1. ## Mapping the Universe

Initial assuption: The universe is finite. An infinite universe would likely mean infinite matter because of the strange relationship between space and matter(as described by GR), and a universe with infinite mass/matter/energy poses serious theoretical problems and violates the conservation laws.

I'm sure this sounds fascinating: Imagine having a map of the universe, but not just an atlas collection containing every region of the universe but a small replica of the universe, analogous to what the a small globe of the world is to the Earth.

The first obvious question is: what is the shape of the universe? I' ll come back to this.

What would a "globe" of the universe look like? If we had every region mapped out we could certainly construct a small replica of the universe.

At this point, some might argue that you can't have a replica-map of the universe because for instance lets say the universe is one HUGE sphere, what is outside the sphere? That's the equivalent of saying what is outside the universe, and we could NOT know because we are inside of it.

Another argument is that lets for example Earth and our Solar System and the Milkyway galaxy is located is the near the center of the universe. Couldn't we just travel travel in a straight line from Earth outward, along a three dimensional radius, and after a long time reach the the outer boundary of the universe? It's as if the universe could really be modeled by a three-dimesional sphere, that would implicate that we would travel in space until we hit a crystal clear shell that prevented us from traveling any further in that direction, or that the universe has an edge where you can travel no more. This is obviously absurd and so my map of the universe represented by a three-dimentional sphere (or a compact/finite two-sphere) is flawed and will not work in representing the universe.

So far, I showed that you can't represent the universe in a small replica-map as a three-dimentional sphere (or a compact/finite two-sphere). Lucky we now have the mathematical tools of topology and this shell-edge problem can be easily fixed.

Instead of one compact 2-sphere representing the universe in our replica-map, it would be two compact 2-spheres joined at one point along the surface.

Now by aligning the two-dimensional manifolds of both three-dimensional spheres, we can travel in any straight line indefinitely through a finite universe (due to the fact that the manifold of a 2-sphere has no boundary).

The implication of the previous statement is that to travel in a straight line all the way across the universe would land you back where you started.

If this theory is correct, then the possible shape of the universe is a 3-sphere, or a three-dimensional manifold that models a four-dimensional sphere(also known as a hypersphere).

Now the easiest way to picture the universe shaped as a hypersphere is the two connected three-dimensional spheres, and this means that if I am correct, than in the far future we will have replica-maps or "globes" of the universe that will look like two spinning connected spheres next to each other that align depending on direction of travel.

2. I agree.
What an excellent point!

3. Off-topic: (meaning me, not you)
I apologise for the delay, seems I can't override the mod for the post count for the image however people can click it to see it for now. You'll be able to sort the image out later once you've hit the magic post count however make sure you put forwards some discussion not just post numbers the locals seem to get a little irate.

Welcome to Sciforums btw, I hope you manage to prepare yourself for a lot of responsive posters that might or might not be cruel or kind or even on topic for that matter.

Btw, heres the image in it's full glory.

4. now the theory{that the universe is a 3-sphere) has been made at least theoretically possible by the recent proof of the Poincare conjecture, because in order to travel in a straight line indefinitely in our universe, the boundary manifolds must be simply connected, and the Poincare conjecture states:
Every simply connected compact 3-manifold (without boundary) is homeomorphic to a 3-sphere.

5. finite universe?
the universe can be mapped by probability and time measurements...with probability of objects being there in that time based on gravitation measurements...wobbling of stars...thermal/x-ray measurements. XYZ map with embedded time scales and probabilities of planets/stars/nebulas existing there from less than 1&#37; to more than 99% probability.

I would call it Hypersphere map.

6. dragon, I see what you're saying but you are trying to map the universe onto four-dimensional space-time, or onto three-dimensional space relative to time.

I'm trying to map the universe spatially, and even though it is expanding, the 3-sphere is homeomorphic and can be stretched without disrupting continuity.

7. im sorry for being unclear, everytime i say 3-sphere, I mean a compact 3-sphere..

8. Camilus:

We can map the universe in our own centric reference frame, which is the easiest.

Millions of galaxies are already mapped and assigned 3-D coordinate positions [solid-angle, distance].

The distance is actually a red-shift measurement, caused by the galaxy's recession from earth in our 'centric' Milky Way reference frame, converted into distance.

We see some discrete galaxies at great red-shift corresponding to distances of roughly 8 billion light-years away [so we see the galaxy as it existed 8 billion years ago in our reference frame]. Most observed galaxies are much closer.

The most distant "object" that we can see is not actually a discrete object, but a continuous 'smear' of hot plasma that is relatively isotropic across the entire sky. Its redshift is roughly 1,000 [corresponding to a recessional velocity of about 0.9999991c]. Thus, the light that we see from that 'object' shows in the microwave frequencies, and is known as the Cosmic Microwave Background. More recent investigations reveal that it is actually slightly anisotropic, likely revealing the formation of even more distant galaxies than those nearer to us.

That plasma is matter separate and distinct from the matter of all of the visible galaxies we see in our telescopes. We cannot see beyond that 'plasma', though we can presume that there is even more matter, even hotter than the 'plasma'. That is the goal of the LHC, to create conditions that existed in the earliest stages of the Universe's development, where matter is much hotter than that distant plasma [in our reference frame - in its own reference frame that plasma has expanded and cooled, and likely formed galaxies].

9. I know what you are saying Walter but that reveals nothing about the shape and structure of the universe as a whole. I'm trying to look at the 'big picture', visualizing it as God must see it.

Tell me guys, do you believe the universe is infinite?

10. Originally Posted by camilus
I know what you are saying Walter but that reveals nothing about the shape and structure of the universe as a whole. I'm trying to look at the 'big picture', visualizing it as God must see it.

Tell me guys, do you believe the universe is infinite?
yes

11. Originally Posted by draqon
yes
incredible. Then the model I described offers you no insight whatsoever into the secrets of the universe.

I believe the universe cant be infinite, because:

Initial assuption: The universe is finite. An infinite universe would likely mean infinite matter because of the strange relationship between space and matter(as described by GR), and a universe with infinite mass/matter/energy poses serious theoretical problems and violates the conservation laws.

12. An infinite universe would likely mean infinite matter because of the strange relationship between space and matter(as described by GR), and a universe with infinite mass/matter/energy poses serious theoretical problems and violates the conservation laws.
Why can't the universe be infinite? The WMAP data says that the universe can be flat, within error bars. If it's flat, then it is infinite, end of story.

13. Originally Posted by BenTheMan
Why can't the universe be infinite? The WMAP data says that the universe can be flat, within error bars. If it's flat, then it is infinite, end of story.
once again, I dont know if I'm just too advanced in the subject or you guys dont see what I'm seeing but listen, I'm trying to map the universe as a whole! what you are describing Ben is just local geometry within the universe, I'm focusing on the global geometry of the universe as a whole.

Originally Posted by Wikipedia
Based on analyses of the WMAP data, cosmologists during 2004-2006 focused on the Poincaré dodecahedral space (Poincaré homology sphere), but also considered horn topologies to be compatible with the data
as you can see, the WMAP data actually suggests the universe is probably spherical, but horn topologies also do not rule out the possibility of hyperbolic universe.

I believe the universe must be spherical, because even the extra six or seven space-like dimensions in String theory are all formulated with compact topology. and the following theorem "every simply connected compact 3-manifold (without boundary) is homeomorphic to a 3-sphere," makes the universe of string theory a hypersphere.

Note: compact means finite in topological terms.

14. do you really believe that the universe is a three-dimensional Euclidian space? extending in the XYZ directions forever?

15. as you can see, the WMAP data actually suggests the universe is probably spherical, but horn topologies also do not rule out the possibility of hyperbolic universe.
This is not right. The dodecohedral sphere thing is dead---it was a wild thought a few years ago.

I am telling you---the flatness parameter is called $\Omega_r$. If it is zero, then the universe is flat---i.e. topologically flat. Two parallel light rays never intersect. Flat in every sense of the word---including ``not a sphere'' flat. The WMAP data give a value of the flatness prameter that is something like 1.01 +/- 0.05 or something (greater than one means closed, like a sphere, less than one means open, and exactly one means flat).

So it is possible that we live in a flat and infinite universe, which poses absolutely no problems for conservation of energy whatsoever.

16. There's no reason to believe anything other than what is consistent with the experiments

17. Originally Posted by BenTheMan
There's no reason to believe anything other than what is consistent with the experiments
first you have to believe in something and that you test it with experiments to prove it.

18. Camilus,
"Now by aligning the two-dimensional manifolds of both three-dimensional spheres, we can travel in any straight line indefinitely through a finite universe (due to the fact that the manifold of a 2-sphere has no boundary)."

You lost me here. How is this so? Can you show how you would travel in a straight line indefinately?

19. Originally Posted by BenTheMan
The WMAP data give a value of the flatness prameter that is something like 1.01 +/- 0.05 or something (greater than one means closed, like a sphere, less than one means open, and exactly one means flat).
Are you sure? I thought the WMAP just showed the relative spacing between matter.

Camilus,
"Now by aligning the two-dimensional manifolds of both three-dimensional spheres, we can travel in any straight line indefinitely through a finite universe (due to the fact that the manifold of a 2-sphere has no boundary)."

You lost me here. How is this so? Can you show how you would travel in a straight line indefinately?
Well, not necessarily a straight line, more like a geodesic, and travel indefinitely similarly to how you can board a plane right now and fly in a straight line aound the earth indefinitely. The 'indefinite' is due to the fact that the sphere is unbounded, you'll never come to an edge where you can say "this is the end of the sphere."

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