The h Bar

0celo7

4:00 PM

@Slereah maybe

But what he doesn't understand is that "constant in coordinates" is not an invariant notion

the metric of the plane in polar coordinates is variable

Slereah

Scalars are invariant, though

John Rennie

Is it related to the fact that the vacuum SET is diag(0,0,0,0) in all coordinates, while the form of the FLRW SET depends on the coordinates?

Slereah

Well any transformation on the 0 tensor is 0

John Rennie

Yes, so does the occurence of multiple vacuum solutions rely on this fact?

That would be a nice simple explanation ...

Slereah

The multiple vacuum solutions are due to what I said

0celo7

4:03 PM

@JohnRennie the General FLRW metric does not depend on the matter model.

The specific form of a(t) does

Slereah

The Riemann tensor depends on the Ricci tensor and the Weyl tensor

Obliv

@acuriousmind $\mathcal{O}_x$ is the equivalence class under the relation ~ for a group element $x \in G$ ($G$ is being acted upon by $H$) Is what I have said so far correct? If so, my deductive reasoning tells me that $f: H \to \mathcal{O}_x$ means that elements in $H$ get mapped to $f(h)$ which means $h \to$ a corresponding element in $\mathcal{O}_x$ Elements in $\mathcal{O}_x$ look like this $(x,a)$ or $(x,h)$ right? Isn't that what elements of an equivalence class look like? SO,

$(x,h) =$ $x$~$h$? Is this the part where I go wrong

0celo7

@Slereah But the Einstein equations contain enough information to determine the Weyl tensor too

Obliv

and so if all of $H$ gets mapped to $\mathcal{O}_x$ injectively (the left regular action is injective) then it's bijective.

Slereah

@0celo7 No they don't

0celo7

4:06 PM

@Slereah Of course they do

Slereah

It is determined by boundary conditions

0celo7

That's implied

FrancescoS

@DavidZ Do you know how to calculate these integrals of partonic distributions? s32.postimg.org/n3dwm4nfp/… the factor in the denominator outside the integrals is irrelevant, so just see it as a known constant. I need to use the PDF's CTEQ6L1

0celo7

@JohnRennie no

Oh, Hmm, is that what you meant by SET?

@JohnRennie can you please clarify?

What do you mean by "the vaccum is homogeneous"

If we wrote in chat like Definition. Theorem. Proof.

Things would work a lot better :P

John Rennie

@0celo7 The stress-energy tensor is isotropic and homogeneous in a vacuum (because it's zero everywhere). The stress-energy tensor is also isotropic and homogeneous in an FLRW spacetime. The vacuum SET produces many solutions, Minkowski, Schwarzschild, etc, while an isotropic and homogeneous SET that is non-zero produces only one solution, FLRW. Why?

Slereah

4:12 PM

It doesn't

0celo7

What does that mean???

Slereah

For a start

You can add a black hole to a FRLW spacetime

0celo7

Isotropy and homogeneity are not properties of the energy momentum tensor

@Slereah link?

John Rennie

@Slereah but then the stress-energy tensor is not (spatially) isotropic and homogeneous.

Obliv

@acuriousmind no the part that is flawed is $h \to (x,h)$. It simply means it gets mapped to $(x,a)$ for some $a \in G$ where $x$~$a$ iff $x = ha$ so that's where $h$ goes.

Slereah

4:14 PM

Why not

0celo7

@JohnRennie you're acting like Duffield.

Slereah

Oh also

One important thing

Flat space IS a type of FRLW spacetime

In the case $a(t) = 1$

John Rennie

@0celo7 no I'm not, because I'm not claiming I'm right. There is obviously something I don't understand and I'm trying to find out what that is.

0celo7

You're not defining stuff

John Rennie

Ok let me try and be clearer.

Slereah

4:15 PM

arxiv.org/pdf/gr-qc/0411033.pdf

^FRW with a different metric

ACuriousMind

@Obliv $\mathcal{O}_x = \{ g\in G\mid \exists h\in H : x = hg\}$. It's just a subset of $G$, its elements don't look special.

John Rennie

Start a stress-energy tensor that is zero. If we feed this into the Einstein equation then there are many different Riemann tensors that satisy the equation.
Does this make sense so far?

Slereah

Yes

0celo7

Perhaps.

Slereah

It's also true if it's not zero

You can add arbitrary gravitational waves, for one thing

0celo7

4:19 PM

Is there a book on gravitational waves

Slereah

Sure

There's a book on generic PP-wave spacetimes, even

Obliv

@acuriousmind that was my fundamental misunderstanding. Now it makes sense why it's a bijection. If a subgroup sharing the same operations and elements of a group is acting on the group, it's intuitive to see that there will be 2 elements in $G$ where one divides the other by $h$

Slereah

(heheheh peepee)

John Rennie

Now take a stress-energy tensor that is diag(\rho(t), 0, 0, 0) - presumably this is only true in comoving coordinates.
Am I still making sense?

0celo7

But once you fix boundary conditions I think you get a unique metric

Brb

Slereah

4:20 PM

No, because

I told you several time

That's not true

Plenty of counter examples

Obliv

@acuriousmind so a group can be represented by the union of the partition of the orbits of the group under the action of a subgroup?

John Rennie

I've lost track of who is talking to whom. @Slereah was your last comment aimed at me?

Obliv

this works for any subgroup no matter the size

Slereah

All of them

ACuriousMind

@Obliv It's a general fact that under an equivalence relation, every set is the disjoint union of equivalence classes.

Obliv

4:22 PM

kk

Slereah

If the stress energy tensor is isotropic and homogeneous, in 4D, there is more than one possible metric

John Rennie

@Slereah as in the paper you linked?

Slereah

yes

John Rennie

@Slereah OK, it was painful, but I think I have my answer. Thanks :-)

Loffen

what is the ligo announcement about

GPhys

4:31 PM

I can tell you what it's probably not about

John Rennie

@Loffen that hasn't been revealed, but obviously it's going to be the detection of more mergers.

Increasing the number of detections is really important, because we need to know if the 30 solar mass black holes in the first detected merger were typical.

If it turns out most mergers are of black holes around this mass there will be some major head scratching amongst cosmologists.

We expect most black hole masses will be either a few solar masses or supermassive.

If it turns out there are lots of black holes with intermediate masses that will take some explaining.

Obliv

@johnR what do you mean by blackhole masses? Don't they have infinite mass at a singularity?

John Rennie

density not mass

Obliv

ah ok. I see many sites/articles confuse mass with density then.

John Rennie

And anyway the singularity is not part of the black hole spacetime

A black hole doesn't have any matter anywhere. It's a vacuum solution.

@Obliv we should try to do better than that :-)

Slereah

4:47 PM

Not if you use distribution valued metrics :p

David Z

5:02 PM

@FrancescoS I assume you mean numerically? In that case it depends on what language and libraries you're using.

If you're on the market for one, I'd suggest LHAPDF which aims to be a common interface to all the PDF sets

John Rennie

The stream is now up!

iframe.dacast.com/b/59062/c/268750

user54412

@JohnRennie do you get anything other than "Sorry, the live stream is offline now."?

FrodCube

refresh the page, it's online now

John Rennie

@ChrisWhite Yes, the stream is up and running fine for me. Maybe it's oversubscribed.

And the sound has just come on.

David Z

I'm getting nothing, just the offline message

You may have to relay the information for the rest of us

ACuriousMind

5:13 PM

I can see it

GPhys

it's online for me and there's audio

John Rennie

What browser - I'm using Chrome

2 minutes!

GPhys

wfm in Safari and Chrome

David Z

Firefox here

FrodCube

Chrome

David Z

5:16 PM

Second confirmation of gravitational waves caused by colliding black holes announced http://bit.ly/23a9cBi #LIGO https://t.co/MGoH8ecHT7

Tweeted by sciam on June 15, 2016 at 5:15 PM

4

0celo7

@JohnRennie Your notion of homogeneity and isotropy is nonstandard so you got a nonstandard answer.

David Z

hm

It's funny watching about a dozen subtly-different tweets about the same thing all flood my Twitter timeline

0celo7

@JohnRennie Given true homogeneity and isotropy FLRW is the only possibility.

I've written two answers on this.

ACuriousMind

Sigh...this is going to be another of those press conferences where we don't get any details, right?

0celo7

(Using some very advanced techniques one can prove isotropy at every point implies homogeneity or something like that.)

Secret

5:20 PM

I wonder if this press conference will trigger another wave of GW questions on PSE?

0celo7

@ACuriousMind Hmm? What's happening

John Rennie

14 and 8 solar masses

user54412

Hmm, 14+8 solar masses

John Rennie

Still on the big side

FrodCube

eww... ugly plots this time

Secret

5:22 PM

no ringdown

0celo7

What are you talking about

GPhys

@0celo7 iframe.dacast.com/b/59062/c/268750

ACuriousMind

@0celo7 How do you manage to talk the entire day in this chat room and not notice the LIGO announcement session?

John Rennie

5-sigma detection

David Z

@JohnRennie I figure they wouldn't announce it otherwise

Nick

5:25 PM

@ACuriousMind I wasn't even in the room. I got a mail :) Thankful for that. But my connection sucks. It's all broken buffering.

John Rennie

Hmm, it's pretty near the detection limit - unlike the first detection ...

Slereah

Hey science dudes, we don't care if you detect the SECOND TIME

There's no medal for second place

David Z

For anyone (else) with bad connections, Twitter is a good secondary source

John Rennie

Further detections are very important - see my ramblings about the black hole masses above

0celo7

@ACuriousMind Oh, that

I'm completely disinterested in physics

(this physics, anyway)

David Z

5:27 PM

Hashtags to follow the #gravitationalwaves news announcement going on right now include: #LIGO #AAS228 #virgo #gravitationalwave

Tweeted by rerutled on June 15, 2016 at 5:23 PM

Nick

@Slereah ... physics much?

GPhys

Christmas detection

ACuriousMind

@GPhys It probably wasn't a black hole, it was Santa's sled passing by ;P

GPhys

probably

0celo7

@Slereah Is that black hole paper you posted just a black hole that is asymptotically FLRW

user2540549

5:31 PM

It seems the web only works with Flash

GPhys

journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.241103

user2540549

Otherwise shows the offline message

GPhys

paper ^

DOI:10.1103/PhysRevLett.116.241103

0celo7

@MAFIA36790 oh I watched an episode of the Flash the other day

David Z

@GPhys better to link to the lead page rather than the PDF file

GPhys

5:32 PM

@DavidZ journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.241103

2

approved in 2 weeks?

that's better :-P

Is that normal

are there any astronomical sources capable to produce gravitational waves shorter than ms scale? (I was curious why the spectrum of gravitational waves shown in wikipedia cuts off at ms)

John Rennie

The third (not quite 5 sigma) detection is also heavy - total mass is 35 solar masses

ACuriousMind

5:35 PM

@JohnRennie Well, if they say the second was close to the detection threshhold, is that really a surprise?

I.e. isn't the point just that we need more sensitive instruments to decide what the "typical" black hole merger looks like?

John Rennie

I guess at the current state of play we simply wouldn't see light mergers unless they were very close

GPhys

LIGO page: ligo.caltech.edu/news/ligo20160615

(links to paper, audio files, data)

0celo7

@ACuriousMind How come you seem so interested?

Slereah

@0celo7 it is also isotropic and homogeneous

0celo7

It's like the first one again, I'm the only indifferent one

@Slereah Not possible because it's not FLRW

Slereah

5:38 PM

Hush you

It totally is

I have decided

Not read it but I have a good feeling

Secret

I know the really long period GW are more important because they will give more info about the early universe, but what about GW shorter than ms?

FrancescoS

@DavidZ thanks. And do you know MadGraph?

John Rennie

0.2 of the extremal spin!

user54412

5:55 PM

@Secret The maximum frequency is, heuristically, the orbital frequency you get by moving at the speed of light around the Schwarzschild radius. For high frequencies you need smaller objects, but since you can't get more dense than a black hole this also means less massive objects and therefore the signal will have a lower amplitude.

Secret

make sense, thanks!

John Rennie

Stupid question!

Still, it gave everyone a laugh

user116211

@0celo7 asked the same question during the 1st LIGO announcement

John Rennie

Incidentally, the LISA Pathfinder mission was a spectacular success.

The sensitivity proved to be even greater than anticipated

user116211

@0celo7 which season?

user54412

6:07 PM

125 W "turns out to be a lot of laser power"... yes, yes it is

0celo7

@Slereah I will read it

And report back

But it's a theorem in like 5 books that FLRW is the unique family of homogeneous isotropic spacetimes

Slereah

I'm pretty sure you can have a homogeneous SET that isn't FRW tho

0celo7

and I've proved it on PSE

I'm done

Slereah

Yes, but that refers to the metric

Not the SET

0celo7

homogeneous has NOTHING to do with the SET

Slereah

6:14 PM

I know

But that's what @JohnRennie talked about

That jerk

Not using proper words

John Rennie

@Slereah :: John reaches for kickmute button ::

0celo7

@JohnRennie is this true

are you using wrong words

John Rennie

0

Q: Why does Ligo's second detection of gravitational waves and a black hole merger look absolutely nothing like the first?

Why does Ligo's reported second detection of gravitational waves and a black hole merger look absolutely nothing like the first detection announced in Februaray? Here is the data from the first LIGO detection of a black hole merger: And here is the data from the second LIGO black hole merger a...

0celo7

3

Q: Proving constant curvature

I'm currently on section 5.1 in Wald's book. He is trying to prove that the cosmological principle implies that space has constant curvature. Given a spacelike hypersurface $\Sigma_t$ for some fixed time $t$, we say that it is homogeneous if given $p,q \in \Sigma_t$, there is an isometry, $\phi$...

general-relativity differential-geometry curvature

John Rennie

Up to his usual tricks I see

0celo7

6:16 PM

wow 81 views and one vote on my answer

Too technical?

> The Postal Service could not locate the tracking information for your request. Please verify your tracking number and try again later.

Crap.

vzn

@MAFIA36790 strange, missed your ping in my inbox. @DavidZ hasnt said when hes ready for next mtg yet, would like to schedule it ~4wks with yuggib jul12

does anyone know roughly how the solar masses are calculated for the collision? is it roughly the amplitude difference between the two measurements at the different observatories (and the quadratic dropoff in intensity)? does that mean mass cant be measured at a single location? wondering

user116211

@vzn I would like to see it in 2nd week of July as was talked earlier.

user54412

@JohnRennie I just tried unpinning my own message, and I think all I ended up doing was adding a star to it. Feel free to try to remove it.

John Rennie

Zappppppp!

user54412

@vzn No, the observatory separation is less than $10^{-18}$ times the distance to the source, and the amplitude precision is ~10%.

ACuriousMind

6:29 PM

3

Q: How were the solar masses and distance of the GW150914 merger event calculated from the signal?

The GW150914 signal was observed, giving us the frequency and amplitude of the event. Because LIGO has two detectors a rough source location could be derived. But how do these three factors allow for the mass of the black holes and their distance to be calculcated? If the wave strengths are in a...

general-relativity black-holes mass gravitational-waves ligo

user54412

(btw the strain drops off linearly, which is a nice feature of using an interferometer rather than an energy detector)

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Did I miss the press announcement?

:(

ACuriousMind

yes

user54412

In addition it is like asking "why does a violin show different waveforms than a Tuba" — anna v 11 mins ago

user54412

<3

user116211

6:33 PM

oldest but wittiest

vzn

@ACuriousMind thx, finding it hard to follow the answers, get the general idea but not specifics, & some of the terms are not defined carefully :(

ACuriousMind

@vzn The "specifics" should be in some of the LIGO papers, a phys.SE answer is not the place to lay out the entire methodology in detail.

user54412

@vzn Here's my off-the-cuff summary: We measure 3 quantities well (amplitude at detector, primary frequency, time-derivative of frequency). We have 3 unknowns (distance, two initial masses). Thus we can solve.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

In theory :P

vzn

@ChrisWhite ok thx. in theory can both masses be measured with a single detector? seems the 2 detectors may be crucial...? or the same calculations can be done at the two different detectors & compared?

user54412

6:45 PM

that answer points out how $A$ is a function of $r$, $m_1$, and $m_2$; you can also use the fact that a different combination of $m_1$ and $m_2$ (the chirp mass) is a function of $f$ and $\dot{f}$; and I think the other ingredient is a maximum frequency being related to a total mass of some sort

vzn

A as amplitude, is(nt) it a function of time?

user54412

@vzn In theory except for two issues: (1) only by cross-correlating signals do they have much confidence that they are not picking up noise, and (2) the detector is a quadrupole antenna, and so its sensitivity is not the same in all directions. That is, direction is perfectly degenerate with amplitude, so you need directional information from a second detector.

user54412

@vzn yeah, but you could pick a single A to characterize the envelope, since the functional form is known

vzn

@ChrisWhite since youre around at moment, any interest as guest speaker? :)

btw does any of your work touch on fluid dynamics in relativistic situations?

user54412

@vzn I think I'll hold off, but thanks :)

user54412

6:52 PM

@vzn all of my work is relativistic fluid dynamics, actually

vzn

@ChrisWhite ok was thinking that from prior conversations, but they were awhile back

have you heard of any analogies of GR to fluid mechanics eg modelling space "density"...?

user54412

mostly only through a few questions on this site

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Is there going to be a meta post evaluating the first AMA?

vzn

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ not bad idea, note we had some immed discussion after the mtg

user54412

at some level GR and fluids are the same -- second-order quasi-linear PDEs describing the evolution of scalars, vectors, and/or rank-2 symmetric or antisymmetric tensors

user54412

6:56 PM

but the communities are somewhat disjoint

vzn

@ChrisWhite yeah exactly there seems to be a strong mathematical correspondence but different vocabularies/ thinking etc & not much cross...

0celo7

7:16 PM

@ChrisWhite so why are the NS equations so much harder to solve than the Einstein ones

user54412

are they?

user54412

The first fluid simulations were done in... the 60s? The first dynamical spacetime simulations were done in 2005.

0celo7

@ChrisWhite We know that we can solve the EFEs

2005???

Whaaaaaaat

How can it be that hard

>:( books that don't have named theorems in the index

Physics Meta

0

Q: Engineering questions and answers that are closely related to Physics

I found an old question asked 5 years ago. How much power to keep surface of aluminum plate at given temperature?. How do I answer this in a physics kind of way? This is my original answer: By running a current through one kilogram of metal using a adjustable D/C power supply 1 volt to 12v and sl...

discussion support scope questions answers

user54412

So I thought I'd be ahead of the curve trying to embed videos in my thesis. Turns out the journal I use started supporting embedded video last month.

0celo7

7:29 PM

Your thesis is not done yet?

Ahhhhh, the Schur lemma is equivalent to the Bianchi identity

Secret

@ChrisWhite Recalling a discussion on the GR vs fluids a year, Slereah and acuriousmind mentioned that they are mathematically similar because they are both nonlinear phenomenon and suggest it is not a fruitful path to consider as the curvature tensor can have mroe complex dynamics than fluids do (4th order vs 2nd order tensors)

0celo7

@JohnRennie I thought I had obtained another proof of the FLRW thingie

But the second one in Wald is equivalent

(and mine was stolen from an obscure '70s paper anyway)

Secret

but IMO, I think we might get something once we mix the two fields together and investigate the relevant GR as fluid literatures more thoroughly

especially in light of the recent discussion of stagnation points in CTCs

One thing that might be interesting is the dynamics of a particle passing through the centre of a CTC, where the stagnation point is located

would such a worldline be spacelike, since at a stagnation point the tangent vector should be not pointing along the time direction...?
there are other also other questions that we can ponder

David Z

7:48 PM

@FrancescoS not really. I tinkered with it a bit many years ago, but I don't remember much of anything.

0celo7

7:58 PM

I wonder what the "compact open" topology is...

How many topologies do we need

David Z

@vzn I think July 12 should be fine.

0celo7

@Obliv Does Prop. 6.1.2 in Kobayashi-Nomizu Vol. 1 imply the conclusion of exercise 7.2 in Lee Riem. Man.?

Obliv

@0celo7 let me check with my crystal ball

it said ask again later :(

0celo7

when

can I get a year on that

Obliv

yeah

now < when < infinity

somewhere in that bound

vzn

8:13 PM

@DavidZ awesome! @yuggib you are clear for takeoff on july 12th. it would be great if you could cook up a meta post similar to slereahs. thx

Obliv

@0celo7 do u know where I can find the original papers by Einstein on SR & GR?

0celo7

@Obliv don't read them

Obliv

why not? i heard they're explained really well and simply

well SR anyway. idk about GR

ACuriousMind

@Obliv From whom?

0celo7

@Obliv they're very confused and out of date

If you want to seriously learn GR, read Zee or Carroll

Obliv

8:15 PM

I think I started reading the SR paper and it defined time or something. Then I couldn't find the paper again when I looked

vzn

@Secret think that this is a very worthwhile prj and a vocabulary/ table/ map of similar/ corresponding terms for both could be built as an early guide. eg CTCs = ? ...

Obliv

@acuriousmind I don't remember. Also nevermind I meant this paper fourmilab.ch/etexts/einstein/specrel/www . I think searching on my phone browser yields unwanted results for whatever reason

vzn

@Secret does the curvature tensor include time dimension? the concept of how time is handled seems a key difference in the two fields. (but possibly "only" a conceptual difference and not a big mathematical difference as far as equivalence...?)

0celo7

@vzn Yes.

dmckee

8:45 PM

@vzn The two detectors give several things: robustness against local noise, time-of-flight input to the direction determination, Slightly different orientation to disambiguate the direction determination. I don't believe you need more than one to 'just' solve the in-spiral parameters problem.

Obliv

8:57 PM

@johnR Can I ask what program/software you use to produce images like the one in this answer?

0celo7

9:17 PM

@Obliv what are the one-dimensional manifolds

how many are there

Obliv

@0celo7 let me get back to you I'm currently busy

@acuriousmind hey just wondering, what are the one-dimensional manifolds and how many are there?

0celo7

>:(

He doesn't know

He doesn't know any manifold theory

He's an algebraist

I'm currently doing a combinatorics proof. I hate my life.

Obliv

I haven't found combinatorics interesting until like yesterday.

0celo7

I'm trying to prove this lemma:

Obliv

Also, I have 0 knowledge of geometry and like 1/1000th of ACM's knowledge in algebra

0celo7

9:20 PM

I have to find all framed cobordism classes and compute that number

Obliv

see you're just talking nonsense. Cobordism sounds like a disease

0celo7

And any cobordism between such 0-manifolds is 1-dimensional

So I have to find all the 1-manifolds

Thankfully there's only a single 1-manifold that works here

good lord this theorem is terrible

It's obvious if you draw a picture lol

Obliv

@0celo7 how many GR books did you read btw?

0celo7

More than you

Obliv

I'm only like 45 pages into this algebra book having done 2 chapters (chapter 1 and the introduction) and have done ~170 exercises

dude this is taking so fucking long. It's a shame because nearly every exercise has taught me something new

0celo7

9:26 PM

Obviously don't do every exercise

Algebra is for chumps

Obliv

but i'm learning!

how many exercises did you do in your GR & geometry books?

0celo7

I told my prof I would write the formal proof of this, I'm regretting that now.

@Obliv The ones that were interesting

Obliv

would it ever assume knowledge from previous exercises, or no?

0celo7

Good books will tell you

And some books like Hawking-Ellis don't have exercises

(thank god)

0celo7

9:41 PM

AHA

$1-1=0$!!!!

Obliv

@0celo7 that's very impressive. Cool to see what 2 years of advanced geometry will let me prove

Danu

9:59 PM

@Obliv that @0celo7 is talking nonsense, of course ;)

0celo7

@Danu Not really, that fact is crucial to my proof

Danu

Proof by nonsense?

0celo7

@Danu No, I need a point with orientation number $-1$ to cancel one with $+1$ :)

So stop being an ass

0celo7

10:26 PM

@Danu My prof's proof sketch was wrong :(

I was right :)

0celo7

11:24 PM

@Slereah There's a mathematician named CTC Wall

0celo7

11:35 PM

I HATE ANALYSIS

@ACuriousMind My definition of "set of measure zero" is one for which, given $\epsilon >0$ there exist a collection of open rectangles $R_i$ such that $\sum V(R_i)<\epsilon$, where $V(R_i)$ is the product of side lengths (volume)

I'm trying to prove that one can substitute rectangles with cubes as follows:

(crap I did it wrong)

good lord my proof was wrong!

Transcript for