The h Bar

John Rennie

17:02

@vzn See:

@JohnRennie I'm afraid I don't get you - there are no creation/annihilation operators for interacting fields. We have to stipulate that the particle come/go to the asymptotic past/future, and that in those asymptotic times, the fields can be treated as free. Then we compute the overlap of the in-state $\langle A,B\vert = \langle 0\rvert a_A a_B$ with the overlap of the out-state $\vert C,D\rangle = a_C^\dagger a_D^\dagger$ where we first evolve the past in-state into a future state.

Understand how the evolution of the asymptotic past state to the asymptotic future state is done and you understand what virtual particles are. And that's my goal.

Or of course you could not bother to make that effort and fill the chat room with misconceived notions that owe little to rational thought.

ACuriousMind

Sometimes, I really don't understand worldbuilding.SE. Case in point: How to realistically explain a creature that eats dreams and nightmares? What does the story gain from explaining this "realistically"? What kind of audience are you writing for that is incapable of a simple suspension of disbelief for the sake of a fantasy story?

John Rennie

Damn, I can't find the chat flag for sense of humour failure :-)

Balarka Sen

I don't even know what worldbuilding.SE is all about.

vzn

@JohnRennie [heresy alert!] to me virtual particles are a strong indication of the existence of the spacetime fabric. there are agreed on understandings, but think (like photons) they are not fully understood. would make excellent blog topic. see eg scientificamerican.com/article/are-virtual-particles-rea scientificamerican.com/article/… discovermagazine.com/2008/may/…

John Rennie

@ACuriousMind I'm currently reading Infernal by Mark de Jager, and while it's the most dreadful tosh (highly entertaining tosh though :-) it does make the effort to make the magic rational and that does improve the story.

0celo7

17:09

@JohnRennie We're following your advice and moving the XRD to the microscope PC

if something breaks we will bill you

John Rennie

@0celo7 Put it on my tab - I have your bank details.

@vzn if you're saying that there are aspects of QFT that we don't fully understand I will rush to shake your hand. If you are just saying we don't understant what virtual particles are then you are just adding to the ill informed debate. They are what QFT defines them to be. They are a computational device.

vzn

@JohnRennie virtual particles have a definition/ usage according to conventional wisdom. we can probably agree on at least that much.

John Rennie

@0celo7 How easy is it to buy stuff these days i.e. what funding is available. In situations like this my immediate reaction is to go looking on ebay for another Dell PC just to run the XRD and your analysis software. You'd get one for $200 - maybe $250.

DanielSank

One of these days someone ought to explain in detail why interacting fields don't have creation ops.

If I have a field interacting with a zero dimensional thingy, I still have those ops.

Where does it all fall apart with interacting fields?

Slereah

@DanielSank Some interacting fields do have creation operators

John Rennie

17:16

@DanielSank I would love to understand QFT well enough to understand that, but I fear your request to explain in detail is incompatible with briefly and comprehensible to non-QFT heads.

Slereah

Sine Gordon has them

John Rennie

I suspect that explain in detail = read a book on QFT

0celo7

@JohnRennie Oh, we could afford another PC, but then we'd need a screen, keyboard and all that other bullshit. Also there's no room.

And all PCs have to get checked by IT and it's a pain

Slereah

The reason is basically just that you can't have a Fourier transform of a non-linear equation?

Well you can, but it won't do much to help you solve the field

John Rennie

@0celo7 Ah, true. But then you could run it headless and connect using RDP or TeamViewer. I take your point though, sometimes yet another PC is more hassle than it's worth.

0celo7

17:18

@JohnRennie Speaking of "briefly in detail," I am considering writing my senior thesis (in 2-3 years) on cohomology.

DanielSank

@JohnRennie In my experience, that's usually not true.

Brevity isn't the thing I'd want anyway.

John Rennie

@0celo7 If it's fun I'd say go for it! You'll always do best what you enjoy most.

0celo7

@JohnRennie I would expect you to read it ;)

John Rennie

@0celo7 Read \ne understand. Anyway i may have died of old age by then.

0celo7

You're what, 70? You've got a few left

John Rennie

17:20

death or reading about cohomology - that's a tough call.

@0celo7 55 - I only feel like 70

0celo7

correct to within an order of magnitude.

John Rennie

Now lets assume I'm spherical and moving in a vacuum

0celo7

hey, you're not a cow

vzn

@0celo7 still have no idea why you dont switch to a math major

0celo7

@vzn I don't want to be useless

vzn

17:22

@0celo7 would a sr thesis on cohomology be "useless"? :P

0celo7

@vzn My other will be on fuel cells or something

crap this measurement will take 45 minutes

John Rennie

Oh, I've noticed the ~~troll~~ orc has gone!

0celo7

time to do some cohomology

oh dear god @ACuriousMind what happened to you

John Rennie

Darth Traya!

starwars.wikia.com/wiki/Darth_Traya

0celo7

I should change my avatar

John Rennie

17:24

Whatever did we do in the days before Google image search?

vzn

@JohnRennie sounds like virtual particles :P

0celo7

Actually I might do it on diff topology @JohnRennie

I want to learn about surgery

and you probably need cohomology for that

John Rennie

@0celo7 maybe I should change my avatar. How about this one:

0celo7

you should

who is that

John Rennie

Me

0celo7

17:30

the hell

something's wrong with your eyebrow...

and you look green

sorry

John Rennie

0celo7

good god man

John Rennie

It was from a pantomime I was in many, many years ago :-)

I was the bad guy. It was enormous fun :-)

Slereah

Please don't

I feel molested just looking at it

John Rennie

The very devil getting the make-up off though. It left me with an increased sympathy for the ordeal women have to go though every day.

0celo7

17:32

AMS TEXTBOOK SALE

YEEEEEES

TIME TO SPEND MY PAYCHECK

John Rennie

Don't you think I make a good villain? :-)

0celo7

you look sick, not evil

pls see a doctor

vzn

lol maybe mimes will help us understand virtual particles :P

John Rennie

@0celo7 I am a doctor

vzn

@JohnRennie you could be cast as JD in a physics play :P

0celo7

17:35

a real doctor, not a PhD doctor

vzn

@0celo7 like a "useless" math phd

John Rennie

@vzn He doesn't look anything like me. You can see him on YouTube if you're curious - from about 03:30 IIRC.

0celo7

oooo

I hate when problems get harder unexpectedly

John Duffield

@vzn : I'm not some "my theory" guy. I don't have a model.

vzn

@JohnDuffield (a candid admission!) wondering, why do you feel so strongly over certain physics issues? (you might find some support in those virtual particle refs above)

peterh

17:47

@JohnRennie Programming can be learned from the internet, physics requires full-time effort around a decade long

@JohnRennie A physicist can go anywhere to find a programming job, the opposite is chanceless.

@JohnRennie Writing HQ programs is not so simple, but in the daily practice I never found such tasks where the real quality of the code had been more important as, for example, the communication/teamwork skills.

John Duffield

@vzn : it's like the future isn't what it used to be. Once upon a time there was so much promise, and so much hope. But now we're into the nightmare scenario wherein there's been no scientific progress for forty years. I feel strongly about this. I'm going to do something about this.

0celo7

You're not doing anything tbh besides annoying a bunch of people on the internet.

vzn

@JohnDuffield lol so now you quote hossenfelder (nice find! reminds me of the "desert" discussed awhile back in here!). bought woits book ~1 decade ago, need to read it sometime, think hes a rare/ valuable iconoclast. anyway what do you mean youre going to do something? what? does it involve something outside of answering Physics questions?

John Duffield

18:03

@vzn : yeah, I'm writing a physics book.

vzn

@JohnDuffield wondering, do you have an undergrad degree? did you say once you worked in software? cant remember

John Duffield

@vzn : I have a BSc honours degree in Computer Science. There's a lot of analysis and logic in computing.

vzn

@JohnDuffield (cool) so can you say anything about your book? whats the main theme? any math? etc

@0celo7 lol "annoying..."

John Duffield

18:18

My working title is The Physics Detective. The chapters so far are 1) the future isn't what it used to be 2) the nature of time 3) the speed of light, 4) how gravity works 4) what is a photon? and 5) what happens in gamma-gamma pair production? There's bits of maths like √(1-v²/c²) and ds² = -cdt² + dx² + dy² + dz² and E=hf. But not much.

0celo7

lol

vzn

@JohnDuffield that reminds me, there is an old legend/ folklore (maybe true? told by hawking? told to me by HS CS teacher) that a publisher told hawking re bestselling "brief history of time" that he would have ~½ the readers for every eqn he put in his book... book became rare bestseller popsci written by hardcore scientist (1980s)... (gives new meaning to "½ life decay"...)

John Duffield

@vzn : I don't think that's really true. IMHO the odd equation doesn't do any harm. IMHO the problem comes when people start slipping into mathematical handwaving as a substitute for evidence and explanation.

vzn

@JohnDuffield have some )( sympathy for that pov. arguably that has been going on ~1century or more re copenhagen interpretation... institutionalized. many topnotch physicists have questioned/ challenged it. the arguments are mostly swept under the rug. black sheep of physics. "omerta" etc

John Duffield

@vzn : I'm not a fan of the Copenhagen interpretation.

0celo7

18:25

of course not

John Duffield

@0celo7 : do you want a real LOL?

1) Who was Feynman's supervisor?

No? OK. Maybe some other time then.

vzn

wheeler (coincidentally am in middle of feynmans bio right now... written by physicist) amazon.com/Quantum-Man-Richard-Feynmans-Discoveries/dp/…

John Duffield

2) Who proposed the geon?

vzn

(clicking on the link) wheeler

(sounds a lot like solitons...)

John Duffield

3) Who didn't know the difference between curved space and curved spacetime?

vzn

18:39

(again clicking on the link, this is all very socratic...) youre a wheeler fan or antifan or something?

John Duffield

4) Who else didn't know the difference between curved space and curved spacetime?

5) What did Percy Hammond say just before the end-note here?

0celo7

@JohnDuffield Wheeler?

@JohnDuffield You

peterh

3

Q: Sum of reciprocal of primes

If $p_n$ is the nth prime, then prove that:$$\frac1p_1+\frac1p_2+....+\frac1p_n$$ is not an integer. Since $p_1 ,p_2,..., p_n$ are all prime their reciprocal is not an integer so the sum should not be an integer. But I am not sure.

Well, I admit the mean level of quality of the MathSE is maybe lower as of the PSE, but I think this communication style, in this question, should be also on the PSE followed. The question is high school level, but has a high quality and the answers, and mainly: the typical attitude, is simply wonderful.

John Duffield

@vzn : not a fan. Sorry, I have to go I'm afraid. Good night.

vzn

@JohnDuffield ok/ why not? you think he misinterprets GR somehow? etc?

peterh

18:53

@JohnDuffield I remember around the "first year"of the LHC, I predicted: it will find the Higgs, but no more. And so has it happened. I think this is sad, but I don't think I would be a vizier. It was predictable not to me.

William Bulmer

19:07

Hi again

WillO

@peterh: It's the toleration of questions like that that keeps me off MSE.

Balarka Sen

I don't see what's so wrong with that question.

WillO

First, it's not a question; it's an order.

Second, it shows absolutely no effort.

Third, it's almost surely a homework assignment

Fourth, the suggestion that since no summand is an integer, the sum should not be an integer, betrays the fact that the questioner didn't giive this a second's thought.

Balarka Sen

First is acceptable. For the second: it does show some effort (although that line of thought is completely useless), but I guess that depends on your defn of effort.

Yeah, homework questions are very well-accepted in MSE. I guess SE culture varies sitewise.

WillO

It shows absolutely no effort. If your idea is that no sum of egyptian fractions with prime denominators can be an integer, and if you haven't doodled enough to notice that 1/3+1/3+1/3 is a counterexample, you've made absolutely no effort.

Balarka Sen

19:17

I did say it depends on your definition of effort :)

0celo7

19:36

for some reason I'm drawing pis with three legs

wtf is wrong with me

William Bulmer

@WillO But if this person is a newbie, maybe they just don't know HOW to think, and so, therefore, don't know how to make the effort. Perhaps they think that mathematical reasoning is like that. I am kind of curious about why they are asking this question in the first place. Are they taking a basic number theory course? Though, I suppose this could be a question asked in a Discrete Mathematics course, which lots of non-mathy people are forced to take...

0celo7

@BalarkaSen I'm dumb.

If I have a basis $v_i$ and a dual basis $\omega^i$, how do I represent a trace using them

$\mathrm{tr}(f)=\sum_i\omega^i(f(v_i))$?

WillO

19:55

@0celo7 : The trace is the evaluation map $V^* \otimes V \rightarrow k$. The choice of basis gives you an isomorphism $Hom(V,V)\approx V^*\otimes V$.

Physics Guy

Hey guys. Has anyone of you ever heard of "Skyrmions" ?

peterh

@WillO It was simply fun to read the question, think on it, and then read the answers. Similarly interesting and useful questions on the PSE are downvoted, closed and deleted.

0celo7

@WillO I don't know what that means

Physics Guy

@peterh Why do you complain about that all the time ? I read interesting questions all the time, and they are not downvoted at all, the question just shouldn't consist of bullsh*t ;)

peterh

@PhysicsGuy And what do think about this MSE question? Don't you find it interesting?

@PhysicsGuy I don't complain always, but now I've checked a little bit of MSE and I think, this question - and the answers, and the general attitude - is an example to follow.

Physics Guy

20:09

@peterh It's a serious question about maths.

Nothing more

Sir Cumference

So if I were to approach any type of black hole, and I somehow wasn't killed by the heat of accreting matter or its magnetic fields, I would inevitably be ripped apart by tidal forces, right?

No matter the size of the black hole?

Physics Guy

The size does matter.

peterh

@PhysicsGuy See the crystall clear logic of the answers! See their perfection! The MathSE is a wonder!

Sir Cumference

@PhysicsGuy Very funny

No but seriously, it really shouldn't

Physics Guy

It does.

Sir Cumference

20:11

Why's that?

Physics Guy

Or, wait....

peterh

@PhysicsGuy You are in denial. The sad truth is, that the PSE simply isn't on this level, the mean quality of the PSE is very far from the level of this question, and it is mainly because the analog questions on the PSE are downvoted, closed and deleted regularly, and their OPs are expelled.

Physics Guy

@SirCumference If you have a supermassive black hole, then you wouldn't be ripped apart immediately, it would take time, but if you have a smaller black hole it would take less time.

Sir Cumference

@PhysicsGuy But no matter what, you'd be torn apart by a black hole, regardless of size

Right?

Physics Guy

Yeah.

peterh

20:14

@SirCumference And, if the supermassive black hole rotates enough fast, and all of them rotates at least a little bit, then the Kerr-metric has a very interesting prediction.

@SirCumference And it that in a rotating black hole, the singularity is not point-like, but it is ring. And, if you falls through this ring, you falls out from a white hole, possibly in another Minkowski-universe.

Sir Cumference

@peterh No. You can't fall through that ring.

Physics Guy

@SirCumference It's very presumably. It isn't well known what exactly happens in a black hole. We just have mathematical formulations that can show us the rough structure of Spacetime inside the BH (see Kruskal-metric)

@peterh You're not right this time.

Sir Cumference

Time dilation would increase as you approach the event horizon. As far as I know, that means the black hole should evaporate from Hawking radiation before you realize it.

Meaning no more black hole.

Or at least it should continue shrinking, until tidal forces can rip you apart

peterh

@SirCumference Unfortunately, the only experimental evidence about the black holes are the spectrum of the infalling interstellar gas. It seems currently totally impossible to send a probe into such a ring.

@SirCumference Why you can't?

Sir Cumference

@peterh What are you responding to?

peterh

20:19

@SirCumference The Hawking-radiation is a QG thing, and no QG has any experimental evidence until now. It is speculation, just as the internal structure of the Kerr black holes.

Physics Guy

@SirCumference Nah, you would reach the singularity right in time, it's hard to explain, but you should think of Hawking radiation as a result of formulating a QFT in curved space near the event horizon. That (easily said) causes the shrinking of the BH. Now we have the information loss problem.

If you want to understand the shrinking of the BH, you should be familiar with the thermodynamics (entropy) of black holes.

peterh

@SirCumference Well, I admit, a considerable proof against the possibility of this "inter-universal travel", that nobody has seen a white hole until now.

Physics Guy

@peterh en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates

peterh

@PhysicsGuy The Hawking radiation hasn't any experimental proof. Nothing. It is a theory, a hiphotese.

Physics Guy

@peterh If black holes exist, then HR exists, too.

That is very presumable.

peterh

20:24

@PhysicsGuy Do you admit that there is no experimental evidence showing the HR?

Physics Guy

@peterh There isn't yet. As I said, it's very presumable.

Sir Cumference

@peterh It astounds me that you're criticizing Hawking radiation for a lack of experimental evidence, yet you just brought up white holes a second ago. If you think the latter is plausible, you shouldn't have any problem with us bringing up Hawking radiation.

Physics Guy

@SirCumference ;)

peterh

@PhysicsGuy Yes, also I admit it is very presumable, but I also admit there is no experimental evidence, and even the predicted HR is with tens of orders below any measurement possibility.

Sir Cumference

Really if we are only talking about what's proven, we can't have much of a discussion about black holes.

peterh

20:26

@SirCumference Exactly. I say, there is no experimental for any of them, as I did some minutes earliy here.

Sir Cumference

@peterh I read what you said. But if you think that white holes are plausible, you shouldn't be criticizing HR for its lack of evidence.

peterh

@Sir Nothing is proven. The existence of the black is proven, not because we had seen them, but because the infalling interstellar gas has a characteristic spectrum, which can't be explained by other processes. It was looked for objects with this spectra, and they were found. Thus, we can say, BHs exist.

@SirCumference I didn't say the WHs are plausible, I only said, that the Kerr-metric has an interesting prediction.

@SirCumference As the HR is also an interesting prediction.

Physics Guy

@peterh But yo misinterpreted that prediction.

peterh

@PhysicsGuy It surprises me, first I've heard it from a prof. Well, he was a QM prof and GR prof, but he was a prof. I.e. a full-time teacher on a university, as I can remember, in docent rank (maybe I didn't translate well the exact status). I think it is much more probable that I misunderstood him as that he had said some silly.

@PhysicsGuy "...it was found that in addition to the black hole interior region (region II) which particles enter when they fall through the event horizon from the exterior (region I), there has to be a separate white hole interior region (region IV) which allows us to extend the trajectories of particles which an outside observer sees rising up away from the event horizon,

@PhysicsGuy along with a separate exterior region (region III) which allows us to extend some possible particle trajectories in the two interior regions." <- He explained some similar. Unfortunately, I am only an avid enhusiast and maybe I misunderstood, but this wiki fragment seems to me quite similar as I've heard.

@SirCumference No, I think thinking on things is very useful!

@SirCumference But it is important to know, what is really proven and what is only widely accepted. For example, it is nearly surely accepted, that the antimatter interacts exactly as the normal one, but unfortunately it couldn't be measured until now. Or, there is also a strong believe that the protons decay with a very long half life.

@SirCumference fix: "antimatter interacts gravitationally exactly as the normal one...

0celo7

20:48

@peterh you're saying it doesn't have negative mass?

Sir Cumference

@0celo7 You're saying it does have negative mass?

0celo7

Yep

Sir Cumference

Care to explain?

0celo7

no, currently doing some math

Sir Cumference

Okay, last I checked, positrons and such have + masses

Hell

Antiproton

The antiproton, p, (pronounced p-bar) is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived since any collision with a proton will cause both particles to be annihilated in a burst of energy. The existence of the antiproton with −1 electric charge, opposite to the +1 electric charge of the proton, was predicted by Paul Dirac in his 1933 Nobel Prize lecture. Dirac received the Nobel Prize for his previous 1928 publication of his Dirac Equation that predicted the existence of positive and negative solutions to the Energy Equation ( E...

Unless you're pulling my leg

0celo7

20:54

lol

Sir Cumference

Ffs the definition of a positron in the dictionary is "a subatomic particle with the same mass as an electron and a numerically equal but positive charge."

0celo7

same absolute value mass, sure

Sir Cumference

No, it clearly distinguished "same" from "numerically equal"

0celo7

That's a typo then

Sir Cumference

I think you're confused

0celo7

20:56

anti means you flip everything

Sir Cumference

I think you're REALLY confused

But I know you're not someone who would be that confused

I dunno what you're trying to do

peterh

@SirCumference I would like to point you to John Rennies wonderful answer:

23

Q: Has the gravitational interaction of antimatter ever been examined experimentally?

I know that the gravitational interaction of antimatter is expected to be the same as normal matter. But my question is, has it ever been experimentally validated? I think it would not be a trivial experiment, because electromagnetic effects have to be eliminated, so neutral particles would be ...

gravity experimental-physics antimatter

@SirCumference Citate from John Rennie: The error bounds are huge - all the team were able to say is that the upper limit for the gravitational mass of antihydrogen is no greater than 75 times its inertial mass!

Sir Cumference

And?

That has nothing to do with what we were talking about

peterh

@SirCumference I only said, that the gravitational behavior of the antimatter isn't measured until now, although it is widely accepted that it would behave as the ordinary one. What is not clear?

@SirCumference I based this statement on the citated answer.

Sir Cumference

@peterh Mass isn't just a measure of gravity, nor is gravity only dependent on mass

peterh

21:00

@SirCumference It is not clear to me, could you make it more clear?

Sir Cumference

@peterh Which part?

peterh

@SirCumference It looks to me some like an ungrounded phylosophical statement.

Sir Cumference

Which part?

peterh

@SirCumference Your this sentence: "Mass isn't just a measure of gravity, nor is gravity only dependent on mass."

Sir Cumference

Massless particles can certainly have gravity

Hell, photons interact gravitationally with black holes

Gravity is dependent on a lot of things, including pressure, mass, energy, and momentum

peterh

21:02

@SirCumference Yes, although a significantly different one. For example, enough strong parallel laser beams can completely ignore eachother, or even distract eachother. Of course, this happens only in extreme cases (the energy density of the laser beams should be enough strong to produce measurable GR effects)

Sir Cumference

Please actually respond to me using the link button, not by writing my name

It makes it harder to know what you're responding to

peterh

@SirCumference ok

Sir Cumference

@peterh How is this relevant? All I said was that gravity is dependent on more than just mass. Other properties of matter can curve spacetime.

In the case of neutron stars, too much pressure can cause one to collapse into a black hole

peterh

@SirCumference Yes, but the widely accepted view about the gravitational behavior of the antimatter isn't a tricky GR thing. It is simply widely accepted that it has a positive energy, i.e. an 1kg anti-iron ball would exactly so fall, as an 1kg massive normal one.

Sir Cumference

The overwhelming consensus among physicists is that antimatter has positive mass.

peterh

21:06

@SirCumference Well, it wasn't thought always so sure, but not it is.

Sir Cumference

I don't see your point.

@0celo7 Back to you, what are you trying to do?

peterh

@SirCumference Yes, and this is also what I think, I only mentioned that it is not measured experimentally, just as the proton decay.

Sir Cumference

You know that's not true

peterh

@SirCumference Or the Hawking-radiation.

@SirCumference What?

Sir Cumference

@peterh That was towards 0celo

0celo7

21:07

@SirCumference Currently trying to prove intersection theory is consistent with (co)homology.

You?

Sir Cumference

@0celo7 I mean regarding the whole "antimatter has negative mass"

peterh

@SirCumference I have the feeling that you are continously trying to disprove something for me, what I never stated.

Sir Cumference

You know that's not true

peterh

@SirCumference I never said this!

Sir Cumference

@peterh Oh my christ, I'm responding to 0celo

You clearly posted an instant before I could

:31732783 It's like when atheists say "Oh God"

Anyways

@0celo7 Again, what are you talking about with the whole antimatter thing?

0celo7

21:10

shrug

Sir Cumference

Goddammit man

You're screwing with my mind

peterh

@SirCumference So, I never stated that HR doesn't exist (I believe: yes, it exists), I never stated that falling through the ring singularity would lead to a different Universe (although I think it is a very interesting possibility), I never stated that the antimatter had negative mass (I think it is quite improbable). These statements exist only in your view. May I ask you, what produces this view for you?

Sir Cumference

@peterh Certainly for the third one, you entered into a discussion and I assumed you were posting something relevant

As in, actually related to what we were discussing

I see I was wrong

Nobody was discussing gravitational interactions with antimatter.

peterh

@SirCumference ...and, what you didn't try to disprove: I think, the proton decay may not exist, but I think it is more probable that the protons decay.

Sir Cumference

@peterh What are you talking about now?

@peterh For the second one, you indeed said "And it that in a rotating black hole, the singularity is not point-like, but it is ring. And, if you falls through this ring, you falls out from a white hole, possibly in another Minkowski-universe."

When I was talking about approaching a black hole

You seemed to sound certain at first, that's all

peterh

21:14

@SirCumference My previous sentence was that it is a prediction of the Kerr-metric!

Sir Cumference

@peterh Dude, you keep bringing up random points in the middle of discussions

I was obviously talking about black holes and tidal forces, yet you suddenly bring up "And, if the supermassive black hole rotates enough fast, and all of them rotates at least a little bit, then the Kerr-metric has a very interesting prediction."

peterh

@SirCumference Ok, no prob. I think only the experimental results are very important.

@SirCumference Yes.

Sir Cumference

I don't even know when we're discussing the same thing

It's like if you were talking about GR, and I suddenly brought up plate tectonics

peterh

@SirCumference I ask on the site many questions about the experimental validation of the theoretical results. I think they are very important and interesting.

@SirCumference I think how the experimental validations are going, makes a very clear distinction, what we know, and what we think. And the difference is very important.

Sir Cumference

@peterh Dude, we're not even talking about that now

We were only talking about how you interrupt with random points

peterh

21:23

@SirCumference I didn't interrupted anything, and honestly I would like much more to talk about the experimental results as that why do you think that I state things surely what I mentioned only as hyphotheses.

@SirCumference I don't think this discourse could lead to any interesting from now. Maybe you should read some interesting, highly upvoted posts on the main site and then initiate interesting talks about them.

@SirCumference If you are searching for them enough well, you can find a lot, mainly between 2013-2014.

0celo7

@Danu If/when you get to the Euler characteristic in GP, try proving that their definition is equal to the alternating sum of Betti numbers. I know of three proofs. Using Poincare duality, using Morse theory, and using geometric analysis. I can't follow the last one, of course.

I just worked out the first one, and the second one is a one-liner.

WillO

How do you define Euler characteristic? I'd have defined it as alternating sum of Betti numbers.

0celo7

@WillO The self-intersection number of the diagonal with itself.

WillO

Okay.

0celo7

It's highly nontrivial to prove it's equal to the Betti number one.

Unless I'm missing something super obvious.

There might also be an involved argument using triangulations.

@WillO Do you want to hear the proofs?

WillO

21:35

Okay.

0celo7

The Morse theory one is easy.

DanielSank

@JohnDuffield What about the proton radius, gravity waves, macroscopic quantum tunneling, and the discovery of the HIggs?

WillO

I don't offhand see any proof.

0celo7

Well, "easy."

You need the fact that both definitions of the Euler char give rise to the Poincare-Hopf theorem.

To get it via Betti numbers, you need Morse theory. There might be an algebraic topological way to do it without Morse theory, but I dunno. I'm a geometer.

WillO

When you say "Poincare-Hopf theorem" do you mean what I would call the Hopf index theorem?

0celo7

21:38

Yes.

So, you get $I(\Delta,\Delta)=\mathrm{ind}(v)=\sum(-1)^ib_i$.

QED.

Wait, you don't even need Morse theory.

You can use Morse theory.

DanielSank

@dmckee @DavidZ @Danu I'm going to start flagging chat messages that would be considered "shitposts" in our chatroom's parallel universe incarnation as a subreddit.

If you'd like me to stop, please just let me know and I will stop immediately.

WillO

Wait. What is v?

0celo7

But there's another proof of Poincare-Hopf without it that uses de Rham cohomology.

@WillO vector field.

WillO

An arbitrary vector field?

0celo7

The index sum of any vector field, yeah

Balarka Sen

21:40

It's independent of the vector field.

0celo7

@BalarkaSen I told you that ;)

WillO

okay. yes.

Balarka Sen

Yes, indeed.

0celo7

Ok, so in GP they show that the index is equal to $I(\Delta,\Delta)$.

In Bott & Tu or Milnor they show it's equal to $\sum(-1)^ib_i$.

WillO

Presumably you need some condition on the zeros of this vector field?

For example, I don't think the zero vector field will work.

Balarka Sen

21:41

They should be isolated, yes.

0celo7

@WillO Finitely many, but you can always find such a vector field.

WillO

Right. Okay.

0celo7

So the index equals both $I(\Delta,\Delta)$ and $\sum(-1)^ib_i$.

That's actually a much easier and better proof than what I was thinking about earlier.

Balarka Sen

@0celo7 (in fact such vector fields are generic in the space of all vector fields on compact manifolds)

0celo7

Dense you mean?

Balarka Sen

21:44

Yes.

0celo7

@BalarkaSen See Hirsch?

Balarka Sen

Huh?

0celo7

22:05

@BalarkaSen I'm ever more convinced GP is an amazing book

It makes the top 5 on my list

Balarka Sen

Good

WillO

What is GP?

Balarka Sen

Guillemin & Pollack

WillO

ah.

Physics Guy

Hey guys.

Aaah, talking about Euler-characteristics.

David Z

22:20

@DanielSank if half a dozen mods from other sites show up and tell you to stop, you should stop.

peterh

I see fast and significant changes on the right side in the starred messages, maybe it is a previously unknown mod/CM effect?

David Z

We clear out starred messages sometimes

peterh

@DavidZ You deleted them?

David Z

Oh, no, sorry - I just meant clearing the stars. The messages are still there.

peterh

@DavidZ Ok-ok.

ACuriousMind

22:41

@JohnRennie indeed it is, although I prefer her as Kreia

@DanielSank What are you flagging them as? Keep in mind that ordinary "spam/offensive" flags are seen by users across the SE chat network without context

ACuriousMind

Kotor 2 as a whole is an interesting commentary both on the binary Jedi/Sith morality and on the almost Nietzschean morality Kreia follows

Of course, as with all great RPGs, it was never finished and plagued by terrible bugs at release.

Emilio Pisanty

22:56

-2

Q: Hurling questions

Consider a rigid rod of length $R$, inserted through a central hole in a projectile. There is a small gap between the rod and the projectile, so that the projectile is free to slide along the length of the rod with negligible friction. The rod is caused to rotate about one of its ends wi...

homework-and-exercises classical-mechanics

CV it with fire?

cf. its original version physics.stackexchange.com/revisions/274759/1

ACuriousMind

@EmilioPisanty If I had any close votes left I would do something :P

Emilio Pisanty

@ACuriousMind ah

I wondered

@ACuriousMind In any case, why edit the tags and LEAVE THE ALL CAPS?!?

=P

ACuriousMind

@EmilioPisanty Yeah, I concede that was a bad/incomplete edit by me

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