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?

[Alien]

I'm afraid I am going off-topic now...

The only way we can talk about the "beginning" is talking about the variable "time". This is because talking about the concept of "beginning" implies a sort of movement in the sense of variable "time". According to our present knowledge about physical laws, we can say that there are two possibilities which fit into these knowledges:

1. time always existed
2. time started at a point t = 0

You can build a scientific theory that fits with assumption #1 above, and you can also build a scientific theory that fits with assumption #2. I will show you that in my view, philosophically, if not scientifically, I see is no difference and this distinction becomes useless.

Look at assumption #1: for any point in time you select, you can always find another point in time that came "before" it. The concept of beginning is a philosophical nonsense because a beginning implies that something that did not exist before, exists now.

Look at assumption #2: if we visualize time as a cartesian axis, we could say that at the point t = 0 there is the origin of the axis. At the left, there is nothing. At the right, there is time. But, one moment, what are we saying? What does it mean "on the left" of time t = 0? It means "before". Everytime we look at the left of a certain t, we mean before time = t.
But, we are spinning! If on the left of time t = 0 means before time, it means that time did not exist yet... Therefore, how can we philosophically define a "before", which is an attribute that has a sense only if the object (time) is defined? How can we say there was something before time if "before" implies an extension along time, and time did not exist?

My conclusion: if we move backwards in time, we are never able to reach a "beginning". We move asymptotically towards a zero or we are just moving. It's the same!
We cannot reach a beginning in any case, even if we are moving according to assumption #1 or #2.
We cannot see any difference between the two assumptions.
There is no beginning of time, there is no beginning of space, matter and universe. We can move backwards towards the singularity, but we never reach it!

Please note that these considerations

- avoid the concept of "beginning"
- avoid any singularity
- are valid either you consider there was nothing before the Big Bang, or there was something

[Ian Parker]

My conclusion: if we move backwards in time, we are never able to reach a "beginning". We move asymptotically towards a zero or we are just moving. It's the same!
We cannot reach a beginning in any case, even if we are moving according to assumption #1 or #2.
We cannot see any difference between the two assumptions.
There is no beginning of time, there is no beginning of space, matter and universe. We can move backwards towards the singularity, but we never reach it!

Please note that these considerations

- avoid the concept of "beginning"
- avoid any singularity
- are valid either you consider there was nothing before the Big Bang, or there was something

If you postulate a "normal universe. It started at t=0. If you postualte a Muliverse it (at least in certain forms) is eternal. From the scientific stand-point what happened before the Big Bang is meaningless. Only t>0 has meaning. The first 3 minutes (Weinberg) are meaningful. What set off the Big Bang? Inflation??

I appreciate there is a difficulty from the point of view of creation of the Universe. Was it created? did it just arise in some way? I have said that (probably the really interesting question is the Multiverse. You see if we have one Universe the conclusion that God created it is indisputable. If we have a Multiverse this can have its constants dictated statistically. In some forms Evolution can take place. A Universe generated within another has some of the flavor of the present Universe.

What is our purpose in life? Darwin proposed that our purpose was to reproduce and have surviving offspring. Maybe our purpose is to build bigger and bigger accelerators to form other universes! Personally I regard this as rather far fetched. However it does illustrate the point that a Universe is inherently a one shot affair unlike Evolution where the unfit are weeded out. If a Universe is unfit that's it!

I suppose, if we base our ideas on String Theory, at some point we will have to say God created strings for the express purpose of creating an anthopic Multiverse.

[otseng]

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".

I'll stop on further debates on singularities in this thread since its not really relevant to the topic. We can perhaps pick it up in another thread.

My opinion is that we cannot define a time = 0.

Actually, I don't believe there really is much of a debate on this. But, I'll save this for a more relevant thread also.

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".

I have already presented evidence that the universe is Euclidean (flat, Omega is 1), so I fail to see how there is no evidence for this option.

I assume what you mean by closed is elliptical non-Euclidean and open is hyperbolic non-Euclidean. If there is no evidence for non-Euclidean at all, then even by splitting them into two does not give it more credence. Furthermore, you dismissed the third possibility, that of being Euclidean. So, given the three options of open/closed/flat, the only one that has any supporting evidence is the flat option.

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.

Oh, OK, I see now. But, though it might make it possible, I think it would be irrelevant to our discussions since it would have no effect with our observable universe. That is, if there is an infinite amount of matter out there that is receding faster than its gravitational effects (or any effects) on our universe, then we can pretty much say it is outside of our universe and outside of our discussions.

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.

I'm afraid you've completely lost me here.

[Alien]

I assume what you mean by closed is elliptical non-Euclidean and open is hyperbolic non-Euclidean. If there is no evidence for non-Euclidean at all, then even by splitting them into two does not give it more credence. Furthermore, you dismissed the third possibility, that of being Euclidean. So, given the three options of open/closed/flat, the only one that has any supporting evidence is the flat option.

My point is that we cannot divide the picture in three separate and equivalent options. The options that are each other equivalent are only two: closed or open. And there are many possibilities about how much could it be closed or how much could it be open. There is only a single possibility about the exact Omega = 1 value, and this possibility is a very specific numerical case, more theoretical and academic than real.

What you call evidence for Omega = 1 is a measurement that gives an Omega closer to 1 compared to previous measurements that indicated a lower value for Omega (more distant from 1). Nothing more, really.

The difference in our viewpoints is now becoming more general: it involves a general principle and we are disagreeing about the general principle.

Let me give you an example: the escape speed from Earth is defined as a borderline numerical value.
Objects that possess a speed > escape speed will never return to Earth; they possess a so-called hyperbolic excess of speed that allows them to still move away at a theoretical infinite distance from Earth; their trajectories are virtually infinite, all with hyperbolic paths.
Objects that possess a speed < escape speed will eventually come back and will never be able to go more far away than a certain maximum limit. Their trajectories are virtually infinite, all with elliptical paths.
In between there is a border situation that is only mathematical: Objects that moves exactly at the escape speed. These objects will reach the theoretical infinite distance from Earth with an excess of speed = zero! Their trajectory is parabolic.

What you are saying is that if we study an object moving away from Earth, by measuring its speed and position (its state variables) we can deduct that it is moving exactly at the escape speed and that the other two possibilities (escape/no escape) are BOTH excluded.

What I am saying is that if we study the object, by measuring its speed and position with a certain accuracy (never absolute), we can deduct that it is moving at a speed that is lower or higher than the theoretical escape speed. But the fact that our measurement is affected by errors, results in an inaccuracy about the open/closed path option, and a small variation in this inaccuracy results in a situation slightly above or slightly below the theoretical borderline. Only two options are significant, not three.

Your conclusion is that our measurement indicates that the object will have exactly zero speed at exactly infinite distance (which is a very academic or theoretical situation).
My conclusion is that our measurement indicates that the object is close to that situation, but we still don't know whether it is below or above (will it come back or not?).

What do you think about my example? If you agree that my example is a good analogy (as I think), then your conclusion must be the same as I have written. If you disagree that my example is a good analogy, then tell me please where is the difference in principle between the an expanding universe that can either expand for ever or revert back, and a flying object that can either escape from Earth of come back. Both cases are ruled by gravity.

In two words, we should use the signs "<" or ">", and never ">=" or "<=".

[Ian Parker]

What do you think about my example? If you agree that my example is a good analogy (as I think), then your conclusion must be the same as I have written. If you disagree that my example is a good analogy, then tell me please where is the difference in principle between the an expanding universe that can either expand for ever or revert back, and a flying object that can either escape from Earth of come back. Both cases are ruled by gravity.

In two words, we should use the signs "<" or ">", and never ">=" or "<=".

In fact for constant expansion you should say > or <=. I see the point you have come from. There might however be a mechanism (such as Inflation) that puts Omega as 1. In fact Hubble has shown an accelerating expansion (the acceleration having started some 8 billion years ago). 2.72K shows Omega=1.

[otseng]

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.

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.

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

[Ian Parker]

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.

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

The Universe is unbounded by the Cosmological Principle whatever the value of Omega. If Omega = 1 there is the possibility that the Universe is finite being wrapped round like the surface of a balloon.

[Curious]

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.

Sorry Otseng but I really have to correct you here. In the case of a satellite, the gravitational force is always equal to the centripetal force because the centripetal force is simply a description of the behaviour of the gravitational force. You would be more correct to say the centrifugal force but this itself is just a description of the satellites inertia (or "desire" to travel in a straight line). If the inertia of the satellite is greater than the gravitational force then the satellite will shoot off into space but it's centripetal force would still equal the gravitational force. If the centrifugal force was less than the gravitational force then the satellite would eventually crash into the planet but the centripetal force would still always remain the same as the gravitational force. I hope you don't mind the correction.

[otseng]

If Omega = 1 there is the possibility that the Universe is finite being wrapped round like the surface of a balloon.

If Omega = 1 (and the universe is Euclidean), how could any "wrapping" occur? Would not this violate Euclidean geometry?

You would be more correct to say the centrifugal force but this itself is just a description of the satellites inertia (or "desire" to travel in a straight line).

Thank you for the correction. It should be centrifugal force, not centripetal force.

[Ian Parker]

[quote="otseng"
If Omega = 1 (and the universe is Euclidean), how could any "wrapping" occur? Would not this violate Euclidean geometry?
[/quote]

Yes it would. General Relativity depends on having a metric which, in general, is non Euclidean. The Scwartzchild equation describes the metric around the Sun and also Black Holes. The prehilion of Mercury precesses which was the first experimental test for GR.

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. Such a wrapping would be a property of the metric. It is inconceivable that with Omega having any other value than 1 such a wrapping could take place.

Experimentally a Fourier Transform of 2.7K has been taken. This shows no sign of a wrap round visible to us. If there were the structures in 2.7K would be repeating giving a spike in the transform.