The universe is Euclidian.

[gib65]

I just learnt that the geometry of the universe has recently been measured. It turns out to be Euclidian after all (as opposed to spherical or saddle-shaped).

 

I learnt it here, a course you can order on cosmology, taught by Mark Whittle.

 

Whittle says this:

 

"The geometry of the universe, as best we can measure, is Euclidian. Giant triangles do add up to 180 degrees. Giant sphere do have surface area 4(pi)r^2, and volumes (4/3)(pi)r^3. All the geometry you learnt in high school applies not only to surveying your property, but also to surveying billion light year galaxies maps."

 

What are the implications of this? Thinking of the 3D universe as the surface of a 4D sphere was convenient because I didn't have to ask where the ends of the universe lay. No matter which direction you travel, you eventually end up back at the same spot you started. Now I have to question what would happen if I kept moving outward indefinitely. Would I end up reaching an area of space that was devoid of matter and energy? Would matter and energy continue to surround you no matter how far out you went (I doubt it considering this would mean an infinite amount of matter and energy exists)? Would I suddenly hit a "wall" - the edge of the universe, so to speak (I doubt this too)? What does this say about the creation of space itself. As the 3D surface of a 4D sphere, one could imagine that space was created with the Big Bang, but in a Euclidian universe, it's hard to imagine how space was created (unless one imagined that there really is an expanding edge to space).

 

Can anyone shed light on these questions?

[michel123456]

I think there are some confusions here.

"the 3D universe as the surface of a 4D sphere" transforms our 3d world into a surface. That means you cannot go "outwards" nor "inwards".When you are thinking a "4D sphere", you are transforming the time dimension into space-dimension. This is not correct (IMO).

IMO, there is another way to introduce the 4th dimension, which is actually the conventional one: introducing time.

 

At the paradoxal risk of not being conventional, you can leave the time dimension as-it-is. By introducing time as the 4th dimension, the 3D space (the sphere) can move, translate, rotate, jump, grow, shrink, etc. Choose wathever motion you want, and ask again.

[insane_alien]

he was talking about spatial dimensions, not temporal dimensions. i would have thought this to be obvious.

 

the numbering of dimensions is arbitrary anyway.

[Sisyphus]

It is approximately Euclidian on the largest scales we can see. It isn't so on every scale, and it still might not be on extremely large scales.

 

However, if it really is "flat" on the largest scales, that presumably just means it is infinite. It specifically does not mean an expanding 3D sphere, and all that implies (an "edge" or whatever). Everything is regressing from everything else at rates proportional to distance, and that isn't consistent with what you would see with an expanding 3D object, like a conventional explosion.

 

So I guess, how does this make it harder to imagine how space was (and continues to be) created? Maybe this analogy could be useful: imagine that the number line is the universe. Obviously, it is infinite in extent (though 1-dimensional), and has no edges. The objects in the universe are located at the integers. For simplicity, imagine they are not moving relative to one another. Now imagine that space is expanding, such that it has doubled in size. Now all the objects are 2 units apart, located at the even integers. They haven't moved, there are still the same amount of them (infinite), but everything is twice as far apart as it was before. The "universe" has "doubled in size" in that sense, though that's only measurable with average distances, and it didn't have a finite size to begin with.

[gib65]

It is approximately Euclidian on the largest scales we can see. It isn't so on every scale, and it still might not be on extremely large scales.

 

Oh, that makes a bit more sense. So then the curvature of the universe must be extremely large, and its rate of expansion in the beginning extremely fast.

[michel123456]

Sisyphus wrote " Everything is regressing from everything else at rates proportional to distance," (OK, I knew that) " and that isn't consistent with what you would see with an expanding 3D object, like a conventional explosion." Could you please explain the second part. Thanks.

[insane_alien]

a conventional explosion has objects expanding from one point. and you can trace the point from the frame of any particle you choose.

 

the universe is expanding uniformly which means there is no starting point because everywhere is the starting point.

 

imagine the universe is an invisible fruit loaf(bear with me here) and you're standing on one of the raisins looking at some other raisins when its baking (and expanding). you would measure the further away raisins to be moving away from you at a faster velocity relative to you. but relative to the bread bit they're not moving at all. universe is closer to that than an explosion.

 

don't read too much into the analogy, it is an analogy to explain the fundemental concept and nothing more reading too much into it will lead to disparities between the analogy and reality that are irrelevant to the point.

[michel123456]

O.K.

So, the difference is about direction, not about intensity, speed, acceleration or wathever.

 

But (to go back on track) I thought that the regular sequence of dimensions were:

1,2,3 Space (Euclidian as it shows)

4 Time

5,6,7,8,9,10,11, abstract dimensions.

 

You cannot avoid Time in the sequence. And transforming the 4th dimension into a spatial one is not correct (IMO).

Edited November 29, 2009 by michel123456

[insane_alien]

the numbering is abstract, you could have time as the first dimension. besides, he didn't say the dimension was the fourth. he just say a 4D sphere which means a sphere with 4 spatial dimensions.

 

also, the 11-D from string theory is nowhere near a certainty and there are plenty of other theories.

[gib65]

Right, and who's to say the fourth dimension isn't time? I sometimes like to think of the radius of the 4D sphere universe as time.

[michel123456]

Right gib64.

 

Time is not a beloved entity. It is not understandable, and once you begin talking about Time, you often fall into the tenebres of philosophy, existentialism, and blah blah.

 

Space is more tangible.

 

Also Time is difficult to be represented on paper. It is so easy with space.

I am surprised that we have now new technologies that make available representations in the time scale, i.e. gif diagrams for example. They are used, and you can find some on the Web, but it is IMO a wonderful new tool that is not utilised as much as it should.