Effort to get us all on the same page (balloon analogy)

GeorgeDishman

I think it is significant that all the results in Fig. 7 are consistent zero curvature other than those that include the BAO result, and BAO is significant in Figure 8 as well. Given the poor agreement between H0 and BAO, I would prefer to resolve the discrepancy before we claim we have strong evidence either way.

marcus

I don't think I posted anything about the WMAP9 report (Hinshaw et al.) what it said about Ω_k . I'll get a link.
http://arxiv.org/abs/1212.5226
Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
G. Hinshaw, D. Larson, E. Komatsu, D. N. Spergel, C. L. Bennett, J. Dunkley, M. R. Nolta, M. Halpern, R. S. Hill, N. Odegard, L. Page, K. M. Smith, J. L. Weiland, B. Gold, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, G. S. Tucker, E. Wollack, E. L. Wright
(Submitted on 20 Dec 2012 (v1), last revised 30 Jan 2013 (this version, v2))

On page 19 you see:
Ω_k= −0.0027^+0.0039_-0.0038 this is using pretty much all the major data sets: WMAP +eCMB+BAO+H
eCMB or "externalCMB" includes SPT but not the LATEST SPT. But that is details.
When you translate their plus/minus stuff it leads to a confidence interval of
-0.0065 < Ω_k < 0.0012

So that is lopsided on the negative Ω_k side, which means FINITE but it also has some zero and positive territory which means spatial INFINITE. Thats how several recent major reports have been going. You can't exclude spatial infinite, at this point.

On page 20 they also have a figure −0.0065 ± 0.0040 which I don't take as seriously but which ostensibly is based on even more data namely WMAP +eCMB+BAO+H + SNe.
That would correspond to a purely negative interval:
-0.0105 < Ω_k < -0.0025
That would exclude the spatial infinite case, at whatever the confidence level is. But this ball is still up in the air.

Hinshaw et al also had other interesting stuff about other issues, like the number of neutrino species and what Dark Matter clouds might possibly consist of. That tended to get people's attention so what they had to say about curvature was less noticed.

RayYates

I may have been one of those that suggested looking at the inside as the past and the outside as the future. This was in response to someone trying to calculate the center of the balloon (aka the universe). It was a way of getting him to visualize that everything in the universe is on the surface, and there is no center on the surface.

The balloon analogy also assumes the balloon is always expanding, which as you point out may not be the case.

As for Black Holes, since time and space are the same fabric and space seems to have been compressed out of existence, time must also have stopped, (or nearly so). In my mind I see this as a point/line extending out away from the balloon into infinity (the future). So in a way, its not part of the balloon but still attached at a single point.

GeorgeDishman

If "time stops" at the event horizon, the radius would then be fixed, so it's more like a thread attached to the inside of the balloon with the other end fixed at the centre. Once it goes taut, the rest of the balloon expands as usual but that small patch gets left behind.

Like any analogy, you can only take it so far.

RayYates

Good "point". (pun intended). I like visual image created by the thread analogy. The beginning point becomes fixed in space-time and the balloon keeps expanding into the future dragging the event horizon with it. That's a very helpful way to imagine it.

Naty1

Jorrie posts:

s:

Very nice!!. And here I thought we exhausted all the 'analogies' with Phinds BALLOON ANALOGY last year. Phinds...you should Add this and Marcus' prior post to your discussion!!


//////////////////


Georgedishman:
I'm pretty sure there is some misunderstanding here:

The 'singularity', not the horizon, is believed to be a point in time where space has been compressed out of existence.

'time stopping' at the horizon is a local, coordinate effect. Only for an accelerating not an inertial [free falling] observer.

The event horizon is a global construct....

Illustrations :


From Kip Thorne in BLACK HOLES AND TIME WARPS
Finkelstein’s Reference Frame

when the star forms a black hole:
Kruskal–Szekeres coordinates
http://en.wikipedia.org/wiki/Kruskal_coordinates

'well behaved' here means using Kruskal-Szekeres coordinates instead of Schwarszchild time does not 'stop' at the horizon.

for further discussion, a separate thread would be appropriate.

GeorgeDishman

Good points, and that is why I said you could only take it so far. Can you create an exact correspondence between coordinates on the balloon surface any any of those you listed?

Naty1

Good question, but above my paygrade for now...

Oddly that issue did not come up in a very long thread started by phinds "Balloon Analogy'....

But the endpoints [coordinates] of paths seems to not be the only issue:

In another discussion I tried unsuccessfully to sort out the idea that the Einstein Field Equations, used in cosmology, deal with geodesics in 4D spacetime. So what does a geodesic of 4D spacetime look like in 3D space? And what does that look like on a 2D balloon surface??

marcus

Before I lose track of the links, I'll try to get something together about current measurments of the spatial mean curvature.
Page 40 of the relevant Planck report ( http://arxiv.org/abs/1303.5076 )
==quote==
With Planck we detect gravitational lensing at about 26σ through the 4-point function (Sect. 5.1 and PlanckCollaborationXVII 2013). This strong detection of gravitational lensing allows us to constrain the curvature to percent level precision using observations of the CMB alone:

100Ω_K= −4.2^+4.3_-4.8 (95%; Planck+WP+highL);
100Ω_K= −1.0^+1.8 _-1.9 (95%; Planck+lensing + WP+highL)

These constraints are improved substantially by the addition of BAO data. We then find

100Ω_K = −0.05^+0.65_-0.66 (95%; Planck+WP+highL+BAO)
100Ω_K = −0.10^+0.62_-0.65 (95%;Planck+lensing+WP+highL+BAO)
==endquote==
Here's an earlier post on the topic of mean spatial curvature:
==quote==
http://arxiv.org/abs/1212.5226
Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
G. Hinshaw, D. Larson, E. Komatsu, D. N. Spergel, C. L. Bennett, J. Dunkley, M. R. Nolta, M. Halpern, R. S. Hill, N. Odegard, L. Page, K. M. Smith, J. L. Weiland, B. Gold, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, G. S. Tucker, E. Wollack, E. L. Wright
(Submitted on 20 Dec 2012 (v1), last revised 30 Jan 2013 (this version, v2))

On page 19 you see:
Ω_k= −0.0027^+0.0039_-0.0038 * * this is using pretty much all the major data sets: * * * WMAP +eCMB+BAO+H
eCMB or "externalCMB" includes SPT but not the LATEST SPT. But that is details.
When you translate their plus/minus stuff it leads to a confidence interval of
-0.0065 < Ω_k < 0.0012

So that is lopsided on the negative Ω_k side, which means FINITE but it also has some zero and positive territory which means spatial INFINITE. *Thats how several recent major reports have been going. *You can't exclude spatial infinite, at this point.

On page 20 they also have a figure −0.0065 ± 0.0040 which I don't take as seriously but which ostensibly is based on even more data namely *WMAP +eCMB+BAO+H + SNe.
That would correspond to a purely negative interval:
-0.0105 < Ω_k < -0.0025
That would exclude the spatial infinite case, at whatever the confidence level is. But this ball is still up in the air.
==endquote==
And here was an earlier post that mentioned the curvature measurement by the SPT:


http://arxiv.org/pdf/1210.7231v1.pdf
==quote==
Perhaps the most remarkable thing is the tilt towards positive overall curvature, corresponding to a negative value of Ω_k

For that, see equation (21) on page 14
Ω_k =−0.0059±0.0040.
Basically they are saying that with high probability you are looking at a spatial finite slight positive curvature. The flattest it could be IOW is 0.0019, with
Ω_total = 1.0019
And a radius of curvature 14/sqrt(.0019) ≈ 320 billion LY.
Plus they are saying Omega total COULD be as high as 1.0099 which would mean
radius of curvature 14/sqrt(.0099) ≈ 140 billion LY.
==endquote==

marcus

I just saw a really classic handling by Bandersnatch of newcomer questions by TigerDave. It is so clear and concise I want to save it as part of "effort to get us on same page"

Here is TigerDave's original post His paragraphs are interspersed in the following by Bander.
==quote Bandersnatch classic response to newcomer==

Is it assumed that the universe, at the time of creation was finite in size (or at least more finite than it is now) prior to the rapid expansion, or was the protoexistance finite in size in an infinite universe? So, did the universe AND its contents expand, or did a collection of mass within the universe expand, creating the physicality we know today?

The universe was either finite or infinite, and it still is one of those. We cannot say which one it is, but if it's finite, then it has got a very large curvature radius(~88 billion ly was the minimum estimate, iirc).
The key part to understand is that whenever you hear of the universe's expansion, it does mean the entirety of it. It's not about some matter expanding into a preexisting space, but space WITH matter and energy, expanding.

I have seen the expansion explained like a balloon. However, if this were true, would not most mass be on the 'outside' of the balloon? Is there content in the middle of the universe, or is there a hollow center that is getting bigger as we get further from the center? I've read that asking about the center is impossible, and that the universe has infinite shape, but if that's true can we say we're expanding? Would there not be an origin point, or is that one of the problems that a physics-uneducated person like myself would be unable to grasp (re: Plato's allegory of the cave).

The balloon analogy is not perfect, as it creates this erroneous intuition that there is something outside(or inside) the balloon, due to the way we imagine it being a three dimensional object.
The analogy requires you to think of only the surface of the balloon as the universe.
There is no centre to a 2d surface(but there is curvature), and the expansion is still easily observable by comparing the distances between any two points on that surface at two different times.

These two pages go into more detail about the balloon analogy, its aims and limitations, all in layman's terms:
http://www.mso.anu.edu.au/~charley/p...DavisSciAm.pdf (first page is blank)
http://www.phinds.com/balloonanalogy/

Can we not use red shift in order to determine the relative center of this expansion? I understand that we observe red shift based upon where we're standing, but should we not be able to calculate from all that where the overall center is? Where are we in regards to this?

You should see from the above links that it is impossible to define a centre of uniformly expanding space.
You can easily define the centre of the observable universe, which is wherever you are standing.

Was expansion more like bread dough? Did the pre-expansion material tear? Was that tearing uneven, that left behind general emptiness in some spots and densely clumped matter in others that led to our original star nurseries?

You are taking the analogy too far. Of course the universe is not made of dough, so it does not tear like dough does. It is important to limit yourself to only what the analogy is trying to convey(i.e., the expansion of space) and not to go overboard with drawing conclusions from it.

Are galaxies considered expanding or collapsing? I've heard that there's supposed to be black holes in the center, so is this local mass "going down the drain" or is this mass being spun off from the center? Is it both? Do we consider galaxies to be generally "on par" with each other in the creation of more complex atomic structures, or do we expect each birth/nova/collapse/rebirth cycle of stellar material to continually generate more complex material, and that individually from galaxy to galaxy?

Galaxies are stable structures, with no significant amount of mass going down the black hole or escaping.
Sure there might be some rogue star gaining enough speed from random gravitational interactions to fling itself into the intergalactic space, and there tends to be some gas falling down the black hole - mostly because it takes so long to actually get there.
But overall, there is no expansion or collapse. The expansion of space does not affect small scale structures(like galaxies), and the black holes are not the voracious vaccuum cleaners of doom that you might sometimes see in the popular media. Most stars stay in pretty much stable orbits around the galactic centre, and it's not going to change much, barring collisions with other galaxies.
All the galaxies coalesced from the same primordial gas, and the laws of physics governing them are the same, so it stands to reason that they are similar.
The difference is in the time scale. As you look farther away, you see younger galaxies, and the younger the galaxy, the less time its stars have had to go through their life cycles and produce heavier elements.
Generally the longer the universe exists, the more heavy elements it contains(in the early universe there was only hydrogen, helium and some lithium).

Second to last, is it possible, in the same way that we view time against the overall amazingness of deep time, that this initial universal expansion was just one bubble in an even larger sea of expanding pockets that we have yet to get close enough to see the evidence of? Not getting into dimensions, but is our universe just one in an entire "hyper-universe" of immense activity, that we can't directly "observe" in the same way that our tiny blip of existence fits in the concepts of deep time?

It's a kind of a vague and dangerously philosophical-sounding question, but I suppose it asks about the multiverse hypothesis?
As you say, it's not observable, therefore not falsifiable, which makes it an empty question really.
The first half an hour or so of this talk by Lee Smolin:
http://pirsa.org/13020146/
touches on the subject.

Finally and most importantly, where should I be aiming myself educationally in order to learn the answers to these questions, and to ask even more?

I'd recommend starting here:
http://www.astro.ucla.edu/~wright/cosmolog.htm
and going through either/both tutorial or/and FAQ.

Stephen Weinberg's "First three minutes" is a classic book concerning the early expansion of the universe. It's a bit dense at times, and getting somewhat old, but still worth reading.

Alan Guth's "The Inflationary Universe" talks about the birth of the idea of inflation, that is a major(if still somewhat dodgy) part of current cosmology.

Finally, understanding Relativity might be necessary. This popular treatment by Einstein himself is a good start:
http://www.gutenberg.org/files/30155/30155-pdf.pdf

You should be able to understand the ideas without any maths knowledge, but once you dig deeper into cosmology, you'll notice that it's at its heart a mathematical science, requiring you to learn higher mathematics to truly understand what's going on.
Unless you do that, you'll have to do with imperfect analogies, so if you have such an option, take calculus and algebra courses.

Finally, you might find the courses/videos on these sites relevant to your interests:
http://www.perimeterinstitute.ca/video-library (you probably want the "public lectures" section)
http://www.academicearth.org/ (try astronomy section)
https://www.coursera.org/ (actual online courses; physics section covers cosmology as well)
https://www.khanacademy.org/ (not a lot on cosmology, but good for learning maths and basic physics concepts)
==endquote Bandersnatch==