Talk:Shape of the Universe

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[edit] Tone of article

The language of this article comes off as highly condescending. Rather than slapping the reader around with "What you think is wrong" it would be more approachable to simply state the generally scientifically accepted notions of space-time. Addressing "the reader" repeatedly also begins to sound didactic and overly bookish. I'll throw this up on my list of pages needing massage, but feel free to go at it before I manage to get to it.

Hope to have a go at Shape of the universe shortly, if no one else does so before me.
Eddie 08:14, 13 Dec 2004 (UTC)
Working on this now --Eddie 21:50, 4 Jan 2005 (UTC)
Done. Please improve and be bold. Old text commented out in this page. --Eddie 23:10, 12 Jan 2005 (UTC)

[edit] A typo in Local geometries

I am not familiar with this but I know that there is a typo at Local geometries (...negative than the...)

There are three categories for the possible spatial geometries of constant curvature, depending on the sign of the curvature. If the curvature is exactly zero, then the local geometry is flat; if it is positive, then the local geometry is spherical, and if it is negative than the local geometry is hyperbolic.

--Iiaiialover 02:31, 11 December 2006 (UTC)

[edit] Merged and redirected Topology of the universe

I've merged and redirected Topology of the universe. Actually, I only redirected, as IMHO that article doesn't provide anything, not already covered here. For the case, someone disagree, I quote the entire old article here:

According to the general theory of relativity, spacetime is a pseudo-Riemannian manifold. The term topology of the Universe is generally used to mean the 3-manifold of comoving space, even though strictly speaking, it should probably refer only to the underlying topology of this manifold. We do not yet know the global topology of the Universe, and in fact may never be able to know what it is. However, cosmologists are trying to measure cosmic topology using data from ground-based and space-based telescopes. Results from the WMAP telescope may give an answer by 2004 or 2005. The adjective global here means that black holes are ignored - only the properties of space on scales of at least hundreds or thousands of megaparsecs are referred to in the term topology of the Universe. A current hypothesis is that the spatial shape of the Universe is homeomorphic to a 3-sphere. See also: shape of the Universe, Poincaré conjecture.

Pjacobi 20:59, 2005 Jan 22 (UTC)

[edit] Open Universe

The open universe with hyperboloid geometry is unclear to me. Being infinite, the universe would continue forever. But if that was so, then either curvature would have to change its sharpness, or stop curving beyond the center, otherwise the curve would continue around until it contacted itself, making a doughnut shape. Is that sensible?--Ansandre 02:17, 1 July 2007 (UTC)Ansandre

[edit] Closed and Open?

I think that the stubs for Closed universe and Open universe probably need to be redirected to this page, the definitions added in here somewhere; but I don't know enough to be confident doing so. The definitions of closed, flat, and open universes would need to be added here to wherever they're relevant, and there would need to be at least a mention of the connection between a closed universe and an eventual Big Crunch. -- ThirdParty 01:24, 6 December 2005 (UTC)

Hi Third Party. If you're keen go ahead. I didn't realise that there are stubs for Closed and Open Universe. Do you think they could be worked up where they are for the time being and then considered for integration here?
You've raised food for thought and I for one am ruminating on it. For instance, you may be well aware, that Olbers paradox is true, so to speak, in a Closed universe? Distant are stars blue shifted - night is as bright as day (the sun/local star being a disc not as bright as the surrounding stars) and everywhere bombarded by x-rays from distant galaxies. --Eddie 08:53, 6 December 2005 (UTC)
I've merged these two stubs into this article and turned them into redirects while I rewrote this article a bit (see 'Rewrite' below). Mike Peel 16:50, 25 February 2006 (UTC)

Is it possible to have a closed hyperbolic universe? If not, why not?

[edit] Multiple images in different age

One of the endeavors in the analysis of data from the Wilkinson Microwave Anisotropy Probe (WMAP) is to detect multiple "back-to-back" images of the distant Universe in the cosmic microwave background radiation. Assuming the light has enough time since its origin to travel around a bounded Universe, multiple images may be observed. While current results and analysis do not rule out a bounded topology, if the Universe is bounded then the spatial curvature is extremely small.


the words in italics:

does any astronomer consider about the light needs time to move ?

yes

so that we can see multiple images of the same object but in different age ?

Yes. However, the multiple "images" from the cosmic microwave background (CMB) that we are most interested in are those on the surface of last scattering - which is essentially a sphere (2-dimensional sphere) centred on the observer (us, at the Sun), defined by the time light takes to travel to us. This is light emitted at the time when the Universe was much denser. Of course, the light went in all directions, but only some of the light particles photons happened to be sent from spatial positions and in directions which turn out to be useful for us as the observer. In other words, for the CMB, the age of the "images" (but they're really fluctuations rather than individual images) are approximately equal. Boud 12:28, 20 February 2006 (UTC)


[edit] stuff removed

from here

[edit] Connectedness of the global manifold

A simply connected space is all of one piece, such as a sphere.

The probability of detecting a multiply connected topology depends not only on the scale of the topology but also the degree of complication in the topology. The observer may have a privileged position near a closed path. In a hyperbolic local geometry, a non-simply connected space is unlikely to be detected unless the observer is near a closed path.

A second endeavor in the analysis of data from the WMAP is to separate any multiple images in the cosmic background radiation from potential "back-to-back" multiple images due to a compact space. Current results eliminate many forms of non-simply connected topologies implying that either we are not near a closed light path or the global geometry is simply connected.


One way of thinking of a multiply connected space has circle-shaped "holes" or "handles". If the global geometry is non-simply connected then at some points in the geometry, near the junction of a "handle", paths of light may reach an observer by two routes, a "closed path" - a path through the main body and a path via the handle.

to here (though some is already edited a bit, sorry)

The π-2 homotopy class of the 2-sphere is non-trivial - just as the circle is a multiply connected 1-dimensional space - so you have to be a bit careful in saying that the 2-sphere is simply connected - better not use it as an example.

The problem with the "hole" or "handle" way of thinking is that it's most relevant for an extremely INhomogeneous universe, whereas in observational cosmology we're thinking of a standard approximately FLRW model universe, which is of nearly the same density (hence, curvature) everywhere. A purely topological approach ignores distances, the metric, you can stretch the space arbitrarily as long as you don't cut or tear it. But that's confusing in this case, unless you explain that you are making extremely radical stretching and that you are thinking from a four-dimensional point of view.

A lot of the explanation for correct development of intuition about the subject has been removed from this page - look in the history to find it if you want to bring it back. Some time when i have a moment free i may do this if noone else does (i guess some of it could be moved to wikibooks - but given people's constant misunderstandings, i don't see how we can avoid having a section on intuition development - an encyclopedia is not supposed to persuade people that they are stupid. Boud 12:51, 20 February 2006 (UTC)

[edit] Rewrite

I've just gone through the article and rewritten it, with the aim of making it more accessible to the non-mathematician, and to make it conform more with the cosmology section. At the same time, I merged the information about open, closed and flat universes into the page - these are the common terms used by cosmologists to describe the universe. The text probably needs further work, but I'm done for now. Mike Peel 16:50, 25 February 2006 (UTC)

The terms "open" and "closed" are misleading, though it's true that they're commonly used. Boud 19:32, 10 July 2006 (UTC)

I'm new to wikipedia, but I couldn't help adding my two cents: I thought this page was tough reading for a lay person. Perhaps some illustrative analogies or simple examples would help. gabekader —Preceding comment was added at 08:31, March 19, 2007

[edit] correcting several errors

i've corrected some errors:

  • figure - omega alone does not determine the overall geometry of the Universe. It's a local property, not a global property.
  • a hypersphere is 3D, not 4D.
  • i removed the following section since it is not a separate case, it is discussed in the preceding three sections on negative, zero and positive curvature universes:
=== Non-Simply Connected Universe ===
This is the case of a multiply-connected, or more generally 
non-simply   connected, topology.

Boud 19:41, 10 July 2006 (UTC)

[edit] various

i've done a bit more cleaning up, trying to preserve the work of people who have tried to help, while also correcting the errors.

Please: anyone making corrections please be careful that you're not changing the scientific sense unless you're reasonably sure that you understand things properly. i'll probably come back to this and start from talking about 3-manifolds, because otherwise everybody will get confused...

Boud 23:31, 30 December 2006 (UTC)

[edit] Why isn't the Mobius Strip in here as a possible shape of the universe?

I read that it's a possibility. MC Escher made a drawing of it with ants crawling along it. 64.236.245.243 15:50, 15 February 2007 (UTC)

good Question, i thought of that also. I am working on new ideas that the universe has no shape and is truly infinite in all dimentions,direction,time and matter/anti matter.... —Preceding unsigned comment added by 209.212.21.182 (talk) 19:02, March 23, 2007

  • I think it's a bit of an outdated model, but it would still be nice to mention it. Also, unsigned comment person: I don't even know what to say to you. Ketsuekigata 14:08, 15 November 2007 (UTC)

[edit] indeed, a great circle on a sphere has circumference only twice its diameter...

I may be wrong, or there's a small geometry mistake here. 202.27.54.3 00:02, 15 March 2007 (UTC) Gerry


Don't think of the sphere in terms of its embedding in 3-dimensional Euclidean space. You have to measure the diameter of a circle within the manifold. As an example, consider the equator of a sphere of radius R. Its circumference is 2πR, its diameter is twice the distance between the north pole and a point on the equator, i.e., πR. Hence, the ratio between the equator's circumference and diameter is two. SwordSmurf 13:13, 15 March 2007 (UTC)

Agreed. Boud (talk) 14:57, 11 February 2008 (UTC)

[edit] Torus

I don't know much, but I don't think the surface of a torus is flat. Why is it listed under the possible shapes of bound flat universe? If it is flat, I request a proof or explanation. Aurora sword 07:24, 22 May 2007 (UTC)

I assume taht they have to have flat surfaces because the other two shapes (Cylinder and Mobius Strip) are flat. Aurora sword 07:26, 22 May 2007 (UTC)
I'm pretty sure a 4D torus can be flat. As far as I understand, a toroidal universe would mean a cubic honeycomb that repeats itself infinitely, but could still be "flat" in 3D (parallel lines neither meet nor diverge, and all that. Unless they go near anything that has mass, but that's another story). :-) - ∅ (∅), 06:41, 18 January 2008 (UTC)
Try drawing a diagram showing Pythagoras' Theorem on a piece of flat paper. Write down the lengths of the 3 sides of the triangle, either numerically or algebraically. Now roll it up to make a cylinder. The three side lengths have not changed. So Pythagoras' Theorem is still correct and the paper is flat. Now define the two ends of the cylinder to be equal to one another, and you have a 2-Torus. Pythagoras' Theorem is still true. So the 2-torus is flat. The embedding of T^2 in euclidean 3-space is just an aid to intuition, it's not part of T^2 itself. Hope this helps. Boud (talk) 14:55, 11 February 2008 (UTC)

[edit] Another shape.

There is another shape (the name eludes me) where it is a spherical universe but it a dip in it. Does anyone know what I'm talking about? —Preceding unsigned comment added by 69.19.14.42 (talk) 02:37, June 24, 2007

[edit] Hyperbolic Universe Consistent with 1998 Measurements?

If you look at the Supernova Cosmology Project's website, it seems that the later conclusions drawn from the 1998 observations support a flat universe with vacuum energy, not with a hyperbolic universe. This article seems to favor the hyperbolic model, whereas my understanding is that the current most accepted model is flat. Ketsuekigata 13:53, 15 November 2007 (UTC)

[edit] Subsections in introduction

Someone boldly deleted the subsections in the introduction and also deleted its subsection on "Well defined 3-dim concept of space". Since the introduction is in development it is important to have a subsectioning. So that people can identify what the introduction is about, what is missing and what contains errors. —Preceding unsigned comment added by Caco de vidro (talk • contribs) 23:18, 17 January 2008 (UTC)

No text was deleted, I merely reverted the following:
  1. the conversion of prose to a list
  2. the addition of useless and distracting section headers
  3. the rewording of one sentence.
See WP:MOS, WP:LEAD and WP:LAYOUT. (Also WP:SIG.) - ∅ (∅), 06:20, 18 January 2008 (UTC)

[edit] Curvature of the Universe?

Shouldn't this be named Curvature of the universe? Its a more commonly used term than shape and is a more accurate description. Or at least redirect it here. ErgoSum88 (talk) 08:11, 30 January 2008 (UTC)

No. Curvature does not fully determine the shape of the Universe. A 2-plane and a cylinder (more formally R times S^1) are both flat spaces. They have identical curvature (zero) but they are different shapes. See the first sentence of the article. Boud (talk) 14:37, 11 February 2008 (UTC)

[edit] CMB Analysis Shows Shape is Flat

This article looks good to me, but shouldn't it be mentioned somewhere that the observed angular size of the CMB temperature variations (as shown by the first acoustic peak) is just what is expected, which implies the angles of the corresponding triangle add pretty close to 180, so the shape of the universe is flat to a fairly high degree of accuracy, at least the universe from here to the surface of last scattering? DCCougar (talk) 01:45, 4 April 2008 (UTC)

[edit] And the answer is.....?

This article yaps on about the theory, but does not provide a simple answer to the question: what is the shape of the universe? I suggest there should be a paragraph at the top which answers this question in simple laymans terms, even if only to say "Nobody knows" or "Different scientists say different things" or "It could be A or it could be B" or whatever. 80.2.206.224 (talk) 00:18, 13 May 2008 (UTC)