# How do we know space is not infinite?

by zeffur7
Tags: infinite, space
 PF Patron P: 4,966 [QUOTE=Tanelorn;3524331] ... I think that the observable universe is small compared to the whole universe because the CMBR is so flat in every direction implying homogeneity.QUOTE] I too think I now get what Chris is saying (and agree w/ him that it is unlikely), but I do NOT get the statement above. Why does homogeneity limit his suggestion in any way, or suggest that the U is much bigger than the OU ?
 P: 694 Phinds, ever since reading Penrose's estimate that the observable universe is just ~10-31 the size of the whole universe, I have been trying to build a mental picture of such a system. It is pretty funny to think that the entire observable universe is an insignificant part of the whole universe.
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P: 4,966
 Quote by Tanelorn Phinds, ever since reading Penrose's estimate that the observable universe is just ~10-31 the size of the whole universe, I have been trying to build a mental picture of such a system. It is pretty funny to think that the entire observable universe is an insignificant part of the whole universe.
Seems quite reasonable to me, but of course the estimates vary all over the place and we don't really KNOW so it gets to be a somewhat theological (i.e. non-falsifiable) discussion.

I'm still interested in hearing your answer to my question of why you think the CMB homogeniaty implies anything about the size of the U beyond the OU.
P: 38
 Quote by vrmuth then please give me the initial conditions to formulate the differential equations, then i will tell you the max and min
In other words, it would be finite. :)
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P: 10,394
 Quote by zeffur7 In other words, it would be finite. :)
Only if the initial conditions were finite. There is no known way to tell currently.
P: 694
 Quote by phinds I'm still interested in hearing your answer to my question of why you think the CMB homogeniaty implies anything about the size of the U beyond the OU.
I am saying that matter homogeneity on large scales of the Observable Universe itself, and the flatness of the CMBR suggests to me, and I believe many others, that the OU is small in size compared to the complete Universe. I think I said this already and I cant think of any better wording!
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 Quote by Tanelorn I am saying that matter homogeneity on large scales of the Observable Universe itself, and the flatness of the CMBR suggests to me, and I believe many others, that the OU is small in size compared to the complete Universe. I think I said this already and I cant think of any better wording!
Thanks. Actually, I worded my question very poorly. What was confusing me was actually the statement
 If the universe has an edge and we are relatively near it, then eventually we would see no more CMBR in that direction because it had all passed us by.
but I think I get it now.
 P: 694 ok glad to help. Lots of if and buts there and a cynic might say that it still needs to be proved. The only truth that counts is the one that can be scientifically proved.
P: 59
 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.
Careful...that is not technically correct. I don't know why I always get into Set Theory here on the Cosmology section, but it seems to come up a lot.

Infinity, in and of itself, is not a number. There are finite numbers (ordinals), and transfinite ordinals. There are finite sets, and infinite sets.

The first transfinite ordinal is omega "w"...which can be considered the next larger number after ALL the Natural numbers. It is the order type of the Set of all numbers preceding it, which is the Set of Natural numbers.

In accordance with Cantor's ordinal arithmetic, w + 1 = w is NOT true. w + 1 is the next ordinal which succeeds w. On the other hand 1 + w = w IS true.

So, a well ordered listing of ordinals that include the Naturals and extend to the first three transfinite ordinals would be: { 0, 1, 2, 3,..., w, w+1, w+2 }
P: 65
 Quote by zeffur7 We also know that that expansion is accelerating.
Have we measured that acceleration ? so that we are also able to calculate its(the acceleration) rate of change, huh?
P: 617
 Quote by vrmuth Have we measured that acceleration ? so that we are also able to calculate its(the acceleration) rate of change, huh?
Yes, several times. The first time was in 1998 as reported here. Several years ago I attended a lecture by a member of this group, Dr. Kirshner, on these results and the presentation was amazing.
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 Quote by vrmuth Have we measured that acceleration ? so that we are also able to calculate its(the acceleration) rate of change, huh?
Do you have some reason for thinking that we have not? The tone of your post seems to imply that. As Chris said, we have.
 P: 186 Maybe space-time’s a compact Lorentzian manifold
P: 65
 Quote by Constantin To measure a diameter you need to be on the edge of the Universe (or any circle or sphere) and that's not possible in any version of the Universe. You can't simply multiply the radius by two and say it's diameter.
And to measure the radius ?
P: 65
 Quote by chrisbaird Yes, several times. The first time was in 1998 as reported here. Several years ago I attended a lecture by a member of this group, Dr. Kirshner, on these results and the presentation was amazing.
 Quote by phinds Do you have some reason for thinking that we have not? The tone of your post seems to imply that. As Chris said, we have.
No i don't have . but i wonder how it's measured and i remember i read in a book that the acceleration is decreasing , if so please tell me whether the rate of change of the Acceleratrion is also measured and can we say that the acceleration will ever reach zero or keep on decreasing ?
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 Quote by vrmuth No i don't have . but i wonder how it's measured and i remember i read in a book that the acceleration is decreasing , if so please tell me whether the rate of change of the Acceleratrion is also measured and can we say that the acceleration will ever reach zero or keep on decreasing ?
I'm on shaky ground here so I hope someone who actually knows what they are talking about will chime in. What I THINK I remember reading is that the acceleration is decreasing asymptotically to a non-zero value and that the acceleration will never drop below that value so we DO seem to be on track for the universe dying by ice, not fire.
P: 476
 Quote by zeffur7 How do we know space is not infinite?
In science we can't know beyond what is observed/measured. The observable universe has a finite radius. You only can speculate beyond that.
 P: 181 IF our universe is infinite, would that rule out the possibility that other universes exist?

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