
#451
Dec712, 07:03 PM

P: 1

This comic does a good job visualising it in an entertaining way: 'The Adventures of Archibald Higgins: Here's Looking at Euclid' 



#452
Dec1812, 11:45 AM

Astronomy
Sci Advisor
PF Gold
P: 22,809

I hope you keep us informed about more clever cosmology stuff from Petit and his "learning without boundaries" project. Today in the "How to prove the stretching of space" thread, I noticed a neat explanation by Brian Powell of how the wavelengths of light get stretched out as distances expand. "...your explanation why λ goes with a(t) is very convincing and new to me, thanks." I think this is an especially nice way to look at it, which doesn't exclude others as well. 



#453
Dec2012, 04:14 PM

Astronomy
Sci Advisor
PF Gold
P: 22,809

The South Pole Telescope (SPT) has given us new narroweddown ranges for the cosmological parameters.
At the highest confidence level these correspond to a cosmos which is NOT "Euclidean flat" and NOT spatially infinite but is the 3D hypersphere analog of the 2D spherical balloon surface model. The SPT curvature estimates translate into an estimated range of the "radius of curvature" namely from 140 to 320 billion light years. This may not be right, the U may not be spatially finite, or it might be finite and these numbers might subsequently be revised. But let's take them at face value and see. After all it is a fine instrument, a respected team, and these are the most recent published estimates. Here's what I posted earlier about it: ==quote post #448== http://arxiv.org/pdf/1210.7231v1.pdf Scroll to Table 3 on page 12 and look at the rightmost column which combines the most data:
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. For Jorrie's A27 calculator the important parameters as estimated by the SPT report are current Hubble time = 14.0 billion years future Hubble time = 16.6 billion years matter radiation balance S_{eq} = 3300 ==endquote== Since I posted that, Jorrie upgraded calculator from A25 to A27, so I made that change in the quote. 2 pi ≈ 6 so you can, if you wish, estimate the CIRCUMFERENCE of the universe simply by multiplying the "radius of curvature" figures by 6. The smallest it could be is 140 x 6 billion lightyears and the largest it could be is 320 x 6 billion lightyears. So if you could stop the expansion process, to make circumnavigation possible, you would have to travel in a straight line for six times 140320 Gly before you'd be back at starting point. If you sent a laser flash off in some direction it would be six times 140320 billion years before it came back at you from the opposite direction. This is just a way of understanding equation (21) on page 14 of the SPT report. Ω_{k} =−0.0059±0.0040. It's a way to get an intuitive feel in your imagination for what it means. Here, again, is the link to the technical paper itself: http://arxiv.org/abs/1210.7231 



#454
Dec2012, 05:48 PM

P: 47

In non technical language.. OMG the scale is mindblowing!




#455
Jan1113, 09:36 PM

P: 177

That's a very disappointing development. Infinite would have been much more aesthetically pleasing to me. Oh well.




#456
Jan1113, 10:07 PM

Astronomy
Sci Advisor
PF Gold
P: 22,809

I love the hypersphere S^{3} the threedimensional analog of the surface of a balloon, so I'm certainly pleased by the South Pole Telescope report, but I have no sense that the thing is finally decided. But for the sake of an example, if we take the SPT findings at face value then (with 95% confidence) the SMALLEST the circumference could be is 6 times 140 billion LY. In other words 840 billion light years. quite a big balloon, so to speak. Would take an awfully long time to circumnavigate, if you could stop it from expanding so that circumnavigation would be possible. 



#457
Jan1313, 02:18 PM

P: 177

So it's not carved in stone yet? There is still hope for infinity? :D YAY




#458
Jan1413, 12:34 AM

PF Gold
P: 1,570

I have a lot of catching up to do on this thread. Thus far the info contained in it has been insightful. Creedos to Marcus on it. I look forward to the finalized draft.
That being said I found the suggestion of thinking that inside the balloon being the past and outside the future useful. The one concern I have with it is in the case of Black holes. The analogy may lead to misconception that due to its infinite density the singularity may reside in the past at the big bang. I know thats not likely lol but its often the way laymen like myself tend to misconstrue analogies. 



#459
Jan1413, 01:04 AM

PF Gold
P: 717

In any case, if the cosmos happens to be spatially flat or slightly hyperbolic, there can't be a notion of 'inside' or 'outside''. However, the balloon analogy would still yield all the correct answers by just considering the observable universe as the surface patch 'visible' to us. The motto seems to be: use the analogy to get our brains around the expansion/contraction issue of the surface; then ignore it and rather use the simple mathematics of the LCDM cosmic model (or use one of the many available calculators to play around).  Regards Jorrie 



#460
Jan1713, 06:15 PM

P: 255





#461
Feb2013, 10:40 PM

Astronomy
Sci Advisor
PF Gold
P: 22,809

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 NineYear 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. 



#462
Feb2113, 10:33 AM

P: 47

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. 



#463
Mar2413, 04:46 AM

P: 255

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



#464
Mar2513, 08:52 AM

P: 47





#465
Apr2313, 02:37 PM

P: 5,634

Jorrie posts:
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!! ////////////////// 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: http://en.wikipedia.org/wiki/Kruskal_coordinates for further discussion, a separate thread would be appropriate. 



#466
Apr2313, 04:11 PM

P: 255

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?




#467
Apr2313, 04:50 PM

P: 5,634

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?? 



#468
May1613, 11:15 PM

Astronomy
Sci Advisor
PF Gold
P: 22,809

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 4point 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: http://arxiv.org/abs/1212.5226 NineYear 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: ==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== 


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