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

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• alae
In summary: Even if they expand by an extremely small rate, the "intfintieth" stake would be moving away, well, at infinite speed. Would... would the infinitieth stake eventually catch up to the rest of the stakes?
alae
how could something infinite expand?
expandig mean geating bigger but if its already infinite how could it get bigger

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).

vanhees71 and alae
alae said:
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.

alae
ergospherical said:
*(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.

Last edited:
alae said:
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.

Lnewqban and ergospherical
Ibix said:
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.

vanhees71 and Ibix
ergospherical said:
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.

vanhees71, phinds, sysprog and 1 other person
alae said:
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, sysprog and Lnewqban
timmdeeg said:
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).

timmdeeg and sysprog
Ibix said:
the Lego Movie notwithstanding
Also, Buzz Lightyear notwithstanding

User2022 said:
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.

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.

Klystron and ergospherical
fresh_42 said:
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.

Ibix said:
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?

weirdoguy and PeroK
valenumr said:
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.

PeroK said:
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.

valenumr said:
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

valenumr said:
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.

PeroK
Ibix said:
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.

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

valenumr said:
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.

valenumr
valenumr said:
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.

phinds said:
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.

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

phinds said:
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.

valenumr said:
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.

phinds said:
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.

valenumr said:
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.

valenumr
valenumr said:
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.

## 1. How do we know that the Universe is expanding?

Scientists have observed that the light from distant galaxies appears to be shifted towards the red end of the spectrum, indicating that they are moving away from us. This phenomenon, known as redshift, is consistent with the expansion of the Universe and is one of the key pieces of evidence for the expanding Universe theory.

## 2. What is the Universe expanding into?

The Universe is not expanding into anything. It is often described as infinite and unbounded, meaning that there is no edge or boundary to the Universe. Instead, the expansion of the Universe is the expansion of space itself.

## 3. How can something that is infinite expand?

The Universe is infinite in the sense that it has no boundaries, but it is not infinite in terms of its size and contents. The expansion of the Universe refers to the increase in the distance between galaxies and other objects, not the increase in the size of the Universe itself.

## 4. Will the expansion of the Universe ever stop?

It is currently believed that the expansion of the Universe will continue indefinitely. However, the rate of expansion may change over time due to the influence of dark matter and dark energy. It is possible that the expansion may slow down or even reverse in the distant future, but this is still a topic of ongoing research and debate.

## 5. How does the expansion of the Universe affect us?

The expansion of the Universe has several consequences for us. It explains the observed redshift of distant galaxies, it affects the large-scale structure of the Universe, and it also plays a role in the evolution of galaxies and the formation of new stars. Additionally, the expansion of the Universe may have implications for the ultimate fate of the Universe and our place within it.

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