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

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- #1

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

- #2

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*(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).

- #3

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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.

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

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

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

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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.

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

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

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

- #8

Gold Member

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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.

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

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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).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.

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Also, Buzz Lightyear notwithstandingthe Lego Movie notwithstanding

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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/

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Mentor

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While it is possible that our universe is spatially finite, the meaning of "expanding" for the universe, and in particular the fact that it doesMaybe because it isn't infinite.

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That is irrelevant to the discussion at hand.Maybe because it isn't infinite.

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

EDIT: I see Peter beat me to it.

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Science Advisor

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

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

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No, it wouldn't. Not in any meaningful sense.Even if they expand by an extremely small rate, the "intfintieth" stake would be moving away, well, at infinite speed. Would it not?

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

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Yes, but finite will never be infiniteOk, thanks. I'm still thinking on it as pertains to uniform expansion of space, i.e. the further the distance, the faster the recession.

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

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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.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.

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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.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.

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

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Understood, but I don't think the original question is vastly different.No. Space could be finite and expanding but still not expanding "into" anything.

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Huh? They are about two radically different things. Finite and infinite.Understood, but I don't think the original question is vastly different.

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

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I was not referring to the expansion but to the size. Finite and infinite just can't be much different.So I don't see much difference between a finite or infinite universe expanding.

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

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

- #31

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

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