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?

[otseng]

As stated many times previous the Cosmological Principle states that the Universe looks the same from any position. Every observer is at the center of the Universe.

From our viewpoint, the universe appears homogeneous and isotropic. But, is that true for all other points in the universe? I would say it is only an assumption that it is true elsewhere.

The Cosmological Principle is the assumption that the universe is homogeneous (the same everywhere) and isotropic (the same in all directions) on large scales (it is obviously not correct on "small" scales, like that of the solar system or galaxies). It is an extension of the Copernican Principle which says that we are not in a special place at the center of the solar system, but just one of nine planets. The Cosmological Principle has not been proven or disproven, but it appears to be consistent with the parts of the universe that have been observed.

http://www.astro.washington.edu/bbeck/2 ... 61796.html

That is, the matter in the universe is homogeneous and isotropic when averaged over very large scales. This is called the Cosmological Principle. This assumption is being tested continuously as we actually observe the distribution of galaxies on ever larger scales.

http://map.gsfc.nasa.gov/m_uni/uni_101bb1.html

Our current Universe exhibits a wealth of nonlinear structures, but the zero-th order description of our Universe is based on the assumption that the Universe is homogeneous and isotropic smoothed over sufficiently large scales. This statement is usually referred to as the cosmological principle.

http://relativity.livingreviews.org/ope ... lesu1.html

cosmological principle - an assumption that the universe is everywhere uniform and looks the same in any direction---it is homogeneous and isotropic.

http://www.astronomynotes.com/glossary/glossc.htm

An assumption that says since Earth is no longer the center of our solar system, Earth has no unique place in our Universe, and that any theory that says otherwise must be flawed. This is a philosophical position (a fancy name for an assumption) taken without evidence.

http://www.allnewuniverse.com/glossary.html

[Alien]

What do you think about my example?

I think your example is a good one. In the case of a satellite and a planet, there are two forces acting on the bodies, the centripetal force (Fc) and the gravitational force (Fg). However, I would argue that there are three possible scenarios. When Fc > Fg, the distance between the satellite and the planet will increase over time. When Fc < Fg, the satellite will eventually crash into the planet. But, when Fc = Fg, the satellite will orbit the planet. So, even here we see that there are three distinct possibilities.

My analogy is focused more on the energy balance than on the forces.

In a gravitational field, an object possesses kinetic energy Ek = 1/2mv2 (depending on its speed) and potential energy Ep = Gm/r (depending on its geometrical position "r" in the field).

Then we have three possible theoretical cases:

- Ek > Ep
- Ek = Ep
- Ek < Ep

If we equalise Ek = Ep, we can find what is the exact value of the escape speed at that body position in the gravitational field.
For Ek < Ep, ie a lower speed, the body will not be able to escape, and the trajectory will be closed (ellyptical).
For Ek > Ep, ie a greater speed, the body trajectory will be open (hyperbolic)

But, my point is: even if we theoretically have three cases, in practice only two are meaningful, ie either Ek < Ep or Ek > Ep. The exact situation by which Ek = Ep can never exist, because it would require an infinitely precise value for Ek and an infinitely precise value for Ep, both depending on an infinitely precise value for the speed (affecting Ek) and an infinite value for the position (affecting Ep). And we know that according to the Heisenberg Principle speed and position cannot be both precisely defined.

Therefore, we can consider two separate and mutually exclusive situations, and not three. We can see that Ek ~ 78%Ep, or Ep ~ 34%Ek.
Our measurements can show that we these two situations are asymptotically approaching, for example we can see that we have Ek ~ 99%Ep or even Ek ~ 99.99%Ep.

In the same way we can see that Omega ~ 0.99 or even 0.9999, but we can never consider the border between them as a third situation in which Omega = 1.

In the same way, there are three possibilities for Omega. Omega < 1, Omega = 1, and Omega > 1. These three are mutually exclusive and distinct. It could be that Omega is close to 1, but this would mean that the universe is non-Euclidean. However, there is no evidence of this. So, the natural conclusion is that Omega is 1.

To throw more evidence that the universe is flat, the WMAP data shows that the universe is flat with only a 2% margin of error.

Therefore, the natural conclusion is that the universe has any value between Omega ~ 0.98 or Omega ~ 1.02. And this value cannot be infinitely precise.

BTW, I am still hoping to see an explanation from Ian about the physical mechanism by which the Inflation maintains Omega close to 1.
In other words, where is the negative feedback mechanism that maintains stable over time the value of Omega?

Let me ask this, if Omega is 1, would it be a logical conclusion then that the universe is bounded?

I don't think so. For the simple reason that Omega can be as close as you like to the value 1, but never exactly 1.

My understanding is that if Omega > 1 then the universe is closed, and if Omega < 1 then the universe is open. In the first case, there is no boundary because the curvature does not allow it. In the second case, the curvature is different and open. With an open universe, there might be a boundary if you consider a finite quantity of matter. An open universe with an infinite quantity of matter would possess no boundaries.

[Ian Parker]

BTW, I am still hoping to see an explanation from Ian about the physical mechanism by which the Inflation maintains Omega close to 1.
In other words, where is the negative feedback mechanism that maintains stable over time the value of Omega?

There is a feedback mechanism during the inflationary phase. Inflation in fact is one of the few things that actually travels faster than light (FTL) although only for an instant. Inflation can be viewed as a change of state in the vacuum. If the Universe were to be collapsing in on itself inflationary pressure would correct this. Similarly for the completely open Universe.

My understanding is that if Omega > 1 then the universe is closed, and if Omega < 1 then the universe is open. In the first case, there is no boundary because the curvature does not allow it. In the second case, the curvature is different and open. With an open universe, there might be a boundary if you consider a finite quantity of matter. An open universe with an infinite quantity of matter would possess no bondaries.

Not quite a logical explanation. The Universe if finite but unbounded iff the metric is such that you come back to the start if you (say) go to where the recession speed is say 0.9c go in the same direction to 0.9c ad infinitum and arrive back where you started. This is purely a though experiment as we are travelling FTL to the same point in time.

[otseng]

But, my point is: even if we theoretically have three cases, in practice only two are meaningful, ie either Ek < Ep or Ek > Ep. The exact situation by which Ek = Ep can never exist, because it would require an infinitely precise value for Ek and an infinitely precise value for Ep, both depending on an infinitely precise value for the speed (affecting Ek) and an infinite value for the position (affecting Ep).

Both Ek and Ep have distinct values. Whether we can or cannot determine the values with complete accuracy does not have any affect that they have those values.

Part of your argument appears to be that since we cannot "measure" the exact value of Omega, therefore it cannot have any exact value. Of course we could never be able to "measure" the value of Omega exactly. Furthermore, we can actually never be able to measure anything exactly either. But, things can still have a certain value, even if we cannot measure what that value is exactly.

In the case of Omega = 1, the main evidence that we have is that is the universe has been determined to be flat. It hasn't been measured to have any curvature at all . So, based on the evidence that we currently have available, it is logical to conclude that Omega = 1.

And we know that according to the Heisenberg Principle speed and position cannot be both precisely defined.

I think this is a misapplication of the Heisenberg Uncertainty Principle. HUP deals with particles on the atomic level, not on the macro level. Determining the speed and position of objects (above the atomic level) happens all the time and is not in violation of any law or principle.

In the same way we can see that Omega ~ 0.99 or even 0.9999, but we can never consider the border between them as a third situation in which Omega = 1.

Again, this is at odds with the empirical evidence that I have presented that shows that the universe is flat. Any deviation from Omega = 1 would be evidenced in that the universe is not flat. Your argument would be more persuasive if there was empirical evidence to support that the universe is either open or closed.

To throw more evidence that the universe is flat, the WMAP data shows that the universe is flat with only a 2% margin of error.

Therefore, the natural conclusion is that the universe has any value between Omega ~ 0.98 or Omega ~ 1.02. And this value cannot be infinitely precise.

No, it's not stating this. It only means that there is a 98% chance that the universe is flat.

Let me ask this, if Omega is 1, would it be a logical conclusion then that the universe is bounded?

I don't think so. For the simple reason that Omega can be as close as you like to the value 1, but never exactly 1.

Let me put it this way, if the universe is flat, then would it follow that the universe is bounded?

[Ian Parker]

Let me ask this, if Omega is 1, would it be a logical conclusion then that the universe is bounded?

I don't think so. For the simple reason that Omega can be as close as you like to the value 1, but never exactly 1.

Let me put it this way, if the universe is flat, then would it follow that the universe is bounded?

No not necessarily. I think we have been going round a little bit in circles. Here are some websites which provide the nice graphics that my postings lack.

Have a read for yourself for some current resources.

No Center
http://www.astro.ucla.edu/~wri ght/nocenter.html

Also see Ned Wright's Cosmology Tutorial
http://www.astro.ucla.edu/~wri ght/cosmolog.htm
http://www.astro.ucla.edu/~wri ght/cosmology_faq.html

WMAP: Foundations of the Big Bang theory
http://map.gsfc.nasa.gov/m_uni .html

WMAP: Tests of Big Bang Cosmology
http://map.gsfc.nasa.gov/m_uni /uni_101bbtest.html

I would like to repeat what I have said before., If the Universe hasn edge, the idea of looking back in time when viewing the distant Universe would be false 2.7 or 2.72...K would no longer represent the history of our corner of the Universe.

[Alien]

There is a feedback mechanism during the inflationary phase. Inflation in fact is one of the few things that actually travels faster than light (FTL) although only for an instant. Inflation can be viewed as a change of state in the vacuum. If the Universe were to be collapsing in on itself inflationary pressure would correct this. Similarly for the completely open Universe.

But now the inflationary phase is well finished. This would mean that the feedback mechanism is over.

In principle, the system can be stable, or may show a static instability or a limited dynamic instability. Therefore, we might have

a statically unstable diverging universe (an open or closed universe)
a statically stable universe (a flat universe)
a statically stable but dynamically unstable universe (an oscillating universe)

If the feedback mechanism is over, how can we see a stable behaviour?

My feeling is that we know too little about numerical values of the parameters in order to put the right category to the universe.

Not quite a logical explanation. The Universe if finite but unbounded iff the metric is such that you come back to the start if you (say) go to where the recession speed is say 0.9c go in the same direction to 0.9c ad infinitum and arrive back where you started. This is purely a though experiment as we are travelling FTL to the same point in time.

Is it not what I said? If Omega > 1 the universe is closed, finite and unbounded. It fulfills your thought experiment.

[Ian Parker]

But now the inflationary phase is well finished. This would mean that the feedback mechanism is over.

Yes but if Omega=1 Omega will always be 1.

If the feedback mechanism is over, how can we see a stable behaviour?

My feeling is that we know too little about numerical values of the parameters in order to put the right category to the universe.

Yes I agree we probably do. I would like to make a quasi political point here. The big money of NASA is going into the Shuttle (which keeps failing and is twice as expensive as expendable rockets) and the International Space Station, where astronauts do housekeeping and little else. The refurnishment mission for Hubble has been cancelled. 2.7K and Hubble provide us with the knowledge we have. Hubble gave the estimate of 13.7 billion years and is suggesting that the expansion of the Universe is speeding up.

How do you do the calculation. Basically what you have to do is to measure red shift and then measure distance by an independent method, such as Cephid variables, or simply size and brightness. Only Hubble can see stars in distant galaxies.

My gripe is that everything is going into useless manned space flight and Science is getting the crumbs.

Not quite a logical explanation. The Universe if finite but unbounded iff the metric is such that you come back to the start if you (say) go to where the recession speed is say 0.9c go in the same direction to 0.9c ad infinitum and arrive back where you started. This is purely a though experiment as we are travelling FTL to the same point in time.

Is it not what I said? If Omega > 1 the universe is closed, finite and unbounded. It fulfills your thought experiment.[/quote]

Even if the Omega=1 there are still choices for the precise metric.

[otseng]

I think we have been going round a little bit in circles.

I feel the same way too. But, I think we are gradually making some headway. As a sidenote, I find it interesting that I haven't been able to find any places elsewhere arguing much about this issue. So, we're sorta breaking new ground with this topic, and as such, we're bound to meander around while in uncharted territories.

No Center
http://www.astro.ucla.edu/~wright/nocenter.html

The page gives little reasoning behind its assertion. I still fail to see how any point is the same as any other.

If the universe is flat (and has always been flat), the Big Bang singularity should be traceable to a single point. I cannot see how it can be any other way if the universe is Euclidean.

If the Universe hasn edge, the idea of looking back in time when viewing the distant Universe would be false 2.7 or 2.72...K would no longer represent the history of our corner of the Universe.

I'll need to ask for more clarification on this. Why would "idea of looking back in time when viewing the distant Universe would be false"?

[Alien]

Both Ek and Ep have distinct values. Whether we can or cannot determine the values with complete accuracy does not have any affect that they have those values.

Part of your argument appears to be that since we cannot "measure" the exact value of Omega, therefore it cannot have any exact value. Of course we could never be able to "measure" the value of Omega exactly. Furthermore, we can actually never be able to measure anything exactly either. But, things can still have a certain value, even if we cannot measure what that value is exactly.

I have two arguments, not only one. We cannot measure any parameter with infinite precision and accuracy, and, in addition, there is no infinite precision and accuracy in any physical parameter.

All parameters change over time. The universe is dynamic. There are fluctuations in mass and energy at each level of magnitude. Now, at 10:45am my mass is ~75.4 kg, and after one hour it might be 75.3 kg.

How can we define exact values for the integral over the whole universe? I remember I have read somewhere that a variation of one single particle generated in a cubic kilometer each year would be sufficient to maintain the universe static as it was in the first Einsteins ideas.
This would mean that the borderline value Omega = 1 has a tremendous dependence on a very little quantity of matter variation over time, giving a huge parameter sensitivity (are there something like 10E80 particles in the whole universe? This would mean that Omega has a parameter sensitivity of 1 over 10E80 per year!).

In addition to that, cosmoligists say that the expansion rate of the universe has not been constant and (related phenomena) both densities of matter and dark energy are not constant. With the increasing of universe volume, its matter density decreases over time.

This would mean that there are second-order effects to be taken into account when computing Omega. Omega therefore cannot be strictly constant over time. Also, there are different theories about the Dark Energy density as function over time: someone says it increases, someone says it decreases...

The conclusion about this is that there are only two future scenarios. Also the NASA link that you provided

http://map.gsfc.nasa.gov/m_uni/uni_101fate.html

deals with two scenarios and not three.

To throw more evidence that the universe is flat, the WMAP data shows that the universe is flat with only a 2% margin of error.

Therefore, the natural conclusion is that the universe has any value between Omega ~ 0.98 or Omega ~ 1.02. And this value cannot be infinitely precise.

No, it's not stating this. It only means that there is a 98% chance that the universe is flat.

I don't think they mean this. The margin of error in a measurement is not the same as a chance.

A measurement is always affected by an error, and this error can be given in adimensional units referred to the units of the measurement itself, ie a percentage. Saying that a body weighs 50kg with a 2% error means that the uncertainty is +/-2% and the actual value lies in the range 49 to 51 kg.

This error is intrinsic into the measurement methodology.

If you then talk about a "chance", then I can say that a chance is a probability level, not an error.

But mathematically we cannot define the chance that an exact value is right: we cannot say Omega = 1 with 98% chance. We can define the chance that the right value lies in a defined range. For example, we could say that 0.99 < Omega < 1.01 with a 98% chance.
Or, that 0.999 < Omega < 1.001, or that 0.7 < Omega < 1.1. Any of these pictures would be unambiguous, but if you dont specify a range, then there is no information.

The only legitimate interpretation is therefore that 0.98 < Omega < 1.02 , and I think this is what NASA refer to in the link you provided.

Let me put it this way, if the universe is flat, then would it follow that the universe is bounded?

I have thought about this question. My conclusion is the following: mathematically, a flat universe is bounded if it contains a finite amount of matter and is unbounded if it contains an infinite amount of matter.

But I have difficulties with the concept of infinite. One of my difficulties is that this scenario implies both an infinite dimension of space (unbounded flat universe) and an infinite amount of matter. But, as we can test, there is a finite amount of density of matter. Because density of matter = (amount of matter)/(space) we would have that a finite quantity is defined as the ratio of two infinites. But we know from mathematics that the ratio infinite/infinte is an undetermined form.

The other difficulty is related to the evolution of the universe itself: how can we say that the universe was smaller than now if it is infinite? How can an infinite volume change its dimensions? Unless it is bounded, but how can you describe such a boundary? Perhaps we should consider the multiverses here...

[Ian Parker]

As a sidenote, I find it interesting that I haven't been able to find any places elsewhere arguing much about this issue. So, we're sorta breaking new ground with this topic, and as such, we're bound to meander around while in uncharted territories.

This is interesting. The way the discussion is going at this moment in time we have rather left the idea of "Debating Christianity" and are rather debating a purely scientific topic in a purely scientific way. Not quite, I have stressed that, unlike Evolution, the Universe is inherently "one shot" and intelligence in its constraction is true intelligence. I have put forward the idea of a hyperuniverse. Nobody has taken me up on it. Hence we my conclude that the Universe is basically theistic since :-

1 Gravitational coupling constant If larger: No stars less than 1.4
solar masses, hence short stellar life spans
If smaller: No stars more than 0.8 solar masses, hence no heavy element
production

2 Strong nuclear force coupling constant If larger: No hydrogen; nuclei
essential for life are unstable
If smaller: No elements other than hydrogen

3 Weak nuclear force coupling constant If larger: All hydrogen is
converted to helium in the big bang, hence too much heavy elements
If smaller: No helium produced from big bang, hence not enough heavy
elements

4 Electromagnetic coupling constant If larger: No chemical bonding;
elements more massive than boron are unstable to fission
If smaller: No chemical bonding

5 Ratio of protons to electrons formation If larger: Electromagnetism
dominates gravity preventing galaxy, star, and planet formation
If smaller: Electromagnetism dominates gravity preventing galaxy, star,
and planet formation

6 Ratio of electron to proton mass If larger: No chemical bonding
If smaller: No chemical bonding

7 Expansion rate of the universe If larger: No galaxy formation
If smaller: Universe collapses prior to star formation

8 Entropy level of universe If larger: No star condensation within the
proto-galaxies
If smaller: No proto-galaxy formation

9 Mass density of the universe If larger: Too much deuterium from big
bang, hence stars burn too rapidly
If smaller: No helium from big bang, hence not enough heavy elements

There were other points made, those related more to the Earth. They are not very good since all they prove is the rarity of Earth not its uniqueness.

If the Universe hasn edge, the idea of looking back in time when viewing the distant Universe would be false 2.7 or 2.72...K would no longer represent the history of our corner of the Universe.

I'll need to ask for more clarification on this. Why would "idea of looking back in time when viewing the distant Universe would be false"?[/quote]

Because the Universe is likely to be different at its edge from the center. For a start matter will aggregate more in the central regions of the Universe. The density will be different too.

One of the central arguments concerning the amount of matter in the Universe is the deuterium / lithium ratio. In the time when the temperature of the universe was similar to that of a thermonuclear explosion. Deuterium and lithium were being turned into Helium. Just like an H bomb. This is a sensitive test. It indicates that the contribution to Omega of protons and neutrons (familiar matter) is round about 0.04. Dark matter is 23% whilst the zero point energy, the energy of expansion is 73%. Indicated by COBE.

If the Universe had an edge stars would have different composition and would evolve differently. 2.7K refects the edge of the Universe. You would expect this to be less dense and aggregate less. We cannot therefore use 2.7K as an indication of aggregation of proto galaxies.

The Chinese are looking at 100 MYr (AUC). They want to look at aggregation and have assumed aggregation to be like our corner of the Universe.

One of the (eventual) tasks of LISA is to look at aggregation at an earlier stage than 2.7K. Oh Dear!

The other difficulty is related to the evolution of the universe itself: how can we say that the universe was smaller than now if it is infinite? How can an infinite volume change its dimensions? Unless it is bounded, but how can you describe such a boundary? Perhaps we should consider the multiverses here.

You have a finite bubble in an infinite Universe getting bigger and bigger, there is no contradiction there. I think the Multiverse should perhaps be considered but not for this reason.