# Finiteness of space

1. Jun 4, 2005

### εllipse

If space is flat or open, does that make it infinite? Is a closed universe the only type that would be finite, or would a flat or open universe also somehow be finite?

2. Jun 4, 2005

### Garth

Welcome to these Forums ellipse!! A good question even if it seems obvious at first.

Generally speaking if space is flat or hyperbolic (like the 'seat' of a saddle shape at every point) then it would be open and infinite and unbounded.
If space is spherical (a 3D analogue of the 2D surface of a sphere ) then it would be closed and finite although still unbounded. Go off in a straight line and hypotheticaly you could return to where you started from. Actually while the universe is expanding you would have to go faster than light to get round and therefore this journey is impossible in standard GR cosmology.

However as I said here (post #26) the evidence of the data of the CMB from WMAP, BALOON and COBE seems to indicate that while the universe appears flat there is some indication that it is also finite in size. As an alternative to my suggestion in that link, this led to the proposal that the universe was like a football (soccerball) with flat hexagonal plates welded together into a 'sphere'. Each plate would be like a space invaders game, go off stage left and you would reappear stage right! I don't think this model has lasted very well.

Garth

Last edited: Jun 4, 2005
3. Jun 4, 2005

### Hurkyl

Staff Emeritus
Not true. It's fairly easy to construct closed, finite topologies that are everywhere flat. For example, the usual model of a 3-D torus.

4. Jun 4, 2005

### Garth

Yes, my "generally speaking" was referring to the three Friedmann models.
The Torus is joined by the cylinder and cone as conformally flat models that are finite.
Garth

5. Jun 4, 2005

### εllipse

The followup question

Thanks, so if space is infinite then would the amount of matter in the universe be infinite? I've read that it's believed matter is evenly distributed throughout the universe, which would seem to suggest an infinite amount of it, but I'm just asking for clarification.

6. Jun 4, 2005

### Garth

Yes, indeed, that would be the inference of an infinite universe, infinite volume but finite (and actually very small) density, and consequently infinite mass.

One point, which many find difficult if the universe is open, is imagining the BB from a zero volume singularity expanding instantly into an infinite volume universe. But that's singularities for you!!

Garth

7. Jun 4, 2005

### yogi

In an infinite Universe, all things would be repeated an infinite number of times - imagine an infinite number of Yogi's to forever perplex all the Hurkyls and Garths

8. Jun 4, 2005

### Garth

And everything that is not forbidden is compulsory!

Garth

9. Jun 5, 2005

### εllipse

Thanks, Garth. I recently read on these forums a "size" of the universe. If I remember correctly, it was around 74 billion light years. Is this correct? And if so, is the term "universe" in this sense being used for something else (maybe the observable universe). I only just now remembered reading the size of the universe, so now I'm confused as to how cosmologists believe there's a good possibility that the universe is open (which would imply an infinite universe as you stated) but still quote a size for the universe. Could you help clear this up? And could you point me to a reputable web reference that covers the probability of the universe being infinite vs finite or atleast the current mainstream views? I fear doing a search on google won't be as valid as something someone here could provide. Thanks again!

edit: I just found a similar thread stating the observable universe is estimated to have a 47 billion light year radius, so I guess that answers my question. I'd still like a good web site to read about this, though, if anyone could help with that. Thanks.

Last edited: Jun 5, 2005
10. Jun 5, 2005

### Chronos

The observable universe is clearly finite. It is enclosed within what is referred to as the Hubble volume, which limits how much of the universe is visible to any given observer at any given time in the universe. It became logically apparent a long time ago that the universe cannot contain an infinite number of stars and be infinitely old. The night sky would otherwise be as bright as the sun. This is referred to as Olbers paradox. It was not clear which aspect was not infinite until the big bang theory arrived on the scence. So we know the universe is not infinitely old, although it could still be infinitely large.

11. Jun 5, 2005

### Garth

Olber's Paradox is dependent on three necessary properties of the universe that were all thought true in pre-GR days since Newton.

1. The universe is infinitely old.
2. The universe is infinitely large.
3. The universe is static.

If any one of these three conditions do not hold the paradox is resolved.
The standard model breaks the first and third of these conditions and it may also break the second if the density parameter Omegatotal > 1.
In the Steady State Cosmology universe conditions 1 & 2 held and 3 was replaced by the Perfect Cosmological Principle. The paradox was then used to place an upper limit on the brightness of the night sky in order to constrain the theory. SSC was consistent with the observed background upper limit.

Garth

12. Jun 5, 2005

### Dr.Brain

First of all, there have been numerous theories on the structure of our universe.Remember that none of those have been proven , only proposed.

Lets assume , if universe was flat ....flat like what?... a sheet of rubber with dents due to large celestial bodies?....or something like liquid in which everything floats?... or more like imaginary flat spacetime fabric ....? ....we just cannot exactly decipher what we mean by 'flat'..

And if it was open ,?...... like a straight plane that extends everywhere randomly?...or more like a hyperbola that never ends....?

On one side we are proposing so many possibilities....who knows a Universe is a speck of dust on somebody's else shoulder?...Maybe The universe rotates around something else?.... Maybe what appears to us so big and vast...is something which is part of something massive?

13. Jun 5, 2005

### turbo

There is a 4th necessary property upon which Olber's Paradox depends.

4. Light propagates through space for infinite distances with no loss of energy.

It can easily be demonstrated that if EM waves interects with the aether of the quantum vacuum (and gradually loses energy in the process), that light from a distant enough source will be redshifted into undetectability. If this effect is real, Olber's Paradox cannot produce a bright night sky even in a static universe that is both temporally and spacially infinite.

14. Jun 5, 2005

### Hurkyl

Staff Emeritus
You still get infinite energy, it's just redshifted to the lower end of the spectrum.

15. Jun 5, 2005

### turbo

Absolutely right. The energy level can be extreme, but when is is redshifted to the point that we can no longer even measure its frequency relative to the ground state, it has essentially joined the ground state of the vacuum. We have no reference to a perfectly empty vacuum from our universe, so we cannot measure the difference between the ground state of our universe and a "perfect" vacuum.

It's analogous to rectifying AC (flattening its oscillation relative to ground) into DC in an old tube audio circuit. The B+ voltage (rail) can be be hundreds of volts above ground, but without access to ground, we cannot measure its magnitude.

16. Jun 5, 2005

### Hurkyl

Staff Emeritus
The doppler effect worries me greatly, though. Suppose in one frame we have this infinite, "undetectable" bath of radiation. If something moves at high velocity with respect to this frame, it would blueshift the radiation. By moving closer and closer to the speed of light, we can blueshift an arbitrarily large magnitude of radiation into, say, the visible range. (and it would all be going in one direction)

17. Jun 5, 2005

### turbo

If we move relative to this ground state (lets call it the CMB just for grins) we might expect to see some anisotropies in the observed temperatures.

18. Jun 5, 2005

### Chronos

I object to your fourth condition on Olbers paradox, turbo. Energy is simply lost in that scenario, which rewrites the laws of thermodynamics. If it is absorbed by some sort of background state, the background temperature should increase over time, not decrease - which is what is observed.

19. Jun 6, 2005

### hellfire

There is a fourth condition. The distribution of light sources is homogeneous and isotropic, or at least, with a fractal dimension greater than two. Otherwise (fractal dimension less than two), the paradox is resolved in a static, spatially infinite and enternal universe.

20. Jun 6, 2005

### Garth

Homogeneity and isotropy are assumed; however, as the darkness of the whole night sky is taken to be isotropic (more or less) could it be otherwise?

Garth