@NeuroFuzzy: I never asked: What is your profile picture?

Existance itself

Doesn't look like a 42 to me.

@0celo7 When will you change your profile image?

@Icosahedron When you finish Shankar.

It's starring into my soul.

andrew lee is deleting his account

@Jimmy360 Who?

Why do we care?

Just kinda interesting.

He posted some really weird stuff.

@Icosahedron You should have the same problem with the new pic ;)

Crackpots come and go, it's nothing out of the ordinary.

True...

@0celo7 I finished shankar.

@Icosahedron Riiiiight

@ACuriousMind Ask him some random intro QM question

@0celo7 Why would I?

Why does chat take so long to change profile pics?

I won't answer it regardless to maintain integrity.

@ACuriousMind To see if he's finish Shankar

@Icosahedron What does that even mean?

Why would he care?

I think that's what he meant.

@0celo7 Because it does only periodically load the content from the parent site - every half hour or so.

@0celo7 Why would I care?

:/

@Icosahedron Fine. Explain what values orbital angular momentum can take on and why.

I said I won't answer anything, though that is a really easy question.

Why won't you answer anything?

Because it's a slippery slope.

Eventually I won't be able to answer one.

You'll keep asking.

@0celo7 What? You thought I really care what d20 knows or doesn't know?

@ACuriousMind No.

I just thought you could come up with a good question.

Uh...I'm not good at coming up with questions, I'd say.

I know everything in the universe.

My first instinct would have been to open one of my old problem sheets :P

@0celo7 I haven't finished shankar yet.

I knew it.

I didn't say I finished it.

@ACuriousMind Interesting. How did you come to discover this?

That was in response to changing your profile image before I finished shankar.

theatlantic.com/technology/archive/2014/05/…

@Icosahedron Ah, the new pic is here!

Looks glorious.

The eye is too tiny to stare into my soul.

Your mom is too tiny

@0celo7 By changing my profile pic, and by observing that the total rep number shown also lags behind the main site.

@ACuriousMind I see.

@Icosahedron My next one will be the Anaconda album art.

Either that or I might pull a @StanShunpike and go through all the Scantraxx Reloaded album arts.

I have synesthesia and your existence as an abstract object appears grey to me.

The album art is annoying unless it's grey.

Is that a reference?

Reference to an external source?

I don't know what you're talking about.

I don't know what you're talking about.

I don't know what you're talking about.

I don't know what you're talking about.

@ACuriousMind Do you have time to look at Fig. 38 in HE?

@0celo7 Yes. Page?

193

cf. the last paragraph on the preceding page.

I don't know why this spacetime fails that condition.

I don't get it either. Where is the more-than-once-intersecting curve?

@ACuriousMind This.

physics.stackexchange.com/questions/186819/… This question is really cool, I remember seeing something like this back when I did chemistry a year ago though I didn't know enough to understand it. (I still don't understand it)

I was thinking we snake a curve up from the bottom, make it null and hit the circle. Then do the same along the top.

Then we make them arbitrarily close?

@0celo7 dude, nice profile pic! :D

They can't touch, but we can make them close.

@StanShunpike Thanks.

Wow! Im blue today

@StanShunpike How do you find those SE profile images?

@Icosahedron Magnets.

I don't follow.

Put a magnet near your CPU.

Trust me.

XD

I trust you.

I think you mean hard drive.

This polarizes the electrons.

No, CPU.

A magnet does not damage a CPU.

If you knew QM, this would be obvious to you.

Damage?

I thought you were trying to troll, which you are, though in a different way.

@StanShunpike I still liked the neon green better

Also, all this talk of pics makes me want to change my pic, too.

@ACuriousMind Do you think the curve I described works?

@0celo7 I'm not sure what you mean.

I've never changed my picture.

@Jimmy360 That is evident :P

@ACuriousMind I'll try to draw it. Brb.

Although I believe @StanShunpike hasn't changed his picture ever, either :D

Imagine the yellow dots match up and the curve is nowhere spacelike.

It should be possible to make the two ends get arbitrarily close at $p$, right?

Okay, how does this curve intersect the neighbourhood more than once?

I feel I haven't understood what this is about at all.

It intersects it once going in and once going out.

Or, just extend the curve so that the bottom part goes out of the circle and the same for the top part.

Then you have 4 points where the curve hits the circle.

Oh, so the number of "intersecting the neighbourhood" means number of intersections with the boundary?

I think so.

Also, why does that curve not violate the causality condition?

It is not closed.

I am beginning to understand this, and I am also thinking your example is the correct one.

Again, I like quantum stuff better than this :D

This would be a lot better if they weren't so damn vague.

@ChrisWhite You around?

nope

@ACuriousMind Wald says that strong causality pretty much means there are no non spacelike curves which come arbitrarily close to intersecting.

I think when counting the "number of intersections" you have to count the number of connected components of the curve that intersect the nbd.

In my example, there's the part coming from below and the part coming from above.

@0celo7 A curve has, by definition, only one connected component, because it is the continuous image of an interval.

@ACuriousMind You know what I meant.

@0celo7 Yes, but I'm still a pedant :D

@ACuriousMind How would you put it?

I remember this confusing me when reading Wald too.

From a different book:

@0celo7 I'm not absolutely sure I've understood it, but: $p$ satisfies the strong causality condition if, for every neighbourhood $U$ of $p$ and every non-spacelike curve $\gamma$, $\gamma \cap U$ is connected.

Holy shit:

I swear I did not see this.

Well, then you can be proud :)

Seeing one's own proof/example in a book is one of the best feelings ever

:)

@Icosahedron @ACuriousMind is correct. I have never changed it :D it does it by itself

@StanShunpike Is there a way to upload a bunch of images and have it change automatically?

@StanShunpike How though?

There is probably a hidden option to change the profile image periodically.

@ACuriousMind Let $V$ be an nbd around $p$ containing $q$. Let $\gamma$ be a curve with $\gamma(0)=q$. If $\gamma$ leaves $V$ at $t=t'$, it may never re-enter $V$ for all $t>t'$.

@0celo7 I'd agree with that.

I'm not entirely sure why the definition in HE and Wald uses two nbds.

@0celo7 To make sure it is a local condition. Note the entire spacetime is also a neighbourhood.

@ACuriousMind Ah. Is that needed in my definition?

We should probably add that to both our definitions

@0celo7 Yes. Remove the closure of a small neighbourhood of a point far away from $p$ from the entire space. This is a neighbourhood of $p$, but finding a curve that violates "your" causality condition on the neighbourhood is rather trivial, I think.

Let $V$ be an nbd of $p$ containing $q$. Let $\gamma(t)$ be a curve with $\gamma(0)=q$. If $\gamma(t)$ leaves $V$ at $t=t′$, it may never enter $U\subset V$ for all $t>t′$, where $U$ is an nbd of $p$.

Yes, that would be equivalent to Wald's definition, I think.

Wald? Do you have Wald?

No, you copied it

@0celo7 Or wasn't that from Wald?

The above picture is from Semi-Riemannian Geometry.

I've read Wald, so I would have seen that picture already. That would be cheating.

Ah, then I misunderstood you, and it is equivalent to whatever-the-hell-that-is-from.

amazon.com/…

@ACuriousMind What curve would that be? I can't quite picture your spacetime.

@0celo7 Take Minkowski space. Take the timelike curve $\gamma(t) = (t,0,0,0)^T$, and remove, for a point $p \neq 0$, the closure of a small neighbourhood around $0$. The curve $\gamma$ leaves and re-enters this neighbourhood of $p$ certainly, does it not?

What is the nbd around $p$? Are you essentially removing a sphere from the space?

Let's keep this to the $t-x$ plane.

@0celo7 Yes, I'm think of removing a sufficently small ball $B_\epsilon$ around $0$ from the space, so that $\mathbb{R}^4 - \bar{B_\epsilon}$ is an open set containing $p$, hence a neighbourhood of $p$ by definition.

@ACuriousMind Ok, so how does the curve leave the nbd if the nbd is the whole space?

It certainly can't leave the manifold.

It leaves it at $\gamma(-\epsilon)$, and re-enters it at $\gamma(\epsilon)$.

Leaves? It can't leave the manifold!

@0celo7 mine just does it for no reason at all. @Icosahedron no idea how or why it does it

@StanShunpike wat

@0celo7 The neighbourhood is $\mathbb{R}^4 - \bar{B_\epsilon}$, not the whole space, but the whole space with the small ball removed!

@ACuriousMind ohhhhhh

So how does using two nbds rectify the situation?

Shouldn't I have said for all $U$ in my definition?

After all, I could pick $U=\mathbb{R}^4-\bar B_{\epsilon+\delta}$.

@0celo7 Exactly, the idea is that the condition holds for all "sufficiently small" neighbourhoods.

@ACuriousMind Gotcha.

Now my next question: How does Definition 11 above imply causality?

Do we simply take the "endpoints" of the closed curve to be the same point?

@0celo7 Yep, I think so.

Great. Time to move on.

@StanShunpike Are you registered with an e-mail?

@Danu alas, the incident was so far in Wikipedia's past that I could not easily find the conversation. The physicist was trying to explain the role of left and right handed electrons, and someone started harassing him for getting angry. By the end of it the physicist was comparing Wikipedia to (I think) old communist block bureaucracies. I was annoyed because at that time, the physicist was essentially the only person on Wikipedia who was writing something meaningful on that topic.

Hi everyone else, conversing with ghosts here... :)

@TerryBollinger It's fine. ;) As @DanielSank likes to say: Chat is an asynchronous communication protocol.

Can it be patched to allow for acausal conversation?

@NeuroFuzzy Yes, that patch is due to come out about 500 BC.

:)

Interesting topology conversation you have going there, I need to look up what started it... causality?

@Icosahedron it doesn't change with that. I've had this convo before. Mine is just weird

@TerryBollinger This was the start.

@TerryBollinger HE := Hawking & Ellis, The large scale structure of space-time (1973)

It's certainly a very interesting book, although calling it "good" is a stretch.

@0celo7 thanks, yes, I just figured that out the haaaaaard way, by tracing the quote in this stream to a Russian link that gave the O'Neill book that I found on Amazon that I peeked inside that I searched for [HE] that I then found was the Hawking/Ellis book... but methinks that saying "uh duh?" might have been more efficient... :)

Hah, you could have asked!

I thought it would be easier, then the challenge took over!

Anywho, I don't have either book, so I remain mostly intrigued but not able to pursue it tonight for sure!

@TerryBollinger How much GR do you know / do you like GR?

I think it can be read without knowing much GR, but you probably won't appreciate it unless you like GR.

@0celo7 Basic calculus and algebra.

I'm more quantum, definitely. Reading about Kip Thorne on black holes drives me a bit nuts, way too many sharp left turns on the interpretations.

@Icosahedron Clearly.

@TerryBollinger This is the classical book that shows how a collapsing star forms a black hole and why there was a Big Bang.

Heh! I don't think I'd be getting too far into either of those books very quickly. But neither do they look boring...

@0celo7 Math is a bit like programming: If you can't answer the big questions, you need to be very, very careful about some of the details. Black holes seem to be having some big-picture concept problems these days?

@TerryBollinger I believe those are quantum-related problems. HE is all about classical black holes.

Classical BHs, especially the really huge ones, are the ones that profoundly bother me. The tiny ones just seem to make sense -- tightly curved space is incredibly hot, so of course it radiates/evaporates. (I'm odd, sorry!)

@TerryBollinger Radiating black holes are not classical.

One of the major theorems proven in HE is the area law: classical effects can never decrease the area of the event horizon.

@0celo7 I know, it's the classical ones that bother me, not the quantum ones.

@0celo7 I checked out the book. Where do you see yourself in HE in, say, three weeks? (The next two are my last two weeks of thw quarter so. Finals!)

@0celo7 I've heard that, but what does it really mean? That adding matter can never decrease the BH area I assume...

@TerryBollinger Adding matter increases the horizon.

If we merge two black holes, the resulting area must be at least the sum of the two previous areas.

I think there are some issues with the proof of the area law involving horizons with cusps...

Here's a simple question about BHs: Even large ones evaporate slowly, right? So how does mass return from the singularity to the event horizon to accomplish that?

They don't evaporate like that. They radiate near the event horizon.

arxiv.org/abs/hep-th/9409195

@0celo7 But that is the catch! Are you saying the singularity has zero mass equivalency? Is all the mass "in effect" still at the event horizon?

This is a good intro to causal structure, quantum black holes, etc.

I'm about half-way through.

@NeuroFuzzy No clue. I think it gets progressively harder.

Ok, but like vague chapter estimate?

@TerryBollinger No, the mass is at the horizon. I'm not sure how much meaning that has.

@0celo7 That one looks familiar, I may even have a copy somewhere. Thanks!

@NeuroFuzzy I'm halfway through chapter 6 right now.

...what does "the mass is at [the horizon/the singularity/in between]" even mean?

@0celo7 Er... you mean the singularity really does have zero mass equivalence?

@ACuriousMind It's at the singularity because any particle can only exist for a finite proper time between the horizon and the singularity.

Like I said, I'm not really sure what that means though.

But for outer observers, stuff never falls in, right? Or something like that?

@0celo7 if that is really accurate, why do we even talk about the singularity, which after all exists only if you accept the argument that switching observer frames is OK?

As I've said before, I don't get why quantum theories are supposed to be weird :P

@ACuriousMind Yes, but that's irrelevant to what is actually happening in the rest frame of the matter.

@ACuriousMind yep!

I still say quantum black holes make lots of sense. "Curved space is hot space"

@ACuriousMind You're on fire!!

BTW, I don't really accept that switching frames _is_valid, because the inbound view quickly bumps into the end of the universe and/or the evaporation of the black hole. He can't get there as far as I can tell...

@0celo7 Oh wow. I'm unlikely to catch up then, but I'll still be reading it

@TerryBollinger "Quantum black holes" don't make much sense to me. After all, they can only be treated in these weird semi-classical approximations

@0celo7 Hell, yes I am. :D

@NeuroFuzzy I'd appreciate you asking questions if you get stuck. I might have overlooked stuff!

@ACuriousMind That's just the programming. No approximate method is safe unless it's bounded by valid higher-level assumption to ascertain and know its limits.

I said all the talk about profile pictures made me want to switch pictures.

And now that danged song is stuck in my head, have to break out some Infected Mushrooms...

@ACuriousMind Cool, but what is that? It's not resolving well here... I'll follow the link.

@ACuriousMind This one is alarming.

Oh, argh, yep!

I'm keeping the trend - it's a character from a rather old and good RPG.

I've had another from this game as pic before.

So, a vote: Do singularities have mass/energy or not? If so, how do they "pump it back" to take care of evaporation?

Oh @ACuriousMind I just saw your msg about the profile picture (I'm on phone)

@0celo7 I saw his (her?) new pic, this is what I thought I should go to hbar and post!

Hence the star.

It's wolfram rule 110. Two simulations. One with the middle bit 0 and one with the middle bit 1 with the difference in blue

@TerryBollinger Evaporation does not work like that.

So it's a "light cone"! Just not.

@TheDarkSide :D

@0celo7 But what exactly do you mean by that? A huge black hole has a huge distance from EH to singularity, I guess nominally infinite.

@NeuroFuzzy Say what?

I want to invent "dark cones"!

@TerryBollinger A (Schwarzschild) black hole has distance $2GM/c^2$ from H to singularity.

Terry no! There are enough cones as is!

TOO many cones!

@NeuroFuzzy Just wait till you discover there are conifolds.

@0celo7 So it's fixed? My very old image is more of a rupture scenario... dunno, been too long.

And conifers!

@NeuroFuzzy Ah, if @JimtheEnchanter were still Jimnosperm, he could contribute his cones

@0celo7 It's my mani-fold destiny...

Anyone cone-fused yet?

@TerryBollinger It shrinks when the BH radiates.

Anyway, I'm a bit burnt out now, so I'll go to sleep.

Sun is rising, anyway :P

Cya!

I'm confused. I have no clue what kind of black holes we're talking about.

bye

Bye! Late here too.

I'll just be here...

@NeuroFuzzy Start reading HE now!

Oh right. Yeah! (I might get to ch 3 and find iut it was all futile)

@NeuroFuzzy Have you done any geometry or topology before?

Quite a bit of point set topology and a little bit of more general topology. Not too much geo.trial by fire.

Point set topology is the stuff you need going in.

@NeuroFuzzy Like I said, ask questions! I just went over this material.

@0celo7 Sorry, you answered my question and I didn't even notice it! (It fell into a black cone?) So, to use the visual analogy, the evaporation at the EH slowly "tightens up" the "elastic membrane" (ouch, this is painfully stretched... oops) and brings the singularity back into real space... Hmph. Doesn't seem like much of a singularity in that view, though, more like just a badly squeezed and well-buried star husk...

@TerryBollinger The singularity is not "brought back", whatever that means.

@0celo7 your comment "it shrinks when the black hole radiates"

@TerryBollinger The event horizon shrinks because the black hole loses mass.

@0celo7 which necessarily also reduces distance 2GM/c2 from H to singularity...

Why aren't you guys explicitly using mathematics in your statements?

I could learn a lot if you did.

I have yet to study this mathematically.

@0celo7 and I'm not sure that for "bringing back the singularity" there's much more to it mathematically than $\frac{2GM}{c^2}$.

@TerryBollinger I don't know what you mean by "bring back the singularity"

@0celo7 Evaporation of the entire mass of the BH.

@TerryBollinger Well, there's a way to calculate the rate of evaporation.

Really must go, literally not able to keep eyes open... (will I recall this?... :)

Yep, again, I'm just interested in the conceptual bounds for the math methods. Where's the mass? How does it move around? Is all the mass energy in the singularity or the EH, or both?

Bye!

@ChrisWhite oooh what city?

@ACuriousMind Yup.

@ChrisWhite Do you like spicy

?

There's a restaurant in Shanghai called HaiDiLao. If you have an opportunity for a meal that hasn't already been scheduled, please go there.

If you like spicy food get that, and if you don't still go and just get something else.

If you don't like it you can punch me in the face.

hey :)

@DanielSank may i ask a question on fluid pressure? :)

@TheArtist ok. I'm not an expert.

That's a diagram, not a question :-)

In this problem, since pressure force acts in all directions, can we simply take the force by finding the pressure at $h_A$ ????

What do you think?

But even then how do u find the area

Also why are there four question marks in your question? Some new syntax? ;-)

The area of what?

my classmate told me that you could find the weight component of the water and the force component which is horizontal at hA

$h_A$ is a distance, so I'm not sure what you mean by "the force component which is horizontal at h_A".

What does the question mean by "reactions"? Does it mean "force"?

@DanielSank oh yes :O reaction at A means , the reaction from the wall ? O.o

What does ":O" mean?

@DanielSank it means "surprised"

Ah.

:)

So it's asking for the force from the wall on the gate?

it must be the reaction from the water?

I think it wants to know the force from the wall on the gate.

reactions from water since they tell " Reactions from perpendicular to the plane of gate"

it says normal to the plane of gate

Yes.

so how do we find? :)

I'm not going to do your homework for you.

This site never does that.

no I'm saying, what is the method

If you have a specific question I will answer it.

Draw a free body diagram.

what is the method :) what concept is used?

Draw a free body diagram.

ok :)

To be honest, I don't understand what the problem is asking.

This kind of thing annoys me. I have a PhD in physics and I can't tell what the problem is asking.

hehe :)

really ? wow its so cool :) you have to do some research in order to get a phD right? :)

Yes.

What is the research that you did ? :) can you tell me?