How do we know space is not infinite?

[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.

 

[juanrga]

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.

 

[Oldfart]

IF our universe is infinite, would that rule out the possibility that other universes exist?

 

[phinds]

IF our universe is infinite, would that rule out the possibility that other universes exist?

Since there is not the slightest knowledge HOW other universes might exist, the question doesn't have much meaning. My guess is it's irrelevant since our universe isn't thought to be expanding INTO anything, it's not like we're going to use up all the room.

 

[Oldfart]

... it's not like we're going to use up all the room.[/QUOTE]

Heh..., here I go again...

Where is this "room"?

 

[phinds]

... it's not like we're going to use up all the room.

Heh..., here I go again...

Where is this "room"?[/QUOTE]

It's the non-existant stuff "outside" our universe that we're not going to use up all of, thus crowding out other non-existant universes. That's my story and I'm sticking with it !

 

[Oldfart]

That's my story and I'm sticking with it !

Okay, thanks, phinds!

But please be careful, I assume you know that you can get your license pulled for talking like that...

 

[Justaman]

It is. There is no beginning, and no end, only transition. Same with time.

 

[Justaman]

IF our universe is infinite, would that rule out the possibility that other universes exist?

One universe, lots of space, infinite potential for infinite configurations beyond that which has become visible to us as of yet.

 

[phinds]

It is. There is no beginning, and no end, only transition. Same with time.

Personal theories are not allowed on this forum. You should read the rules. This is a physics forum, not a theology forum.

 

[maggiemaeu]

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.

assuming the definition of infinity in use here is immeasurably great, then it makes sense to imply that it has a defined starting point to measure from. however, the word is in my opinion and possibly in fact a paradox, so saying anything about measuring infinity or infinity getting bigger is just contradictory. that is not to say it's not argueable though.

 

[maggiemaeu]

Personal theories are not allowed on this forum. You should read the rules. This is a physics forum, not a theology forum.

not neccessarily a personal theory; could simply be a professional theory you obviously haven't heard of yet. that is one explanation of many that i have heard concerning infinity. don't mean to cause trouble :)

 

[phinds]

... the word is in my opinion and possibly in fact a paradox, so saying anything about measuring infinity or infinity getting bigger is just contradictory. QUOTE]

ANOTHER Personal theory and this one DEFINITELY contrary to the facts.

 

[Justaman]

Personal theories are not allowed on this forum. You should read the rules. This is a physics forum, not a theology forum.

Hi Phinds- my statement wasn't intended to be theological in any way- quite the contrary actually.

Quite simply, I don't think time ever began or will end, and that space continues for an infinite distance in all directions.

Considering infinite, how does time either start or end? With the freezing of a cesium atom? I don't think so, as the duration of it's condition is still real. Even beyond observable space (expanding at light speed) if no matter exists beyond some distance, wouldn't an object that moves into this space continue indefinitely until acted upon? How we currently measure time and space may become obsolete, but I don't think this suggests a beginning or end to either.

With infinite time comes infinite possiblities, so it seems unlikely to me that all matter sat in singularity eternally until 13B yrs ago.

Rather, I think (there I go again) the expansion/contraction cycle is a continuous and infinite process- the contraction cycle including material collisions of increasing frequency with decreased proximity, arriving at and passing a "central gravitational point" (thus entering expansion phase) at inconsistent intervals around the central (and dynamic) point.

This would then mean that expansion/contraction exists with or without a "big bang" event, and that all matter only occasionally (though repeatedly) forms an instantaneous singularity that, once again, "bangs".

Not even light could escape the gravitational pull at singularity, so the OU would be quite small. Would this mean that space-devoid of matter even 2 feet away- would be finite? I personally would not consider it so, making it infinite in all directions correct?

Assuming infinity of space and time, it seems likely that an infinite number of expansion/contraction/big bang cycles would be occurring at all times, of course located well beyond our OU, but part of a larger "universe".

As with cells in our body, it seems these universes must occasionally interact with/effect each other in some way, just as cells in our own body do.

Associated by proximity, would this then make our universe part of a finite "organism" which, on a universal scale taken to infinity, co-mingles with an infinite population of similar "organisms"? And so on, and so on...

I think so. But there I go again...

Sorry to go on so in responding.

 

[Constantin]

It's easy to imagine time as finite. Actually it's much harder to imagine anything as being infinite. How do you imagine an infinite thing ?
Your problem arises from not being able to imagine time having limits. These limits, edges of the time dimension, beginning and end of time.

But if you consider time being just another dimension, you might find that easier.

Imagine the normal space dimensions. The Observable Universe is finite.
It has a center, any observer being at the very center of his own Observable Universe. And it has an edge, the furthest away it is possible to see. That edge is moving away and the Universe is expanding, but it's still finite.

Same thing with time. It has a beginning, the Big Bang. And an edge, the "current moment". The "current moment" is continuously moving, same as the edge of the Observable Universe. So the time spent since the Big Bang keeps increasing, but it's still finite.
Also don't consider the future as part of the time dimension. The future doesn't exist, yet.

If you imagine this analogy between space and time dimensions, you'll find it easier to understand the concept of finite time or space.

 

[Justaman]

The Observable Universe is finite.
It has a center, any observer being at the very center of his own Observable Universe. And it has an edge, the furthest away it is possible to see. That edge is moving away and the Universe is expanding, but it's still finite.

Thanks, I well understand this, and how it serves to assert that the entire universe (consisting of everything beyond our OU) is indeed infinite. Since the OU that exists at the edge of my OU is twice as far away from me...and so on.

Same thing with time. It has a beginning, the Big Bang. And an edge, the "current moment". The "current moment" is continuously moving, same as the edge of the Observable Universe. So the time spent since the Big Bang keeps increasing, but it's still finite..

It's clear that a finite number of seconds have passed since the last big bang, but not that time did not exist/advance prior to it. So all matter in the universe existed in a single point and then simply exploded? How long would it have maintained this state? Of course, that duration would have been real and measurable.

 

[Constantin]

There's no proof there was anything before the Big Bang. So it's pure speculation.

Just use the concept "what you can't see does not exist". It simplifies things quite a lot and avoids speculation.

We can't see before the Big Bang, so nothing existed before that. We can't see beyond the edge of the Observable Universe, so nothing exists beyond that edge.

Can't get simpler than that.

 

[Constantin]

"So all matter in the universe existed in a single point and then simply exploded?"

Matter did not exist at the very beginning, just a huge amount of energy. That energy created the matter.

 

[Drakkith]

Quite simply, I don't think time ever began or will end, and that space continues for an infinite distance in all directions.

That's fine. Current models don't care whether the universe is actually infinite or whether it wraps back on itself or something.

With infinite time comes infinite possiblities, so it seems unlikely to me that all matter sat in singularity eternally until 13B yrs ago.

Nonsense. If something is impossible now, it is impossible always. The sun has zero chance of violating conservation of energy and suddenly losing all of it's mass and energy and turning into a bowl of soup. As for all matter sitting in a singularity until 13 billion years ago, I don't know of anything in the standard model that says it did. In fact the model simply stops making predictions past a certain point. There are several other theories that try to go beyond the standard one and predict what happened during and before the big bang but none of those are accepted yet.

Rather, I think (there I go again) the expansion/contraction cycle is a continuous and infinite process- the contraction cycle including material collisions of increasing frequency with decreased proximity, arriving at and passing a "central gravitational point" (thus entering expansion phase) at inconsistent intervals around the central (and dynamic) point.

Unfortunately our observations show that unless something changes this is not the case.

This would then mean that expansion/contraction exists with or without a "big bang" event, and that all matter only occasionally (though repeatedly) forms an instantaneous singularity that, once again, "bangs".

I don't know what you call sudden expansion of the universe from a possible singularity, but I believe it's called the Big Bang.

Not even light could escape the gravitational pull at singularity, so the OU would be quite small. Would this mean that space-devoid of matter even 2 feet away- would be finite? I personally would not consider it so, making it infinite in all directions correct?

Our knowledge of physics breaks down at the singularity point, so there's no way to answer your question.

Assuming infinity of space and time, it seems likely that an infinite number of expansion/contraction/big bang cycles would be occurring at all times, of course located well beyond our OU, but part of a larger "universe".

As with cells in our body, it seems these universes must occasionally interact with/effect each other in some way, just as cells in our own body do.

Associated by proximity, would this then make our universe part of a finite "organism" which, on a universal scale taken to infinity, co-mingles with an infinite population of similar "organisms"? And so on, and so on...

None of this even makes any sense. I recommend that you take some time and understand current models of the universe before posting anything like this nonsense again. And remember that PF isn't the place for personal beliefs or theories.

 

[Constantin]

A very good argument against the repeated "expansion/contraction/big bang cycles":

Evidence shows the Universe is expanding at an accelerated rate, so it will never contract again.

 

[Justaman]

A very good argument against the repeated "expansion/contraction/big bang cycles":

Evidence shows the Universe is expanding at an accelerated rate, so it will never contract again.

Begs the question: What's out there, pulling it? I mean this in a purely scientific way. But obviously a topic for a different board. Sorry for the intrusion...

Thanks all, very interesting (and at times entertaining) thoughts.

 

[Drakkith]

Begs the question: What's out there, pulling it? I mean this in a purely scientific way. But obviously a topic for a different board. Sorry for the intrusion...

Thanks all, very interesting (and at times entertaining) thoughts.

http://en.wikipedia.org/wiki/Cosmological_constant

 

[maggiemaeu]

... the word is in my opinion and possibly in fact a paradox, so saying anything about measuring infinity or infinity getting bigger is just contradictory. QUOTE]

ANOTHER Personal theory and this one DEFINITELY contrary to the facts.

sorry, didn't mean it as an opinion, just presenting a problem in the arguement. honestly, there are many definitions of the word that are contradictory. the fact being that infinity is an argueable word, you have to narrow it down a little more. how could this be contrary to the facts? it is a fact that the word has different meanings and which ones you use is your business, not mine. all I'm saying is that specifics are needed in discussing infinity to avoid confusion.

i do admit i should have been more careful about how i conveyed that.

 

[maggiemaeu]

A very good argument against the repeated "expansion/contraction/big bang cycles":

Evidence shows the Universe is expanding at an accelerated rate, so it will never contract again.

is this the theory that states there are multiple events similar to the big bang? sorry, I'm not sure

 

[phinds]

sorry, didn't mean it as an opinion, just presenting a problem in the arguement. honestly, there are many definitions of the word that are contradictory. the fact being that infinity is an argueable word, you have to narrow it down a little more. how could this be contrary to the facts? it is a fact that the word has different meanings and which ones you use is your business, not mine. all I'm saying is that specifics are needed in discussing infinity to avoid confusion.

i do admit i should have been more careful about how i conveyed that.

There is nothing contradictory about infinity being able to get bigger. It can and does. This is a standard part of any reasonable definition of infinity and if you think otherwise, you might find it interesting to study up on the subject.

 

[Constantin]

Mathematically infinity can get bigger, smaller, and you can joggle with it in different ways.

But can you give any example in physics of something that was proven to be infinite ? Because I don't believe there is such an example.

 

[phinds]

Mathematically infinity can get bigger, smaller, and you can joggle with it in different ways.

But can you give any example in physics of something that was proven to be infinite ? Because I don't believe there is such an example.

I believe that most (but by NO means all) models have the universe as infinite AND haveing size added to it all the time but that IS the only thing I am aware of.

And I think that talking about infinity getting bigger or smaller is probably incorrect. You can add to it or take away from it, but that does not change the fact that it is just "infinity".

 

[khemist]

A simple way to think of infinity.

Consider all the real numbers -> 1, 2, 3, 4, etc...

One would certainly consider that an infinite set (give me any number, and I can get another number by simply adding 1). Now, take all the real even numbers -> 2, 4, 6, etc...

That is certainly an infinite set as well, but it has half the values as the original set!

 

[phinds]

A simple way to think of infinity.

Consider all the real numbers -> 1, 2, 3, 4, etc...

One would certainly consider that an infinite set (give me any number, and I can get another number by simply adding 1). Now, take all the real even numbers -> 2, 4, 6, etc...

That is certainly an infinite set as well, but it has half the values as the original set!

No, it's the same number. It SEEMS like half as much but that's that thing about infinity ... you can't treat it in normal mathematical operations as though it were like other numbers. Half of infinity is still infinity, as is twice infinity. Very UNintuitive.

 

[khemist]

No, it's the same number. It SEEMS like half as much but that's that thing about infinity ... you can't treat it in normal mathematical operations as though it were like other numbers. Half of infinity is still infinity, as is twice infinity. Very UNintuitive.

That is what I am saying... Although the even set has half the numbers, it is still infinity. Read what I wrote a bit more closely :)

 

[phinds]

That is what I am saying... Although the even set has half the numbers, it is still infinity. Read what I wrote a bit more closely :)

DOH ! misinterpretaion alert ! (by ME, I mean, not you)