# How can the Universe grow if it is infinite?

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Our general understanding of the universe is that it is infinite, so how can it be growing? If the universe is everything then what is it growing into?

MantleMan

## Answers and Replies

PeroK
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Our general understanding of the universe is that it is infinite, so how can it be growing? If the universe is everything then what is it growing into?

"Growing" or "expanding" can also mean simply that the distances between points is getting larger with time.

If you know a little mathematics, you could imagine an infinite plane (the x-y plane, say) and a mapping that expands the distance between any two points over time. The x-y plane is simply mapped to itself by this process. There is no outside to grow into and no outside is needed.

FactChecker, fresh_42, acidmatic and 1 other person
"Growing" or "expanding" can also mean simply that the distances between points is getting larger with time.

If you know a little mathematics, you could imagine an infinite plane (the x-y plane, say) and a mapping that expands the distance between any two points over time. The x-y plane is simply mapped to itself by this process. There is no outside to grow into and no outside is needed.
As far as we are able to realize for the moment... Who knows...

Our general understanding of the universe is that it is infinite, so how can it be growing? If the universe is everything then what is it growing into?
Ever hear of the balloon analogy?

acidmatic
As far as we are able to realize for the moment... Who knows...

That we don't need any 'outside' (mathematicaly) is a fact.

Ken G
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That yours is a common question can be seen if you look at the similar thread "Infinite vs. Expanding" just above yours, and the answers there.

I'd suggest, Sen, that the question you put forward here may strictly belong more to philosophy than to physics. It arises because the finite (i.e. 'us'; at least in how we observe and think of ourselves) can have no realistic comprehension of 'infinite'. I.e. we can only possible think in terms of limitation. Thus since we have no prospect of defining (at least) one of the terms of the question, it is rendered meaningless. Sorry, I don't mean to be a killjoy.

I'd suggest, Sen, that the question you put forward here may strictly belong more to philosophy than to physics. It arises because the finite (i.e. 'us'; at least in how we observe and think of ourselves) can have no realistic comprehension of 'infinite'. I.e. we can only possible think in terms of limitation. Thus since we have no prospect of defining (at least) one of the terms of the question, it is rendered meaningless. Sorry, I don't mean to be a killjoy.
Sen is not asking about how it's infinite (or how to comprehend it), but rather how something infinite can expand. This can be explained easily through the balloon analogy, as long as one does not begin to think that the universe is on a curved 2 dimensional plane, such as the balloon.

Sen Turner and Daisyroots
phinds
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@Sen Turner , google "Hilbert Hotel". "growing" and "infinite" are fully compatible.

I also recommend the link in my signature

Ken G
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Personally, I think the problem stems from taking our concepts, like "finite" and "infinite", too literally. They are both merely tools for understanding, with their various benefits and limitations. They are both mathematical notions, attributes of models. I'd say they are more like templates we hold up to our observations to make sense of them, so the question "but how can it really be like that" is always answerable by "of course it's not actually like that, but this is a useful way to think about it, our best current model." That holds just as much for a finite model as an infinite one. If we had detected positive curvature, and modeled the entire universe as a finite sphere with no boundaries, wouldn't people ask "how can a finite universe expand, what is it expanding into if it is already everything?" So it goes. Any "how can it really be" question is like that, they can be used to stimulate new thinking, but they never actually have an answer.

phinds
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I'd suggest, Sen, that the question you put forward here may strictly belong more to philosophy than to physics. It arises because the finite (i.e. 'us'; at least in how we observe and think of ourselves) can have no realistic comprehension of 'infinite'. I.e. we can only possible think in terms of limitation. Thus since we have no prospect of defining (at least) one of the terms of the question, it is rendered meaningless. Sorry, I don't mean to be a killjoy.
Not true at all. His question is very clear and has a definite answer. Google "Hilbert Hotel"

Daisyroots
Not true at all. His question is very clear and has a definite answer. Google "Hilbert Hotel"
Hi Phinds

I looked at 'Hilbert's Hotel' as you suggested and I see that the idea uses as its basis a never ending series of numbers, extending, then, naturally, into infinity. But the question that occurs to me is, is a uni-directional 'infinity' plausible? I.e. can you have a viable idea of infinity that possesses, yet, a start point?

Sen is not asking about how it's infinite (or how to comprehend it), but rather how something infinite can expand. This can be explained easily through the balloon analogy, as long as one does not begin to think that the universe is on a curved 2 dimensional plane, such as the balloon.
But if in the course of inflating my 'balloon' the one-way air valve should fail, where does all the 'universe' end up then? Presumably in the same 'space' it was in the process of 'moving into' anyway(?).

phinds
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Hi Phinds

I looked at 'Hilbert's Hotel' as you suggested and I see that the idea uses as its basis a never ending series of numbers, extending, then, naturally, into infinity. But the question that occurs to me is, is a uni-directional 'infinity' plausible? I.e. can you have a viable idea of infinity that
possesses, yet, a start point?
What "start point" ? If the universe is infinite it has always been infinite and there is no starting point to the growth other than infinite. If it is not infinite now, then it did not start out infinite.

What "start point" ? If the universe is infinite it has always been infinite and there is no starting point to the growth other than infinite. If it is not infinite now, then it did not start out infinite.
Well, I was just pointing to what looks like a hole in Hilbert's 'hotel' idea. The 'hotel' has rooms of infinite numerical extension, but the numerical series starts at room #1. Therefore the particular variety of 'infinity' indicated is unidirectional. I agree with you that a unidirectional infinity is a nonsense. It's what I meant.

But if in the course of inflating my 'balloon' the one-way air valve should fail, where does all the 'universe' end up then? Presumably in the same 'space' it was in the process of 'moving into' anyway(?).
There's no one on the other side actually pumping their carbon dioxide breath into a latex sheet. The balloon analogy is simply an analogy. And just as much as the balloon analogy is an analogy, the universe is still expanding. It isn't "failing".

phinds
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Well, I was just pointing to what looks like a hole in Hilbert's 'hotel' idea. The 'hotel' has rooms of infinite numerical extension, but the numerical series starts at room #1. Therefore the particular variety of 'infinity' indicated is unidirectional. I agree with you that a unidirectional infinity is a nonsense. It's what I meant.
I just don't follow you at all. The choice of which of the existing infinite number of rooms to choose to call "1" can be arbitrary so you are setting up a strawman to knock down. How would YOU label the elements of an infinite set that has the same cardinality (Aleph null) as the integers?

There's no one on the other side actually pumping their carbon dioxide breath into a latex sheet. The balloon analogy is simply an analogy. And just as much as the balloon analogy is an analogy, the universe is still expanding. It isn't "failing".
Thanks, Comeback city, I appreciate that it's an analogy. It's just that it's an analogy that doesn't (for me anyway) explain the 'pressure' that must surely be requisite for expansion whether or not there's a 'balloon'.

phinds
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Thanks, Comeback city, I appreciate that it's an analogy. It's just that it's an analogy that doesn't (for me anyway) explain the 'pressure' that must surely be requisite for expansion whether or not there's a 'balloon'.
It's not supposed to. It describes the expansion rather than explains it. No on knows what dark energy is, so you're hardly alone in that.

Comeback City
I just don't follow you at all. The choice of which of the existing infinite number of rooms to choose to call "1" can be arbitrary so you are setting up a strawman to knock down. How would YOU label the elements of an infinite set that has the same cardinality (Aleph null) as the integers?
Hmmm... I see we are running into difficulty. The way I'm viewing it is from the perspective of an ongoing numerical count. I can see that the 'count' has the potential to go on forever, but at any point in time it is necessarily (as I see it) specific. So, as you rightly point out, the name of any of them is of course an irrelevance, but Hilbert is effectively forever adding 1 to infinity. The fact is, I think, 'infinity' is an un-graspable concept. Thanks for your effort with me. :)

stoomart
So basically the prevailing view is that the universe has an infinite amount of space AND an infinite amount of matter that is fairly evenly distributed throughout the universe. I think the infinite matter aspect is often not emphasized strongly enough. This should help dispel the misconception among laymen of infinite space but with all the matter concentrated in a region of the universe and expanding outward into the empty space surrounding it.

Sen Turner
It's not supposed to. It describes the expansion rather than explains it. No on knows what dark energy is, so you're hardly alone in that.
But does it 'describe the expansion'? The thread question was 'How can the universe grow if it's infinite?' In your view (I ask genuinely) has our little conversation around the question moved us on at all, as yet?

I can see that the 'count' has the potential to go on forever, but at any point in time it is necessarily (as I see it) specific.
What do you mean by it has to be specific? As in it has to be a defined number?
but Hilbert is effectively forever adding 1 to infinity.
If my understanding is correct, then the whole point of Hilbert's hotel is to show that adding one to infinity still gives you infinity.

PeroK
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Hmmm... I see we are running into difficulty. The way I'm viewing it is from the perspective of an ongoing numerical count. I can see that the 'count' has the potential to go on forever, but at any point in time it is necessarily (as I see it) specific. So, as you rightly point out, the name of any of them is of course an irrelevance, but Hilbert is effectively forever adding 1 to infinity. The fact is, I think, 'infinity' is an un-graspable concept. Thanks for your effort with me. :)

Well, "finite" is a simple enough concept. And "infinite" means "not finite". And that's about all there is to it!

stoomart
PeroK
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What do you mean by it has to be specific? As in it has to be a defined number?

If my understanding is correct, then the whole point of Hilbert's hotel is to show that adding one to infinity still gives you infinity.

Not at all. The point of Hilbert's hotel is to show that an infinite set can be mapped one-to-one to a proper subset of itself. This can't be done for a finite set.

Infinity is not a number and hence cannot be subjected to a numerical operation such as addition.