How Can an Infinite Universe Expand?

[fmichel]

I sometimes read that we know that the universe is in expansion and that we don't know if the universe is finite or infinite. I have some difficulties to understand the notion of "infinite universe" and to see how an infinite universe could be in expansion.

Assume the universe is infinite.

Does it mean that the universe has an infinite size?
Does it mean that the quantities of matter and energie are infinite?
Therefore there are an infinite number of galaxies, stars...

How an universe with an infinite size could be in expansion?

Thanks in advance for any explanations, precisions...

Franck

 

[Chronos]

Good argument. It suggests it is illogical to assume the universe is both infinitely old and contains an infinite number of stars.

 

[EL]

Hi fmichel.
There is no problem for a spatially infinite universe to expand.
What is ment by "expansion" of space is that the distance between any two objects increases with time.
To make an analogy: consider a two dimensional toy universe consisting of dots (representing galaxies etc) on an infinitely large paper sheet (so there'll be an infinite number of dots). Now stretch the paper and you'll see that the dots are moving away from each other.

 

[MeJennifer]

I sometimes read that we know that the universe is in expansion and that we don't know if the universe is finite or infinite. I have some difficulties to understand the notion of "infinite universe" and to see how an infinite universe could be in expansion.

Assume the universe is infinite.

Does it mean that the universe has an infinite size?
Does it mean that the quantities of matter and energie are infinite?
Therefore there are an infinite number of galaxies, stars...

How an universe with an infinite size could be in expansion?

Thanks in advance for any explanations, precisions...

Franck

There is no problem here. Think of expansion as in expansion in terms of spatial separation.

For instance consider the infinite set of integers, 0, 1, 2, 3, 4, etc. Each member is separated with a distance of exactly 1. Now expand the scale say 100%. Now we still have the same set but each member is now separated by exactly 2, so we have 0, 2, 4, 6, 8 etc. It is similar with an infinite universe.

 

[fmichel]

Ok thank you. I do undestand now how an infinite universe could be expanding.

About my other question: if the universe has an infinite size, does it mean that there is an infinite number of stars? (instead of the number of stars, I could as well have used the total amount of energy, the total quantity of matter... as infinite values)

Or does it mean that the size of the universe is infinite, but the number of stars is finite?

 

[EL]

If the matter is homogeneously distributed (as it seems to be in our universe), then of course there is an infinite amount of matter in an infinite universe.
Anyway, one should be careful to speak in terms of what the universe looks like beyond what we can observe. Surely our observable universe, which is the only thing we really can say anything about, is finite.

 

[fmichel]

Is that true that at the Big Bag (time t=0), the size of the universe was zero?

I have difficulties to imagine how the universe can:
- have an infinite size since t>0
- has matter at any location in space since t>0
- was concentrated on one point at t=0

It would means that there was an infinitely fast expansion from a universe reduced at one point at t=0 to a universe with infinite size at any time t>0. It would mean that the matter has moved at an infinite speed, i.e. quicker than the celerity of ligth which is impossible.

Moreover, we know that the universe is expanding. Do we know the speed two objects (for example stars) are increasing their distance now? If this speed was infinity at t=0, is should be finite and <c now. Does this speed depend on the distance between the two objects? Is there a formula giving this speed in terms of the distance between the objects?

 

[EL]

Is that true that at the Big Bag (time t=0), the size of the universe was zero?

The simple answer: no!
According to GR the universe started from a singularity (infinitly dense state), but not necessarily from "one point". But note that we do not know what physics hold at the very earliest time, and hopefully there's some new physics helping to avoid any singularity. The Big Bang singularity just poppes out after using GR in a place were it probably doesn't work very well.
What the Big Bang theory tells us is that in case the universe is infinite, it once was in a much denser state, but still infinite in size.

I have difficulties to imagine how the universe can:
- have an infinite size since t>0
- has matter at any location in space since t>0
- was concentrated on one point at t=0

So the lines above should clear these conserns out.

Moreover, we know that the universe is expanding. Do we know the speed two objects (for example stars) are increasing their distance now?

The speed is propartional to the distance beween the objects, v=Hd, where H is the Hubble parameter. This is called Hubbles law.

Note that in GR it is perfectly ok for galaxies to move away from us with "speeds" exceeding "c", without contradicting SR. This topic has been discussed frequently here before, so do a search if you're interested.

 

[fmichel]

According to GR the universe started from a singularity (infinitly dense state)
[...]
What the Big Bang theory tells us is that in case the universe is infinite, it once was in a much denser state, but still infinite in size.

Ok the universe has an infinite size since the beginning, but there was an "infinitely dense state" at t=0. What does it mean?
Does it mean that all the matter was concentrated in one point?

In that case, at what time was the matter present everywhere in the infinite space? In the past, was the expansion speed the same as now? In case no, do we have a time-dependent formula for this speed? Is Hubble parameter a known function of the age of the universe?

 

[EL]

Ok the universe has an infinite size since the beginning, but there was an "infinitely dense state" at t=0. What does it mean?

It means that the energy (matter) density (that is mass per volume unit) was infinite all over space.

Does it mean that all the matter was concentrated in one point?

No. (But our observable universe was concentrated to one single point.)

This reasoning is kind of mindboggling, since what we are doing is sort of adding and subtracting infinites, which not really makes that much sense. But the math of GR is capable of describing the situation.
One shouldn't though spend too much time thinking about this since fact is we know GR can't hold at the very first times, and thus the prediction of a singularity is pure speculation. Hopefully new physics (perhaps string theory) has a better answer.
We know the universe once was in a very dense state, but not that it was infinitly dense.

In the past, was the expansion speed the same as now? In case no, do we have a time-dependent formula for this speed? Is Hubble parameter a known function of the age of the universe?

The Hubble parameter is a function of time.
Read more here: http://en.wikipedia.org/wiki/Hubble's_law

 

[jmnew51]

Hi all
I'm new to the board. Just been kind of reading and learning. Mainly in chemistry though. But this thread intruiged me somewhat. This dimension we call the universe, if it is infinite, by virtue of the definition "infinite" is (let's think of it as) already expanded to a state of infinity and cannot be expanded. This is of course aside from the fact that there is matter in it or not that is spreading apart or not. So if the question is posed "Can or does an infinite universe expand?" the answer has to be in my opinion "no"

Just my $.02

 

[hellfire]

Hi all
I'm new to the board. Just been kind of reading and learning. Mainly in chemistry though. But this thread intruiged me somewhat. This dimension we call the universe, if it is infinite, by virtue of the definition "infinite" is (let's think of it as) already expanded to a state of infinity and cannot be expanded. This is of course aside from the fact that there is matter in it or not that is spreading apart or not. So if the question is posed "Can or does an infinite universe expand?" the answer has to be in my opinion "no"

Just my $.02

This might be a problem of the definition of the term "expansion". You seam to assume that expansion has something to do with borders or a dynamics within a embedding space. This is however not the case as was already explained. In cosmology, expansion means the increase of the distance between two points of space. Note that this definition is related only to internal attributes of the universe.

 

[fmichel]

The Hubble parameter is a function of time.
Read more here: http://en.wikipedia.org/wiki/Hubble's_law

Ok according to this article, the Hubble parameter depends on a function H(t) who is unknown.

I would like to learn more about the possible structure of the universe and about its evolution. Are there interesting books, articles, or documents on the Internet? All suggestions are welcome. Thanks.

 

[hellfire]

I would like to learn more about the possible structure of the universe and about its evolution. Are there interesting books, articles, or documents on the Internet? All suggestions are welcome. Thanks.

Ned Wright's cosmology tutorial:
http://www.astro.ucla.edu/~wright/cosmolog.htm

 

[FunkyDwarf]

A great book i used for some uni courses was this: Universe 7th edition by Freedman and Kaufmann III. don't know if its avaliable where you are though.

part of the unit that used this a lot was about cosmic and stellar evolution and this book is jam packed with cool info about it. good, easy read too, well written

 

[EL]

As some of you may have noticed, I'm rather found of citing Wikipedia. Although it's sometimes not perfectly complete, and in a few cases even wrong or missleading, it's most of the times a very good source of knowledge for non-experts.
Hence I recommend you to start with
http://en.wikipedia.org/wiki/Physical_cosmology
and navigate through the links you find interesting.

 

[Flatland]

Hi fmichel.
There is no problem for a spatially infinite universe to expand.
What is ment by "expansion" of space is that the distance between any two objects increases with time.
To make an analogy: consider a two dimensional toy universe consisting of dots (representing galaxies etc) on an infinitely large paper sheet (so there'll be an infinite number of dots). Now stretch the paper and you'll see that the dots are moving away from each other.

Actually, there is a problem. What if you reversed time and ran the scenario backwards? The dots would all surely merge right? How can an infinite series of dots merge? How would that be physically possible?

 

[hellfire]

I think that the answer is that standard cosmology does not consider t = 0. If you plug t = 0 into the RW metric for any reasonable model of the scale factor you certainly get zero distances between any two points. However, it is known that general relativity does not properly describe the t = 0 state and therefore it is usually assumed that a spatially infinite universe was already infinite at its "origin" (we are able to describe) at an instant after t = 0.

 

[petm1]

Anyway, one should be careful to speak in terms of what the universe looks like beyond what we can observe. Surely our observable universe, which is the only thing we really can say anything about, is finite.

I would think that if the laws of physics work in our visible universe we could talk about the infinite universe as long as we compare them to ourselves, and hold to these laws.

The Big Bang singularity just poppes out after using GR in a place were it probably doesn't work very well.

I was under the impression that singularities pop up in more than one place in GR and that is one of the reasons Dr. Einstein added his constant. Could you go into more details as to where this "place" is.

This dimension we call the universe, if it is infinite, by virtue of the definition "infinite" is (let's think of it as) already expanded to a state of infinity and cannot be expanded. This is of course aside from the fact that there is matter in it or not that is spreading apart or not. So if the question is posed "Can or does an infinite universe expand?" the answer has to be in my opinion "no"

But for the duality of motion and matter I could agree with this, because at the same time that your ideal infinite universe reaches its expanded form it is no longer infinite it is now just a part, either as a wave or as matter, of an infinite universe.

I think that the answer is that standard cosmology does not consider t = 0. If you plug t = 0 into the RW metric for any reasonable model of the scale factor you certainly get zero distances between any two points. However, it is known that general relativity does not properly describe the t = 0 state and therefore it is usually assumed that a spatially infinite universe was already infinite at its "origin" (we are able to describe) at an instant after t = 0.

I believe that t = 0 is talking about time, or how we measure motion at t=0 you would have no motion. SR states that there is nowhere in our visible universe that there is absolutely no motion, in an infinite universe there could be more than one. So I would take it as all the mass in our visible universe measured as a volume of space with no motion, at a ratio of 1 meter/1 second.

Think of fireworks, with the mass of the universe as the fuel, and only one gravity well, now start the burn (motion) at the center of the gravity well. Because we think of the duality of matter we could also think in terms of waves. You could think of the motion starting infinitely small and not needing matter at all in the beginning, because all matter is made up of energy and it could have been formed by motion, but for this you would also need resistance to the expanstion to explain the changes to the motions direction. I like the fireworks because I think the galaxies look like the burning embers expanding out, and because I like to think that we are all just cosmic ash.

 

[FeynmanMH42]

I understand all of this, but there's one problem: a lot of what I read on quantum fluctuations and inflation seems to suggest the Universe must have originated at a point for it to have appeared through a quantum fluctuation. This I understand with a closed universe but our Unverse is clearly flat - so... does this mean that our cherished ideas about the Universe forming from a quantum fluctuation at a point are wrong?

 

[EL]

I would think that if the laws of physics work in our visible universe we could talk about the infinite universe as long as we compare them to ourselves, and hold to these laws.

That's what we do when we talk about what's beyond our observable universe - we extrapolate the part we can really see. But strictly we can't know what's beyond what can be observed, so that's pure speculation.

I was under the impression that singularities pop up in more than one place in GR and that is one of the reasons Dr. Einstein added his constant. Could you go into more details as to where this "place" is.

Singularities for example also arise inside black holes.
Einstein added a cosmological constant in order to allow for a static universe (which was the preferred model until Hubble observed the expansion). To what I know it has nothing to do with singularities.

 

[kant]

Hi fmichel.
There is no problem for a spatially infinite universe to expand.What is ment by "expansion" of space is that the distance between any two objects increases with time.
To make an analogy: consider a two dimensional toy universe consisting of dots (representing galaxies etc) on an infinitely large paper sheet (so there'll be an infinite number of dots). Now stretch the paper and you'll see that the dots are moving away from each other.

I have a hard time understanding the word "infinity" in your definition. What does the word "infinite" have in a universe that has a begnning(big bang). I can imagine space like a inflated bolloon. We humans are like ants on that surface of that bolloon, and that that bolloon is "expanding". Where does the word "infinite" come into play in this model?

Do you mean the universe is infinitly big? If so, then the universe can t be expanding, because there is nothing to expand into. If there was something to expand into, then that would only mean universe in increasing in size, and not infinite.

 

[kant]

Perhaps some one can help me clarify "Infinite universe". How can any physical process be infinite.

 

[EL]

I can imagine space like a inflated bolloon. We humans are like ants on that surface of that bolloon, and that that bolloon is "expanding". Where does the word "infinite" come into play in this model?

You're right that your analogy doesn't describe an infinite universe. Instead your "balloon-universe" is analogous to a spatially closed and finite universe.
That's why I didn't mension any balloon, but instead a plane!
When we go backwards in time, the points on the plane will get closer and closer, and eventually we'll get an enormous density, corresponding to the Big Bang. What is important is though that the plane is still spatially infinite.
I think most of your conserns may come from that you think of the BB singularity as a spatially finite point, which it doesn't need to be. The BB singularity just corresponds to an infinite density.

Do you mean the universe is infinitly big? If so, then the universe can t be expanding, because there is nothing to expand into. If there was something to expand into, then that would only mean universe in increasing in size, and not infinite.

There's no need for the universe to have anything to expand into. It may sound odd at first time, but that's just because our minds are used to the ordinary every day euklidian world. In theory (GR) there is no need for any embedding.

 

[kant]

You're right that your analogy doesn't describe an infinite universe. Instead your "balloon-universe" is analogous to a spatially closed and finite universe.
That's why I didn't mension any balloon, but instead a plane!
When we go backwards in time, the points on the plane will get closer and closer, and eventually we'll get an enormous density, corresponding to the Big Bang. What is important is though that the plane is still spatially infinite.
I think most of your conserns may come from that you think of the BB singularity as a spatially finite point, which it doesn't need to be. .

Not at all. I perfer to go slowly, and define my vocab along the way. You analogy of two point on a plane is indeed insightful, but that does not explane/describe the world "infinite" in connection with any physical processes. What do you mean by "spatially infinite universe". Suppose, i am a life form living in a 0-dimension(=spatial dimension 0) space, i wouldn t be able to to move anywhere.Suppose perhaps i was an ant living in a 1_dimension, then the only world i can see and going is left, and right. When you say "infinite spatial dimension" do you mean that one can move in any direction in space?

The BB singularity just corresponds to an infinite density

Take your analogy, If two points on a plane are continuous moving apart, then that would imply that at one time, the two point must be together? All the matter in the universe would be compressed to a single point. Surely, the density would be great, but that does not mean infinite. Let start from the density equation in grade school. d( density)= m(mass)/v (voloumn/space). If d is infinite, than v must be very close to zero. That does not implies v can be zero, so d must be less than infinity.

The points themselves are not really moving apart, but rather the spaces themselves are stretching, which perhaps gives the illusion that the two point are moving apart. Are the space themselves in a sense stretching? If so, What are they stretching into? Where do the "space" itself come from? Surely, space itself must itself be defined some how. if all the universe, including the space itself came out of the big bang, then space must undergo it` s own expansion. Would there be any meaning in referring to anything 'outside" space. ( I know the absurdity in the use of 'outside' in the sentence, but that is perhaps just a limitation on natural language, not ideas!).

 

[EL]

Suppose perhaps i was an ant living in a 1_dimension, then the only world i can see and going is left, and right. When you say "infinite spatial dimension" do you mean that one can move in any direction in space?

The 1-dimensional space is spatially infinite if the ant can start walking in one direction (left or right) without ever coming back to its starting point.

I'm sorry but I'm not able to get anything out of your second part.

 

[kant]

The 1-dimensional space is spatially infinite if the ant can start walking in one direction (left or right) without ever coming back to its starting point.

I see, than perhaps i was mistaken that what you mean by "infinite spatially dimension" was actually a infinite physical process. Perhaps what you mean by "infinite spatial dimension" was just a fancy way of talk about the geometry of space in the universe. Is that correct?

I'm sorry but I'm not able to get anything out of your second part

I do not know what you mean by infinite density at the SS.

 

[SpaceTiger]

I see, than perhaps i was mistaken that what you mean by "infinite spatially dimension" was actually a infinite physical process. Perhaps what you mean by "infinite spatial dimension" was just a fancy way of talk about the geometry of space in the universe. Is that correct?

An infinite universe (in this context) is one that is infinite in spatial extent. This is not the same as saying that it has an infinite number of spatial dimensions, and I don't think EL ever said that it did.

 

[kant]

Well, should i thank you for clarifying on EL behalf?

 

[EL]

Ok, now I think I get what you mean.
As ST said, in a "spatially infinite" universe the space is infinitely large, which has nothing to do with the number of dimensions at all. A n-dimensional universe can be spatially infinite for any n=1,2,3,..., although our universe seems to have n=3.
(And I can't find where I have mensioned "infinite spatially dimension" as you claim I have done?)