Age versus Size of the Universe

[marcus]

My question: Does the cosmological principle imply that the universe is infinite?
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Wiki clearly states: "The cosmological principle implies that at a sufficiently large scale, the universe is homogeneous; different places will appear similar to one another."

Well then, in whichever direction and however far I travel, I will see more of the same. What’s the difference between that and infinity?

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Big difference!

It is the easiest thing in the world for a spatially finite universe to satisfy homogeneity. To make it simple imagine that space is one-dimensional, with one dimensional galaxies, and the 1D creatures find that if they travel long enough and far enough in one of the two possible directions they find themselves back where they started.
(They discover they live in a finite 1D space with "ring" geometry.)

And then think of the analogous thing in 2D. Space is 2D with 2D galaxies scattered about, and the 2D creatures discover (by exploring and measuring triangles and stuff) that they live in a finite "balloon surface" geometry.

You can't take geometry for granted, you can't assume it is standard Greek Euclidean, you have to find out empirically, by measuring, what the geometry you live in really is. Cosmology is the business of finding out the largescale geometry. Just like the 1D and 2D creatures had to do in the examples.

Now think of the analogous thing in 3D. Imagine space is 3D with 3D galaxies scattered about more or less homogeneously. And suppose we 3D creatures start measuring very large scale triangles to find if there is a very slight deviation from 180 degrees. If there is a consistent pattern of getting very slightly MORE than 180, this will indicate that we live in a finite 3D analog of the "balloon surface" geometry.

So far the measurements have not been conclusive but there are some recent measurements that lean in the direction of that kind of spatial finiteness.

Maybe you should click on the "balloon" link I keep in my signature, and watch the movie a few times. Think about the experience of being in one of those 2D galaxies you see in the movie, with the other galaxies receding from it. finite volume, but no boundary anywhere.

 

[Johninch]

Big difference!

It is the easiest thing in the world for a spatially finite universe to satisfy homogeneity...
Maybe you should click on the "balloon" link I keep in my signature

I did and I also read the rest of Ned Wright's tutorial. The animated sphere has a boundary, so it doesn't help.

You have to see that these pictorial illustrations are doomed to failure, because you can't draw a finite universe without boundaries. It's impossible - you may come to the edge of the paper or let the ink fade out, or draw anykind of complex geometrical shape but you can't demonstrate absence of a boundary with an illustration. And if it can't be shown on paper, this is an indication of the problem.

The oft repeated analogy of the balloon's surface is not translatable to 3D in my mind.

I also want to emphasize that I came off the idea of a crossable boundary some time back. I hope I made it clear that I am only imagining lack of galaxies and other observables from a vantage point within the universe. The problem of the word boundary is that it implies something on the other side and that is not what I mean.

In the meantime I have done more searching and have found a couple of very interesting threads in this forum on this very subject in 2006 and 2007. I have the impression that several posters treating the subject of BBT, expansion, finite/infinite universe, boundary, and so on from a logical point of view were not satisfied before those threads were locked.

I thank everybody for their efforts and I will for sure keep my eyes open for further insights into BBT. As far as I am concerned, the thread can be closed. "Locked" is so aggressive!

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[marcus]

I did and I also read the rest of Ned Wright's tutorial. The animated sphere has a boundary, so it doesn't help.
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The point of the animated sphere analogy is that it has no boundary. All existence is concentrated on the 2D edgeless surface. The 2D creatures living there cannot point their fingers in any direction that is not on the sphere.
There is no "inside" or "outside" to the sphere.
You have to concentrate in order to get the help from the analogy.

You as a 3D creature cannot point your finger in a 4th spatial direction. In fact we may live in a 3D analog of the 2D sphere. But so far we have no evidence of any "inside" or "outside" or any boundary. No more would 2D creatures living in a universe in which all of existence was concentrated on that animated sphere.

About locking this thread, I am not a moderator or mentor, so I don't decide about those things. Personally I see no reason to lock. If you are dissatisfied or bored you can always drop out. But at this point it's possible someone else might be reading and have questions or comments they want to make. I'm happy with the thread so I think I will hang around a while longer, and see.

Plus you might conceivably change your mind and want to discuss some more. Who knows?

 

[Naty1]

Johnich

...I came off the idea of a crossable boundary some time back... I am only imagining lack of galaxies and other observables from a vantage point within the universe...

Well one CAN imagine being able to look out waaaaaay beyond the current 46bly sphere from which we receive the most distant light. why not...if Einstein could imagine catching up to light we can imagine an 'empty' portion of the universe...

I think I already posted about the fact that each day we receive new CMBR...and it's like yesterdays. No surprises there. Each additional bit looks like the prior homogeneity with small fluctuations...

There may in fact be a 'lack of galaxies' out, say 100 times or 1,000 or 10,000 times further than we can observe today. Nobody can prove that one way or another. But then you should have some reason for such a hypothesis. I can't think of any, we have no such model, but such things don't make it impossible.

It's fun to speculate, to do thought experiments, and then see if they 'pan out' or not. Or whether you can even justify a thought one way or another. The great Richard Feynman noted something to the effect that 'a successful physicist succeeds by making just about every imaginable mistake before arriving at a correct solution.' [I don't mind being shown to be wrong here; I am used to it because my wife does it every day!]

 

[Mordred]

I don't think anyone has a wife that doesn'l lol. Trying to describe outside the universe is like trying to describe non existence. As many are pointing out.

 

[Naty1]

In my next life I'd like to be right all the time...like my wife in this life!

 

[Johninch]

Well one CAN imagine being able to look out waaaaaay beyond the current 46bly sphere from which we receive the most distant light. why not...if Einstein could imagine catching up to light we can imagine an 'empty' portion of the universe.

It is generally accepted that the universe probably extends far beyond the 46 bly observable portion. I do not imagine being able to “look beyond” it, as you suggested, because that is impossible by definition.

I imagine being physically beyond it in another observable portion.

I wasn’t aware that it’s possible to catch up to light – please explain how “Einstein imagined catching up to light”.

I also don’t know what you mean by “an empty portion of the universe”. Do you mean a bubble? A bubble as large as our observable portion would offend the cosmological principle and wouldn’t be compatible with the CMBR measurements as far as I know.

If you mean an empty portion adjacent to a boundary, I don’t think this makes sense. On the one hand it would be merely changing the shape, i.e. ‘drawing in’ the boundary. On the other hand I am doubtful that there could be an empty portion at all. As far as I know, in modern cosmological theory there is no such thing as empty space. Please explain how “we can imagine an empty portion of the universe”.

To repeat, and I hope that I don’t have to repeat this again, my thought experiment was standing at a point in the universe, a long way outside of our observable portion. I look at the sky with the best instruments possible. In a big portion of the sky, say half of it, there is nothing to be observed. I would conclude that there is nothing in that direction and that the universe does not extend any farther in that direction.

There may in fact be a 'lack of galaxies' out, say 100 times or 1,000 or 10,000 times further than we can observe today. Nobody can prove that one way or another. But then you should have some reason for such a hypothesis.

It is not a hypothesis, it’s a question related to the geometry of the universe and whether it can be infinite or not. Marcus has given me good feedback, which you applauded, and I need to digest it, as he suggested. At the moment I am still stuck on the idea of a finite universe with a size and I still don’t accept an infinite one.

Trying to describe outside the universe is like trying to describe non existence. As many are pointing out.

Mordred: I think it is silly to try to describe outside the universe and/ or non-existence. So please don’t attribute these ideas to me.

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[Naty1]

It is generally accepted that the universe probably extends far beyond the 46 bly observable portion. I do not imagine being able to “look beyond” it, as you suggested, because that is impossible by definition.

Ah, but you can in fact see further each time you look!

Next year you will be able to see 'one additional light year' distant...
That's not an actual number but an illustration...But you can do calculations
using the Jorrie on line calculator and figure out such things for yourself...in fact just read Marcus' posts...he has already done many illustrative calculations.

check out the last few pages here for examples:

Look 88 billion years into future and see cosmic event horizon shaping up
https://www.physicsforums.com/showthread.php?t=634757&page=3

please explain how “Einstein imagined catching up to light”.

This was supposedly a 'thought experiment' when Einstein was a teenager...from it, he began his later work on special relativity...refuting the then popular 'aether' theory and instead taking as a given that the speed of light is the same for all intertial observer frames.

 

[Mordred]

No problem just wanted to make sure that all the comments on outside observation were merely a thought experiment.

 

[Johninch]

Ah, but you can in fact see further each time you look!

HaHa! Better than your wife joke!

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[Naty1]

No joke.

You should READ the link so you understand.