The h Bar

ACuriousMind

12:00

@Secret When you're not "sure what type of math object it is", you can't claim that you can define anything about it rigorously.

Secret

ooops. sorry about that

But one thing is clear, whatever R is, it basically contain the information of all equations and x has to satisfy at least one of them

in some restricted sense,one can view R as a set of equations that have physical relevance and x are the given unknown

ACuriousMind

But "equations that have physical relevance" is horribly ill-defined!

Secret

Indeed, that's why I am suspecting we cannot really measure the size of this set...

ACuriousMind

You're free to think about this, but you're always trying to make things have some formal mathematical sense. This doesn't. It's philosophy, and vague philosophy at that. Don't pretend it's math.

Slereah

Well first let's create a measure of physical significance

And then we find the kernel of the function of measure, to find equations that have 0 physical significance

Secret

12:06

for that to work, the kernel has to be some kind of measurable set, or in some sense, "smaller"...?

I wonder if there's a theorem that guareentee that in set theory

ACuriousMind

"measurable set" only has meaning when you already have a measure, and has not really something to do with size. What are you talking about?

Slereah

(It's a joke)

Secret

https://en.wikipedia.org/wiki/Non-measurable_set

O great, I mixed up this guy with the notion of cardinality of a set

hence the mistake aucirousmind pointed out
Blagh, vagueness of concepts prevent them from being able to write them in math formalilsms

-_-

ACuriousMind

@Slereah I know you're joking, but I don't think Secret is :P

Secret

@ACuriousMind I have a habit of playing along with a joke, because there exists jokes that can acutally made serious and some sensibel ideas given the correct thnking

huffingtonpost.com.au/entry/…

for example, we austrlians knew that drop bears are a joke to scare foreigners (but we always say them them that they are out there)

But imagine the twist and craziness (and high) that can be produced if the joke is made partially real, in the sense that it matches the behaviour except that they don't look like koalas)

Slereah

12:12

It is partially real already.

Dropbears are based on koalas.

Secret

> I am kinda like a weird drug addict. I get more high the more a joke gets real. Thsi is because most people don't take jokes seriously, thus it is a guareentee shock to them (This is my mischevious side of my personality)

and so far, nature seemed to play along well

Besides the high, there's also a degree of seriousness in that some jokes do offer insights on some problems that are not found elsewhere

hence my "weird" attitude to jokes

Secret

So for the "pseudomaths" example above, we knew that the vagueness of a concept prevent them to be defined rigorously in mathematical language

thus even if there is a slim possibility that there exists a sensible way to rigorously define them, it must be hard to find (possibly nontrivial)

@ACuriousMind But you are right about one thing: This attitude can be a big problem, espeically in having a higher chance to write nonsensical things withour realising that the vagueness is ignored by accident

Slereah

mb focus more on learning the physics

Do some basic physics exercises

The point mass in a gravitational field

The point mass with friction

The linear spring

The pendulum

The point charge

The dipole

The spherical charge

The wire current

The adiabatic process

The harmonics on a string

The deadlift

The squats

The push ups

Secret

NB to reader: The last 3 items are not in the same classification (I refuse to use the word "category" to not upset the mathematicians) as the others, thus it is a joke

However it can be argued that they are not a joke if one considered the biophysics of physical exercise, which can be simplified to a lever problem

Therefore (joke) the last three items are in a superposition of $|Joke\rangle$ and $|Non joke \rangle$

(Unless I am missing something, or that vagueness kills me (in that you cannot treat a joke in any manner that is consistent to a state), the above nested joke should be a sensibel joke)

Slereah

Oh hush

Secret

12:27

Ok back to point: I have done a couple of these, the point mass with friction seems kinda new, I might try it

Slereah

That is just a falling mass with a friction term

Secret

I wonder how we can compute this with GR..

Slereah

Of the form $\vec F_{friction} = - k \dot{\vec{v}}$

Secret

In the context of GR, is friction part of the stress energy tensor?

given how friction is a disspative force thus can contribute to the energy of the system?

Slereah

don't focus on fancy things.

Just try solving those types of problems first.

Secret

12:31

for point mass with friction, what quantity do you want me to compute, the time taken to fall, the height, the final velocity?

Slereah

Solve the force equation, for a start.

$m\frac{d^2 x}{dt^2} = mg - k\frac{dx}{dt}$

Basic things

0celo7

> A timelike hypersurface contains a timelike vector field. Take an everywhere future-directed timelike vector field on the hypersurface and construct an integral curve. But no points in an achronal set may be connected by a timelike curve.

How does one write that more elegantly?

Slereah

Put it in unitless form and then solve it

0celo7

@Slereah let's get Penrose

Slereah

Errr

Road to reality?

0celo7

12:44

no the other one

Slereah

Or do you mean the topology one

0celo7

yes

Slereah

oh yes

it's pretty good

It's basically proto-HE

Although it's a bit poorly constructed

0celo7

does it cover different things

Slereah

Feels more like class notes than an actual book

Yes

Secret

12:47

@ Slereah i.sstatic.net/cFoQ7.jpg

0celo7

don't you hate reading the intro to a book

and they talk about shit

and you don't know if you're supposed to know that or if they'll explain it later

Slereah

>reading the intro

Man skip the first section

always

Secret

Wait, how come I don't get the prediction of terminal velocity here (x should tends to a const as t gets large)?

O nvm, that's displacement, not velocity...

In that case, as $t\rightarrow \infty$ $v\rightarrow\frac{mg}{k}$ as expected for terminal velocity

Slereah

Terminal velocity isn't done with $t \rightarrow \infty$

Oh wait

0celo7

yes it is

Slereah

12:54

do you just mean the velocity it converges to eventually

ACuriousMind

@Slereah oO

Secret

yes

Slereah

Then sure

0celo7

Wow

0

Q: Is Schwarzschild spacetime globally hyperbolic?

Is the Lorentzian manifold $\mathbb{R}\times(\mathbb{R}^3-\{0\})$ together with the Schwarzschild metric a globally hyperbolic spacetime?

Shortest question evar

Probably gonna get closed.

ACuriousMind

You could have shown a little effort :P

0celo7

12:57

Like what?

Slereah

More importantly what is the metric inside the horizon

0celo7

Put in the definitions?

Slereah

I mean I guess the inside metric is also a fine solution

ACuriousMind

@0celo7 Yes and elaborate on where exactly the problem in determining whether it is globally hyperbolic or not lies

Slereah

But at the horizon, what metric are we supposed to use?

Can't be Schwarzschild

Wrong signature at the horizon

0celo7

12:59

@ACuriousMind it lies in the fact that I have literally no clue how to do it

wait

I think I have a better question, will I be able to undelete this one later?

ACuriousMind

@0celo7 The naive guess would be to just foliate the spacetime radially (w.r.t. the coordinate that is "radial" inside/outside the horizon)

@0celo7 Yes, you can delete and undelete your own posts however you like.

0celo7

@ACuriousMind So?

ACuriousMind

@0celo7 So you should explain what the problem with that naive guess is?

0celo7

That's not what globally hyperbolic means

Slereah

You can foliate non-GH spacetimes

0celo7

13:00

^

ACuriousMind

Ah, I meant something different

0celo7

Like Minkowski with a fucked up metric

ACuriousMind

But I expressed that very badly

0celo7

i.e. Gödel

Slereah

Or just Minkowski with a point removed

Gödel isn't foliable!

0celo7

13:01

@Slereah allegedly.

Slereah

GH is that every causal curve crosses every Cauchy surface exactly once

ACuriousMind

Okay, my naive guess for the Cauchy surface would be any of the leaves of that foliation (perhaps only those outside the horizon, come to think of it)

0celo7

@ACuriousMind And that's true

Slereah

foliating by $t$ isn't a very good idea because it's spacelike inside the horizon

0celo7

But how does one prove it

Slereah

13:02

You need to foliate it along a timelike curve

Maybe using Gullstrand-Painlevé coordinates

I dunno

0celo7

@Slereah you foliate using KS coordinates, I'm pretty sure.

or whatever the coordinates in a Penrose diagram are

ACuriousMind

@0celo7 Ok, so you're not actually confused about whether or not that spacetime is globally hyperbolic, but you want to know how to show a surface is Cauchy?

Slereah

Can also work, yes

Although be careful about the domain of definition

0celo7

@ACuriousMind Point taken, I should have put way more effort into this :P

Slereah

KS is usually done in the maximally extended spacetime

Make sure you have only the specific range

0celo7

13:04

@ACuriousMind yes, I'm now asking a more general question of how to do that for a general spacetime

ACuriousMind

Now that's a better question :)

0celo7

In fact, HE has a little picture of the Cauchy surface.

Getting my totally legal digital copy out now to take a screenshot...

Slereah

Cauchy surface in KS is just

horizontal line in the Penrose diagram

IIRC

Maybe slightly curved?

I forget

0celo7

0

Q: How does one determine if a spacetime is globally hyperbolic?

A spacetime $M$ is said to be globally hyperbolic if it is strongly causal and if the sets $J^+(p)\cap J^-(q)$, for all $p,q\in M$, are compact. (For more information, see the Wiki article on causal structure.) It may be shown that global hyperbolicity is equivalent to the existence of a Cauchy ...

general-relativity mathematical-physics differential-geometry causality

@ACuriousMind Better?

Should I just add the Schwarzschild thing on the bottom or make a new one?

> We are finally led to consider what can be said about Lorentzian analogues for the rest of the Hopf-Rinow theorem. Here, however, every conceivable thing goes wrong.

@ACuriousMind Have you heard of the Nomizu-Ozeki theorem?

DeNiSkA

13:20

if a light passes through a mirror, is it correct to say that photons have passed through the mirror(like some spirit in movies)[this is second time i am asking, so sorry]

Slereah

Either that or they were absorbed and reemitted in the same direction

0celo7

@Slereah BBE doesn't even define the metric they're so badass

they start on the first page with the connection

Slereah

Well HE also starts like that?

Defining the connection first

Not on the first page tho

0celo7

yup

wait, are we counting the intro chapter?

Slereah

Intro chapters don't count

you just skip those

0celo7

13:28

ok, they define the connection on page 2

ACuriousMind

@0celo7 no

Slereah

intro chapters are always BACK IN THE 19TH CENTURY blablabla

0celo7

and even that's because they have an intro to the second chapter as well :V

Slereah

You've read one you've read them all

0celo7

@ACuriousMind look it's up, pretty cool theorem that no one mentions

@Slereah this one starts with IN 1973 HAWKING AND ELLIS WROTE A BOOK

barrycarter

13:30

Should I respond to a user's complaint about me in meta, or let the situation play itself out?

Slereah

@0celo7 Good idea

Give credit to the only proof reference

0celo7

They seem to reference HE and Penrose equally

John Duffield

@JohnRennie : Don't put me in the same box as Jokela Turbine. He's some my-theory guy, I'm not. I give rock-solid references to back up what I say, for example to the Einstein digital papers. Einstein said x, and I reiterate it. And if you disagree with x, that means it isn't me imposing idiosyncratic views. Instead it's you. Like with your "definitive" "authoritative" "canonical" answers that are factually incorrect. Perhaps you'd like to discuss them on meta?

0celo7

Lol!

@Slereah GR book not using Einstein summation, why??

ACuriousMind

@barrycarter Not really, since meta posts should not be about specific users (and explicit references to specific users will be removed)

Slereah

13:32

@0celo7 Coordinate free?

0celo7

@Slereah they do remain coordinate free for the most part

barrycarter

@ACuriousMind OK, but it's pretty clear from the links in the meta post as to my identity. So, if I respond, my entire response will be deleted because it reveals my identity?

0celo7

but you have to write down the geodesic equation in coordinates

Slereah

Coordinate free isn't too bad

0celo7

and when they write it in coordinates they have a bunch of sums

coordinate free is amazing

but there's nothing wrong with going to coordinates every now and then and using Einstein summation

Slereah

13:34

Newman-Penrose is best tho

0celo7

no

one does not need 10 equations for every calculation

ACuriousMind

@barrycarter Uh...I don't actually know what the mods will do if you respond. Usually, such questions will be answered in a general way of what to do in the situation described in the meta question, without judgement whether that's actually an accurate description of the specific incident.

If you want a mod's take on this, you could always ping them here about it

barrycarter

@ACuriousMind I'm trying to avoid blowing this up too much. I feel the natural need to defend myself, while, at the same time, realizing that it may just make things worse. I do appreciate your opinion.

0celo7

You know a GR book means business when they don't define $\otimes$ or $TM$ or anything

have I found a truly advanced GR book?

ACuriousMind

@barrycarter That's...way more considerate than what we usually get with drama on meta :)

barrycarter

13:38

@ACuriousMind Oh great. Now I feel like I should add to the drama just so I can be one of the guys :)

0celo7

NO

@Slereah want some references where the metric is a distribution?

Slereah

Sure

It's not too common

But it sure beats most other formalisms for Schwarzschild

$R = M \delta(r)$

The best

0celo7

Parker (1979), Distributional Geometry, J Math Phys 20, 1423-1426

Taub (1980), Spacetimes with distribtion-valued curvature tensors, J Math Phys 21, 1423-1431

those look any good?

I can't access the articles because I'm at home

Slereah

dunno

0celo7

they use $\tau$ for the Ricci scalar

> One of the folk theorems in general relativity asserts that the spacetime metric is determined up to a conformal factor by the set of null vectors.

Slereah

13:53

IS IT NOT???

0celo7

no, it's true

BEE is just being weird

whoops only one author is B

I'm too used to BBS

Physics Meta

14:21

-1

Q: Should we discourage "canonical" questions with "canonical" answers?

We've recently had John Rennie asking "canonical" questions which he's answered himself: What is time, does it flow, and if so what defines its direction? What is time dilation really? What is the proper way to explain the twin paradox? He says his answers are intended to be definitive and au...

discussion

yuggib

it's so silly that is not even worth comments.

0celo7

That's not very nice you guys

ACuriousMind

I never thought of myself as a medieval theocrat. Now I have an odd desire to go burn a witch.

3

yuggib

a little excerpt "It is in essence saying “mine is the right answer and all other answers aren’t worth looking at”. It’s imposing an orthodoxy, and it’s the sort of hubristic mindset that gets in the way of scientific progress."

while his usual viewpoint is:"mine is the right answer and all other answers aren’t worth looking at"

0celo7

@ACuriousMind The last recorded witch burning was in 1682.

Not necessarily "medieval."

yuggib

14:30

@0celo7 I've never been a nice person

ACuriousMind

@0celo7 That only shows how hard we medieval theocrats are to get rid of!

Danu

@yuggib Gotta love the rhetoric

yuggib

@Danu I don't like politicians so much; so actually, no :-þ

0celo7

@Danu there any geometers on HSM

Secret

The Librarians (2014 TV series)

The Librarians is an American television series developed by John Rogers that is broadcast on TNT, and premiered on December 7, 2014. It is a direct spin-off of The Librarian film series, sharing continuity with the films. On February 12, 2015, TNT renewed the series for a 10 episode second season. The second season of The Librarians began on November 1, 2015 on TNT. On December 15, 2015, TNT renewed the series for a 13-episode third season. == Plot == The series follows four people, Eve Baird (Rebecca Romijn), who is chosen by the Library to be a new Guardian, as well as Ezekiel, Cassandra and...

0celo7

14:32

^ good show

Very cheesy, but good

Secret

It's the first show that taught me about magic

0celo7

...what

In 2014??

How old are you

3?

Secret

It's the first show (I watched) that taught me about magic

I am of course in my 20s

yuggib

^why the "of course"??

0celo7

Wtf, what about Star Wars, Harry Potter, fucking Disney?

Secret

14:33

Before that, I rarely pay attention to the 3rd branch of social culture: Esoterism

Danu

@0celo7 Sure

Secret

@0celo7, oops, you are right, harry potter is the first ,then

0celo7

@ACuriousMind why is my cat complaining

Secret

but The Librarian flesh it out a lot more, including other types such as paganism etc.

For one thing, there depiction of magic is not the "pew pew" type and actually follows folklore depictions, thus more accurate in presenting this culture

ACuriousMind

@0celo7 I'm a physicist, not a veterinarian

0celo7

14:34

you're neither

technically

John Duffield

@barrycarter : don't respond, I've done an answer instead. But do make sure that any further comments you make are well-thought-out.

Secret

So I argue that, yes harry potter taught me the concept of magic, but it is The Librarian that taught me the culture as depicted in folklore and historical accounts

Danu

@0celo7 Relevant

Secret

...as a (bad?) side effect of the show, I became more curious on esoterics now.

Although to keep myself form being kicked out and locked up by the physics community, I tend to be very careful not to mix science and esoterics, (especially in the physics community, best known for being extremely sensitive to cranky phenomenon)

0celo7

@Danu do you know why the exponential map in Riemannian geometry is called that (yes, I looked it up, but ACM says the standard answer is wrong)

Secret

14:38

@ 0celo7 In particular, I will always answer "This is too naive of a generalisation" whenever peopel start raising quanutm mystism

0celo7

I asked an HSM question last night on his suggestion

Danu

@0celo7 Ok. Note that getting answers on HSM may take longer... About 2-5 days usually.

dmckee

^ Small, and a growing culture of really well researched answers.

0celo7

@Secret what?

Secret

Put it in another way, it is nonsense (unless proven otherwise)

Danu

14:44

@dmckee Yeah. It's really nice when we do get answers: They tend to be quite good.

However, the fact that most answers really require research makes it complicated to grow the user base

Secret

However, I rarely say to people directly his/her idea is nonsense, because there's always something I can make use of from their ideas

In fact, the way I deal with nonsense is I ignore them, and often the other person won't notice it (because of how I blur the lines between using the idea and ignore it)

This is how I can keep my religious, esoteric and science friends all happy

[parasite mode] while I continue to extract from them what truly matters

Secret

In all 3 branches of social culture, there are things that are useful to ponder about.

However, because my curiosity on the 3rd branch came by so late, there is still a lot to learn about its worldview as Iam not famialr with it

As for the 1st and 2nd branch, I am learning as usual, such as doing the physics problems as covered with Slereah a few minutes ago, and discusisng purpose with my religious friends

> crap accidently killed chat...

> looks like I am still off from the perfect moment on the insertion

barrycarter

15:18

@JohnDuffield Thanks!

David Z

15:41

@barrycarter official word: probably not. It's not against the rules to say that a complaint is about you.

The thing is, 99% of the time, the whole point of bringing up an issue on meta is to develop guidelines for future incidents of that time. Questions like "barrycarter did blah blah blah, what are you going to do about it" aren't useful. But a question like "Should blah blah blah be allowed? I think not, and here's why: ..." is useful.

Experience has taught us that when people focus on the specific instance of blah blah blah, or on the person who did it, we wind up getting into arguments. That's bad. That's why we try to strongly discourage posts that pick on the specific details of one incident, and encourage posts that address the long-term implications.

So, as for responding to the post about whatever you did (I don't even remember): if you can respond in a way that contributes something useful toward deciding on a future policy, go for it. Sometimes it's really valuable to get a perspective from the person involved.

But if you want to respond just to defend yourself, that's probably not useful. Honestly, nobody cares that much. Our memories are short, for the most part, and whatever you did, it's surely not the most pressing thing we have to deal with even at this moment.

Oh, and if you do post something that gets deleted, it doesn't necessarily reflect badly on you. When we delete things to defuse arguments, we're not doing it to punish the people who posted them.

barrycarter

16:02

@DavidZ I'm reasonably happy with how the issue has been handled so far policy-wise, so I shall hold my peace for now.

David Z

Sure, up to you

John Rennie

16:43

@barrycarter For what it's worth, the vast majority of people answering questions on this site do so out of a desire to be helpful. They may or may not be successful in this, but even if you feel an answer is not helpful downvoting it is a poor way to reward the effort someone has put in on your behalf.

barrycarter

@JohnRennie OK, but if the answer (to someone else's question in this case, not mine) is actually incorrect, isn't downvoting and making a comment re why the answer is wrong the correct way to proceed?

Danu

@barrycarter Sure it is.

Holy crap a long first answer

John Rennie

@barrycarter If I see an answer that I think is well intentioned but incorrect I will add a comment explaining why I think this, or even add a reply of my own explaining what I think the correct answer is.

I would normally only downvote if I thought the answer was lazy or careless.

barrycarter

@JohnRennie I was hoping to add an answer of my own later, but I felt that commenting and downvoting right away was important to alert the original asker and anyone else who sees the answer.

John Rennie

You shouldn't underestimate how upsetting it is to receive downvotes. In effect you're being told: you don't know what you're talking about. It happens to me regularly, and even when it's a fair cop I still don't like it.

When I feel the downvote is undeserved it can really prey on my mind.

Remember no-one is paid to answer questions here. No-one gets a prize or mentions in the newspapers. We all do it becauise we are trying to help.

hubot

16:49

Hello!

How is your reactions on downvotes?

barrycarter

@JohnRennie To be fair, that is the message I was trying to convey. The answerer was fairly rude to me and effectively said the same thing to me. Of course, I realize that two wrongs don't make a right, but, in this case, I don't feel bad that I made the answerer feel bad.

hubot

*to

John Rennie

I don't feel bad that I made the answerer feel bad - I'm afraid I fundamentally disagree with that attitude.

barrycarter

How about "I don't feel bad that I made the answerer feel bad since the answerer made me feel bad"?

Danu

@hubot Just don't react, unless something valid was pointed out.

ACuriousMind

16:51

@JohnRennie But...the score is what tells people how trustworthy an answer is! If the answer is already sitting at -1 or -2, I can understand not piling on, but as long as an answer that is (in your opinion) wrong is sitting at a positive score, downvoting is the right thing to do.

Danu

@ACuriousMind No, the current score should be completely irrelevant IMO.

Always downvote if it's bad.

John Rennie

@ACuriousMind the score shows what anonymous and unaccountable voters think of the question. On the other hand a contrary answer from a respected site member shows what a respected site member thinks of the answer.

hubot

How is your reaction when your teacher says that you has given minus something points?

John Rennie

@hubot I used to argue with the teacher - I was popular with the teachers at school :-)

hubot

Do I feel bad that I've given minus for example 10 points from my educator?

Danu

16:54

That moment when you (explicitly) abandon coordinate invariance in GR:

-4

A: How do we measure Schwarzschild coordinates?

In general relativity, you can take whatever coordinate system you want That's what people tend say, but it isn't true. Imagine your coordinate system is blue. You can adopt a new coordinate system if you wish, but that's blue too. You can have any coordinate sysem you like, so long as it'...

ACuriousMind

@JohnRennie And...site members become respectable through the accumulation of anonymous and unaccountable votes?

Danu

"respectable" :P

ACuriousMind

Really, the reason for the voting system, aside from gamification, is that I can express my opinion about an answer without having to write a "Well done!" or "no, this is wrong"

John Rennie

@ACuriousMind Ok, I take your point, but signal to noise improves in the long run

hubot

*when instead that

ACuriousMind

16:56

@JohnRennie Of course, because the bad answers are downvoted and the good ones upvoted!

barrycarter

@JohnRennie I think we have a fundamental philosophical disagreement here. If I see an answer that's wrong, I'll at least comment on it, even if I don't post my own answer. If the answer is wrong in some fundamental way, I'll downvote it as well.

John Rennie

I realise that I'm probably on the wimp side when it comes to downvoting, and I'm not sure my attitude is entirely defensible. It's just that given we are a community it's important to encourage as well as criticise.

hubot

Should I feel bad when I've given minus for example 10 points from my educator? - correct

barrycarter

@JohnRennie I felt the poster was wrong, arrogant, and rude. I think downvoting can sometimes discourage people like that, which is the intent.

John Rennie

@Danu We need a canonical Q/A on the subject. I'll get started right away!

barrycarter

16:59

@JohnRennie I concede that I was not driven entirely by benevolence.

ACuriousMind

@JohnRennie I don't disagree with that last statement. Good answers should be rewarded, and especially if the fault in an answer is minor, commenting often solves the issue better than a downvote if the answerer is reasonable. But there are answers which are just wrong, not just with some mistakes, and those ought to be downvoted.

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