The discussion centers on the concept of the universe's expansion, particularly how something infinite can expand. Participants clarify that expansion refers to the change in scale of space rather than a physical expansion into another space. Key concepts include the FLRW metric scale factor and the idea that any finite subset of an infinite space can increase in size over time. The conversation emphasizes that while distances may grow locally, the nature of infinity means there is no definitive "infinitieth" point in an infinite sequence.
PREREQUISITESAstronomers, physicists, mathematicians, and anyone interested in the theoretical implications of cosmic expansion and the nature of infinity.
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: