

@vzn The ocean is older than the ocean floor. The rings as an overall feature are older than the material that comprises them. They change and reform

@vzn Dense periodic orbits and positive Lyapunov exponents cover most systems that one would call chaotic. Chaos theory is an active field of study but you're once again trying to make something seem mysterious that is not.

@Jim can you stay tuned for the answer? If not, run to the nearest university library and get adsabs.harvard.edu/abs/2008gady.book.....B, p. 556.

5:25 PM

I'll stay tuned

Are all chaotic phenomenon will slowly develop a fractal like pattern once you run the simulation long enough?

@Jim exactly as stated earlier

I'm curious to learn what part of a bh formation is considered a collision

I know lorenz attractors has a fractal liek structure, but I am not sure if all chaotic phenomenon form fractal like structures

@ACuriousMind think you should look into recent literature on subj, might dig up something sometime but dont like your attitude, you dont really seem to want to learn but instead just prove me wrong :(

5:27 PM

@vzn the point is that they easily could cease to exist. They just don't because there is enough going on around to sustain them. Look at jupiter, it's rings come and go over time.

@Jim again, it depends on your pov on time scale... zen question, is billions of years long, or short? stable, or choatic/ unstable?

@vzn Yes, I do want to prove you wrong because you continue to fill this chat with unsubstantiated vague assertions and hunches, then get upset when someone calls you out on their vagueness, and most of your references, if indeed you give some, are pop-sci articles.

If you claim that there is some connection between stability and chaos, then do something to back that up, instead of hiding behind "these terms are difficult to define"

@vzn Given that the universe is only 13.8 billion years old, I'd say it's fair to call a timescale on the order of billions of years as objectively a long time

@ACuriousMind as stated, solid popsci writing is based on real science. its just a summary. it doesnt mean its wrong. maybe you should give up on the (physics) crackpot attack jihad, it seems futile to me...

@ACuriousMind might dig up a ref for someone (else?) who asks nicely & apparently sincerely wants to learn

@vzn And what expertise do you have to tell "solid" writing from nonsense? What "jihad"? Are you saying I should stop asking you to make your claims precise and back them up?

5:33 PM

> ...what expertise do you have to tell "solid" writing from nonsense?

@ACuriousMind Jim was just off on his estimate of saturn ring age by billions of years by not being familiar with (very) current state-of-the art scientific research on the subj... even obviously misinterpreting his own citation... you have no comment and and now you want me to be more precise and back up claims? ok

@vzn See, that's a typical pattern with you - instead of addressing the question posed to you to quickly want to switch the attention to something else. What has what Jim does or does not do to do with you, or that you should back up your vague assertions?

@ACuriousMind you have some "typical patterns" also but now feel like am wasting my time :(

Well, I don't know what I expected...

anyway it appears expert scientists themselves are a bit off in their thinking (to say the least!) if they just recently revised their best estimates of saturn rings by billions of years but guess nobody (else) finds that very notable... yawn

@vzn again, the age of the rings is usually a measure of the age of what comprises it. The seafloor is hundreds of millions of years old, the rings are a hundred million. There were rings around at all times, but it was not the same rings. The current rings are not billions of years old

5:41 PM

@Jim think you are now playing semantics. there have been rings around saturn for (probably) billions of years (exactly as stated earlier). their composition is always changing. just like your body. which will last far less long. etc

Not the same rings, not in the same structure. It even said in the article that they aren't the same rings and that these rings are young

yes, one might be tempted to date structures by their materials composition, and that typically would work in most cases, but as we see here its not so simple is it? exactly like with another one of my examples, the jupiter red spot etc

@ACuriousMind What is that?

even the greeks understood this concept that might be lost on some...

> you cant step twice in the same river —Heraclitus

I'm not going to touch the red spot. But this is like asking how old the craters on the moon are. There have been craters on the moon since it was made, but you only date them by the craters on top, not the (now erased) craters beneath them.

5:45 PM

@Jim the arguments about evaporation of gravitationally bound systems assume that the objects are point particles so no two bodies can ever collide. Effectively a gravitating ideal gas. Any object of a finite radius spoils this if the radius is significant compared to the length scales in question.

The age of the craters on the moon is not the age of the first time it was pock-marked

So there's nothing special about a black hole in this context.

anyway, not to be obtuse about this, agree the rings of saturn have probably undergone substantial shifts in structure over billions of years... but overall they seem to be "stable" by all our human povs

@JohnRennie I'm lost. Are you saying black holes don't count because they're too small?

The argument is this: total energy is conserved so KE + PE = constant.

Two gravitating point particles can get arbitrarily close so they have arbitrarily large (negative) PE.

So there is an arbitrarily large amount of KE to be shared.

5:48 PM

0

Q: Low-quality answers

A bunch of answers just came into the review queue (coincidentally, many by the same user...) and they all share one characteristic: they are incorrect, but they do attempt to answer the question. Just to confirm: because they attempt to answer the question, I should click "looks OK"? Side note:...

discussion answers flagging

If the system is ergodic there is a non-zero probability that enough of that energy is concentrated in one body to eject it from the bound system.

So given these assumptions every n body system will evaporate until only two bodies are left.

@JohnRennie I'm not even sure the ergodicity condition is necessary?

makes sense, it simply doesn't cover the extremely unlikely but not impossible case where all the point particles converge at once and develop enough mass in a small enough volume to become a black hole, without colliding.

also, collisionless? Way to take all the fun out of it

Ah, OK, though that's being reeeeeeeeeeally pedantic :-)

In practice for a globular cluster the assumption of pointlike collisionless masses is pretty good, and the evaporation of global clusters is reasonably well understood.

@JohnRennie I don't think so. It's the difference between saying all n-body systems will dissolve and saying most n-body systems should dissolve

5:52 PM

@ACuriousMind Is the category of smooth vector bundles with smooth vector bundle homomorphisms an abelian category?

The timescale for a single collision (e.g. getting close enough to start talking about making a BH) between two particles in a typical stellar system is much longer than the timescale for the system to fall apart from evaporation.

Well, OK, if we were mathematicians I'd be praising your rigour ...

@JohnRennie I consider myself praised

@Jim not exactly following the distinction you are making. each crater has an age of impact and then of course other dust settles on top of it from other impacts. maybe thats your point. ok. seabed top layer is recent. etc. but the rings dont nec have layers... thats harder to figure out. but an interesting hypothesis to test. (eg could their locations correlate with age? etc)

@jim are all chaotic dynamics give rise to some kind of fractal structure after letting the system to run for a very long time?

5:54 PM

@Jim Meanwhile I shall finish off this Jim doll that I've been creating. Now, where did I put those needles?

@0celo7 no

@vzn rings are distinct and more/less separate. Each ring has its own age. The total ring structure is as you describe, but, for instance, the C ring would have an age associated with it and may not be around in 100My

@ACuriousMind Well then I can't use the five lemma!

So back to square one!

0

Q: Matrix diagonalization in SU(2) and SO(3)

I'm currently using Nadri Jeevanjee's book on group theory for physicists to understand quantum mechanics. I came across these two pages that left me stuck: Example 4.19 $SU(2)$ and $SO(3)$ In most physics textbooks the relationship between $SO(3)$ and $SU(2)$ is described in terms of th...

group-theory group-representations lie-algebra

This question is clear and hq to me

@JohnRennie Ow! Must have been bitten in the back by a damn bug

5:55 PM

@WillO you liar

@JohnRennie Well I'm a...an engineer

@0celo7 You can, just view it as a subcategory of the Abelian category of sheaves :P

@vzn I strongly doubt that.

@JohnRennie Right, but, "point masses"? Come on...

@Jim you seem to be mixing up two different ages: age of origin and age left. yes, rings nearer to saturn are more unstable presumably ("falling from orbit"), something like that. but they might all have similar age of origin. etc

@DanielSank well air molecules aren't points either, but the ideal gas approximation describes air at STP exceedingly well.

@DanielSank how else do you find stable orbits? numerical simulations? agreed those can converge but its a random convergence etc

5:59 PM

Anyway, my armchair and a beer await. It's actually hot in (my bit of) the UK today so a cold beer is especially welcome.

this now reminds me of that web-based orbit video game secret got a high score on...

@vzn I'm not confusing ages. The specific rings in the structure are younger, more in line with the roche limit theories. Most sources agree that the age of any specific ring is relatively low. The ring ceases to exist and then the material can be recycled into a new satellite and eventually it will replenish the rings when it enters the roche limit

@Jim ok. not following. not an expert! is any of this described in the wikipedia article?

Each ring is young and transient. Damn saturn has too many moons though. If it were more like neptune or jupiter, it would have periods of no rings

@vzn yes, I think so

scratch that, it just mentions the two dissimilar theories and says it's not clear which is correct

@Jim so you are saying there is a conjectured cycle where a satellite is shredded passing thru roche limit, material scatters (into rings), material somehow eventually reconverges into a satellite? it sounds very questionable to me, against thermodynamics/ entropy

6:05 PM

nasa and university course pages provide more detailed reviews

@vzn I'm not the astrophysicist. If you disagree with the fact that they say it, then argue with me. If you disagree with what they say, take it up with them

ah, wikipedia does have some on dating

> Saturn's rings may be very old, dating to the formation of Saturn itself.

@Jim where is it said? can you find it in the wikipedia article?

it seems to me satellite shredding (agree that is a likely source of the rings) is an irreversible process so to speak...

@ACuriousMind what the fuck you just said it isn't abelian

@0celo7 : ?

Scrolling back, the answer to "is the category of vector bundles abelian?" is of course no.

@WillO ACM says the category of vector bundles isn't abelian so the 5-lemma doesnt apply

Of course?

I don't know what an abelian category is

0celo: In the case at hand, it suffices to check exactness on each fiber. The fibers are vector spaces, which form an abelian category. So the five lemma applies just fine.

A map of vector bundles is an isomorphism if it's a fiberwise isomorphism. That's all you needed to check.

That suffices to make the five-lemma applicable. Here is a completely different reason: The category of vector bundles imbeds in the category of coherent sheaves, which is abelian.

Either argument will do.

6:21 PM

@0celo7 So? "Abelian" is not a property that subcategories inherit.

For those still interested in the N-body thing, here's my contribution, such as it is: physics.stackexchange.com/a/274528/11053

4

And I won't let "I don't know what Abelian means" be a valid excuse because by now you had ample time to search for the definition.

@ACuriousMind The definition is meaningless to me

0celo: In practice, in this case, it means that the quotient of vector bundles need not be a vector bundle.

And that there is no alternative construction that has the desired universal property.

But once again---none of that matters. If you're checking something on fibers, you're working with vector spaces, where you have all the constructions you need.

Hmm

I'm not sure that I care enough to follow up on this any further

I clearly need more category theory than I care to know

6:26 PM

@vzn : IMHO she doesn't understand GR or electromagnetism, she doesn't know the difference between virtual particles and vacuum fluctuations, she doesn't know the difference between curved space and curved spacetime, and she censors any comments that might suggest she is not God's gift to physics. I am not a fan.

@Secret : I know exactly what it is.

What is the difference between curved space and curved spacetime?

Why does it matter?

curved spacetime is more general than curved space. You can have spacetimes that cannot be foilated, thus cannot be described as hyperspatial slices wrt time

@Secret I want to hear JD explain it

@DavidZ @JohnRennie @dmckee I want to remark that I consider such statements as made by JohnDuffield above, in particular asserting "she doesn't understand GR or electromagnetism", about an accomplished academic to be insulting and inappropriate for this chatroom.

Insulting?

6:35 PM

@0celo7 Yes, implying a physicist doesn't understand basic aspects of her field is an insult unless accompanied by substantial evidence.

2

Number of theories that gravity and magnetism are interrelated: innumerable. Number of people who were right about it: zero. Amount this has caused physicists to distrust any new similar theories: 100%. Probability your interpretation is correct: >0%. Probability anyone will adopt it without a mathematical basis or endorsement from someone with a degree: 0%. It's unfair, but the fact that we see so many "theories" claim gravity and magnetism are linked means that we unfairly dismiss new ones. — Jim 1 min ago

too harsh?

@Jim Uh, string theory clearly links the two.

Different modes of the string.

@0celo7 sir, you are technically correct (a bit outside of context, but correct). The best kind of correct

@ACuriousMind Even with substantial evidence, it's an insult. Accurate and deserved, but insulting

@acuriousmind do all chaotic systems give rise to fractal like structures in their dynamics?

@0celo7 How electromagnetism (or any gauge theory for that matter) arises from string theoretic models is a bit more subtle than "mode of the string"...

6:40 PM

@0celo7 : curved spacetime is inhomogeneous space wherein the inhomogeneity is non-linear. It's akin to this picture of the inhomogeneous ocean, but where your plot of speed v depth is not a straight line. Instead it's curved in line with the inverse square rule.

user image

@ACuriousMind I've forgotten all of that, forgive me.

If you want to remind me, cool

@Jim Well, thank you clarity czar for pointing that out!

What's the thing you put pasta through to get the water out

@Secret Many, but not all (and there are non-chaotic fractal attractors). For details you'll have to find someone who actually knows chaos theory

@0celo7 A sieve?

fml there's an e in there!?

6:43 PM

@ACuriousMind I never wanted to be your Czar. The people demanded it and I serve to the best of my ability.

ah, the ol' Caesar argument

@ACuriousMind : it isn't insulting. It's true. See this: "But there are also waves on the surface of the sea. The waves are like “virtual” particles; they are fluctuations around sea level that come out of the sea and fade back into it". Virtual particles are not the same thing as vacuum fluctuations.

@0celo7 I promise I will relinquish this power you have granted me once our crisis has ended

@Jim if you get a salad named after you, keep your power as long as you want

(I know Bajoran will point out the salad was not named after the Roman)

Every time I make a salad with romaine lettuce, bacon, and croutons, I name it after the roman

6:49 PM

Bacon?

It has, at most, chicken.

Anything more is a bastardization and you should be ashamed

have you never ordered a caesar salad from a restaurant? They always have bacon

@0celo7 One should NEVER be ashamed of bacon

2

@Jim : yes. in the current-in-the-wire the linear and rotational electromagnetic forces don't quite balance, and the result is a weak rotational force. We call it a magnetic field. When you stop the current, the forces still don't quite balance and the result is an even weaker linear force. Only we don't call it a magnetic field any more.

@Jim Had one yesterday.

And the day before

I am a Caesar salad daemon

But how can we trust you if you're ashamed of bacon?

I'm Muslim

6:53 PM

@JohnRennie Never said otherwise.

@0celo7 Then you don't eat it, why are you ashamed?

@vzn Who said anything about finding orbits? The question is whether or not particles from the "clump" can or do ever eject from the clump.

@Jim I'm not ashamed, I'm saying you should be ashamed!

but I'm not muslim

Assuming "eject" means "become unbounded" I would think one can answer the question without solving for orbits.

6:54 PM

I don't see what that has to do with anything

it has to do with eating bacon. That seems fairly important

I'm saying you should not put bacon in a caesar salad, and should be ashamed if you do.

Why is that so controversial

your reasoning for being ashamed was that you're muslim. I'm not, ergo I lack the reason that should make me ashamed

No, that's not my reasoning

@ACuriousMind : and perhaps you'd care to comment about "This means that the virtual particle pairs can only exist for a short time, and the more energy they carry, the shorter the duration of their existence"? Particularly after your reference to stories in this answer.

6:56 PM

@0celo7 stop being so unclear

@ACuriousMind I thought you had JD on mute? Why did you reverse that decision?

@JohnDuffield Many physicists choose to tell such stories in their pop-sci articles. I'm not a friend of that, but it's a lie-to-children - I'm fairly certain most of these physicists know that that's not what rigorously happens in the theory.

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