How could something that is infinite (the Universe) expand?

[alae]

how could something infinite expand?
expandig mean geating bigger but if its already infinite how could it get bigger

 

[ergospherical]

Expansion of space means a change in scale* of space, rather than the image you might have of "something expanding into something else".

*(you marked this thread as "A Level", in which case the relevant ideas are that of e.g. the FLRW metric scale factor, the expansion scalar, etc., but I don't think these will be helpful ideas for you right now).

 

[PeroK]

how could something infinite expand?
expandig mean geating bigger but if its already infinite how could it get bigger

Mathematically and physically "expand" might mean that any finite subset gets bigger over time. The "size" of an infinite space may not be not well-defined in any case.

 

[fresh_42]

*(you marked this thread as "A Level"...).

Corrected.

Imagine a potato chip of unlimited size, like a hyperbola. Now forget about the surrounding space, the chip alone is all we have.

 

[Ibix]

how could something infinite expand?
expandig mean geating bigger but if its already infinite how could it get bigger

Plant a row of stakes in the ground. If the stakes move apart, the ground is expanding - something you can detect locally whether there's an edge to the ground or it's infinite.

 

[ergospherical]

Plant a row of stakes in the ground. If the stakes move apart, the ground is expanding - something you can detect locally whether there's an edge to the ground or it's infinite.

Done! Can confirm that the ground is not expanding. However, the gardener looks pretty miffed.

 

[fresh_42]

Done! Can confirm that the ground is not expanding. However, the gardener looks pretty miffed.

You have to measure it at night after the last call. The expansion rate is $Pub(G)=\dfrac{\dot{a}(G)}{a(G)}$ where $a(G)$ denotes the amount of Guinness that you have had.

 

[timmdeeg]

how could something infinite expand?
expandig mean geating bigger but if its already infinite how could it get bigger

Infinite is not a large number which means you can't calculate with infinite as it would be a large number. E.g. 5 times infinite is still infinite. So if you watch an expanding infinite rubber band at a certain place you see locally that distances are growing while the rubber band is and stays infinite.

 

[Ibix]

Infinite is not a large number which means you can't calculate with infinite as it would be a large number. E.g. 5 times infinite is still infinite. So if you watch an expanding infinite rubber band at a certain place you see locally that distances are growing while the rubber band is and stays infinite.

This is an important point, OP. In my stakes in the ground example it's very easy to wonder what happens to the infinitieth stake, but you can't do that. Any stake you are thinking of is a finite numbered stake, and there are always infinitely many stakes beyond it. There is no "infinitieth" last stake in an infinite chain of stakes (the Lego Movie notwithstanding).

 

[phinds]

the Lego Movie notwithstanding

Also, Buzz Lightyear notwithstanding

 

[User2022]

how could something infinite expand?
expandig mean geating bigger but if its already infinite how could it get bigger

Maybe because it isn't infinite.

https://www.quantamagazine.org/what-shape-is-the-universe-closed-or-flat-20191104/

 

[PeterDonis]

Maybe because it isn't infinite.

While it is possible that our universe is spatially finite, the meaning of "expanding" for the universe, and in particular the fact that it does not mean expanding into some pre-existing surrounding space, is the same whether the universe turns out to be spatially finite or spatially infinite.

 

[phinds]

Maybe because it isn't infinite.

https://www.quantamagazine.org/what-shape-is-the-universe-closed-or-flat-20191104/

That is irrelevant to the discussion at hand.

EDIT: I see Peter beat me to it.

 

[martinbn]

Think of the universe being modeled mathematically by a pair $(M,h)$. The first part is the space, which can be the Euclidean three dimensional space, so it is infinite in the sense that you think it is. The second part is a Riemannian metric, which is something that tells you how to measure distances and angles. It need not be the Euclidean metric that you know from school geometry. It also can change with time. For example if it is $h$ now, and it becomes $3h$ in a billion years, then all distances have tripled in that time. In this sense the universe have expanded, three times in the example.

 

[valenumr]

Corrected.

Imagine a potato chip of unlimited size, like a hyperbola. Now forget about the surrounding space, the chip alone is all we have.


View attachment 297370

I've never seen a Pringle used as an example.

 

[valenumr]

This is an important point, OP. In my stakes in the ground example it's very easy to wonder what happens to the infinitieth stake, but you can't do that. Any stake you are thinking of is a finite numbered stake, and there are always infinitely many stakes beyond it. There is no "infinitieth" last stake in an infinite chain of stakes (the Lego Movie notwithstanding).

Even if they expand by an extremely small rate, the "intfintieth" stake would be moving away, well, at infinite speed. Would it not?

 

[PeroK]

Even if they expand by an extremely small rate, the "intfintieth" stake would be moving away, well, at infinite speed. Would it not?

No, it wouldn't. Not in any meaningful sense.

 

[valenumr]

No, it wouldn't. Not in any meaningful sense.

Ok, thanks. I'm still thinking on it as pertains to uniform expansion of space, i.e. the further the distance, the faster the recession.

 

[phinds]

Ok, thanks. I'm still thinking on it as pertains to uniform expansion of space, i.e. the further the distance, the faster the recession.

Yes, but finite will never be infinite

 

[Ibix]

Even if they expand by an extremely small rate, the "intfintieth" stake would be moving away, well, at infinite speed. Would it not?

There's no such thing as the infinitieth stake - that's the point. Any stake is a finite numbered one, with infinitely many stakes beyond it.

 

[valenumr]

There's no such thing as the infinitieth stake - that's the point. Any stake is a finite numbered one, with infinitely many stakes beyond it.

Well, I get that you can't pick one stake to be the "infinitieth", so perhaps talking about limits rather than discrete would be useful.

 

[valenumr]

Sorry, I'm off topic. I guess this is one of the many questions related to what space expands "into".

 

[Ibix]

Well, I get that you can't pick one stake to be the "infinitieth", so perhaps talking about limits rather than discrete would be useful.

You can talk about a stake arbitrarily far away from you, which is receding arbitrarily fast, yes. The next stake is receding faster and the recession rate grows without bound, yes.

 

[phinds]

Sorry, I'm off topic. I guess this is one of the many questions related to what space expands "into".

No. Space could be finite and expanding but still not expanding "into" anything.

 

[valenumr]

No. Space could be finite and expanding but still not expanding "into" anything.

Understood, but I don't think the original question is vastly different.

 

[phinds]

Understood, but I don't think the original question is vastly different.

Huh? They are about two radically different things. Finite and infinite.

 

[valenumr]

Huh? They are about two radically different things. Finite and infinite.

Well, I don't find it hard to conceive of an infinite universe. For example, one could conceive of an observer at the distant edge of our observable universe. Should they not see a similar observable universe of the same size? And that can be carried out ad infinitum in a single direction. So I don't see much difference between a finite or infinite universe expanding.

 

[phinds]

So I don't see much difference between a finite or infinite universe expanding.

I was not referring to the expansion but to the size. Finite and infinite just can't be much different.

 

[valenumr]

I was not referring to the expansion but to the size. Finite and infinite just can't be much different.

Fair point. But what I mean is that either way, the frequent question is, again, what does the universe expand "into". Infinite or not.

 

[Ibix]

Fair point. But what I mean is that either way, the frequent question is, again, what does the universe expand "into". Infinite or not.

I think that's best answered by pointing out the 4d nature of spaetime. "Space now" is a 3d slice through it. "Space a moment later" is a different 3d slice - so nothing is actually expanding. You're looking at different parts of spacetime with different scale factors.

 

[jbriggs444]

Even if they expand by an extremely small rate, the "intfintieth" stake would be moving away, well, at infinite speed. Would it not?

If a thing does not exist then it is meaningless to speculate on its properties. It cannot even be correctly referred to. The "infinitieth stake" falls into this category. It cannot properly be referred to.