Cosmo-torun February 2006

cosmo-torun@cosmo.torun.pl

4 participants
4 discussions

money (FNP)
by Boud Roukema 23 Feb '06

23 Feb '06

hi cosmo-torun, Ajk recommends that we consider looking at the many different sorts of funding possible from the FNP: http://www.fnp.org.pl/ Two applications made to FNP last year for Eastern European cosmology visitors to spend some time here were rejected. pozdr boud

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the shape of the universe (fwd)
by Boud Roukema 20 Feb '06

20 Feb '06

hi everyone, We have a media question :). i don't want to spam people, so anyone interested, please respond on cosmo-media@ ... rather than cosmo-torun. Below are my proposed "compact" answers. Any corrections before i respond "officially"? Remember the number one rule of the dependent media: "anything you say may and will be misquoted against you". Which is why having this on the cosmo-media archive will at least, in principle, provide some defence... i don't know what time frame the journalist has in mind - but presumably the sooner the better for any answers. IMHO probably a day or two should be OK. pozdr boud > ---------- Forwarded message ---------- > Date: Wed, 15 Feb 2006 23:38:49 +0100 > From: t.rozek at fz-juelich.de > To: boud at astro.uni.torun.pl > Subject: the shape of the universe > > Dear Sir, > > I'm a physicist and scientific writer. Within the new project of Axel Springer publishing house (editor of Newsweek in Poland and Die Welt in Germany) in Poland I would like to invite you to the discussion about the shape of the universe. > > As I know scientific group you are the leader, in 2004 went public with the information that in the microwave background radiation picture there are some indications, that our universe has a shape of dodecahedron. > > Questions I'm asking you are the same like these I have sent to other expert in this field. I will not hide, that his opinion about the shape of the universe is different than your. > > I will be pleased to get from you compact answers to questions which are listed below. Please keep in mind that new Axel Springer daily will be addressed to nonspecialists in physics or astronomy. > > Let me thank you in advance for time you will spend to answer my questions. I'm looking forward to your respond. > > With the best regards > Tomasz Rozek ---------------------------------------------------------------------- > Questions: > 1. Analysis of the microwave background radiation are the only way > - I guess - to collect information about the shape of the > universe. Isn't it risky to draw conclusions resulting from only one > experiment ? Yes, it is risky to draw conclusions from only one experiment. We expect other scientists to read our paper carefully and make their own analyses of microwave background and other data. The most independent test of our work will be testing the prediction that the average, total density parameter of the Universe, including ordinary matter, dark matter and dark energy together, should be about 0.9% to 1.1% higher than the density which would make the Universe perfectly flat ("flat" means that Pythagoras' Theorem is true). This type of test is highly independent of our analysis method. > 2. Why this is commonly believed, that data from WMAP probe, brought > down the concept of flat and infinite universe ? The flat and infinite universe model is still consistent with the WMAP data. It is not the best model, but it is still consistent with the data and most observational cosmologists still take it as the best approximation we have. Please remember, however, that no theoretical cosmologists take the flat and infinite model as a serious model of the entire Universe - it is only treated as a limiting case inside the observable sphere. > 3. There are many ideas concerning the shape of the universe. Maybe > it is like a sphere, cylinder, funnel, but it can also be like bell, > horn or dodecahedron. Why do you claim that space is > dodecahedron-like ? We don't. The first misunderstanding is that "shape" means the shape of *space itself*, not the shape of *space inside of space*. Our intuition is developed to think of objects inside of three-dimensional, Euclidean, infinite space. In order to understand what is meant by the shape of the Universe, you first need to develop a method of thinking about the shape of space itself. A good place to start would be http://pl.wikipedia.org/wiki/Ksztalt_Wszechswiata . One example of a shape of space itself is a space with the name "Poincare dodecahedral space" (PDS). One "ordinary" shape, inside of space, which helps to think about the PDS, is the dodecahedron. The second misunderstanding is that so far our group only claims to have a "hint" of that the shape of space is the PDS. Our analysis follows that by Jean-Pierre Luminet's group. Ralf Aurich's group and Jesper Gundermann have also found similar (though not exactly identical) results. > 4. What are the errors or defects of the idea of horn-like space ? None as far as I am aware of. > 5. Could you in the very easy way explain the expression, that space > has a shape ? Imagine that space only has two dimensions, instead of three. Now we can use our existing intuition about three-dimensional space to imagine many different possible two-dimensional spaces inside of three-dimensional space. In this way, we use one dimension as a purely psychological dimension. It's used by our brain, but has no physical meaning for the two-dimensional space we're thinking about. Of course, real space has three dimensions (we can ignore the time dimension for discussion of "the shape of space"), so if you can now start thinking in four dimensions, then you can use the fourth dimension as a psychological dimension and think of differently shaped spaces, each having three dimensions. > 6. Do efforts to establish a shape of the universe have any > practical meaning or you are doing that just to know ? Both. It is practical to know the shape of a footpath or a tree or a mountain or an atom or a molecule, so it is practical to know the shape of the Universe. But it is also good to knowing the shape of a work of Picasso or a beautiful woman or man, even if this has no practical use. > 7. Did universe have a beginning, and ones will have the end ? The standard hot big bang model is very well established, and this model has a limiting time we can call "time equals zero". If we start today and think backwards towards "time equals zero", then our model of the Universe becomes more and more speculative as we get towards "time equals zero". So it is more realistic to say that we have a standard model which goes *towards* having a beginning rather than saying the Universe actually "had" a beginning. However, theoretical cosmologists have some ideas of universe models extending earlier than "time equals zero". ----------------------------------------------------------------------

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120 cell
by Jeff Weeks 06 Feb '06

06 Feb '06

Dear Boud et al., You intuition is correct -- there are some additional in-between layers. The attached images show layers 1 through 5. Layers 6 through 9 are of course symmetrical as you work your way towards the south pole. Note that the cells in layer 5 sit "vertically" with respect to the equatorial hyperplane (i.e. they're orthogonal to the equatorial hyperplane) which is why they appear flat in the attached image (each dark blue hexagon is the 2D shadow of a 3D cell when you project from 4D space to 3D space). Anyhow, here's the accounting: layer 1 1 layer 2 12 layer 3 20 layer 4 12 layer 5 30 layer 6 12 layer 7 20 layer 8 12 layer 9 1 ----------- total 120 Note that all numbers are "dodecahedal numbers", respecting the dodecahedral symmetry of the whole construction. The 120-cell is quite beautiful, isn't it? Best wishes to all of you, Jeff

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MG11 - Topology of the Universe (fwd) (and PDS - how many tiles?)
by Boud Roukema 06 Feb '06

06 Feb '06

hi everyone, The following is self-explanatory - you can reply to Marek directly - here is his email in antispam format (this list is publicly archived so better not write people's email addresses in ways that robots can read them): Marek.Demianski at fuw edu pl > ---------- Forwarded message ---------- > Date: Mon, 6 Feb 2006 15:02:38 +0100 (CET) > From: Marek Demianski > Subject: MG11 - Topology of the Universe > > > Dear Colleague, > > I have been asked to organize a parallel session on "Topology of the > Universe" at the XI Marcel Grossmann Meeting in Berlin, July 23 > - 29, 2006. If you are planing to attend the meeting and would like to > present a contribution at this session please let me know. Please spread this > information among your friends and collaborators. > > More information about the Meeting (and on line registration) you can > find at www.icra.it/MG/mg11. Please register by May 31 > to save 50EURO on the conference fee. > > Sincerely yours, > Marek Demianski BTW: i have a question on PDS (Poincare Dodecahedral Space) intuition which someone might be able to answer. A tiling of S^3 by the PDS has 120 copies of the PDS. If we think of this tiling starting from "here" at the "North Pole" (sorry Marcelo, this is North bias ;) (image 1) and we "stick" a copy (image 2) of the PDS next to itself along a North-Pole-South-Pole axis (e.g. X), and then moving along the X axis, we stick another copy (image 3) next to image 2, and then another and so on, then it seems to me that image 6 covers the "South Pole" and is the "antipode" copy of image 1. In other words, the "distance" between the poles is 5 copies of the FD. This allows an easy order of magnitude check on the total number of copies, since the "radius" of one hemi-hypersphere is 2.5 "copies", so that the total volume is roughly (using flat space arithmetic): 2* (4\pi/3) (2.5)^3 \sim 2* 2^2 * (5/2)^3 = 5^3 = 125 which is a good approximation to 120. (AFAIR, Jeff Weeks showed me how to do this - this is not original.) Now for my question: We have 6 "layers": North pole - 1 FD layer 2 - 12 FD's layer 3 - n FD's layer 4 - n FD's layer 5 - 12 FD's South pole - 1 Clearly layer 3 or 4 has more than 12 copies, there are some spaces that need to be filled. But the value required for the total to be 120, i.e. n= 47, is an odd number. Intuition says that everything should be even and symmetric. Can someone give a nice intuitive explanation for why n is odd and why this 12-symmetry is broken? Maybe a nice diagram? In fact, i have a partial answer: it seems to me there are some in-between layers, which we might call 2.5 and 4.5 and i guess also 3.5. But it's difficult for me to imagine them, and it's still difficult for me to imagine how the 12-symmetry is broken. It would be nice if someone had a nice diagram or intuitive explanation of how the 12-symmetry is broken. Going to a 122 tiling would save the tiling symmetry, but intuition says that 120 is better than 122. On the other hand, 2 * (1 + 12 + 48) = 122 seems simpler in terms of tiling symmetry. In the Nature paper, 120 is quoted: http://arxiv.org/abs/astro-ph/0310253 (After all, we *have* made a few minor mistakes in the past in our subject - e.g. when we said that there were uncountably many negatively curved 3-manifolds, and eventually, at MG IX (?), Jeff explained and showed us that the number was countably infinite - the classification is complicated and unfinished, but the number is countable.) cheers boud

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Cosmo-torun February 2006