@heather In my opinion, bra-ket notation is useful when you're doing linear algebra in general. It's not just a quantum mechanics thing.

It's useful because it clearly expresses dot products matrix multiplication.

@DanielSank, yeah. I probably just need to get used to it.

@DanielSank we should do linear algebra in GR notation

I noticed in the conversation about matrix multiplication you were using bra-ket notation.

@heather Let me ask you this: suppose I have two vectors $u$ and $v$, and a matrix $T$. How would you express the dot product of $v$ and $Tu$ without bra-ket notation?

@0celo7, what does general relativity notation look like? I didn't even realize general relativity used linear algebra?

@0celo7 I wouldn't be opposed to that, but I think it might be hard to use that from the start.

@heather Don't worry about that quite yet.

@DanielSank, well, you'd do $v \cdot Tu$, right?

That's a slightly subtle issue.

@heather That certainly works, yes.

In braket notation it's $\langle v | T | u \rangle$.

Of course, then you've got two kinds of multiplication going on in one expression.

But, wait, let me try to figure out your expression:

What's a bit nice about this is that if you see a left bracket and a right bracket with stuff inside, you know the whole thing is a number in the end.

You have a $\langle$, which means row vector, and $\rangle$ which means column vector

I never really understood all the big deal about notation. I think most things work equally well in standard linear algebra notation, in bra-ket notation and in component notation.

You just have to know what you're doing in each case :P

@heather manifolds are just spaces on which you can do calculus

@ACuriousMind Notation is the source of like 90% of all confusion in the universe, dude.

Notation matters a lot.

And calculus is basically linear algebra with topology

@0celo7, still don't know what topology or a manifold is =P

But okay.

@DanielSank Sure, but it's not like one is "better" than the others. I think it is much more consistency and careful application of your chosen notation that matters than what notation you use

@ACuriousMind The fact that you call it "component notation" is a great illustration of why notation confuses people. I don't think of $A_{ij} u^i$ as having anything to do with "components".

A manifold is a locally Euclidean space

@DanielSank but that's wrong lol

@ACuriousMind Sure. Consistency is very, very important.

@heather Yeah, and everything in my expression is just matrix multiplication.

@ACuriousMind, well, unfortunately I don't know what component notation is, and bra-ket I'm barely familiar with, so I prefer standard linear algebra notation.

And if you multiply $\langle |$ by $| \rangle$, then you get a matrix...

@heather What you call "standard" isn't really standard to any of us though ;)

@DanielSank, really?

@heather Huh? I don't think that's true.

@heather Well, the GR people all use "index" or "component" notation.

@DanielSank, that's what I thought, I'm probably wrong, I thought I read that somewhere.

Or maybe we should do GR in Bradley notation

@heather Oh, well, if you have a ket (column vector) $|v\rangle$ and a bra (row vector) $\langle u |$, then $|v\rangle \langle u |$ is a matrix.

@DanielSank, oh, that's what I mixed up.

That's easy to see though because if you multiply an $n \times 1$ matrix by an $1 \times n$ matrix, you get an $n \times n$.

Huh, then I'm stuck with knowing there's a column and row vector, I'm not sure what putting the matrix in between means.

Hmm

What's the Riemann tenor in barley notation

@0celo7, uh, isn't barley a grain? =P

Dirac is barley in English

Everything in $\langle v | T | u \rangle$ is matrix multiplication.

I gotta go.

ciao

@DanielSank, I have to say that it is neat, but I think the other way is just as neat and clear. Well, I mean, I'm just saying that because I'm more familiar with it.

@DanielSank Well

And, how is everything matrix multiplication? You still are doing a dot product.

I think the whole point is that it isn't matrix multiplication

@DanielSank, adios!

@heather I believe Daniel's idea is that if you apply the standard rule of matrix multiplication to row and column vectors as $1\times n$ and $n\times 1$-matrices, then you get that their "matrix multplication" is just the dot product.

@ACuriousMind, I'm not sure I quite follow, but okay, it makes some sense.

$\begin{pmatrix} a_1 & a_2 \end{pmatrix}\cdot\begin{pmatrix} b_1 \\ b_2 \end{pmatrix}$. Now think of the first as a $1\times 2$-matrix and the second as a $2\times 1$-matrix and multply away - you get a $1\times 1$-matrix whose entry is just the dot product.

@0celo7 yes we'll, let's not get into that just now, eh?

@ACuriousMind, oh...yeah, that makes sense! Thanks!

@0celo7, did you ever go see a doctor for your eye?! (Just read the transcript behind the intriguing starred message saying "Send us a photo of the front door of a hospital..." - rather an eye-catcher.)

Oh, sorry, that was a really bad, unintended pun.

lol

=P

@heather no

Tomorrow

nvm I guess it's back up.

I don't know how I'm going to get there

@0celo7, man, I could whack you right now, except I can't via the computer. Get to a doctor!

I don't have time

@0celo7 finish your hw then play FNV THEN go to the doctor. priorities man

@0celo7, equivalent statement: "I don't have time to save my life" (to which my response would be, well, you're gonna have a whole lot less time in a minute).

@Obliv, don't encourage 0celo7...=P

I'm not playing FNV

Good

I never should have played that shitty ass game

yeah play last of us instead

You are walking to a hospital, yes?

It basically ruined my life

Or at the very least an eye doctor

@JohnRennie, hello!

@heather the only time they would take me is tomorrow at 2:30. I'm going to mod the QM exam review

And I don't know when I'm going to study

@0celo7, there's a reason there's the emergency room.

And it's going to be real hard to study half-blind!!

Luckily I've pissed off Rebecca so she won't want to go out with me tonight

@heather hi Heather. Just a brief visit ...

And yes, that required bolding.

@0celo7 Will you answer my messages for the love of god

So I have to do homework tonight

@JohnRennie You should be in bed by now Mr.

@BernardMeurer what fucking messages

@JohnRennie, I just wanted to talk about your potential homework physics site.

@BernardMeurer soon. 5 a.m. is 8.5 hours away.

@JohnRennie Like a clockwork :p

@heather I can chat for a few minutes. I start work at 05:00 (8.5 hours from now) so I need to get to bed fairly soon.

But I don't think there's a lot to say anyway. I did see your comments earlier.

@JohnRennie, okay.

Do you think it would be possible to incorporate your proposal into the reworking of the homework policy, or is that not going to happen? I do like the idea.

@heather not going to happen.

Allowing homework basically destroyed the Math SE and there's huge resistance to the same thing happening here.

As for reworking the homework policy, we been trying to do that for five years with no obvious outcome.

@JohnRennie, okay, I kind of thought that, but. So I guess my main question is how to distinguish this from Math SE and MathOverflow? Because I'm partially worried it might turn into that.

Actually I don't think it's a bad idea if it does end up like the Math SE/Math Overflow split.

Though we'll still welcome beginners here ... just as long as they don't ask about their homework :-)

@JohnRennie I don't think we have critical mass for that

@BernardMeurer the point is that the Physics SE is already closer to Math Overflow than to the Math SE.

Though the MO tend to frown on noobs, and we'll never do that.

@JohnRennie Only if you look at the attitude towards homework. We have very different userbases, and unlike MO, we don't expect a certain "level" from questions.

@heather what's your fear? How do you think a split would make this site worse?

I think you can't meaningfully compare the MO/math.SE split to what you are proposing

@ACuriousMind agreed, though we do expect a degree of effort from OPs i.e. that they have thought about what they are asking and made some attempt to research it.

Whereas it appears you can ask anything in Math SE and someone will answer.

@JohnRennie Eh, that varies wildy. We have never codified whether or not "insufficient effort" is really a close reason and many of our popular questions show a blatant lack of research effort.

@ACuriousMind hmm, yes, the curse of the HNQ

In any case, my intention with a new site wouldn't be to take the load of the PSE or push it in a more rigorous direction. It would purely be to allow more flexibility in the answering of some homework questions.

@JohnRennie MO eats noobs for breakfast

My plan for the next few days is to go back though closed questions and see if there really are enough of them that I think could be usefully answered on a sister site. It's entirely possible I'll decide there just aren't that many homework askers who are genuinely interested.

@JohnRennie, hmm, yes, that makes sense. I just like the way physics falls inbetween math and math overflow, allowing newbie questions but also keeping out some of the junk that gets on math. My one worry about this is that it would cause such a split and result in physics turning int a death for newbie questions zone.

Though from what you are saying, it sounds like that wouldn't happen, in which case I wholeheartedly support your proposal, and would be glad to help however I can.

@JohnRennie that's a good idea. If the scopes of the two sites have to start overlapping for the new one to be sustainable, it probably isn't a viable idea

@heather I think it's exceedingly important we encourage the next generation of physicists, and be loathe for that to stop happening on the physics SE.

@JohnRennie, it might be a good idea to start a meta post or chat room where people can discuss what would or wouldn't be on topic, and discussing close reasons, and such. (If you determine there is enough people who would be interested.)

@heather Area 51 has facilities for doing that.

@JohnRennie, I know, but to start getting a feel for where this is heading, and to raise awareness about it on the physics community, it might be good. (Or it might not be.)

If I decide to go ahead I'll post in the meta here asking for contributors then we'll use the new proposal on Area 51 for the discussion.

@heather well I've discussed it here, but the reality is that few of the people here are interested (for the very good reason that they have physics to work at).

@JohnRennie, well, I hope it does get off the ground.

Anyhow I'm off to bed. 5 a.m. is getting ever closer :-)

Thank you for the conversation, and good night!

=)

@ACuriousMind Goes a generic Hilbert space have a nontrivial isometry group?

@0celo7 does a hilbert space have a 'metric' ?

That's what a Hilbert space is...

I thought it was an infini-dimensional complete vector space

complete in what?

limits exist on it @0celo7

what does that mean?

how are the limits defined?

It's continuous? @0celo7

what is continuous?

@0celo7 The field? So like there is an infinite amount of elements in the set?

Huh?

what does it mean for a field to be continuous then? @0celo7

i have no clue what you're talking about

$\Bbb Q$ is a field but certainly not "continuous"

it has an infinite number of elements

it must have an infinitely small metric b/t elements then? @0celo7

huh?

Is there a maximum mass limit for black holes in any GR solution?

not in static ones

but maybe in some dynamic ones

Then how about the Oppenheimer-Synder model?

@SirCumference There are limits on charge/mass ratios and stuff like that.

@0celo7 Yeah, but someone asked me about a mass limit

In reality, there's a practical limit to how much mass a black hole can accrete before it has no more surrounding mass, but I'm looking for a theoretical answer

@0celo7 So does there appear to be a mass limit in the Kerr metric?

If you don't want a naked singularity, yes

Or maybe it's a minimum mass given a certain angular momentum. Check the usual references

@0celo7 Er, elaborate?

Later maybe

@0celo7 Probably idiotic of me, but if we have a small enough angular momentum, there shouldn't be a problem, right?

Correct

@0celo7 So then why would there be a mass limit? I don't see how that would give us a naked singularity

@0celo7 did u do your lab writeup

@SirCumference, is this paper of any assistance?

@SirCumference, ah, wait, I think I figured out why:

@heather I think that's talking practically

@Obliv dude

they're due Tuesday

I do them Monday

It's saying the $M_{bh}$ -$σ$ relation will prevent such black holes from accreting matter at a certain point

@SirCumference let's check

The black hole won't have anything nearby to eat

Do you have Wald?

@SirCumference, yes, but I think I figured out a different line of reasoning, from a purely theoretical standpoint. Rotating black holes can have two event horizons in some cases, right? And this results in an ergosphere, which draw closer together as the spin of the singularity increases. When the outer and inner event horizons merge, they shrink toward the rotating singularity and eventually expose it to the rest of the universe. Thus, a naked singularity.

> two event horizons in some cases

Are you talking about the absolute and apparent horizons?

Oh wait, nvm

ok, I have it

you need $e^2+a^2\le M^2$

So there's a lower mass limit

And then, with the Kerr metric, disappearing event horizons are a possibility, if the angular momentum is high enough.

^exactly

@0celo7 Well, I'd imagine, since we have the Tolman-Oppenheimer-Volkoff limit

Nothing to do with that

That's a dynamic thing coming from stars and shit

@0celo7 oh i thought yours were due wednesday? I'll just keep asking every wednesday I guess

Yeah, just realized what you're talking about

I'm saying for a Kerr black hole to be "black" one must have that above inequality

I was thinking purely of stars

So to connect with a black hole's mass,

beats me what the hell the units are there btw

(ergh, sorry, I had this page up and then I accidentally exited it)

probably some $c$s missing.

@0celo7 SI?

some $G$s too

@SirCumference certainly not

actually I mean dimensions

that equation works in natural units

Yeah, just realized how stupid that sounded...

or natural dimensions

ahhh whatever the hell I mean

$c=G=1$ units

or dimensions

I don't know any more

Probably electron charge = 1 too

All right, screw Kerr black holes

Let's talk about the Schwarzschild metric

no limit

Can we just keep adding mass to a Schwarzschild black hole indefinitely?

Damn

that's a much harder question

if you "add" mass it's not a static situation

Well, a Schwarzchild black hole has no angular momentum...hmm.

and you get horrible PDEs that I don't understand yet

Is that another reason the Big Crunch hypothesis can't happen? Because Schwarzschild black holes don't exist in nature

(I understand the PDEs but not the functional analysis)

@SirCumference huh?

@0celo7 Cosmology

A schwarzschild black hole can't exist in nature for several reasons

@0celo7 Yes, I know

The most basic one is that there is other stuff around

and a Schwarzschild black hole solution is one in which the black hole is the only thing around

Big Crunch: basically the universe recollapses, if I remember right. But I think the cosmological constant's value prevents that from ever happening.

My point is that since only static black holes wouldn't have a limit, and our Universe doesn't have static black holes, is the Big Crunch hypothesis impossible?

Fuck it. Someone must have flagged me because it's making me wait like 10 seconds before posting each time

@heather The second law of thermodynamics does too

So I'll just stop posting

Entropy would have to increase with each cycle, if the Universe is oscillating

@0celo7 That happens to everyone

It's just SE's chat preventing spam