## How can the universe be infinite?

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?
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 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.
 Recognitions: Gold Member Science Advisor Staff Emeritus 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.

## How can the universe be infinite?

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.
 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.

 Quote by 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.

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

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 Quote by Tanelorn 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_b...tml#Section8.2

See subsection 8.2.9.
 Ben, they mention spatial curvature several times but they dont spell out size of the universe. Maybe the two are connected?

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 Quote by Calimero Once infinite - always infinite.
This definitely isn't a theorem of differential geometry. Is it really a theorem of GR?

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 Quote by Tanelorn Ben, they mention spatial curvature several times but they dont 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.

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 Quote by Calimero 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.
 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 ;-) )

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 Quote by 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.
This is incorrect. There is no edge.
 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.

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 Quote by 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.
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/p...DavisSciAm.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.

 Quote by bcrowell ("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?

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