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]

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

There are two ways that a space can be unbounded and Euclidean.

1. It could be infinite.
2. It could be a form of a torus.

I believe that we can rule out that our universe is infinite.

I think that most cosmologists agree with you there. Not only is the mater and the energy of the universe finite, but spacetime is as well. The Big Bang was not a singularity that exploded in a pre-existing three dimensional space. The Big Bang was the origin of the actual space that we inhabit.

For a (finite) torus, how would that be Euclidean?

Remember the old arcade game asteroids? It's universe was a flat (euclidean) screen where if you go off one side, you immediately re-enter the other. This is topologically equivalent to a torus.
As I understand the current model, the universe is like that, except the 2D screen has been replaced with an expanding regular solid.

[otseng]

According to your model, then if anything, photons will be blue-shifted not red-shifted!

I could entirely be wrong since I just came up with this on my own. But I don't see why it would be blue-shifted.

Are you saying that the gravitational field would be the strongest in the center?

OK, you'll probably think I'm "fobbing you off", but I think the best way for you to understand the answers to your questions is to follow Ned Wright's Cosmology Tutorial.

How about this. I'll read through the article and when I have questions, I'll ask those.

(It's his centenary this year so pardon me for inserting a minor homage)

I didn't realize that Auden knew so much about science!

[QED]

According to your model, then if anything, photons will be blue-shifted not red-shifted!

I could entirely be wrong since I just came up with this on my own. But I don't see why it would be blue-shifted.

Are you saying that the gravitational field would be the strongest in the center?

In an idealized model, Gravity cancels out at all points inside a hollow sphere: At the exact center of a sphere, there will obviously be an equal gravitational effect from every point on the outer shell of the sphere. Moving from the center to some other point inside the sphere, as the point approaches one edge, the forces from that side become stronger than the other. However, there is a compensating change taking place as the amount of mass behind the point gets larger, and this cancels out exactly as described by Gauss's law. At any point inside a homogeneous sphere the gravity only depends on the mass within a sub-sphere whose radius ends at that point. All mass beyond this radius can be considered as collection of spherical shells as per the limiting case of the hollow sphere, and hence contributes nothing to the field inside the radius.

In your spherical universe with the Earth at the centre, a photon at any point would appear to be accelerated towards the mass of the sub-sphere centred on the Earth and ending at the photon. Such an acceleration would tend to shift it to the blue end of the spectrum.

OK, you'll probably think I'm "fobbing you off", but I think the best way for you to understand the answers to your questions is to follow Ned Wright's Cosmology Tutorial.

How about this. I'll read through the article and when I have questions, I'll ask those.

OK, I appreciate that -- but remember -- I'm not a professional Cosmologist so I can't guarantee to be able to answer everything.

It's his centenary this year so pardon me for inserting a minor homage)

I didn't realize that Auden knew so much about science!

His father was a physicist.

[Beto]

The Big Bang was not a singularity that exploded in a pre-existing three dimensional space. The Big Bang was the origin of the actual space that we inhabit.

I remember reading somewhere about theories of how the early universe worked, right after the Big Bang. They said "time" didn't start immediately after. They even used the expression "before time began". That one cracked me up. The universe expanding into spacelessness also confounds me a great deal. Not that it takes much...

[otseng]

For a (finite) torus, how would that be Euclidean?

Remember the old arcade game asteroids? It's universe was a flat (euclidean) screen where if you go off one side, you immediately re-enter the other. This is topologically equivalent to a torus.
As I understand the current model, the universe is like that, except the 2D screen has been replaced with an expanding regular solid.

I would not agree that they would be "topologically equivalent". But, no matter, here's some questions:

If I approach a "side" and come out on the other "side", how would the two points be causally connected?

Also, could such a side even exist if we could not perceive of crossing a side and reentering another side? If other words, how would it be detectable that a side even exists?

[otseng]

In an idealized model, Gravity cancels out at all points inside a hollow sphere:

Why a hollow sphere? I would think an idealized model would be a sphere uniformly filled with points. Or even a solid sphere.

The Hubble law generates a homologous expansion which does not change the shapes of objects, while other possible velocity-distance relations lead to distortions during expansion.

It made a jump here to a metric expansion of the universe. How did it get from the Hubble recession to metric expansion?

Since we actually see the same redshift-distance law in all directions, either the redshift-distance law is linear or else we are at the center which is anti-Copernican.

As far as I know, the Copernican principle is only an assumption.


I am stuck at understanding the red light cone in this space-time diagram. What exactly does the red line mean?

[QED]

In an idealized model, Gravity cancels out at all points inside a hollow sphere:

Why a hollow sphere? I would think an idealized model would be a sphere uniformly filled with points. Or even a solid sphere.

You must have missed the transition from hollow to "solid" (homogeneous) in my explanation above:

At any point inside a homogeneous sphere the gravity only depends on the mass within a sub-sphere whose radius ends at that point. All mass beyond this radius can be considered as collection of spherical shells as per the limiting case of the hollow sphere, and hence contributes nothing to the field inside the radius.

The reason for starting out the explanation with a hollow sphere is to make clear the cancellation effect that accords with Gauss's law by considering a limiting case.

The Hubble law generates a homologous expansion which does not change the shapes of objects, while other possible velocity-distance relations lead to distortions during expansion.

It made a jump here to a metric expansion of the universe. How did it get from the Hubble recession to metric expansion?

Because the extremes of red-shift seen in distant galaxies can only be due to cosmological expansion.

Since we actually see the same redshift-distance law in all directions, either the redshift-distance law is linear or else we are at the center which is anti-Copernican.

As far as I know, the Copernican principle is only an assumption.

It's only an assumption that you and I are typical human beings, that neither of us live at the place on the planet where life first evolved (or God placed Adam and Eve if you will). And I've already pointed out how the view from the centre of an explosion would give the game away. What physical process could you possibly have in mind whereby all the material in the cosmos was first assembled where our galaxy is now and then ends up being distributed uniformly around our galaxy -- which is the only one not to have moved?

I am stuck at understanding the red light cone in this space-time diagram. What exactly does the red line mean?

Do you understand Space-Time Diagrams? The "cosmic speed limiter" prevents lines of distance/time exceeding 45 degrees on the diagram as that angle has been chosen to represent light-speed. So for any point we might place ourselves at, such as the one at top center, then looking out and back in time, information beyond the (red) line at 45 deg, to the normal cannot reach us.

[Openmind]

QED, I doubt I'm the first to say this, but your scientific understanding is amazing. Are you a scientist by living?

[QED]

Member spotlight - QED will answer your question Openmind. What little I know of Cosmology is gleaned from an interest in amateur Astronomy and a pile of paperbacks. I am deeply envious of those who are smart enough to do it for a profession.

[Openmind]

Thanks for the link, it was quite interesting.

Good to know that there is someone the forums with an advanced understanding of science.

Thanks