# How do we know space is not infinite?

by zeffur7
Tags: infinite, space
 P: 38 How do we know space is not infinite? How can we be sure that the objects we see moving through space aren't just moving away from each other through space, rather than 'expanding space' as they change positions in outer space?
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P: 6,332
 Quote by zeffur7 How do we know space is not infinite? How can we be sure that the objects we see moving through space aren't just moving away from each other through space, rather than 'expanding space' as they change positions in outer space?
You have a fundamental misconception here if you think "moving away IN space" and "moving away due to space expanding" cannot be happening at the same time.

We do NOT know for sure that space is or is not infinite but we DO know that space is expanding. If I understand it correctly, all galaxies are moving IN space in random directions but their motion relative to each other (small) is totally dominated (NOW) by their apparent motion (LARGE) due to the expansion of space.

EDIT: if galaxies were NOT moving IN space in random directions, and in particular if they were all moving away from US (or from ANY single point) IN space, this would imply a point-position for the big bang and I don't think you'll find any support in science for that point of view.

FURTHER EDIT: Just in case you don't get another point, expanding space and infinite space are NOT in any way contradictory terms.
 P: 617 The observable universe is finite. The big bang happened about 14 billion years ago, so light from points in space that are 14 billion-light years away (actually 46 because of expansion) are just now reaching us and showing us the big bang. If we try to see farther than 46 billion light years away, we can't, because there is a wall of light caused by the big bang we are trying to see passed. The unobservable universe may be infinite, but we can't know because we can't see it. But even if we could, how can you prove something like "infinite". It would take an infinite amount of time to measure something infinitely large.
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P: 6,332
How do we know space is not infinite?

 Quote by chrisbaird The observable universe is finite. The big bang happened about 14 billion years ago, so light from points in space that are 14 billion-light years away (actually 93 because of expansion) are just now reaching us and showing us the big bang. If we try to see farther than 93 billion light years away, we can't, because there is a wall of light caused by the big bang we are trying to see passed. .
Zeffur, the "wall of light" mentioned here is best understood if you look up "surface of last scattering"
 P: 1 Just to be a bit more concise...yes, the Observable Universe is always finite, but also increasing every year. At present the Comoving Distance has a radius of about 47 billion light years, while the diameter is, of course, doubled to around 93 billion light years. We can't actually see objects 93 billion light years away in one direction.
P: 186
 Quote by zeffur7 How do we know space is not infinite?
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 Quote by Imax Cosmic microwave background radiation?
The CMB tells us absolutly nothing about whether the universe is infinite or not. What is it that makes you think it does?
P: 56
 Quote by phinds The CMB tells us absolutly nothing about whether the universe is infinite or not. What is it that makes you think it does?
but does infinite expand? i mean it's already infinite and it's getting bigger infinite?
 Sci Advisor PF Gold P: 9,445 Infinite is unbounded, so I fail to see your point.
P: 1,666
 Quote by zeffur7 How do we know space is not infinite?
I suspect it will turn out to be more like a paradigm shift. Doesn't that make more sense rather than the two options of finite or infinite especially when you consider how our views of the Universe have changed in history? Our understanding of Nature I'm optimistic will continue to improve, perhaps we'll replace General Relativity with something more broad, new discoveries will be made, and our views of the Universe will change once again. It may not be just more of the same like 2000 years ago when one considered walking along the "flat" earth. The spherical earth was a paradigm shift and resolved the paradox of "falling" off. Perhaps will will reach another in the future which may resolve our puzzle about the "size" of the Universe. That to me makes more sense than wondering if it's finite or infinite.
P: 534
 Quote by Rishavutkarsh but does infinite expand? i mean it's already infinite and it's getting bigger infinite?
Infinitely large can expand to still be...well...infinitely large. For example, the set of all natural number has the same "size" as the set of all even natural numbers. Check out the idea of cardinality of infinite set.
P: 534
 Quote by jackmell I suspect it will turn out to be more like a paradigm shift. Doesn't that make more sense rather than the two options of finite or infinite especially when you consider how our views of the Universe have changed in history? Our understanding of Nature I'm optimistic will continue to improve, perhaps we'll replace General Relativity with something more broad, new discoveries will be made, and our views of the Universe will change once again. It may not be just more of the same like 2000 years ago when one considered walking along the "flat" earth. The spherical earth was a paradigm shift and resolved the paradox of "falling" off. Perhaps will will reach another in the future which may resolve our puzzle about the "size" of the Universe. That to me makes more sense than wondering if it's finite or infinite.
It is possible that the universe is finite but with non-trivial topology.
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 Quote by Rishavutkarsh ... it's already infinite and it's getting bigger infinite?
exactly
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 Quote by phinds exactly
Bigger infinite?? Wouldn't that imply a bounded space?
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 Quote by Oldfart Bigger infinite?? Wouldn't that imply a bounded space?
Why would it imply a bounded space? Forget about the universe for now and read about Hilbert's Hotel.
P: 191
 Quote by yenchin Why would it imply a bounded space?
Well, it just seemed to me that if space was already infinite, it would be meaningless to consider that it was becoming infiniter. Anyway, thanks -- I read about Hilbert's Hotel, no joy. I evidently have a personel conceptual problem with infinity, possibly stemming from incorrectly thinking that if something increases, it increases from a defined point in space and time. and the amount of increase would be measured from that point.
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P: 6,332
 Quote by Oldfart Well, it just seemed to me that if space was already infinite, it would be meaningless to consider that it was becoming infiniter. Anyway, thanks -- I read about Hilbert's Hotel, no joy. I evidently have a personel conceptual problem with infinity, possibly stemming from incorrectly thinking that if something increases, it increases from a defined point in space and time. and the amount of increase would be measured from that point.
Yes, that is DEFINITELY a misconception when it comes to infinities. Do you have a problem with the following algebraic statement?

infinity + 1 = infinity

The thing represented by the word "infinity" is EXACTLY the same on both sides of the equation. If you can't get your head around this, then you will not get any further with the concept of infinity. This, by the way, is just an algebraic version of Hilbert's Hotel.
P: 191
 Quote by phinds Yes, that is DEFINITELY a misconception when it comes to infinities. Do you have a problem with the following algebraic statement? infinity + 1 = infinity The thing represented by the word "infinity" is EXACTLY the same on both sides of the equation. If you can't get your head around this, then you will not get any further with the concept of infinity. This, by the way, is just an algebraic version of Hilbert's Hotel.
Oh, I can get my head around that equation OK. The hard part is ascribing meaning to it. Like, what's the point? Can infinity be increased? Or is infinity plus 1 senseless?

My problem, not yours.,,

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