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 said:
Corrected.ergospherical 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.alae said:
Done! Can confirm that the ground is not expanding. However, the gardener looks pretty miffed.Ibix said:
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.ergospherical said:Done! Can confirm that the ground is not expanding. However, the gardener looks pretty miffed.
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.alae 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).timmdeeg said:
Also, Buzz Lightyear notwithstandingIbix said:
alae said:
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.User2022 said:
That is irrelevant to the discussion at hand.User2022 said:
I've never seen a Pringle used as an example.fresh_42 said:
Even if they expand by an extremely small rate, the "intfintieth" stake would be moving away, well, at infinite speed. Would it not?Ibix said:
No, it wouldn't. Not in any meaningful sense.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.PeroK said:
Yes, but finite will never be infinitevalenumr 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.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.Ibix said:
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 said:
No. Space could be finite and expanding but still not expanding "into" anything.valenumr said:
Understood, but I don't think the original question is vastly different.phinds said:
Huh? They are about two radically different things. Finite and infinite.valenumr 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.phinds said:
I was not referring to the expansion but to the size. Finite and infinite just can't be much different.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.phinds said:
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 said:
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.valenumr said:
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.
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.
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.
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.
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.