B How can the Universe grow if it is infinite?

[Sen Turner]

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?

 

[PeroK]

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.

 

[acidmatic]

"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...

 

[Comeback City]

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?

 

[weirdoguy]

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]

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.

 

[Daisyroots]

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.

 

[Comeback City]

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.

 

[phinds]

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

I also recommend the link in my signature

 

[Ken G]

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]

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?

 

[Daisyroots]

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]

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.

 

[Daisyroots]

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.

 

[Comeback City]

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]

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?

 

[Daisyroots]

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]

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.

 

[Daisyroots]

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. :)

 

[lifeonmercury]

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.

 

[Daisyroots]

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?

 

[Comeback City]

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]

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!

 

[PeroK]

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.

 

[Daisyroots]

What do you mean by it has to be specific? As in it has to be a defined number?
Good question. And very interesting: because I do indeed mean that it must consist in a particular quantity; but at the same time, as I think you point out, any specified number is an irrelevance.

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.

Lol... I can't argue with that, Comeback city.

 

[Comeback City]

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

That makes a lot of sense actually.

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

That is basically what I said (even though as you pointed out, is not the main idea of Hilbert's hotel). 1 + infinity = infinity

 

[Daisyroots]

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

Hi PeroK. It's nice to know somebody knows what infinity represents.

 

[PeroK]

That makes a lot of sense actually.

That is basically what I said (even though as you pointed out, is not the main idea of Hilbert's hotel). 1 + infinity = infinity

Infinity + 1 is undefined.

Infinity is not a number.

 

[Daisyroots]

Can we say then that finite can effectively be represented by '1' and infinite by 'not 1'? (Hope that doesn't sound too ridiculous!)

 

[PeroK]

Hi PeroK. It's nice to know somebody knows what infinity represents.

There are a few of us about!

 

[Comeback City]

Lol... I can't argue with that, Comeback city.

Why are you misquoting me now? Not sure where that middle part even came from

 

[Comeback City]

Infinity is not a number.

Yes, I know.

 

[Daisyroots]

Why are you misquoting me now? Not sure where that middle part even came from

Sorry, I'm not aware of having added or removed anything. I was just saying that I couldn't argue with your observation. Ignore me. :)

 

[Comeback City]

Sorry, I'm not aware of having added or removed anything. I was just saying that I couldn't argue with your observation. Ignore me. :)

Comeback City said: ↑
What do you mean by it has to be specific? As in it has to be a defined number?
Good question. And very interesting: because I do indeed mean that it must consist in a particular quantity; but at the same time, as I think you point out, any specified number is an irrelevance.

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.
----------------
That was the portion (in bold) I did not write. Was this your answer to the question?

 

[phinds]

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 recommend the link in my signature.

 

[russ_watters]

Ever hear of the balloon analogy?

I'm not following how the balloon analogy applies; I thought it was describing a finite yet boundless universe?

 

[phinds]

I'm not following how the balloon analogy applies; I thought it was describing a finite yet boundless universe?

The balloon analogy describes the expansion without regard to whether finite/infinite. It doesn't explain it in the sense of saying what dark energy is or whether the universe is finite/infinite. You can think of it as describing what goes on in the observable universe.

 

[Comeback City]

I'm not following how the balloon analogy applies; I thought it was describing a finite yet boundless universe?

Exactly what @phinds said above. It describes the distance between galaxies getting larger and larger, regardless of the universe being infinite or finite.

 

[Daisyroots]

Comeback City said: ↑
What do you mean by it has to be specific? As in it has to be a defined number?
Good question. And very interesting: because I do indeed mean that it must consist in a particular quantity; but at the same time, as I think you point out, any specified number is an irrelevance.

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.
----------------
That was the portion (in bold) I did not write. Was this your answer to the question?

Yes, Comeback, that was my answer to the question. Sorry. I obviously pressed something wrong. I'm not used to the system having only just joined the forum. It's lively chat!

 

[Comeback City]

Yes, Comeback, that was my answer to the question. Sorry. I obviously pressed something wrong. I'm not used to the system having only just joined the forum. It's lively chat!

No problem. And welcome to PF!

 

[Daisyroots]

I recommend the link in my signature.

Thanks for that. Very helpful.

 

[Ken G]

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.

We should be careful though, no scientist is claiming we have evidence either that the universe is infinite, or that it contains an infinite amount of matter. All we can responsibly say is we have no evidence that it is finite and no evidence the matter shows a boundary, so we can successfully apply an infinite model without encountering any problems. We should always recognize the crucial difference between the attributes of a successful model, and statements about what is, because the latter requires the assumption that the model will never need to be changed. Certainly the history of science has taught us not to do that, unless we have a strong urge to have future generations condescend to our naive notions! And even if humanity goes extinct without ever improving the model, that is still no guarantee that we simply had not the time or technology to take the next step.

 

[russ_watters]

The balloon analogy describes the expansion without regard to whether finite/infinite. It doesn't explain it in the sense of saying what dark energy is or whether the universe is finite/infinite. You can think of it as describing what goes on in the observable universe.

Exactly what @phinds said above. It describes the distance between galaxies getting larger and larger, regardless of the universe being infinite or finite.

Fair enough guys/whatever helps a layman, but can you explain how? I'm not seeing the connection made, so my admittedly layman brain immediately tries to visualize an infinitely large sphere, causing a stack overflow. I can't get past it.

To be a little more technical, I was under the impression that the rubber sheet and balloon analogies were mutually exclusive: that curved=finite and flat=infinite. Is that not the case/can the opposites be true? Indeed, I have always favored the balloon analogy, but I'm getting the perception that scientists are leaning toward flat/infinite, which would imo make the rubber sheet analogy superior.

Looking at marcus's thread, he doesn't list being able to describe an infinite universe as one of the features of the balloon analogy, but he does list "finite but boundless".

Also, the Insight article (which I admittedly hadn't looked at before...) seems problematic and maybe contradictory:

The analogy should ONLY consider a portion of the balloon’s surface — it does not make any statements about the size or shape of the universe (other than it is getting bigger). Forget that the surface of the balloon is curved. That’s NOT intended to be representative of the actual universe. It is actually more reasonable to think of a flat sheet of rubber that is being stretched equally in all directions. That would be a better analogy, but you’d have to confine the analogy to only a section of the sheet. Edges would NOT be part of the analogy. The analogy is not intended to comment in any way on the shape of the universe, whether it is open or closed, flat or curved, or ANY of those things. Those are NOT part of the analogy. The universe not only has no center, it has no edge, but that does not imply that it is necessarily infinite, it could be finite but unbounded (like the surface of the Earth, for example).

Much of that seems contradictory:
1. How can we see it as finite if we aren't supposed to visualize the whole balloon?
2. How is the curved shape not a part of it/differentiate it from the rubber sheet? If we're only supposed to think of the expanding balloon as a flat rubber sheet, why bother with it at all?

Heck, I have an easier time visualizing an infinitely large flat rubber sheet than I do an infinitely large balloon!

 

[phinds]

Russ, have you read my article on it? Link in my signature.

 

[Comeback City]

Fair enough guys/whatever helps a layman, but can you explain how? I'm not seeing the connection made, so my admittedly layman brain immediately tries to visualize an infinitely large sphere, causing a stack overflow. I can't get past it.

To be a little more technical, I was under the impression that the rubber sheet and balloon analogies were mutually exclusive: that curved=finite and flat=infinite. Is that not the case/can the opposites be true? Indeed, I have always favored the balloon analogy, but I'm getting the perception that scientists are leaning toward flat/infinite, which would imo make the rubber sheet analogy superior.

Looking at marcus's thread, he doesn't list being able to describe an infinite universe as one of the features of the balloon analogy, but he does list "finite but boundless".

Also, the Insight article (which I admittedly hadn't looked at before...) seems problematic and maybe contradictory:

Much of that seems contradictory:
1. How can we see it as finite if we aren't supposed to visualize the whole balloon?
2. How is the curved shape not a part of it/differentiate it from the rubber sheet? If we're only supposed to think of the expanding balloon as a flat rubber sheet, why bother with it at all?

Heck, I have an easier time visualizing an infinitely large flat rubber sheet than I do an infinitely large balloon!

Just keep in mind, this whole dark energy/ universal expanding concept came from the observation that galaxies were getting farther and farther away from each other. Yes, the rubber sheet model works just as fine of an analogy as does the balloon model. The whole point behind it, as phinds mentions in his insight, is that galaxies are getting farther apart from each other. Maybe you are overthinking it a little bit.

As for the shape of the universe, I agree with what Marcus wrote: you cannot count out a finite/curved universe. But if this were the case, the universe would have to be INCREDIBLY large so that the overall curve of spacetime is not noticeable to us (since most observations show our universe is mostly flat).

 

[russ_watters]

Russ, have you read my article on it? Link in my signature.

Unless I'm missing something, the link in your signature doesn't contain an article, it only contains a link to the Insight article you helped write (and other 3rd party articles) -- as I said (and quoted!), I read that article. Is there more content I'm missing?

 

[russ_watters]

Yes, the rubber sheet model works just as fine of an analogy as does the balloon model.

So you are saying the two analogies are equivalent?

The whole point behind it, as phinds mentions in his insight, is that galaxies are getting farther apart from each other.

There is definitely more to these analogies than just that galaxies are getting further apart.

Maybe you are overthinking it a little bit.

Maybe I am, but I asked a few specific questions - I'm really interested in hearing the answers:

As for the shape of the universe, I agree with what Marcus wrote: you cannot count out a finite/curved universe. But if this were the case, the universe would have to be INCREDIBLY large so that the overall curve of spacetime is not noticeable to us (since most observations show our universe is mostly flat).

So again; how do those different geometries relate to the analogies?

 

[Comeback City]

So you are saying the two analogies are equivalent?

There is definitely more to these analogies than just that galaxies are getting further apart.

Maybe I am, but I asked a few specific questions - I'm really interested in hearing the answers:

So again; how do those different geometries relate to the analogies?

Just to clarify: are you thinking of the two analogies in this way...
Balloon = curved/finite
Rubber Sheet = flat/infinite
?

 

[phinds]

Unless I'm missing something, the link in your signature doesn't contain an article, it only contains a link to the Insight article you helped write (and other 3rd party articles) -- as I said (and quoted!), I read that article. Is there more content I'm missing?

Sorry, I missed that you had read it. Yes, I meant the Insights article. If that doesn't explain to you how really simple the balloon analogy is, really, then I can't add anything. You seem to want to be taking the analogy to places it wasn't designed to go.