# A Closed Universe?

1. Aug 1, 2015

### Neptune2235

This is probably a silly question, but it's summertime and I can't ask my professor. If the universe turned out to be closed (even in light of WMAP's findings), would it be possible to consider the entire universe a closed system?

2. Aug 1, 2015

### marcus

Why not? but you would not have an energy conservation law.

Sean Carroll has a nice wide-audience essay called "energy is not conserved in an expanding universe"
you can google it by title if you want. John Baez has more explanations at his website--basically the energy conservation "law" depends on Noether's theorem the conditions of which are not met in GR. So GR does not have global energy conservation.

So I would say "closed system" YES. but the U might not have features which we are used to associating with "closed systems"

3. Aug 1, 2015

### Chronos

Einstein was, in fact, quite attached to the closed universe idea having realized GR is rather awkard in an open universe - re:http://mathpages.com/rr/s7-01/7-01.htm

4. Aug 1, 2015

### Chalnoth

Those are two very different things.

It's not unreasonable to consider the observable universe to be a closed system, because the observable universe is approximately homogeneous: it's the same everywhere. So that if energy flows out of one region, just as much energy flows back in. Thus overall, it acts thermodynamically much like a closed system.

Closed, as the term is used to deal with the universe, deals with one of two different issues:
1. Shape. A universe that is closed in shape (technical term: topology) wraps back on itself.
2. Curvature. A closed universe has positive curvature, like a sphere.

These two are related but distinct. The curvature only refers to what we can measure in the observable universe, so if it varies outside of our observable patch, then it doesn't say whether or not the universe wraps back on itself.

The overall shape (topology) is hard to measure at all. I've seen some attempts performed using ultra long-wavelength photons, but so far nothing has been detected. If the universe is closed, it wraps back on itself on a scale much larger than the observable universe, and we probably won't ever be able to to detect that.

5. Aug 2, 2015

### Neptune2235

Thank you all for your insights! I've just started reading about the possible shapes of the universe and find it all quite fascinating.

6. Aug 4, 2015

### grauitate

Regarding the conundrum "closed or not" I think a crucial and important observation fact should be amended here:

It is well known (although not always considered) that the angular size of objects which are
observed at distances z > 1 are tending to become larger again.
Up to z ≈ 0.7 the angular size ist decreasing monotously like in an euklidian, uncurved space.
Here, normal galaxies reach a minimum angular size of approx. 0.3....0.7" (arcsec).
Between 0.7 < z < 1.2 the angular size is nearly constant.
Then, at distances larger than z ≈ 1.2 and especially at larger z in the range of 2...3...5...7...9 the angular size
again increases to 1.0"...5.0", provided of course that the galaxies are observed in the corresponding
spectral range, which must be chosen as λobs = λo(1+z).
By comparing the angular size of a galaxy at e.g. at z = 0.1 that has a max. emission let say at λ = 0.8 μm
with a distant galaxy at e.g. z = 5, this must be observed at λ = 0.8(1+5) = 4.8 μm, which precisely can
be done best with the IR-Space Observatories like Spitzer, WISE, Planck, Herschel, and in future may
be James Webb.
An example is shown here (page 2): arXiv:1502.05399[/PLAIN] [Broken] P.A.Oesch et al.: A Spectroscopic Redshift Measurement...

So, it is left to the community to decide, wether the angular size growth comes from

a.) a expanding flat an not curved universe, with the explanation as follows: the more far away the galaxies
are and were emitting their light in the earlier and therefore smaller universe, the more near to us
they were at that time and the more larger they appear to us. ​

or

b.) a curved (and possibly closed) and not expanding universe, where naturally occuring enlargement
effect become more and more relevant in distance ranges approx. larger than the half of the curvature
radius (these effects locally are well kown by Einsteins lensing phenomena, where far distant objects
are enlarged and enhanced in luminosity by gravitationally acting masses (galaxies and clusters) in
the foreground. This effect can be, at least theoretically, transferred to the entire universe.​

Although this reply would better fit into the forum "Beyond the standard model" I will reply here,
because I think it would help discussing the Thread-Question "A Closed Universe?"

Last edited by a moderator: May 7, 2017
7. Aug 4, 2015

### Chalnoth

If you use a class of observers where the universe appears homogeneous and isotropic, then that creates a specific separation between space and time. Then, we can divide the total space-time curvature into a space-only component and the rest.

The space-only component has been measured to be less than one percent of the total space-time curvature.

Sure, if they really wanted to, a clever person might come up with a different set of observers that sees a lot of spatial curvature. But there's no reason to do that. It doesn't mean anything. All of the predictions of using this set of observers would be identical, but the math would be a lot more complex.

So yes, the nearly-zero curvature is a result of an ambiguous choice (the set of observers who see the universe as homogeneous and isotropic), but there's no deeper meaning in making a different choice (and the math would be a lot harder).