Is the universe bounded or unbounded?

[otseng]

In the Light, stars, and creationism thread, I proposed a theory to reconcile a young earth with being able to see stars that are billions of light years away. The theory assumes that the Big Bang is true, however, it also assumes that the universe is bounded. In typical cosmology, it is assumed that the universe is unbounded.

Bounded means that the universe has a boundary to it. There exists an "edge" to the universe in which beyond this boundary, our universe does not exist.

In an unbounded universe, there is no "edge". The universe "wraps" around itself. So, if you are to go in any direction in a straight line, you will eventually come back to the starting point.

This is hard to conceptualize, but can be explained like a surface of a sphere. On the surface of a sphere, if you start at any point and then go in a straight line, you will eventually come back to the starting point. Now, instead a 2-D surface on a sphere, the universe is a 3-D topology that curves in on itself.

The ramifications of either of these two assumptions make for drastically different cosmological conclusions.

So, the questions are:
1. Is the universe bounded or unbounded? Why?
2. What are the ramifications of whether it is bounded or unbounded?

[ST88]

There's something called Oblers' Paradox, which asks the question: if the universe is infinite, why are there not an infinite number of stars visible in the night sky? In fact why is there even night? An infinite number of stars would take up every single spot of space in every direction and glow as brigthly as daylight.

Even without the Hubble observations of Doppler red shifts (indications that other galaxies are moving away from us), we can theoretically conclude that the universe is expanding at such a rate that the light from the most distant stars racing away from us is going so fast, so close to the speed of light itself, that the light can't reach us. And if the universe is expanding, that means it is contained in a finite space.

Complicating this is the fact that light does not travel infinitely fast, so when we look up at the stars, we are actually seeing them as they existed in the past. What this means is that in a finite, unbounded universe, if we looked hard enough, we would be able to see the point in space that we now occupy as it existed billions and billions of years ago (or a figure equal to that of the warp of space).

But this also means that a finite, unbounded universe violates Oblers' paradox. Not only would we be seeing the light from our neighbor stars, we would be able to see the light from the distant past with equal magnitude, and the light that wrapped around the universe could theoretically create a feedback loop that would burn up the sky like a Bude light.

I don't know if I even buy the theory of the dimensional warp of space. Not the localized gravitational warp observed by astrophysicists, but the bending-back-on-itself warping that would chracterize our universe as a mobius strip or a five-dimensional sombrero.

In a bounded universe, we would expect to see galaxies rushing away from us at an accelerated pace not just because we are rushing away from them also, but because the edges of the universe expand in all directions in three dimensions, like the surface of a balloon being inflated. Any two points on the balloon will accelerate away from one another more quickly as it expands. Similarly, the farther away something is, the faster it will accelerate away from you. And this is what we see.

Hubble's research revealed that distant galaxies recede from us more quickly than closer ones in direct proportion to how far away they are. We now recognize this as the expansion of space itself, launched by the Big Bang.

http://www.nap.edu/html/oneuniverse/fro ... 2-173.html

And don't get me started on string theory...

[otseng]

But this also means that a finite, unbounded universe violates Oblers' paradox. Not only would we be seeing the light from our neighbor stars, we would be able to see the light from the distant past with equal magnitude, and the light that wrapped around the universe could theoretically create a feedback loop that would burn up the sky like a Bude light.

Right. If the universe was unbounded and started from the Big Bang, why would the sky at night be dark? Even if there was only one star in the universe, we would see light from this single star all around us all the time.

Let me illustrate it this way. Suppose the entire 3-D universe is represented by the surface of a sphere. I am standing at one point on the sphere. On the other side of the sphere there exists a light source. The light source would radiate light in all 2-D directions. And I would see light from the light source coming at me from all 2-D directions. And I would still experience this even if the sphere was expanding (as long as it's expanding less than the speed of light).

So, based on this, the universe cannot be unbounded since we don't see light from all around us.

[Rancid Uncle]

So, based on this, the universe cannot be unbounded since we don't see light from all around us.

I don't see how light is the only thing that consitutes universe. I do agree there isn't an infinite amount of matter but the universe has to go on forever. If there is an edge to the universe what's on the other side? It seems like you're imply the lack of light or matter means an area doesn't exist.

There exists an "edge" to the universe in which beyond this boundary, our universe does not exist.

Then what exists? Nothing is one option but if you brought something there then there would definetly be something. If you can't bring something there then there has to be something to stop it.

[otseng]

So, based on this, the universe cannot be unbounded since we don't see light from all around us.

I don't see how light is the only thing that consitutes universe.

I'm not saying that light is the only thing that constitutes the universe. I'm saying that if the universe is unbounded, then what we should see in the sky is light all around us.

I do agree there isn't an infinite amount of matter but the universe has to go on forever.

Not if you believe in the Big Bang. According to the BB, the entire universe started in a finite volume and then rapidly expanded, and is continuing to expand even now. So, the universe cannot be infinite. There is no way to start from a finite volume and then for it to become infinite.

If there is an edge to the universe what's on the other side?

Who knows? Perhaps another dimension?

It seems like you're imply the lack of light or matter means an area doesn't exist.

No, I'm not saying that.

Some more thoughts on an unbounded universe. If the universe is unbounded, then it would follow that the universe has a non-Euclidian geometry. More precisely, the universe would have an elliptic geometry. But, as far as I know, all rocket scientists use Euclidian geometry to determine how to fly a spacecraft in space. Also, an elliptical geometry universe would mean that all triangles that exist in the universe is greater than 180 degrees. Perhaps in our small part of the universe, we can approximate all triangles to have 180 degrees, but in fact, all triangles would have more than 180 degrees.

[otseng]

If the universe is unbounded, then what is expanding is the space itself. It's like stars painted onto the surface of a balloon and it is getting blown up. So, the effect is that we see stars receeding from us. But, if space itself is being expanded, then it leaves open several issues.

What is the force that is causing the expansion of the "space fabric"?

If space is being expanded, then each point in space must also be expanding in three dimensions. So, not only is the space between the stars expanding, but so is the space where stars exist are expanding. And so is the space occupied by the computer in front of you, your entire body, the entire earth, everything. I cannot expect that gravitational forces are strong enough to keep your body together if the space in the body is actually expanding.

[ST88]

If the universe is unbounded, then what is expanding is the space itself... If space is being expanded, then each point in space must also be expanding in three dimensions.

I don't follow this. I understand the concepts, but I don't get how you can prove one thing from the other. Do you have a reference?

So, not only is the space between the stars expanding, but so is the space where stars exist are expanding. And so is the space occupied by the computer in front of you, your entire body, the entire earth, everything. I cannot expect that gravitational forces are strong enough to keep your body together if the space in the body is actually expanding.

I'm not sure where you're going with this. Are you trying to say that an unbounded universe requires stretching some kind of unchanging "space fabric" so loosely that it would eventually rip apart? If so, there are other ways of creating an unbounded universe that does not require the stretching of space fabric.

[otseng]

If the universe is unbounded, then what is expanding is the space itself... If space is being expanded, then each point in space must also be expanding in three dimensions.

I don't follow this. I understand the concepts, but I don't get how you can prove one thing from the other. Do you have a reference?

Here is one reference - uniformity of expansion of the universe. Though it explains that the earth is not expanding, I don't see why not.

Are you trying to say that an unbounded universe requires stretching some kind of unchanging "space fabric" so loosely that it would eventually rip apart?

No, I'm trying to show that the universe cannot be unbounded.

If so, there are other ways of creating an unbounded universe that does not require the stretching of space fabric.

Please present those theories.

[ST88]

If the universe is unbounded, then what is expanding is the space itself... If space is being expanded, then each point in space must also be expanding in three dimensions.

I don't follow this. I understand the concepts, but I don't get how you can prove one thing from the other. Do you have a reference?

Here is one reference - uniformity of expansion of the universe. Though it explains that the earth is not expanding, I don't see why not.

I agree with your theory, but not with your example. It is not necessarily true that in an unbounded universe, every point in space must expand in order to explain the universe's expansion.

If so, there are other ways of creating an unbounded universe that does not require the stretching of space fabric.

Please present those theories.

1. An unbounded universe can expand the same way that a bounded universe can, simply by pushing the boundaries at the unimaginable speed of 70 km per second per megaparsec. Remeber that the balloon universe in an unbounded state would actually be a fourth- or fifth-dimensional balloon. Still expanding, but also still circular. This would also mean that the straight line that connects us to ourselves by going around the universe, is itself expanding. That is, we are getting farther away from ourselves all the time.

And also don't forget that the reason the balloon expands is because matter is pushed into it. In this case, we can explain the expansion not in terms of a singularity, like the balloon hole where air goes in, but as a fourth- or fifth-dimensional hole, where matter is either spontaneously created or is converted from one state to the other. This could be the answer to the theoretical form of "dark matter". In an expanding universe, the dark matter could be transforming itself into usable matter, such as star clouds or interstellar dust.

But I don't think you can make a distinction between the expansion of a bounded universe and the expansion of an unbounded universe -- the two states of expansion would not necessarily be different enough to make a conclusion about one or the other based on observation.

2. An unbounded universe does not necessarily need to expand "outward" - it can expand in any of a number of dimensional directions, creating the effect of expansion while also maintaining the same size-to-matter ratio that keeps it stable.

3. The term "unbounded" impies a kind of mobius-strip-like property where there would be no edge even if we looked for one. If such is true, then think of it as the paper of the strip not thickening, but expanding on a different dimnesional plane at every curve on its surface. That is, the expansion is not uniform, but is directed at specific places that would maintain its shape, which was the original shape from the priordial creation event.

4. An unbounded universe that would produce the kinds of observations that we see from galaxies rushing away from us does not necessarily need to be expanding at all. The measurement is the amount of redshift in the Doppler measurements, which could be accounted for in a number of ways. In an unbounded universe, we would not necessarily expect that galaxies would be occupying their stationary parts of space, they may simply be in the process of rotating away from us in the grand circular scheme. All points in space would appear to be rushing away from each other at an increasing speed, ironically because of the increased redshift. And because the galaxies receding from us are actually preceived by us as their image from billions upon billions of years ago, they would have appeared closer in earlier times despite the fact that they might not have been actually closer. Also, don't forget that Doppler measurements are wavelength measurements. Is it possible that wavelengths change over great distances? If so, it would mean that the rest of the universe is not receding at all (this is unlikely, as observations of supernovae have given us new perspectives on Doppler measurements).


ed to add: additional theories.

[otseng]

1. An unbounded universe can expand the same way that a bounded universe can, simply by pushing the boundaries at the unimaginable speed of 70 km per second per megaparsec.

I do not see how an unbounded universe can have a boundary to push.

And also don't forget that the reason the balloon expands is because matter is pushed into it.

If matter is spontaneously created, this would violate the first law of thermo.

2. An unbounded universe does not necessarily need to expand "outward" - it can expand in any of a number of dimensional directions, creating the effect of expansion while also maintaining the same size-to-matter ratio that keeps it stable.

If we can look at our universe from a higher dimension then we could see that it is expanding "outward". However, from our perspective, we would simply see space growing larger.

If space is not increasing in all directions at all places, then the customary example of a balloon being blown up is not appropriate. If only certain points are expanding and also not expanding in all 3 dimensions, then it would be almost impossible to conceptually visualize. And it would be even harder to explain why it would behave that way.

3. The term "unbounded" impies a kind of mobius-strip-like property where there would be no edge even if we looked for one. If such is true, then think of it as the paper of the strip not thickening, but expanding on a different dimnesional plane at every curve on its surface. That is, the expansion is not uniform, but is directed at specific places that would maintain its shape, which was the original shape from the priordial creation event.

Again, from our perspective, the only thing that could be expanding is space.

4. An unbounded universe that would produce the kinds of observations that we see from galaxies rushing away from us does not necessarily need to be expanding at all.

I agree that there could be other explanations for the redshift other than an expanding universe. But why even theorize an unbounded universe when a bounded universe is the most simple and elegant model?