Universe - finite or infinite?

lionking

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lionking
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I'm currently reading a book about Poincare's Conjecture by Mathematics Professor Donal O'Shea.

Okay, I know the OP is a bit ingenuous because obviously nobody knows. BUT, O'Shea very early in the book states that it is highly unlikely that the universe is infinite because "space and matter are intimately related, and the assertion that the universe has an infinite amount of matter causes serious theoretical problems", and leaves it there.

What theoretical problrms arise which makes an infinite universe unlikely?

I have done a Google search with not much luck, so it is a serious question and I do not have any other agenda.
 
Having only a non-mathematical person's grasp of cosmology, I'll hazard that it would be related to the amount of matter necessary for the universe to collapse into a "big crunch".

Also, an "infinite" amount of mass could not have been the result of a "bang" event, as it would still have to be going on....
 
lionking said:
Okay, I know the OP is a bit ingenuous because obviously nobody knows. BUT, O'Shea very early in the book states that it is highly unlikely that the universe is infinite because "space and matter are intimately related, and the assertion that the universe has an infinite amount of matter causes serious theoretical problems", and leaves it there.

What theoretical problrms arise which makes an infinite universe unlikely?
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We can only see part of the universe because the speed of light is finite and the universe has only been transparent for a finite time (call it 14 billion years). As a result, everything we see today is or was within a sphere of about 14 billion lightyears in radius centered on the earth. So we can't ever know for sure whether the universe is finite or infinite.

That said, we have some models for the universe on large scales which are simple, arise from simple and elegant theoretical principles, and explain what we see. Those models make the assumption that the universe is homogeneous and isotropic on average (meaning every point and every direction is equivalent on average, and so the earth doesn't occupy any unusual or special location). If that assumption is correct, there are only three possibilities: the universe is finite and has positive curvature and the spatial geometry of a 3D spherical surface (a hypersphere), or it's infinite and has zero spatial curvature (a hyperplane), or it's infinite and has negative spatial curvature (a hyperhyperboloid).

The data might never distinguish between those for certain (again because we only see part of the space), but it is consistent with flat space. Since that's the simplest possibility - the other two have an extra parameter, their curvature - it's the one currently favored.

Are there problems with it? No, not really, except perhaps confusions that arise from having an infinite number of regions and therefore an infinite number of possible observations. But if we live in an (appropriately defined) typical region, those problems go away, and might even make the model more predictive.

Bikewer said:
Having only a non-mathematical person's grasp of cosmology, I'll hazard that it would be related to the amount of matter necessary for the universe to collapse into a "big crunch".

Also, an "infinite" amount of mass could not have been the result of a "bang" event, as it would still have to be going on....
Click to expand...

If the universe is infinite the big bang is still going on in a sense - that sense being that new parts of the singular hypersurface become "visible" every moment. But because the universe was opaque early on, that manifests itself simply as the arrival of more cosmic microwave background photons.
 
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sol invictus said:
We can only see part of the universe because the speed of light is finite and the universe has only been transparent for a finite time (call it 14 billion years). As a result, everything we see today is or was within a sphere of about 14 billion lightyears in radius centered on the earth. So we can't ever know for sure whether the universe is finite or infinite.
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Is it feasible something might have been outside that sphere 14by ago, but has since entered it?
 
Soapy Sam said:
Is it feasible something might have been outside that sphere 14by ago, but has since entered it?
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Completely, but we can't see those outermost parts as they are now of course.

(In fact, as a nitpick, the sphere isn't really 14 billion light years across. It's much bigger now, thanks to the universe having expanded. The first light year the light crossed way back then is now much bigger than one light year)
 
This is the inflationary event? I had thought that was earlier/ shorter- I mean in the first coffee break after god flipped the switch or something.
 
Soapy Sam said:
This is the inflationary event? I had thought that was earlier/ shorter- I mean in the first coffee break after god flipped the switch or something.
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No, just the general continuing expansion of the universe.
 
edd said:
Completely, but we can't see those outermost parts as they are now of course.

(In fact, as a nitpick, the sphere isn't really 14 billion light years across. It's much bigger now, thanks to the universe having expanded. The first light year the light crossed way back then is now much bigger than one light year)
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I'd say it like this: everything we see today in inside the past lightcone of the earth today. Visualize a spacetime cone opening down (i.e. back in time), with its apex on the earth now. The radius of that cone 14 billion years ago is 14 billion light years (that's really a definition of the radius, but it's a perfectly reasonable one). Any event that occurred inside that cone might be visible, any event outside it is certainly not.

What edd is saying is that stuff that was on the edge of that cone 14 billion years ago is now much further away from us than 14 billion light years, which is true (for example the light it emits now will take much more than another 14 billion years to reach us, if it ever does at all). But when that stuff emitted the light we are seeing today it was 14 billion light years away.
 
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While the Universe is over 180 billion light years in circumference, the continuing expansion of the Universe, as far as we know, is likely infinite.
 
When scientists look towards the beginning of the universe, which direction do they point their telescopes ?

What happens if they have to point the opposite direction - to the outer limits of the universe and look ahead as far as they look back, what do they see?
 
As Sol said, the universe is homogenous and isotropic, so it doesn't matter where the telescope is directed.

And welcome to the forum.
 
thinkerofmuchthought said:
When scientists look towards the beginning of the universe, which direction do they point their telescopes ?

What happens if they have to point the opposite direction - to the outer limits of the universe and look ahead as far as they look back, what do they see?
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Welcome, any where you point your telescope, although you have to be able detect the faint light, The CMB Cosmic Microwave Background it beleived to be from ~300,000 years into the big bang event.

http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation
 
Infinite, in space and time. And no, not talking about the visible universe as defined by the speed of c.
 
Dancing David said:
So how do you know the current universe is infinite in time?
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Zeuzzz doesn't need evidence, he just knows.

leon_heller said:
I think it was Einstein who first mentioned that the universe was finite but unbounded.
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Einstein found that in his theory it was possible for the universe to have finite volume (at any given time) but not have any edges, much like the surface of the earth. But he didn't know if that was in fact the case, and we still don't.
 
The Universe is both infinite and finite.

The Universe is both infinite and finite.

Don't think of it in 3d space. You cannot build a 3d model of the universe like you can a globe.

THink of it as 5D with the 4th dimension being time.

Does it sound like nonsense? Sorry about that. But it isn't.

The universe was created everywhere. There is no middle to the universe and there is no edge. But, yes, it is limited.

Consider this. If you travel on earth in a straight line will you ever reach the end of the earth? Of course not, you will loop back to where you began. Does that mean the earth's surface is infinite? No it is not. Well, yes and no. You can walk forever on it on a straight line. But the surface area is limited.

Space is like that but on a higher level of dimensions. If it were possible to go faster than light and if you traveled in any direction in a straight line, you would end up eventually back to where you started.

It is hard to grasp, I know, but it was once difficult for people to imagine that the world was round. Then it seemed impossible and difficult to think it was real.

Just as it is not possible to have an accurate flat map of a globe, it is not possible to have an accurate 3 dimensional map of space and the universe.
 
Zeuzzz said:
Due to the law of conservation of energy. And numerous cause and effect arguments.
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The law of conservation of energy does not (AFAIK) mean that the universe is infinite in time, i.e. has existed forever and will exist for ever. Can you give a source for this statement?

Can you give a list or citation to your "numerous cause and effect arguments"?
The physical facts (Hubble law, CMB, etc.) show that the observable universe had a beginning.
 
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