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?

[McCulloch]

I wonder why you say this? It works for a flat sheet of rubber just as well -- only we don't have a familiar model like the balloon for visualizing a sheet that gets uniformly stretched in all directions. Incidentally, I prefer the "cookie dough" model over the balloon because the expansion takes place in all three dimensions.

Wouldn't though a flat sheet of rubber be more consistent with an Euclidean bounded geometry? Wouldn't also the cookie dough analogy be bounded?

In the analogy, the lump of cookie dough represents a part of the universe not the entire thing. It is an analogy about the expansion not about the borders or lack thereof.

Incidentally otseng, if you're thinking that galactic red-shift is due to a "conventional style explosion" centered on our galaxy, projecting galaxies away from us in all directions, then I'm wondering how you account for Hubble's law relating the degree of redshift to the distance of the galaxies?

It could simply be that distant objects are moving faster instead of the space between expanding.

Do you have a model which adequately explains that? It would seem to me that if there was a finite universe in an infinite space that started with a conventional explosion, then the expansion should be slowing down due to gravity. There would be no reason to believe that the objects further away from the source of the explosion would be moving at a greater rate of speed.

[QED]

Wouldn't though a flat sheet of rubber be more consistent with an Euclidean bounded geometry? Wouldn't also the cookie dough analogy be bounded?

Yes, but when you stated that "the expanding balloon analogy would only work if the universe was non-Euclidean" I wanted to make sure you knew that the separation of points would look the same (i.e. from any given point, distant points will appear to travel away faster than closer points as the amount of intervening space increases proportionally to distance).

Like McCulloch says, the expanding dough is not meant to convey any analogy about boundaries. The flat sheet can be either a small patch on a balloon, or a part of a perfectly Euclidean plane, but neither is it meant to convey anything about boundaries.

I read through the wiki article, but I still don't see the observational evidence of the metric expansion of space.

http://en.wikipedia.org/wiki/Metric_exp ... l_evidence

Incidentally otseng, if you're thinking that galactic red-shift is due to a "conventional style explosion" centered on our galaxy, projecting galaxies away from us in all directions, then I'm wondering how you account for Hubble's law relating the degree of redshift to the distance of the galaxies?

It could simply be that distant objects are moving faster instead of the space between expanding.

Isn't that rather contrived compared to metric expansion when General Relativity lends support to the latter? The wiki article says

Further studies have since shown the expansion to be extremely isotropic and homogenous, that is, it does not seem to have a special point as a "center", but appears universal and independent of any fixed central point.

I guess you might like to say that this only holds if we're not at the epicentre of the cosmic explosion? I would rather expect to see the equivalent of a huge crater there myself!

[otseng]

In the analogy, the lump of cookie dough represents a part of the universe not the entire thing. It is an analogy about the expansion not about the borders or lack thereof.

That is why I like the balloon analogy better, because it seems to me the most logical way of representing the entire universe that is unbounded. Though I do understand that it's easier to visualize 3 dimensional expansion with cookie dough than a balloon. Yet if we take the analogy at face value, it would point more to a bounded universe than an unbounded.

It could simply be that distant objects are moving faster instead of the space between expanding.

Do you have a model which adequately explains that? It would seem to me that if there was a finite universe in an infinite space that started with a conventional explosion, then the expansion should be slowing down due to gravity. There would be no reason to believe that the objects further away from the source of the explosion would be moving at a greater rate of speed.

No, I don't have a model to explain it. But, I can give one guess. It could be dark energy.

In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe.

The gravitational repulsive effect of dark energy's negative pressure is greater than the gravitational attraction caused by the energy itself. At the cosmological scale, it also overwhelms all other forms of gravitational attraction, resulting in the accelerating expansion of the universe.

http://en.wikipedia.org/wiki/Dark_energy

It would appear that dark energy acts upon matter, not upon the space-time fabric. So, the expansion of the universe would be due to the movement of matter, rather than the stretching of space.

[otseng]

Yes, but when you stated that "the expanding balloon analogy would only work if the universe was non-Euclidean" I wanted to make sure you knew that the separation of points would look the same (i.e. from any given point, distant points will appear to travel away faster than closer points as the amount of intervening space increases proportionally to distance).

Yes, I understand that point.

The wiki article says

Further studies have since shown the expansion to be extremely isotropic and homogenous, that is, it does not seem to have a special point as a "center", but appears universal and independent of any fixed central point.

I guess you might like to say that this only holds if we're not at the epicentre of the cosmic explosion?

It would hold if we are at the center of a bounded universe. And I think that's why the most basic question we need to answer is - is the universe bounded or unbounded? If we determine that the universe is bounded, then there's only one logical conclusion, that we are at the center. If the universe is unbounded, then the Copernican principle holds.

I would rather expect to see the equivalent of a huge crater there myself!

What would constitute the "crater"?

[Goat]

Yes, but when you stated that "the expanding balloon analogy would only work if the universe was non-Euclidean" I wanted to make sure you knew that the separation of points would look the same (i.e. from any given point, distant points will appear to travel away faster than closer points as the amount of intervening space increases proportionally to distance).

Yes, I understand that point.

The wiki article says

Further studies have since shown the expansion to be extremely isotropic and homogenous, that is, it does not seem to have a special point as a "center", but appears universal and independent of any fixed central point.

I guess you might like to say that this only holds if we're not at the epicentre of the cosmic explosion?

It would hold if we are at the center of a bounded universe. And I think that's why the most basic question we need to answer is - is the universe bounded or unbounded? If we determine that the universe is bounded, then there's only one logical conclusion, that we are at the center. If the universe is unbounded, then the Copernican principle holds.

I would rather expect to see the equivalent of a huge crater there myself!

What would constitute the "crater"?

Your conclusion is wrong.

Let us have you climb the tallest mountain .. and have you look around, When you look round, you see things in equal direction in everyplace you look. Does that mean you are at the center of the earth?

Nope.

[otseng]

Your conclusion is wrong.

Let us have you climb the tallest mountain .. and have you look around, When you look round, you see things in equal direction in everyplace you look. Does that mean you are at the center of the earth?

Nope.

I believe we've covered this before.

On the earth, we know that the surface of the earth is non-Euclidean. Yet there is no indication that the universe is also non-Euclidean. So, your analogy would not be appropriate.

[McCulloch]

Let us have you climb the tallest mountain .. and have you look around, When you look round, you see things in equal direction in everyplace you look. Does that mean you are at the center of the earth?

I believe we've covered this before.

On the earth, we know that the surface of the earth is non-Euclidean. Yet there is no indication that the universe is also non-Euclidean. So, your analogy would not be appropriate.

So imagine yourself in a Euclidean unbounded or bounded three dimensional space. Your view in any direction is better for close objects and becomes more limited as you get further away. The limit of your ability to detect objects is about the same in every direction. Do you conclude from that, that you are at the center of this space? Or might there be another possible or even probable explanation?

[QED]

It would hold if we are at the center of a bounded universe. And I think that's why the most basic question we need to answer is - is the universe bounded or unbounded? If we determine that the universe is bounded, then there's only one logical conclusion, that we are at the center.

Then what would your resolution to Olber's paradox be? The consensus explanation requires a finitely old and metrically expanding universe.

I would rather expect to see the equivalent of a huge crater there myself!

What would constitute the "crater"?

I'm sure you'll correct me if I'm wrong, but I think you have very literal big-bang explosion model in mind where all the material in the universe was blasted out from a central point in all directions. For some reason you seem to want to place our solar system (one of trillions) at the epicentre of this material explosion, a place where the temperature and pressure would have been at a maximum. I think you'll find that the physics of this model simply won't work. With no frictional resistance to prevent material travelling outwards, the appearance of the epicentre today would not look anything at all like what is actually seen around us. Our local group of galaxies is typical in appearance to what is seen at the furthest reaches of our instrumentation. Your model would imply a vast empty region... just... like... the one recently reported Well, that's being played down a bit now and it certainly isn't on our back doorstep.

[Goat]

Your conclusion is wrong.

Let us have you climb the tallest mountain .. and have you look around, When you look round, you see things in equal direction in everyplace you look. Does that mean you are at the center of the earth?

Nope.

I believe we've covered this before.

On the earth, we know that the surface of the earth is non-Euclidean. Yet there is no indication that the universe is also non-Euclidean. So, your analogy would not be appropriate.

It is , on a very local scale. So is the universe, on a local scale. There are indications that there are 'bumps' in the time/space fabric (known as matter), and things are non-Euclidean there. The evidence of that is the bending of light around the Sun.

And, the main point is, from an observer, he is at the 'center' of things relative to himself. From an outside observer, the outside observer is at the center, and not the first person. (relative to himself)

[otseng]

So imagine yourself in a Euclidean unbounded or bounded three dimensional space. Your view in any direction is better for close objects and becomes more limited as you get further away. The limit of your ability to detect objects is about the same in every direction. Do you conclude from that, that you are at the center of this space? Or might there be another possible or even probable explanation?

Yep, that's what we're trying to figure out.

Then what would your resolution to Olber's paradox be? The consensus explanation requires a finitely old and metrically expanding universe.

I'm not sure what you're driving at. I'm not arguing that the universe is infinite in size and age. And why would it require a metrically expanding universe?

Your model would imply a vast empty region...

Well, my model is not as simple as matter just "exploding". I believe our Earth is much too complex to simply arrive by random chance. So, there would have been an intelligent cause for the formation of the Earth.

But, let's get back to a question I asked earlier. How can the universe be unbounded and Euclidean?