Thread: Ep. 78: What is the Shape of the Universe?

1. dcl
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Originally Posted by suyuti
So let me get this straight.
According to the flat universe, the shape is like paper(as NASA said) or as a table or a book one can say or is the comparison wrong? Thats the closest we can get to imagining it right? Or like how the people in the past believed in the flat Earth?
I agree though that the universe must be finite, otherwise it can't be expanding! After all, nothing can be added to infinite.
That comparison is not valid. Both of your examples you cited, the paper, table, and book cover, are flat, but they are only two-dimensional, so citing them is oversimplifying the picture of what we suspect our Unvierse to be. In geometry, "spaces" can have any dimensionalities and be either flat or curved. In this sense, flatness refers to properties that determine, for example, what the angles of triangles add up to. In a flat Universe, theser angles add up to precisely 180 degrees, and those of rectangles, including squares, add up to precisely 360 degrees. Three- and four-sided figures that we still call triangles and rectangles can be drawn on surfaces of spheres, but their angles add up to more than 180 and 360 degrees, respectively.

Conceptually, there are spaces with these properties, and in fact, many people, including me, suspect that we have our Universe exists in such a space. One of the purposes for which the Wilkinson microwave anisotropy probe (WMAP) was created and put into orbit at enormous expense was to determine whether the three-dimensional space in which the Universe that we perceive is "flat", meaning not curved in that sense. WMAP data have thus far not been able to detect any curvature. This has led many people to conclude that space is flat. Actually, that conclusion is premature. Space may still possess such a curvature so slight that WMAP has thus far not yet yielded data precise enough to enable it to detect any curvature that may exist. I believe there is plausible reason to expect that WMAP will detect some slight curvature after it has accumulated data with small enough uncertainty to enable it to do so. My belief is based on the fact that the integral of the product of two finite variables must be finite, those variables in the present case being the age of the Universe, found by WMAP to be about 13.71 billion years, and the expansion rate, believed to have always been finite, even during the inflation era when it is believed to have been many times the speed of light but always finite.

I hope the above dispels your confusion regarding the meaning of "flatness" when applied to the geometry of space. If it doesn't, I hope you will ask more questions. Hopefully, one of us can resolve your uncertainty.

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Ok i get it thanks. Then someone ought to tell NASA to remove that comparison!

3. dcl
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Originally Posted by suyuti
Ok i get it thanks. Then someone ought to tell NASA to remove that comparison!
NASA is made up of people, and people tend to be guilty of lazy or sloppy thinking, me included although I try to not be.

4. Here is a website that describes these concepts in pretty much the simplest terms possible:

THE SHAPE OF SPACE

5. dcl
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Originally Posted by speedfreek
Here is a website that describes these concepts in pretty much the simplest terms possible:

THE SHAPE OF SPACE
The website you cited oversimplifies the matter. It describes the 3-torus, the dodecahedron, and a multiply-connected thing that might fascinate a topologist but not a cosmologist. The 3-torus is merely an example of a finite but unbounded space but cannot be taken seriously as a model of the Universe because it suggests that the universe has the shape of a cube with reentrant opposite faces. The same can be said of the dodecahedron but more so. I feel that the only finite but unbounded shape that seems even remotely plausible for the shape of the Universe is the four-dimensional hypersphere that I described in my thread entitled "The Shape of the Universe". It is not original with me. I would welcome a plausible alternative, but I have yet to see one. Certainly Dr. Gay's doughnut, a crude variant on the 3-torus, is not one.

6. Do you think that papers like Extending the WMAP Bound on the Size of the Universe are based on concepts that cannot be taken seriously? The team involved considered those non-trivial topologies described in The Shape of Space as possible candidates for the shape of the universe too, and the conclusions of that paper are based on their search for them.

They found no evidence for matching circles in different directions, and hope to extend their search to the edge of the observable universe, thus proving that the fundamental domain of the universe is larger than our observable part of it, but they consider multiply connected space as a valid enough model to search for evidence.

7. dcl
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Originally Posted by speedfreek
Do you think that papers like Extending the WMAP Bound on the Size of the Universe are based on concepts that cannot be taken seriously? The team involved considered those non-trivial topologies described in The Shape of Space as possible candidates for the shape of the universe too, and the conclusions of that paper are based on their search for them.

They found no evidence for matching circles in different directions, and hope to extend their search to the edge of the observable universe, thus proving that the fundamental domain of the universe is larger than our observable part of it, but they consider multiply connected space as a valid enough model to search for evidence.
The 3-torus, described in the second reference listed above, likening the shape of the Universe to that of a cube, seems so improbable to me that I find it amazing that anyone would take it seriously and actually search the sky for such circles.. I would have been surprised if any evidence for such circles had been found. As I've said in my thread entitled "The Shape of the Universe", the shape that I regard as most plausible is that of a four-dimensional hypersphere that expanded from a point at its center and with the Universe that we see located in its three-dimensional "surface".

8. You might find that paper, "Extending the WMAP Bound on the Size of the Universe" quite enlightening.

As for the 3-Torus describing the universe as a cube and thus seeming implausible, consider what happens when you take a soap bubble and press other bubbles against it so they "join". Where the bubbles connect they have apparently flat faces...

Can a Hypersphere describe a non-trivial topology or multiply connected space and if so how would it manifest itself to us if light could propagate throughout? If not, does your Hypersphere have an edge where the stars stop?

The question really boils down to whether the whole universe has an "edge" or not.
Last edited by speedfreek; 2008-Jun-09 at 05:51 PM. Reason: typo

9. I'd vote for the hypersphere (S3) over the hypertorus (S1XS1XS1) - how ridiculous can this get? BTW, neither have "edges".

10. dcl
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Originally Posted by speedfreek
You might find that paper, "Extending the WMAP Bound on the Size of the Universe" quite enlightening.

As for the 3-Torus describing the universe as a cube and thus seeming implausible, consider what happens when you take a soap bubble and press other bubbles against it so they "join". Where the bubbles connect they have apparently flat faces...

Can a Hypersphere describe a non-trivial topology or multiply connected space and if so how would it manifest itself to us if light could propagate throughout? If not, does your Hypersphere have an edge where the stars stop?

The question really boils down to whether the whole universe has an "edge" or not.
The paper you cited appears to have examined the WMAP data for the possibility that the Universe has the topology of a 3-torus. I don't understand why a rational person would even begin to consider analyzing WMAP data for the possibility that the shape of theUniverse would in any way resemble that of a cube rather than of a sphere. The 3-torus is interesting as a subject in topology, but the idea that the Universe might have that shape is nothing short of preposterous.

11. They were searching for evidence for a lot of different models including the dodecahedral space first proposed by Henri Poincaré (soccer ball universe). Was his a preposterous idea too?

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im still going for blazing edges...lol simple ...WAP!!

tho they are receding at LS so you could never reach one......

what a sight

im not going for all this complicated 4d jib jab

if the universe (as we defined it as the bubble that started 13.7 billion years ago) is as large as it well my be you would be very unlikley to be near an edge....

its not an unreasonable viewpoint ... and you cant prove it is wrong.... (can you?)

i mean do you really think if you set off in one direction and kept going that you would return to your starting place????
Last edited by damian1727; 2008-Jun-09 at 09:01 PM. Reason: i dont have one i just felt like it

13. dcl
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________________________________________
speedfreek: As for the 3-Torus describing the universe as a cube and thus seeming implausible, consider what happens when you take a soap bubble and press other bubbles against it so they "join". Where the bubbles connect they have apparently flat faces...

dcl: It's surface tension that causes the interface between two conjoined soap bubbles to be flat. There is no analog of that in the Universe and no reason to suppose that a pair of spherical universes would have such an interface if they were in contact with each other.

speedfreek: They were searching for evidence for a lot of different models including the dodecahedral space first proposed by Henri Poincaré (soccer ball universe). Was his a preposterous idea too?

dcl: It seems to me that there is no reasonable or logical basis for supposing that the Universe has the shape of a cube, a 3-torus, a dodecahedron, or Dr. Gay's doughnut. Poincaré's backing that idea makes it no less preposterous.

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