univgeometry

[infoseeker]

Hello,

Those of you who have any knowledge about the shape of the universe, would you please come forward and share? The main idea seems to be that the universe is flat. And this has been proved by WMAP related experiments. Now what exactly does a flat universe mean?? and if you have any links on the shape of the universe and related information, please send them.

[Severian]

Have a look at this:

 

http://map.gsfc.nasa.gov/m_uni/uni_101bb2.html

[ed84c]

when people say a saddle shaped uinverse is infinate; how?, look at omega<1. If you follow the ends (i.e. those ends to the left and right) they will eventually converge surely?

[Severian]

when people say a saddle shaped uinverse is infinate; how?, look at omega<1. If you follow the ends (i.e. those ends to the left and right) they will eventually converge surely?

 

No they won't. It is parabolic: y=x^2 so the ends would never meet.

[infoseeker]

thanks severian. but i already know that link...but that flat universe..where do you see it??...like for flat you need 2D..but how can a 3D space like the universe be flat is my question..

[Severian]

Questions of geometry are sometimes confusing. It is best to think in terms of 'what happens if I go in a straight line'. If two people start walking (or better, travelling in a space ship!) parallel to each other at the same speed and in a straight line, what happens to the distance between them. In a flat universe it stays the same, in an open one it becomes more, while in a closed one it becomes less.

 

That is really all that the different geometries say: it is really just telling you how to measure distance. The reason that you are having difficulty is because the 2d representations that one always sees are embedded in a 3d space, but one cannot in one's mind embed a 3d space into a 4d one. In fact, one really shouldn't even view it this way, because our (3+1)d universe is (presumably) not embeded in a (4+1)d universe in this way (there may be extra dimensions, but they would be compactified).

 

Similarly I think it is dangerous to think of general relativity purely as a spacte-time geometry effect, because of the associated preconceptions we carry about in our minds. It is better to think of the metric as a rule for measuring distance, rather then describing some curvature of space-time. (This is of course the definition of 'curvature', but the word itself carried too much baggage imho.)

[Martin]

thanks severian. but i already know that link...but that flat universe..where do you see it??...like for flat you need 2D..but how can a 3D space like the universe be flat is my question..

 

"flat" means, for example, that if you pick any 3 points that make a triangle, and measure the angles (sighting from each point at the other two) that the angles add up to 180 degrees.

 

a 3D space can be flat in that sense

 

in a 3D space that is flat in that sense, ordinary geometry stuff will work out as you expect

 

when they say "flat" they usually say (if they are being careful)

SPATIALLY flat

 

 

it is only the 3D slice at a particular time which is flat

 

also if they are being careful they stipulate that the 3D space at this particular moment, the slice, is only APPROXIMATELY flat in largescale.

 

it is not flat locally because gravity curves it

if you take 3 points around the sun and measure angles they will not add up exactly to 180 degrees because the sun distorts the geometry slightly

 

and our galaxy distorts it a little too

 

but on very large scale, space looks approximately flat,

 

also they are not sure it is PERFECTLY flat even at very large scale.

 

so there are a hell of a lot of provisos and reservations and caveats

and conditions on this flatness. its spatially flat all right but dont take that too literally or seriously

[infoseeker]

Alright. Thanks martin, that was somewhat clear. I'm wondering if you know any links where i can get more information on that..in detail. that would be good