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?

[Ian Parker]

[quote="Alien"
About critical density:
How can we be so sure to say that the universe is flat and its density has EXACTLY the critical value? This value is a borderline, a theoretical boundary that discriminates exactly two behaviours. It's more a philosophical boundary than a really suitable possibility. The value of this boundary has to be exactly defined or measured. Mathematically, a fraction of 10E-100 or even less, would influence the final destiny of the universe! A single electron more or less in a cubic inch would make the difference! Why should the universe possess an exact value that is only mathematically defined?
As we have already seen examples by which a measurement can never be 100% accurate, and Nature shows us inaccurate phenomena, I would not agree with the absolute statement that "the universe is flat". We can discuss whether it is open or closed, and whether a certain consideration or measurement tends toward one direction or the other, but it would be impossible to claim that the density of the universe is EXACTLY the critical value.
[/quote]

This depends on whether or not you agree with Inflation. Inflation assumes a value of exactly 1 for Omega. A universe that can, in principle, be finite. It is a matter of inflationary theory rather than experimental determination.

There is one thing that I feel I ought to add here, and that is that the Early Universe will be flatter than the Universe is now. If Omega was slightly less than 1 the Universe will have been flat at 3000K, but won't necessarily be flat now. In fact Hubble seems to indicate that the expansion of the Universe is speeding up. Hubble relates specifically to the modern era.

[palmera]

It is physically, mathematically, and logically impossible for the universe to be flat. Pardon the short response, but really.

[otseng]

I am very reluctant to accept singularities.

Could you give a little more detail on this? You do not accept that the Big Bang started from a singularity?

How can we be so sure to say that the universe is flat and its density has EXACTLY the critical value?

For Omega to be even close to 1 is on a verge of a miracle. Why would it even have to be close to 1? Furthermore, how do we know if it is exactly 1? Well, that is perhaps the key point of debate of this thread. And as I've presented from the Boomerang data, the evidence points to the fact that the universe is flat and Euclidean. So, evidence suggests that Omega is exactly 1.

Pictures of the early Universe

Scientists have produced the best evidence yet to show that the Universe is "flat".

This means the usual rules of Euclidean geometry taught in schools are observed in the cosmos: straight lines can be extended to infinity, the angles of a triangle add up to 180 degrees and the circumference of a circle is equal to 2pi times the radius, etc.

The precise geometry has been the subject of much debate since Albert Einstein suggested that the Universe might actually be "curved". Some cosmologists have championed spherical and even hyperbolic (saddle-like) models.

It's more a philosophical boundary than a really suitable possibility.

Only if your philosophical framework precludes it as a possibility.

The value of this boundary has to be exactly defined or measured. Mathematically, a fraction of 10E-100 or even less, would influence the final destiny of the universe!

Right, any deviation and most likely we wouldn't even be here to discuss its geometry.

Why should the universe possess an exact value that is only mathematically defined?

Because of its statistical improbability, this would be another indication of an intelligent designer.

Are we saying that beyond what we call an "edge" there is another universe? What would define if you are on one side or the other? Would the edge be part of this universe or the other?

I don't know what would be beyond the "edge". But I see no other possible conclusion if the universe has finite energy/matter and is flat. Is there any other topology that can fulfill these criteria?

The universe might be infinite only in one sense: it contains an infinite quantity of matter in an infinite dimension. An infinite quantity of matter in a finite dimension would give an infinite averaged density, and an infinite density would not match with an expanding universe.

I'm having difficulty grasping your meanings here of infinite quantity of matter. How could there be an infinite quantity of matter?

#1
the universe is "closed", ie homogeneous, with spherical curvature, unbounded, with finite matter, simply connected, and will reverse its expansion
#2
the universe is "open", ie homogeneous, with hyperbolic curvature, unbounded, with finite matter, non-simply connected, and will continue its expansion for ever

Let me ask this. What evidence do you have that the universe is non-Euclidean?

It is physically, mathematically, and logically impossible for the universe to be flat. Pardon the short response, but really.

I've already presented several articles that states that the universe is flat, so you'll have to present your counter-arguments to support your assertion.

[Ian Parker]

How can we be so sure to say that the universe is flat and its density has EXACTLY the critical value?

For Omega to be even close to 1 is on a verge of a miracle.

Why should the universe possess an exact value that is only mathematically defined?

Because of its statistical improbability, this would be another indication of an intelligent designer.

Flat is in fact shorthand for Omega=1. The angle between 3 geodesics does indeed = Pi, although the statement is a little bit meaningless because the Universe is expanding and light travels at a finite speed. As far as Omega = 1 being evidence for Intelligent Design is concerned most cosmologists take it to be evidence for Inflation. Inflation is self adjusting and Omega is 1. There is evidence for ID in terms of physical constants. If you have only one shot it shows the hand of God. The Hyperuniverse gives you a number of choices. This Universe in anthopic because nobody is looking at the other universes. This was why I raised it earlier.

Are we saying that beyond what we call an "edge" there is another universe? What would define if you are on one side or the other? Would the edge be part of this universe or the other?

I don't know what would be beyond the "edge". But I see no other possible conclusion if the universe has finite energy/matter and is flat. Is there any other topology that can fulfill these criteria?

The normal view of a Multiverse is that it is multidimensional. String Theory has 9 spatial dimensions. These are rolled up in our normal space. There are dualities in ST dimensions hence... To some extent it is a question od "Do you believe in String Theory?" Personally I have grave doubts.

I'm having difficulty grasping your meanings here of infinite quantity of matter. How could there be an infinite quantity of matter?

It can be infinite because it is receding. Olbers in fact applies to gravity as well as light.

[Alien]

Could you give a little more detail on this? You do not accept that the Big Bang started from a singularity?

The idea of a singularity disturbs my feeling about a simple and somehow homogeneous universe. Introducing a singularity is a sort of "giving up" and looks like "sorry, but I have no better ideas". A singularity implies infinite temperature, infinite density, time = zero... It introduces more problems than it solves. And, in addition, it looks like a totally static scenario, from which in no way we can explain how something started to happen and the singularity evolved from a totally static situation to a dynamic situation.

As far as I know, the singularity is the extreme mathematical behaviour of Relativity Theory equations. It's actually a mathematical singularity, and this does not mean that it was a physical singularity. Probably the model does not work very well in these extreme conditions.

However, the so-called Big Bang might have been originated in a way that does not imply any singularity. What about a previous universe that was collapsing and then, before reaching a singularity, just expanded again?

What I also don't like about this singularity is that it implies time = 0. Philosophically, stating that the universe had a beginnnig is a nonsense.

Because of its statistical improbability, this would be another indication of an intelligent designer.

Not necessarily. You are using the Anthropic Principle as an indication of ID. It's a reverse angle perspective.

If we assume that intelligent life can evolve only in a universe with Omega = 1 (exactly), then, just because we are here, we have the proof that Omega = 1. No need to rely on any ID.

We should not confuse "cause" with "aim".

1) The Earth is at the right distance from the Sun just to aim to human life (Subjcective induction, ID theory)

2) Human life is on Earth because the Earth is at the right distance from the Sun (Objective deduction, science)

Statement #1 implies that you see A->B in the sense that A is designed to B. This is a totally subjective induction and has no basis.

Statement #2 implies that you see A->B in the sense that B comes from A. This is a deduction that can be made objective by scientific analysis and observations.

Let me ask this. What evidence do you have that the universe is non-Euclidean?

None. I am saying that there is only a precise possibility that the universe is Euclidean, against other possibilities that cover a range, a whole spectrum of non-Euclidean universes.
Unless, as Ian says, Inflation is a sort of mechanism by which the average density of the universe is maintained constant and exactly equal to the critical value. But this would require a physical mechanism to explain this "stability" of the universe. I can't see it. Can you?

Flat is in fact shorthand for Omega=1. The angle between 3 geodesics does indeed = Pi, although the statement is a little bit meaningless because the Universe is expanding and light travels at a finite speed.

This is my point.
If Omega = exactly 1 then you have that your angle is exactly pi. But you know that pi cannot be exactly defined: it is an irrational number, incommensurable. How can you relate an exact value to an irrational number? In my view, Omega (as any physical parameter in the universe) cannot possess an exact value. Exact values simply do not exist in this universe. This would be 100% deterministic, and we do know our universe is not really deterministic.

[Ian Parker]

There are a number of points here. No it is not possible that the Universe is pulsating. Omega has been measured not to be >1. It might be possible to have a Universe that does not originate in a singularity, although most cosmologists are adamant that it did. The singularity was expanding with Omega=1 in that epoch so it was not a black hole. It would be possible to construct a compact (but finite) Universe, but this would find favor with few cosmologists.

As far as Design is concerned. The physical constants are evidence for Intelligent Design iff there is no Multiverse. The distance of the Earth from the Sun I am afraid is not because we simply pick a planet for Evolution that is. There are billions of planets and stars by the way.

As far as Pi is concerned the fact that you cannot express it as a fraction is neither here nor there, what is much more important is the expansion of the Universe, and the fact that Space itself is moving. This is important when we are considering Inflationary expansions that are faster than light.

[otseng]

I'm having difficulty grasping your meanings here of infinite quantity of matter. How could there be an infinite quantity of matter?

It can be infinite because it is receding. Olbers in fact applies to gravity as well as light.

Could you go into more detail on this also? I don't see how receding bodies can account for an infinite quantity of matter. Also, how does Olbers apply to gravity?

The idea of a singularity disturbs my feeling about a simple and somehow homogeneous universe. Introducing a singularity is a sort of "giving up" and looks like "sorry, but I have no better ideas".

I would not consider "disturbing your feelings" as sufficient grounds for scientifically rejecting something. Also, is "sorry, but I don't believe in singularities" any better than "sorry, I have no better ideas than singularities"?

What I also don't like about this singularity is that it implies time = 0. Philosophically, stating that the universe had a beginnnig is a nonsense.

Again, it seems like you are rejecting something purely based on your philosophical framework, rather than on any objective evidence.

Furthermore, even if the Big Bang did not start off as a singularity (perhaps it was a giant ball), it does not remove the fact that time must have had a beginning.

If we assume that intelligent life can evolve only in a universe with Omega = 1 (exactly), then, just because we are here, we have the proof that Omega = 1.

I'll defer discussions on AP to this thread.

Let me ask this. What evidence do you have that the universe is non-Euclidean?

None.

So, since there is evidence that the universe is Euclidean and there is no evidence that the universe is non-Euclidean, then the only logical conclusion is that the universe is Euclidean.

How can you relate an exact value to an irrational number?

I do not see your point here. Because pi is an irrational number, therefore the universe is not Euclidean?

In my view, Omega (as any physical parameter in the universe) cannot possess an exact value.

Why cannot Omega exactly equal 1? Again, it would appear that you only reject it on philosophical grounds.

[Ian Parker]

I'm having difficulty grasping your meanings here of infinite quantity of matter. How could there be an infinite quantity of matter?

It can be infinite because it is receding. Olbers in fact applies to gravity as well as light.

ding.
Could you go into more detail on this also? I don't see how receding bodies can account for an infinite quantity of matter. Also, how does Olbers apply to gravity?

In fact there may be a slight misunderstanding here what I should have said is that recession makes an infinite amount of matter possible not that it causes. Some people have asked whether we live in a black hole, or why a compact Universe was not a black hole. It was, and is not, a black hole because it is expanding. As I said before space itself is expanding.

How does Olbers apply to gravity. Let us look at the problem in a slightly different way. The General Relativity way is to move space. If you look at this in terms of the exchange of gravitation waves (quantum gravitodynamics) it is clear that as we move into regions of recession the gravitational effect is less.

How can you relate an exact value to an irrational number?

I do not see your point here. Because pi is an irrational number, therefore the universe is not Euclidean?

I used radians instead of degrees. Would that remark have arisen had I said 180 degrees?

[Alien]

I would not consider "disturbing your feelings" as sufficient grounds for scientifically rejecting something. Also, is "sorry, but I don't believe in singularities" any better than "sorry, I have no better ideas than singularities"?

You are right, but what I am saying is that a singularity is, if you like, "a very bad mathematical model that does not fit very well (or even contradicts) with our present scientific knowledge about the behaviour of physics". (Uhm, I have tried to give a definition that justifies my doubts about the "scientificity" of a singularity). However, many cosmologists don't like this Big Bang singularity. I come to the conclusion that it is not scientific. And this conclusion is based on the fact that Science does not deal with physical parameters that take the numerical value "infinite" ("infinite" is not a number! That's it.).

What I also don't like about this singularity is that it implies time = 0. Philosophically, stating that the universe had a beginnnig is a nonsense.

Again, it seems like you are rejecting something purely based on your philosophical framework, rather than on any objective evidence.

Furthermore, even if the Big Bang did not start off as a singularity (perhaps it was a giant ball), it does not remove the fact that time must have had a beginning.

My view is different.

However, this is a separate and probably huge topic: up to you the decision whether or not move it to a different thread.

My opinion is that we cannot define a time = 0. This opinion is not really an individual opinion, but it is based on the fact that philosophically a point t = 0 is a nonsense.
If you assume that time had a zero, you are contradicting yourself: you cannot define what was before this time = zero simply because, being time non-existing, the concept of "before" is a nonsense.
You can imagine something similar to t = 0, but this would be a mathematical asymptote. I mean, if you consider to go back in time, approaching the so-called "beginning", you can rewind the film of the universe going back as you like, asymptotically approach t = 0, but you will never reach the point. This is the same as saying that there was no t = 0 and no beginning.

I think this is a mathematical model that avoids any singularity and fits into our understanding of the universe history.

Unless, there was something before the Big Bang. In this case, time existed also before and my model is not necessary.

So, since there is evidence that the universe is Euclidean and there is no evidence that the universe is non-Euclidean, then the only logical conclusion is that the universe is Euclidean.

I see the picture as if there are no evidences for any option. But my options are not "Euclidean/non-Euclidean", they are "open/closed".

How can you relate an exact value to an irrational number?

I do not see your point here. Because pi is an irrational number, therefore the universe is not Euclidean?

I am not saying this: I am stopping before this conclusion "universe = non-Euclidean".

I took Ian's example to support a consideration from mine. This example sounds like "Being pi the ratio between a circle and its diameter, we see that its value changes if we consider a Euclidean geometry or a non-Euclidean geometry".
Then I say "In a Euclidean geometry, pi is an irrational and trascendental number, therefore incommensurable".
This means that a tiny deviation, as small as you like, surely unmeasurable and unquantifiable, in this pi value, changes totally your picture and the geometry becomes non-Euclidean.
My consideration is: how can we pretend to give an exact sense, an exact value, a "digital", discrete, definition (Euclidean/non-Euclidean) to something (geometry applied to the universe) that is mathematically an "analogue" quantity, a continuum that cannot even be measured (chaotic components)?
We should not apply discrete logic to mathematical analogue models (like Euclidean/non-Euclidean geometry). My conclusion is simply that this non-legitimate operation is misleading and we can never reach a precise measure of Omega = 1.
Therefore, not being able to define the discrete value "1", I would talk about the options Omega > 1 and Omega < 1.
If we divide a continuum in two parts, we should accept the fact that we can never exactly define a third part as a unique discrete entity, comparable with the other two. In order to do that (an absolute, precise measurement), you would need infinite resolution, and we all know that infinite resolution is impossible and therefore not viable.

To measure a parameter like Omega = 1 (or anyone else) with absolute precision, you would need to measure the exact quantity of all matter in the universe and its exact position, and the Heisenberg Principle does not allow you.

In my view, Omega (as any physical parameter in the universe) cannot possess an exact value.

Why cannot Omega exactly equal 1? Again, it would appear that you only reject it on philosophical grounds.

Please see above.
My considerations are both mathematical and pragmatic, they are not really philosophical.

[Ian Parker]

What I also don't like about this singularity is that it implies time = 0. Philosophically, stating that the universe had a beginnnig is a nonsense.

Again, it seems like you are rejecting something purely based on your philosophical framework, rather than on any objective evidence.

Furthermore, even if the Big Bang did not start off as a singularity (perhaps it was a giant ball), it does not remove the fact that time must have had a beginning.

My view is different.

However, this is a separate and probably huge topic: up to you the decision whether or not move it to a different thread.

My opinion is that we cannot define a time = 0. This opinion is not really an individual opinion, but it is based on the fact that philosophically a point t = 0 is a nonsense.
If you assume that time had a zero, you are contradicting yourself: you cannot define what was before this time = zero simply because, being time non-existing, the concept of "before" is a nonsense.
You can imagine something similar to t = 0, but this would be a mathematical asymptote. I mean, if you consider to go back in time, approaching the so-called "beginning", you can rewind the film of the universe going back as you like, asymptotically approach t = 0, but you will never reach the point. This is the same as saying that there was no t = 0 and no beginning.

.

The normal theory of the Universe postulates t=0. There really is no argument about that. It may, to some people, be philosophically difficult. But there it is. Are you proposing the Infinitely Old Multiverse? If we are going to be ripped apart in 20 billion years the rip has got a certain symmetry with the Big Bang about it. I had hoped that the Multiverse was what we would eventually come round to discussing.

t=0 also has another consequence, it means that we cannot propose the influence of aliens in our creation. Any aliens evolved in the same timeframe we have, so how did they originate?