How can the universe be infinite?

[steveclay]

Hi. Went to a lecture by Brian Greene a few days ago. He started his talk by discussing the logical consequences of the universe being infinite. But I'm really puzzled: the universe has been expanding at various rates - all finite even when very large - for a finite length of time (13.7 billion years) so how can the sum of {finite rates} * (finite time = 13.7 billion years) be infinite? Perhaps an infinite number of big bangs? Anyone got any information or ideas about this?

 

[Calimero]

Hi steveclay. You almost answered your question yourself. Once infinite - always infinite. We really don't know size of the universe, but we precisely know size of our observable patch. So, if you sometimes hear things like 'universe once was size of an atom' it can only refer to the size of observable universe, because nobody knows size of the whole thing, neither now, neither at the time of Big Bang.

 

[bcrowell]

Basically I agree with what Calimero said, with one reservation. We can, in principle, find out whether the universe is finite or infinite. The CMB data can tell is that -- in principle. In reality, the data happen to straddle the line between finite and infinite, but that could change tomorrow.

 

[Calimero]

Yes, but only if we detect spatial curvature. I think that things will not go that way, it will always look flat, with possibility of curvature being hidden between error bars, but that is just my guess.

 

[Farahday]

If existence is the result of cause and effect and had a beginning in time, then unless it inflated at an infinite rate or for an infinite time, it would necessarily be finite.

Only something that exists can change - act or be acted upon. This means cause and effect is a FUNCTION OF the phenomenon of existence. No phenomenon can be the result of its own subordinate derivative, so the reverse can't be true. Existence (the cosmos) didn't "begin", hence it need not be finite.

 

[Tanelorn]

Basically I agree with what Calimero said, with one reservation. We can, in principle, find out whether the universe is finite or infinite. The CMB data can tell is that -- in principle. In reality, the data happen to straddle the line between finite and infinite, but that could change tomorrow.

Ben, Can you please enlarge greatly on this? How can CMB help is determine the size of the rest of the universe?

 

[bcrowell]

Ben, Can you please enlarge greatly on this? How can CMB help is determine the size of the rest of the universe?

http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.2

See subsection 8.2.9.

 

[Tanelorn]

Ben, they mention spatial curvature several times but they don't spell out size of the universe. Maybe the two are connected?

 

[Hurkyl]

Once infinite - always infinite.

This definitely isn't a theorem of differential geometry. Is it really a theorem of GR?

 

[bcrowell]

Ben, they mention spatial curvature several times but they don't spell out size of the universe. Maybe the two are connected?

("They" is me :-) Yes. The sign of the curvature determines whether the universe is finite or infinite.

Once infinite - always infinite.

This definitely isn't a theorem of differential geometry. Is it really a theorem of GR?

It's certainly a feature of all the common families of cosmological models. I believe that the only assumptions that go into those models are homogeneity, isotropy, and some kind of equation of state for the matter fields. I think this leads to the Friedmann equations, and then the only difference bewteen, e.g., an FRW solution and a ΛCDM model is the equation of state that you plug into the Friedmann equations.

As far as I can imagine, converting an infinite universe into a finite one or vice-versa would mean that cosmological redshifts would go to zero or infinity at some point in time. The only way that the Friedmann equations could make that happen would be if there was a singularity in the scale function a(t), but that would be a Big Bang or Big Crunch singularity. Since the singularity isn't a point on the manifold, I don't think GR allows you to connect a spatially finite spacetime onto a spatially infinite one by gluing at the singularity.

[EDIT] Deleted incorrect idea about definition of manifold.

 

[ejushol]

Hi. Not taking parallel universes into consideration, surely finite? At the 'edge' of the universe in any direction you will have your last piece of matter within a galaxy. Beyond this just photons that have been emitted/travelled for 13.7 billion (or at least from the point where photons were possible). As photons have no mass, these will travel in a straight line with the absence of gravity.

There are some interesting theories (recent horizon programme) on what is reality in the first place. If they are correct, it may be possible we are all holograms emitted from the edge of the universe. Something to do with our higher dimension universe being emitted from a 2 dimensional source (the opposite way around from our 3d structure being converted in a black hole as 2d information. Need to watch it again ;-) )

 

[bcrowell]

Hi. Not taking parallel universes into consideration, surely finite? At the 'edge' of the universe in any direction you will have your last piece of matter within a galaxy. Beyond this just photons that have been emitted/travelled for 13.7 billion (or at least from the point where photons were possible). As photons have no mass, these will travel in a straight line with the absence of gravity.

This is incorrect. There is no edge.

 

[ejushol]

For something that was finite and thence had an 'edge', this exponentially expanding universe must still have an 'edge', or an end. It is not infinite.

 

[bcrowell]

For something that was finite and thence had an 'edge', this exponentially expanding universe must still have an 'edge', or an end. It is not infinite.

Cosmological models that are spatially finite don't have an edge.

Here is a good article to get you started on cosmology: http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

A book that I recommend to a lot of people is Relativity Simply Explained, by Gardner. It's somewhat out of date, but other than that it's a great, accessible intro.

 

[Tanelorn]

("They" is me :-) Yes. The sign of the curvature determines whether the universe is finite or infinite.

Ben, my sincere apologies for not seeing you as the author, a very impresssive piece of work, and also thankyou for sharing it with us. I know I am in the right place to ask questions now, hopefully the right ones!

So is the sign such that you can see the universe is finite, and if so, do you gain a perspective on just how much larger than the obervable universe the rest is?

 

[bcrowell]

So is the sign such that you can see the universe is finite, and if so, do you gain a perspective on just how much larger than the obervable universe the rest is?

Current measurements of the spatial curvature are consistent with zero.

-Ben

 

[Tanelorn]

Ben, wouldn't this be the least expected result in that from the standard model we expect more and more of the universe to be luminously disconnected from us over time? Meaning the rest of the universe is much bigger than the observable universe?

 

[steveclay]

Ben - thank you very much indeed for the link to the Scientific American article, I get it now in a way I never have before. So thanks very much. Now - to try your other link- the one to your own article - which looks like it might be a bit harder ... I will try... :)
Cheers
Steve

 

[andrewkirk]

I don't want to take this thread off topic, so please let me know if my question does so and I'll start a new thread.

I've been wondering whether there is any physical reason why there could not be an infinite amount of matter in the universe. Earlier posts in this thread talk about whether the universe might be closed or open. I suppose (maybe wrongly) that if it is closed then there is a finite amount of space so it couldn't contain an infinite amount of matter. But if it is open then I presume there's an infinite amount of space so an infinite amount of matter is possible without requiring infinite density.

But are there any reasons why there could not be an infinite amount of matter? For example I was wondering about a gravitational version of Olbers' Paradox. If there was an infinite amount of matter, even though distributed through an infinite spacetime manifold, would the gravitational forces be infinite everywhere and thereby make complex organisms impossible?

Or does inflation save us from this by making us only affected by gravitational forces from of bodies within the event horizon (if that's the right term) of our local patch of space?

 

[bcrowell]

I've been wondering whether there is any physical reason why there could not be an infinite amount of matter in the universe. Earlier posts in this thread talk about whether the universe might be closed or open. I suppose (maybe wrongly) that if it is closed then there is a finite amount of space so it couldn't contain an infinite amount of matter. But if it is open then I presume there's an infinite amount of space so an infinite amount of matter is possible without requiring infinite density.

It's not just that it could have an infinite amount of matter, it would have to have an infinite amount of matter. Cosmological solutions are homogeneous, so you have a constant density. A constant density in an infinite volume is definitely an infinite amount of matter,

But are there any reasons why there could not be an infinite amount of matter? For example I was wondering about a gravitational version of Olbers' Paradox. If there was an infinite amount of matter, even though distributed through an infinite spacetime manifold, would the gravitational forces be infinite everywhere and thereby make complex organisms impossible?

GR doesn't describe gravity as a force. By the equivalence principle, a gravitational force or field can always have any value you like at any point in spacetime, including zero for a free-falling observer. For example, our solar system is free-falling.

You could worry about whether infinite amounts of matter would create infinite curvature, but they don't. Open cosmological solutions have finite curvature.

Although Newtonian concepts don't really apply to cosmology, it may be helpful to realize that in Newtonian physics, tidal forces would have to be zero by symmetry in a homogeneous and isotropic universe.

 

[andrewkirk]

Thank you for satisfying my curiosity.
I find these questions absolutely fascinating.

 

[1dominator1]

For something that was finite and thence had an 'edge', this exponentially expanding universe must still have an 'edge', or an end. It is not infinite.

Unless space is in a spherical formation (much like a 2d surface on the inside of a paper ball, except with 3 dimensions instead of 2).

 

[StateOfTheEqn]

As I understand the current consensus model, all observers see themselves as the center of a Euclidean (flat) 3-ball with the fireball as near the outer boundary. The outer boundary is the big bang 'singularity' which would make it a 2-sphere. Behind (or outside) the 2-sphere big bang 'singularity' is the multi-verse possibly containing other fireball universes.

When people talk about the universe being infinite, I take that to mean the multi-verse but it is sometimes difficult to know exactly what is meant.

 

[bcrowell]

As I understand the current consensus model, all observers see themselves as the center of a Euclidean (flat) 3-ball with the fireball as near the outer boundary. The outer boundary is the big bang 'singularity' which would make it a 2-sphere. Behind (or outside) the 2-sphere big bang 'singularity' is the multi-verse possibly containing other fireball universes.

When people talk about the universe being infinite, I take that to mean the multi-verse but it is sometimes difficult to know exactly what is meant.

No, this is all incorrect. There is no boundary that has any special physical characteristics. The part about the multiverse is completely wrong.