How do we know space is not infinite?

[jbar18]

I like the theory that the universe might be some weird 4-D shape. If you travel in the same direction on the 2-D surface of the earth, you would eventually end up in the same place. It's not infinite, but you would never find a boundary. If the universe were 4D it could be that you could keep going in one direction through 3D space, and in a similar way never find a boundary, just end up in the same place. I guess that would make it bounded in the 4th dimension, but unbounded in the other 3.

That may even lead to ideas like all of the other galaxies we see are just our own galaxy from the various times in the past, with the light having passed different distances through the whole universe before we see it again.

Pure speculation really, I don't think there's any evidence for it, there may in fact be evidence to the contrary. I just think it's quite a neat, wacky idea that seems to tie in quite nicely. How could it be tested?

 

[phinds]

I did not think I made such an assertion.

OK, I guess I misunderstood you.

... Consider the conjecture that the big bang was a singularity that began to expand at some position ...

That is a totally incorrect description of what is currently believed to be the case, in that there was no "position" in space that the expansion happened from, it happened everywhere at once.

 

[yenchin]

I like the theory that the universe might be some weird 4-D shape. If you travel in the same direction on the 2-D surface of the earth, you would eventually end up in the same place. It's not infinite, but you would never find a boundary. If the universe were 4D it could be that you could keep going in one direction through 3D space, and in a similar way never find a boundary, just end up in the same place. I guess that would make it bounded in the 4th dimension, but unbounded in the other 3.

That may even lead to ideas like all of the other galaxies we see are just our own galaxy from the various times in the past, with the light having passed different distances through the whole universe before we see it again.

Pure speculation really, I don't think there's any evidence for it, there may in fact be evidence to the contrary. I just think it's quite a neat, wacky idea that seems to tie in quite nicely. How could it be tested?

Note that what you are talking about doesn't have to require extra spatial dimension, just imposing non-trivial topology will do. For example on some video game, you disappear into the right side of the screen and emerges from the left, effectively that world is *the same* as a cylinder, obtained by gluing left and right edges of the computer screen. Such a topological effect can be looked for via brute force statistical methods (like you say, essentially by looking for patterns which correlate at different directions, not just galaxies but also CMB), but we have not found anything conclusive yet. See e.g.

http://plus.maths.org/content/os/issue10/features/topology/index"

http://www.csulb.edu/~scrass/Teaching/math355/articles/dodecaSpace.pdf"

http://www.maths.lse.ac.uk/Personal/mark/topos.pdf"

 

[vrmuth]

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.

yes i accept infinite can get bigger infinite. But no finite thing can become infinite after finite amount of time (or after finite number of steps). for example the sequence {nc},n=1 to infinity (where c is a positive real number, in case you want the sequence to grow faster you can choose a big c ) after any finite number of steps, never becomes infinity . then after 14 billion years how could the universe become infinite ? starting from a point?
my point is " some thing infinite can get bigger or smaller but it could have not been finite in the past, and will never become finite in the future "

 

[Imax]

I like the theory that the universe might be some weird 4-D shape. If you travel in the same direction on the 2-D surface of the earth, you would eventually end up in the same place. It's not infinite, but you would never find a boundary. If the universe were 4D it could be that you could keep going in one direction through 3D space, and in a similar way never find a boundary, just end up in the same place. I guess that would make it bounded in the 4th dimension, but unbounded in the other 3.

I like this idea too, and it's possible that 3D space at the last scatering surface was compact. You don't need 4D space, only 4D spacetime.

 

[Constantin]

I see the Universe's "diameter" mentioned in two above posts.
I'm pretty sure the Observable Universe only has radius, and not diameter. 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.

 

[Constantin]

I'll quote these two above posted arguments as very convincing:
---

"how can you prove something like "infinite". It would take an infinite amount of time to measure something infinitely large."

"The observable universe is finite. Given that is the only part observationally accessible, the rest is scientifically irrelevant until an observationally detectable effect on the observable part is confirmed."

---
The first argument can be given against anything being infinite, not just the Universe.

 

[phinds]

I see the Universe's "diameter" mentioned in two above posts.
I'm pretty sure the Observable Universe only has radius, and not diameter. 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.

Now that's just silly. The OU is not a physical object, it's just a way of describing the sphere which represents the fartherst out in any direction that we can "see". To say that it has a radius but no diameter is profoundly nonsensical.

 

[zeffur7]

No one knows right now, our technology is to young to discover if the Universe is infinite or finite. The only thing we know is, it is expanding and we already proved that.

We also know that that expansion is accelerating.

 

[zeffur7]

yes i accept infinite can get bigger infinite. But no finite thing can become infinite after finite amount of time (or after finite number of steps). for example the sequence {nc},n=1 to infinity (where c is a positive real number, in case you want the sequence to grow faster you can choose a big c ) after any finite number of steps, never becomes infinity . then after 14 billion years how could the universe become infinite ? starting from a point?
my point is " some thing infinite can get bigger or smaller but it could have not been finite in the past, and will never become finite in the future "

If the big bang reverses at some point & then become the big crunch (i.e. a singularity), what say ye of the min & max of that system, if it were true?

 

[Tanelorn]

The observable universe is finite. Given that is the only part observationally accessible, the rest is scientifically irrelevant until an observationally detectable effect on the observable part is confirmed.

Chronos by observable universe do you count the CMBR sphere or just the highest redshifted galaxies?

The observable universe is shrinking all the time and eventually only our local group will be visible from our position. However isn't it pretty certain that the unobservable universe still exists both now and at that later time - unless we believe that the universe not homogenous and isotropic?

 

[phinds]

The observable universe is shrinking all the time and eventually only our local group will be visible from our position. However isn't it pretty certain that the unobservable universe still exists both now and at that later time - unless we believe that the universe not homogenous and isotropic?

Seems to me that statement is both right and wrong. The OU isn't actually shrinking in terms of the number of light-years it encompasses, but it IS "shrinking" in the way you mean, which is that it contains less and less stuff because everything is moving out of it.

What Chronos has said in other posts is that there basically ISN'T anything outside the OU because we can't TELL directly whether there is or not, but I think that's an overly restrictive point of view. I think the UN-observable universe exists now and will continue to exist but in practical terms, that doesn't seem to mean much since as Chronos always points out (correctly) we just can't detect it.

It's not at all clear to me that there will EVER be any way to detect it, although I have heard, vaguely, that there are some theories that say there will be / may be observational evidence left over from the earliest times after the singularity that we WILL be able to observe remnants of. I don't get how this works but it would be neat if such things ARE ever observed.

 

[Tanelorn]

Perhaps I wasnt being clear. Try less of the matter in the universe will be observable in the future. However this wasnt the point I was trying to make.

 

[vrmuth]

If the big bang reverses at some point & then become the big crunch (i.e. a singularity), what say ye of the min & max of that system, if it were true?

then please give me the initial conditions to formulate the differential equations, then i will tell you the max and min

 

[vrmuth]

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.

Ok now tell me will you take infinite amount of time to say "The set of all natural numbers" is finite or infinite? Actually only if you want to prove an Infinitely large thing as "Finite" you will take infinite amount of time

 

[chrisbaird]

Ok now tell me will you take infinite amount of time to say "The set of all natural numbers" is finite or infinite? Actually only if you want to prove an Infinitely large thing as "Finite" you will take infinite amount of time

I meant it is not possible to physically prove something is infinite. A mathematical proof is a different beast. We can go ahead and make mathematical models of the universe and from some postulates mathematically prove it is infinite. But to see if our model matches reality, we have to do physical experiments and make observations. No physical experiment can measure something infinite. If the universe is finite, then we could measure it. If the cosmic background radiation stopped coming at a certain point in time, that would tell us the universe is finite. The last glimpse of CMB radiation would be coming from the literal edge of the universe. Such a finding would shake the cosmology world up a bit, but I doubt it will happen.

 

[phinds]

... If the cosmic background radiation stopped coming at a certain point in time, that would tell us the universe is finite. The last glimpse of CMB radiation would be coming from the literal edge of the universe. Such a finding would shake the cosmology world up a bit, but I doubt it will happen.

Uh ... say WHAT? Could you elaborate on that, please. I'm certainly willing to believe it's just me, but that makes no sense to me.

 

[chrisbaird]

Uh ... say WHAT? Could you elaborate on that, please. I'm certainly willing to believe it's just me, but that makes no sense to me.

That me try to do better. Imagine that the universe is finite spatially, and always has been, and is not periodic (it does not wrap around and connect to itself). In other words, imagine that there is a physical edge to the universe beyond which nothing exists. Shortly after the big bang, the cosmic background radiation is created effectively uniformly at all points in the universe and spreads out from each point in all directions. CMB radiation that travels a long ways before hitting a planet or space probe's camera needs a longer time to do so, and is thus absorbed/observed at a much later time than the big bang. The CMB radiation created at points in space close to the Earth were absorbed long ago by the Earth (or were not absorbed and long ago zipped away from the earth, out of our region of interest). But CMB radiation created at points very far away from the Earth are just now reaching us and being detected. If there were a physical edge to the universe, there is a physical limit to points in space that were in existence to create CMB radiation. After enough time has elapsed that the CMB radiation created at one edge of the universe has had a chance to travel to the opposite edge of the universe, it will be gone. All of it will have been absorbed or flowed beyond the universe's edge at this point. (Unless the edge of the universe consists of giant and perfect mirrors, so that the universe in a giant resonant cavity.) While I do not believe this to be the case in reality, I am trying to imagine the implications of a finite universe. Have I gone wrong anywhere?

 

[Tanelorn]

Chris, I think I understand what you are suggesting. 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. I suppose we can keep looking!

I think that the observable universe is small compared to the whole universe because the CMBR is so flat in every direction implying homogeneity. However, if there was an edge of some kind I would not expect it to be a sudden transition either, there again we cannot discount any possibility, however remote, when we cannot make any observations.

 

[phinds]

... 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 ?

 

[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.

 

[phinds]

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.

 

[zeffur7]

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. :)

 

[Drakkith]

In other words, it would be finite. :)

Only if the initial conditions were finite. There is no known way to tell currently.

 

[Tanelorn]

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 can't think of any better wording!

 

[phinds]

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 can't 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.

 

[Tanelorn]

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.

 

[Deuterium2H]

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 }

 

[vrmuth]

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?

 

[chrisbaird]

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 http://iopscience.iop.org/1538-3881/116/3/1009/pdf/1538-3881_116_3_1009.pdf". Several years ago I attended a lecture by a member of this group, Dr. Kirshner, on these results and the presentation was amazing.

 

[phinds]

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.

 

[Imax]

Maybe space-time’s a compact Lorentzian manifold

 

[vrmuth]

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 ?

 

[vrmuth]

Yes, several times. The first time was in 1998 as http://iopscience.iop.org/1538-3881/116/3/1009/pdf/1538-3881_116_3_1009.pdf". Several years ago I attended a lecture by a member of this group, Dr. Kirshner, on these results and the presentation was amazing.

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 ?

 

[phinds]

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.