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?

[Beto]

"The story of our universe is vastly more unlikely than the most unlikely story imaginable. First of all, the energy of perfect symmetry had to arise out of the "quantum vacuum." This energy had to arise within the limits of the conservation or energy, which are set according to Heisenbergs Uncertainty Principle. Energy must always be conserved within the boundary of uncertainty. The vast energy of the Unified Field could never arise objectively out of the zero-energy field of the vacuum, since such an energy could not persist for the minimum duration dictated by the Uncertainty Principle. The probability of such an event is zero it is impossible. The universe can only be a possibility, according to the laws of physics, that is to say, it can never truly emerge from the field, although it can exist as a possibility within the field."

From here .

Existing only as a possibility, it would make the universe both bounded AND unbounded, wouldn't it?

[QED]

So do you think that all the galaxies are rushing away from us (apart from a few local ones)?

I do think that the galaxies are receding from each other. And I'm not saying that I believe that tired light is totally correct, but it might have some merit.

We had lost several posts due to the hack, so I'd like to bring back up the discussion - are there Euclidean geometries that would not be bounded?

Well, here's what Einstein has to say:

We already know from our previous discussion that the behaviour of measuring-rods and clocks is influenced by gravitational fields, i.e. by the distribution of matter. This in itself is sufficient to exclude the possibility of the exact validity of Euclidean geometry in our universe. But it is conceivable that our universe differs only slightly from a Euclidean one, and this notion seems all the more probable, since calculations show that the metrics of surrounding space is influenced only to an exceedingly small extent by masses even of the magnitude of our sun. We might imagine that, as regards geometry, our universe behaves analogously to a surface which is irregularly curved in its individual parts, but which nowhere departs appreciably from a plane: something like the rippled surface of a lake. Such a universe might fittingly be called a quasi-Euclidean universe. As regards its space it would be infinite. But calculation shows that in a quasi-Euclidean universe the average density of matter would necessarily be nil. Thus such a universe could not be inhabited by matter everywhere; it would present to us that unsatisfactory picture which we portrayed in Section XXX.

If we are to have in the universe an average density of matter which differs from zero, however small may be that difference, then the universe cannot be quasi-Euclidean. On the contrary, the results of calculation indicate that if matter be distributed uniformly, the universe would necessarily be spherical (or elliptical). Since in reality the detailed distribution of matter is not uniform, the real universe will deviate in individual parts from the spherical, i.e. the universe will be quasi-spherical. But it will be necessarily finite. In fact, the theory supplies us with a simple connection 1 between the space-expanse of the universe and the average density of matter in it.

(you might like to glance at the other two pages under the heading of "Considerations on the Universe as a Whole")

I think where we might be getting hung-up is the way in which we interpret the qualitative and quantitative differences between Euclidean and non-Euclidean universes. What geometry do we have on the surface of a sphere having infinite radius for example? This comes back to what is meant by "flat". FAPP "flat" can be "flat" yet still be inscribed in a non-Euclidean geometry. Different Topologies can then provide a finite yet unbounded space that looks and behaves as though it was "flat".

[QED]

From here .

Existing only as a possibility, it would make the universe both bounded AND unbounded, wouldn't it?

Not too sure about that. I've never noticed Mark Germine before, but having read his piece in your link, he seems to be talking along the lines of Wheeler: Collapse of the Multiverse - J.A. Wheeler's Participatory Anthropic Principle. Interesting stuff, but I think it deserves a topic of its own if we are to debate it.

[otseng]

This in itself is sufficient to exclude the possibility of the exact validity of Euclidean geometry in our universe. But it is conceivable that our universe differs only slightly from a Euclidean one, and this notion seems all the more probable, since calculations show that the metrics of surrounding space is influenced only to an exceedingly small extent by masses even of the magnitude of our sun. We might imagine that, as regards geometry, our universe behaves analogously to a surface which is irregularly curved in its individual parts, but which nowhere departs appreciably from a plane: something like the rippled surface of a lake.

True, the universe is not "perfectly" Euclidean. But it would be more like a surface of a lake.

On the contrary, the results of calculation indicate that if matter be distributed uniformly, the universe would necessarily be spherical (or elliptical).

If it was spherical (or elliptical), it would be non-Euclidean.

I think where we might be getting hung-up is the way in which we interpret the qualitative and quantitative differences between Euclidean and non-Euclidean universes. What geometry do we have on the surface of a sphere having infinite radius for example? This comes back to what is meant by "flat". FAPP "flat" can be "flat" yet still be inscribed in a non-Euclidean geometry. Different Topologies can then provide a finite yet unbounded space that looks and behaves as though it was "flat".

I can agree that if it was modeled as the surface of a sphere with an infinite radius, then it would be Euclidean and unbounded. But, wouldn't this require that the size of the universe be infinite?

[QED]

I can agree that if it was modeled as the surface of a sphere with an infinite radius, then it would be Euclidean and unbounded. But, wouldn't this require that the size of the universe be infinite?

Yes it would. But where does it become detectable? Our instruments are probably going to give-out on us long before we detect spherical geometry in a universe having a finite but very large radius. The limiting case of an infinite radius is an extreme which helps us understand the way things may be headed.

[Greatest I Am]

If we were to say that the universe was bounded, we would have to indicate what was bounding it.

What could possibly be bounding it?

Regards
DL

[otseng]

I can agree that if it was modeled as the surface of a sphere with an infinite radius, then it would be Euclidean and unbounded. But, wouldn't this require that the size of the universe be infinite?

Yes it would. But where does it become detectable? Our instruments are probably going to give-out on us long before we detect spherical geometry in a universe having a finite but very large radius. The limiting case of an infinite radius is an extreme which helps us understand the way things may be headed.

Well, it would also depend on the age of the universe. If the universe expanded from a singularity, then the larger the universe, the faster it would have had to expand to get to its current size. But I guess if the universe can expand faster than light, then any size is possible. This also goes back to the concept that space is stretching, which again I don't see any evidence for.

Another thing. If something is not detectable (either directly or indirectly), of what value would it be in our discussions? And how would it be falsifiable?

[otseng]

If we were to say that the universe was bounded, we would have to indicate what was bounding it.

What could possibly be bounding it?

... the boundary?

Right now, I have two ideas on the boundary.

One is that the boundary is the edge of matter/energy in the universe. Beyond this, there is no matter/energy. However, space can still exist outside of this boundary. So, there could be infinite space. And within infinite space, our universe is expanding.

Another idea is that the boundary is the edge of matter/energy/space. It is impossible for any observer to go beyond this. So, it would be meaningless to ask what is beyond the boundary because it would never be possible. Just like it would be meaningless to ask what would it be like to go faster than light.

[QED]

Well, it would also depend on the age of the universe. If the universe expanded from a singularity, then the larger the universe, the faster it would have had to expand to get to its current size. But I guess if the universe can expand faster than light, then any size is possible. This also goes back to the concept that space is stretching, which again I don't see any evidence for.

Well, the evidence is there. Redshift of distant galaxies was the first piece of evidence that got people to realize the universe wasn't static. An early astronomer called Zwicky proposed that the redshift was due not to Doppler but to "tired light". But this can't explain other observations made since his proposal. For example, distant supernovae seem to explode in slow motion compared to relatively nearby supernovae. This is predicted along with red-shift in an expanding universe that accords with General Relativity. It's not explained by tired light. Tired light theory, on the other hand predicts the blurring of distant objects which we do not see.

But I guess you might want to say that the reason we see galaxies moving away from us in all directions is not because space is expanding (i.e. the raisins in cookie dough model) but because our galaxy was the centre of a big explosion in space.

This is one of those questions that gets raised all the time. Here's a typical response from a physics FAQ

... but if the Big Bang was an explosion
In a conventional explosion material expands out from a central point. A short moment after the explosion starts the centre will be the hottest point. Later there will be a spherical shell of material expanding away from the centre until gravity brings it back down to Earth. The Big Bang as far as we understand it was not an explosion like that at all. It was an explosion of space, not an explosion in space. According to the standard models there was no space and time before the big bang. There was not even a "before" to speak of. So, the Big Bang was very different from any explosion we are accustomed to and it does not need to have a central point.

If the big bang were an ordinary explosion in an already existing space we would be able to look out and see the expanding edge of the explosion with empty space beyond. Instead we see back towards the big bang itself and detect a faint background glow from the hot primordial gases of the early universe. This Cosmic Microwave Background Radiation (CMBR) is uniform in all directions. This tells us that it is not matter which is expanding outwards from a point but rather, it is space itself which expands evenly.

It is important to stress that other observations support the view that there is no centre to the universe, at least in so far as observations can reach. The fact that the universe is expanding uniformly would not rule out the possibility that there is some denser, hotter place that might be called the centre, but careful studies of the distribution and motion of galaxies confirm that it is homogeneous on the largest scales we can see, with no sign of a special point to call the centre.

Another thing. If something is not detectable (either directly or indirectly), of what value would it be in our discussions? And how would it be falsifiable?

Effectively you just asked how we could falsify something that was unfalsifiable! I would say that any idea that isn't, in principle, falsifiable should not be taken seriously. Ideas that, in practice, aren't falsifiable need more work doing on them before they're taken seriously.

[Greatest I Am]

If we were to say that the universe was bounded, we would have to indicate what was bounding it.

What could possibly be bounding it?

... the boundary?

Right now, I have two ideas on the boundary.

One is that the boundary is the edge of matter/energy in the universe. Beyond this, there is no matter/energy. However, space can still exist outside of this boundary. So, there could be infinite space. And within infinite space, our universe is expanding.

Another idea is that the boundary is the edge of matter/energy/space. It is impossible for any observer to go beyond this. So, it would be meaningless to ask what is beyond the boundary because it would never be possible. Just like it would be meaningless to ask what would it be like to go faster than light.

Two things that come to mind. Faster than light travel is possible. It would just take more energy than is available in our universe. There could then be interesting ideas to come from the question of FTL travel.

As to your energy, matter, space boundary, this sounds like the ether that Einstein said that the universe expanded into.
It is not material and can hardly be said to bound the universe because at a local level we could travel beyond this limit in space. There is nothing preventing it.

Regards
DL