"The universe is expanding" & "the universe is infinite"

.....

can someone explain how these two statments fit together? They seem to be in contradiction to me.. How can you expand upon something infinite?

Chronos

The universe is thought to be expanding because distant galaxies are receding from our galaxy. That does not constrain the size of the universe. An infinite universe is just as free to expand as a finite universe. But I think the more important issue is the size of the observable universe [i.e., the only causally connnected part]. For more information, google on 'hubble bubble'.

.....

How?? I don't understand this at all.. by definition something infinite can't get any larger..

infinity + 1 = infinity

right?

εllipse

Place two particles at a finite distance away from each other, which impose no forces on each other. As time progresses, the expansion of the universe accelerates these two particles in opposite directions, causing them to move apart. In an infinite universe, the size of the universe won't grow due to expansion, but the distances between bodies, which are not being held together by a force stronger than the universe's expansion, tend to grow.

.....

I see... so the "universe" referred to in the first statement actually means the bodies within the universe.. not some border of the universe itself?

εllipse

Well, that's not what I meant to imply. In a finite universe, I believe the size of the universe itself is actually expanding, as well as the distances between bodies. But in an infinite universe, the only measurable effects are the distances between particles because we don't have tools, nor the comprehensive abilities, to measure an infinite size.

I think it may be most accurate to say "space" is expanding. Any two points in space will tend to accelerate apart from each other. This includes, in a finite universe, the two points representing the largest distance possible in the universe. In an infinite universe, it's still reasonable to state that space can expand, but what changes is it's no longer meaningful to talk about two points seperated by the largest distance possible in the universe.

pervect

An expanding universe doesn't necessarily have the property that any two points accelerate away from each other. It is sufficient that any two "comoving" points move away from each other at a constant velocity. You can think of "comoving" points as points that are at rest with respect to the cosmic microwave background radiation, i.e. points from which the universe and all physical prameters such as the previously mentioned cosmic microwave bacground appears to be the same in all directions.

It is the fact that "comoving" points get further and further apart from each other as time goes on that allows one to say a universe is expanding.

If one accepts the standard cosmological models, in our universe at the current point in time, any two points do accelerate away from each other. However, it is possible for the rate of expansion to be constant, accelerating, or deaccelerating - this is measured by a cosmological parameter q', the deceleration parameter. The sign of this parameter, which can change as the universe evolves, determines the sign of the acceleration between two neighboring points.

εllipse

I was under the impression that a constantly expanding universe would still accelerate points away from each other. When Hubble observed that galaxies were all redshifted he found that the further away he looked the faster the galaxies were moving, and based on this most concluded at the time that the expansion was constant. But even though the expansion itself was thought to be constant, it still explained galaxies moving faster away from each other the further away they got (accelerating).

If two points didn't accelerate away from each other, I'd find it hard to prove any sort of expansion at all. It'd be impossible to prove or disprove in an experiment. If the expansion just theoretically kept particles moving at a constant velocity away from one another, all one would have to do is "push" two particles, giving them a velocity in the opposite direction, so that they would remain equidistant. But how then do you have a reason to call the universe expanding?

pervect

The Hubble parameter H is not generally constant with time in an expanding universe.

If you consider the flat FRW (Friedmen Robertson Walker) universe modelled by the metric

ds^2 = a(t)^2 (dx^2 + dy^2 + dz^2) - dt^2


the Hubble parameter H as a funciton of time is (da/dt)/a(t). See for instance

http://web.mit.edu/8.033/handouts/cosmology.pdf

(You may notice their metric appears in a slightly different form. I'm assuming k=0, and I'm using x,y,z instead of r, theta, phi. My form of the metric is given later in the file if you look closely.)

An expanding universe without acceleration would be represented by

a(t) = Kt

In such a case the Hubble parameter H would be represented by H = 1/t, i.e. the Hubble parameter would be the inverse of the age of the universe.

You can see that any two points maintain a constant relative velocity in this case- as the size of the universe doubles, the Hubble parameter cuts in half.

Crosson

Here is a set that is both infinite and expanding:

Consider the set of positive odd numbers (1,3,5,7...).

Now put the positive even numbers in the set one at a time

Gumbo72203

i think this is something people misinterpret all the time.

When you say "the universe is expanding" what that means is that the CONTENTS of the universe, all of its disparate entities that MAKE UP the universe, is expanding.


Okay, think of the universe as a basketball suspended in mid-air in an empty room. The basketball is the universe, and the empty room is space. The universe can expand, but its expanding in an infinite space. So, in a sense there IS a boundary to the universe. But there is no boundary to space. Space is infinite. There is no possible way that it couldn't be.

To me, the universe does not include ALL of space, only what is contained within the universe. The universe is the stuff that makes up the universe. Empty space does not make up the universe. It simply contains it.

Like, go back to the basketball in the room: The basketball is the universe, suspended in space. Yes? Okay, but the basketball also CONTAINS space.

So, when you have the 2 phrases "The universe is expanding" and "the universe is infinite" the problem is that the definition of the "the universe" is not consistent; there are two different frames of reference.


So, basically, there are 3 things that we are dealing with:

1. the entire physical contents of the universe
2. the interstellar space that the contents exist in
3. whether or not the concept/definition of "the universe" includes both, or only one



So, lets say that in all of space, there is 6 galaxies, positioned to represent a sphere, and that we're using #1 for defining "the universe", in that it means the entire physical contents that exist, anywhere.

Now, from the center point of the sphere of galaxies, "space" extends infinitely in all directions.

so, if these galaxies expand, then the it SHOULD be said that "the universe" is expanding THROUGH space. The universe can expand, and the space WITHIN the universe is also expanding, but ALL of space is NOT expanding. So, SPACE is infinite; the universe is not. The universe DOES have a boundary; space does not.


i hope this all makes some sense to you people, haha. it makes sense inside my head, but its impossible almost, for me to take the visual image of this entire concept, and then try to convey and explain it with words. gah.

eha

I'm thinking the same way you do Gumbo. Universe occupies a certain volume within endless space. Universe is never gonna fill up the entire space, no way, even expansion lasts forever.
Another thing that I recently hear a lot about shape of the universe. I was just realizing this basketball or baloon model with the diameter of 156 billion light years wide, with inside of baloon is empty which represent the past, outside is empty and represent the future, just surface area of baloon holds all matter, galaxies, stars and everything else. That is our universe, spherical, but inside is empty. I was thinking of what part of the surface area represent our observable universe, it should be 14Gly in radius? Then I heard universe should be in flat-open shape like sheet of paper according to latest critical density findings. Now i'm trying to imagine how is this flat universe expanding?what is the size of it? Hubble constant should be still valid but how does it work?

marcus

You are saying in effect that "Einstein was wrong" and radically contradicting conventional cosmology, although you don't seem to have any evidence for why we should throw out the usual picture based on General Relativity and adopt yours.

You should realize that you are giving us is an idiosyncratic personal vision. My feeling is that you are welcome to it. People should be free to believe whatever they choose. Unless they are motivated to actually learn and are trying to understand conventional science.

There is a question about whether it is appropriate to discuss non-standard private visions here in this particular part of Physics Forums. In Astro/Cosmo we usually stick pretty close to ordinary professionally researched models. There is a department for Independent Research for non-standard stuff. The staff (mentors and admins) decide how to sort things out.

marcus

Eha, I get the impression that you are the kind of person who is asking questions and trying to understand the regular science version. There are some mental stretches to make, you'll probably find it helpful here if you keep asking, at least I hope so.

The balloon model is just a 2D analogy for 3D space. To use the analogy you have to think of space as 2D and whatever stars galaxies creatures as approximately flat 2D things. Nothing inside or outside the balloon, just the pure surface.

It is possible that our 3D space is infinite and to include that possibility with the balloon analogy (it's hard but you have to) think of the balloon as really huge, but still expanding.
So huge that to a creature on the surface it seems perfectly flat, but still expanding. Effectively like an infinite flat sheet of rubber which even though it is already infinite is still expanding. I know that's hard to understand, but it is how you include the infinite space possibility in the balloon analogy.

All expansion means is that distances between stationary points increase according to Hubble law. It doesnt mean there is any "outside" that space expands out "into". Expansion is measured internally by the record of increased distances.

You are right about the observable being a round patch on the balloon. The present radius is 45 Gly. That is the current radius---what it is now. If you could freeze expansion it would take 45 billion years for light to travel it.

Because distances expand light that has come along way is always farther from its source than it could have traveled by itself in a non-expanding universe. Light now arriving as the microwave background has been traveling for 14 billion years, but the presentday distance to the source matter is 45 billion lightyears.

To get some hands-on experience with the standard model cosmos, google "wright calculator" and type in 1090 for the redshift. That is the redshift for the CMB (cosmic micrtowave background) radiation. The calculator will tell you the current distance of 45 Gly and how long the light has been traveling, 14 Gy. It helps to keep the two things straight.

Well flat with infinite volume is one possibility consistent with the WMAP data. But all they said was nearly flat. The data allow a generous possibility that space is finite, just very large. The most recent authoritative report on this was the March 2008 WMAP report by Komatsu et al, and they said that if the universe is spatially a hypersphere (like the balloon except 3D instead of 2D) then the circumference is, with 95 percent confidence, at least 600 billion light years (that is, current presentday distance---if you could freeze expansion then light would take 600 Gy to travel all the way around.)

If you want a link to the technical report, let me know.

So if someone tells you the U is spatially flat, infinite volume, do not believe them. We don't know. The issue really is not settled yet! But the successor to the WMAP spacecraft was launched in May, its the Planck mission. It will refine the curvature estimate and may help settle the issue.

rmatheny

Isn't space curved around matter? So isn't there a limit? When you travel to the edge of the universe you cannot keep going, as space is dependent on matter. Yes that boundary will expand as the universe keeps expanding but space doesn't go on forever.

marcus

Check out the automatic link for "edge of the universe". It is a common misconception about cosmology that the universe has an edge or boundary. If you follow the link in your post they'll have something to say about it.

eha

Thanks Marcus, you explain real good. Now I started to follow up WMAP studies on cosmology except those formulas. So far what I understand is; we are gonna keep baloon model for awhile, and we adopt the rule of "density of universe equals to critical density" which means universe is flat open, and we apply this to our model because our baloon is so big we can count it's surface almost flat.