does the universe have a shape... or is it just a blob... or is it continous... hmmm... theoratically it would be a four dimensinal shape but it's impossible to make a four dimensional figure... could it be a cube with a fourth dimension branching off and never ending...

Originally posted by atreides1977
does the universe have a shape...I never read this anywhere, but I heard that Einstein thought it would have a bananna shape. I don't know what is meant by this.




Originally posted by atreides1977
...or is it continous...It depends on what you mean. All classical theory has, as one of the postulates, continuity. Quantum mechanics seems to screw with this idea a bit, but not in the sense of cosmology.




Originally posted by atreides1977
theoratically it would be a four dimensinal shape...What theory? Special relativity makes no speculation to the "shape" of the universe, except that space is hyperbolic to time. General relativity would require more dimensions than four (I think it's either 9 or 10) if you want to attribute the quality of shape to the universe.




Originally posted by atreides1977
...it's impossible to make a four dimensional figure...Are you sure? I haven't seen any engineering diagrams that very adequately represented a 4-D figure, but the abstraction is perfectly sound, even with a non-Euclidean metric. The ability to <i>draw</i> the figure may be a hard-won bragging right, but a computer, for instance, can handle such things just fine.




Originally posted by atreides1977
could it be a cube with a fourth dimension branching off and never ending... This would be a 4-D "tube" or "cylinder." At least, these are the two terms for it that I see most often. I happen to believe that there's a beginning and an end in time, as well, which would be more like a 4-cube. Some call this a tesseract (as in "A Wrinkle in Time," which I DON't recommend). There are also higher dimensional analogs. Don't forget about n-spheres; that would probably be my first conjecture. They're easy to define, too. In n-dimensional space, the n-sphere is the set of all points "the same distance" from the point designated to be the center. The only problem is the concept of distance; that's what the metric is for.

Originally posted by atreides1977
does the universe have a shape... or is it just a blob... or is it continous... hmmm... theoratically it would be a four dimensinal shape but it's impossible to make a four dimensional figure... could it be a cube with a fourth dimension branching off and never ending...

I think that given the postulate that the cosmological principle holds true throughout the entire universe, there are a limited number of possible shapes. If the geometry of the cosmos is indeed flat on average and space is simply connected, it is infinite, so obviously would have no shape. If flat and multiply connected, I believe there are also limited possible shapes. It has often been said that the 3 torus, or doughnut shaped universe is the simplest of those.

Originally posted by Beercules
I think that given the postulate that the cosmological principle holds true throughout the entire universe, there are a limited number of possible shapes.What cosmological principle?




Originally posted by Beercules
If the geometry of the cosmos is indeed flat on average and space is simply connected, it is infinite, so obviously would have no shape.There is nothing wrong with a "flat," simply-connected topology with finite extension. The simplest example I can think of is a straight line segment. It's flat and simply connected. It may be open or closed, but, I think it must be open to be a complete continuum.

Maybe I'm not sure what you mean by flat. <i>I</i> mean that parallel lines remain parallel. The 1-D example is a line itself (the only line), so satisfaction of this requirement is trivial.




Originally posted by Beercules
If flat and multiply connected, I believe there are also limited possible shapes. It has often been said that the 3 torus, or doughnut shaped universe is the simplest of those. It looks like you're suggesting multiple connectedness on a cosmological scale. I don't think we can probe for something like that. I do think that the universe is multiply connected even at the microscopic scale, though. I don't see how this would limit the shape.

Calibi-Yau?

An interesting point about relativity, time and the shape of the universe - The edge of our viewable universe is 13-14 billion light years away (give or take). Supposedly, the farther we "look" the farther back in time we are seeing, so looking beyond the farthest galaxies, we can see the remnants of the beginning. We must remember though, what we are seeing is 13-14 billion years old. The place we are seeing has had 13-14 billion years to evolve stars, planets, black holes, life?. In actuality, if you were on a planet 13-14 billion light years away, you could look back toward Earth and also "see" the remnants of the beginning. Anyway, that is all common knowledge...The interesting thing is that on this planet 13-14 billion light years away, you could see 13-14 billion light years in the opposite direction as well! You would be able to see space that does not even exist from our (on Earth) perspective. Hypothetically, if you had an instantanious teleportation machine, you could continue like this forever.

If you think about it, this really does make each one of us the center of his/her own universe.

- KitNyx

Originally posted by errandir
What cosmological principle?

The principle that the universe is homogeneous and isotropic, and this assumption is the basis for considering the shape. Though the cosmological principle seems to hold true whever we look in the sky, it might not hold everywhere in a very large universe. But from this assumption that it is, some shapes can be ruled out, such as a normal sphere.

There is nothing wrong with a "flat," simply-connected topology with finite extension. The simplest example I can think of is a straight line segment. It's flat and simply connected. It may be open or closed, but, I think it must be open to be a complete continuum.

It would violate the cosmological principle. A hypersphere is possible for a simply connected universe, though omega seems too low for that to be the actual case.

Maybe I'm not sure what you mean by flat. <i>I</i> mean that parallel lines remain parallel. The 1-D example is a line itself (the only line), so satisfaction of this requirement is trivial.

Yes, flat as in Euclidean.

It looks like you're suggesting multiple connectedness on a cosmological scale. I don't think we can probe for something like that. I do think that the universe is multiply connected even at the microscopic scale, though. I don't see how this would limit the shape.

Oddly enough, there is currently a search for exactly that. Repeated images in the sky, only consistent with a small multiply connected shape is the goal. There should still be an article at the NY Times website (http://www.nytimes.com/2003/03/11/science/space/11COSM.html?pagewanted=print&position=top) though registration is required.

I'm on vacation, so this is going to be brief. After this post, I don't think I'll be making it back for a while.


Originally posted by Beercules
The principle that the universe is homogeneous and isotropic, and this assumption is the basis for considering the shape. Though the cosmological principle seems to hold true whever we look in the sky, it might not hold everywhere in a very large universe. But from this assumption that it is, some shapes can be ruled out, such as a normal sphere.I don't see how a sphere is ruled out. At any poin on the sphere, every direction would appear indistinguishable. I don't even see how homogeneity would influence the shape.




Originally posted by Beercules
It would violate the cosmological principle.The open segment wouldn't, unless "isotropice" put some stipulation on the "amount of space" in a particular direction. In that case, I can see that, only at the middle of the segment would isotropy be satisfied.




Originally posted by Beercules
A hypersphere is possible for a simply connected universe, though omega seems too low for that to be the actual case.Here, I will display some vast ignorance. What is omega? The cosmological constant?




Originally posted by Beercules
Repeated images in the sky, only consistent with a small multiply connected shape is the goal. There should still be an article at the NY Times website (http://www.nytimes.com/2003/03/11/science/space/11COSM.html?pagewanted=print&position=top) though registration is required. I'll read this article (if I find time) before I comment on this.

Check this out:

http://starchild.gsfc.nasa.gov/docs/StarChild/questions/question35.html

I am not going to register to the Times. I did not find the other site very insightful.