Is the Universe Infinite or Finite? I was having that debate with a friend of mine today. My position was that it is finite because it is expanding. My logic was that the fact that is expanding indicates that it must be finite, because how could something be infinite and getting bigger?

His position was that it was infinite though he couldn't really explain why he thought that. (to give you some context, he also believes his daily horoscope offers him meaningful guidance and that aliens built the pyramids).

You may have guessed by now that neither one of us are physicists, so to settle the argument, I proposed that we contact an expert.

Confident of my correctness, I suggested to my buddy that we should have friend of this here site @seanmcarroll (the brilliant physicist and author of "From Eternity to Here") give us an answer.

I tweeted at Sean the subject line of this thread and he was kind enough to tweet me back in a matter of minutes. He said:

"Nobody knows. Sometimes that's the answer."

He then tweeted

"There may not even be an answer. de Sitter space (e.g.) can be finite or infinite depending on how you slice it."

So not wanting to badger Sean with follow up questions, I ask you: If we know the Universe is continually expanding (which to me suggests that it has a finite size that is increasing), how can it be labeled as anything other than finite?

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I think it could be either. Since the universe was "created" and is expanding, it is finite. BUT, since the universe created itself and can keep expanding forever, could it possibly be infinite while being finite? Wow, this is making me think... I'll have to come back to this discussion after I figure out if that is even possible. What do you guys think? Can something be infinite while also being finite?

I wouldn't say the universe was created, which implies a creator. I would use the word "happened," which is far less committal. 

"Forever" implies some sort of process which is ongoing. While it's easy to slip into the view that time is some sort of stream with an existence of its own, like a river, it is really more the opposite, isn't it? Time is created by things happening. There was no time in this universe before it began. It's not like a cosmic clock was ticking, waiting for The Big Bang. Once things started happening, time began. When things stop happening, when a state of absolute entropy happens, there will be no more time. But there will be no one to perceive time long before then.

BTW, on Wonders of the Solar System, the physicist/cosmologist Brian Cox said that the end of the universe, absolute entropy, was unimaginably far off. How many years off? He said that if we assigned every atom in the entire cosmos to a year, we'd run out of atoms long before we ran out of years. 

That's a good point. The universe did "happen", I was just implying that the universe had "created" itself. I'll correct myself on that, though.

And that is also true. If you think about it, time doesn't really exist. Time was created by us to give a specific event a certain place in history. Time before the Big Bang is kind of like the expression, "If a tree falls in a forest and nobody is around to hear it, was there a sound?" Since there was no one there to witness it, time wasn't a factor. That's the closest I could get to describing it.

That's really cool! I have never seen that but I'll be sure to check it out. It's amazing to think that the universe has that long before entropy happens.

Thanks for the response!

An amusing demonstration here. We have words like infinity and in fact some definitions of the term and three kinds of mathematical infinity. Yet when we try to use the terms we have to use other language to say why the consequences of the words are wrong. Even explaining the issue requires an analogy.

To wit, evolution. Essentially all discussions of it are in terms of competing for resources or "evolving" characteristics for some advantage or other. All of these imply there is some kind of goal or objective. But as soon as someone runs with that idea we have to stop them and use other terms to explain there is no objective or purpose.

Yeah, animism (or some would say agency) is a pretty powerful metaphor. It's often easier to explain the behavior of inanimate things as if they had a will of their own. I think that may be how human concepts of gods and spirits started, way back before we even had words for them. (Is that what you're talking about?)

Speaking of evolution and universe(s), some people might be interested in conjecture about

CNS, Cosmological Natural Selection (fecund universes)

I think that may be how human concepts of gods and spirits started, way back before we even had words for them. (Is that what you're talking about?)

Yes more or less. Until people realized and then mainly only scientists realized that nature did not work in terms of the motivation of living things there was really only one way to look at things. But even if they tried, nature works in so many different ways that are not obviously connected that not figuring out the non-animate nature is more than understandable.

My favorite example is Newton. Falling objects, gravity, those were not his "discoveries". Galileo had done that. His discovery was universal gravitation. Poetically said, as on earth so also in heaven. For the first time the domain of "god" the heavens was shown to be no different from earth. All that old "heavenly realm" and crap was not meant to be poetic. It was not metaphor. It was intended as a literal and correct distinction between down here and up there.

My second favorite example is living water but I haven't figured out how to make that as clear but moving water was living water which was different from non-moving water. River v swamp. Drinkable and necessary against disease.

It seems to have a beginning and a measurable age, so it's most likely not infinite. Given the proper technology, we could even visit the edge.

All we know is that the "local space" (ie. known universe) appears to be expanding.

The funny thing about the expanding universe is that it is just the space that's expanding. Physical objects in space are not expanding. You and I and our refrigerators are not expanding along with the universe, other than in the sense we are along for the ride.

Partly in answer to @Matt "The semantics do not work. The physics cannot work. What kind of an answer can a physicist give?"

The way I've understood a closed (finite), expanding universe includes a couple of concepts.

1) Wherever one travels to in the universe, it will always seem like that place traveled to (and traveled from, and all places in between) is the "center" of the universe. In that sense, it's easier to accept the idea that no matter where you travel in the universe, you'll never get closer to any kind of "edge" of the universe.

2) The universe only seems to be expanding from our point of view, and is not actually "expanding" into some space that's "outside" of the universe. Perhaps an easier way to describe this more succinctly is that "distances between everything is increasing". This concept makes more sense if you realize it in the context of the first concept (above).

An interesting (but only slightly) relevant outcome, is that the longer one waits before taking a trip through the universe, the farther one will have to travel (and the longer it will take) to get there. This is might seem irrelevant, but it helps me conceptualize time at the speed of light, since photons experience no aging, even if they travel for billions of years. (Hmm, but I think a light wave will lengthen, over time. Damn, it almost seems like light itself acts as a spring to cause expansion? Ok, beer might fix this confusion.)

If I think about it I may find more appropriate but let me start with this.

We all know the idea of an infinite number of integers, as in 1, 2, 3 ... infinity, there is always one more.

Now let us take the number space between 0 and 1. I can always assign a unique number between 0 and 1 for every number in the child's game of infinity plus one.

For every integer between 0 and infinity I can assign a unique number between 0 and 1. You probably never thought about that but it is not so hard to get your head around the idea. It is simply infinite extent compared to infinitely divisible.

Now here is where the mind blows. For every two, three, four or N-dimensional point in space I can assign a number between 0 and 1.

But lets back up. Every point on a 1 by 1 square can be assigned a unique number between 0 and 1 even though every point on the square can be equally divided into an infinite number of numbers. The same is true for a 1x1x1 cube and for a 1x1x1x1 hypercube and for a cube with an infinite number of dimensions as a 1x1x1...x1 to infinity. To infinity there is a unique point on a number line from 0 to 1.

Get your head around that idea.

The number line of integers is the 0th order of infinity. The unique points between 0 and 1 is the 1st order of infinity. If I were better at this I could give examples and explain why transcendental number which have an infinite number of terms constitute the 2nd order of infinity. 

Now, when asking about anything infinite what is the meaning of infinite you are using? I have an infinity between 0 and 1 which can assign a unique number to every point the the four dimensional universe as it exists today and for all the billions and trillions of years we currently project for its infinite future.

Now that was weird. But let us ignore WHEN the big bang occurred and ask where it occurred.

I know where it occurred. Without time to separate events it happened EVERY PLACE. It happened in every sub-atomic particle that makes up your body, my body and the farthest star.

There is no joke about time is what prevents everything from happening at once. If we ignore time the where is here, EVERY here. So my 0th order infinity is not the 0th order but the infinitesimal point of the big bang is on this scale the -1st order infinity. Every point in space that was there at the beginning is what we live in. It is what we exist in every day.

So what is a finite universe? As it "finiteness" is as a minimum defined by the first photons after bang time and where they are there is NO WAY to ever physically catch up with them. If we cannot catch up and look we cannot know. That is what KNOW means. Talking about "EDGE" instead of furthest extent that we cannot get to is semantics.

But if we ignore time then we ARE the furthest extent. And if we are the furthest extent then all of this talk is nonsense. Just as the point of origin of the universe is every place without time, with time we are its greatest extent.

To assume otherwise says time exists before the expanding universe gets there. It is saying that at the time of the bang today existed and 100 billion years from now existed at bang time.


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