Shape of the universe

[Cap'n Refsmmat]

Everyone wants to know the shape of the universe. It's a rather interesting question. But: is there a practical application of the knowledge? If I find out that space is a sphere, what does that allow me to do besides change our textbooks?

[I_Pwn_Crackpots]

I don't know, and I don't know if there will ever be an answer to that question. Just keep in mind that it took us over 1500 years before we could actually find an application for the fact that the world was round. So while there may not be an immediate application, it's nice that we know one more fact about the universe in general.

 

 

Plus, I think the reason that this is of great interest is because depending on the model, we can make predictions for how the universe will evolve in the future. A flat universe, to take an example, will most likely not collapse on itself.

[stuartdenley]

The shape of the universe is like the shape of the egg of ostrich. Which is not completely circle. I have the interest about astronauts let discuss more about. Thank you.

 

Stuartdenley

 

http://www.marijuanaaddictiontreatment.com

[iNow]

Is it even possible to describe the visible universe as shaped? I mean, there is nothing "outside" of the visible universe by which to compare said "shape."

 

I know there are studies talking about saddle shapes and ovals and whatnot, and I recognize that you are asking why this discussion of shape is relevant and where it helps us, but I am sort of questioning the validity of assigning shape in the first place.

 

 

Hmmm... Where's Martin when you need him?

[I_Pwn_Crackpots]

All a shape implies is that the universe is curved. It doesn't have to look like anything.

[pioneer]

If the universe is expanding uniformly in all directions, as it is claimed, then it looks spherical with dimples. Here is the logic. A sphere is a locus of points equidistant form a given point in 3-D. So the universe is composed of spheres centered on every point. If we superimpose all this up is looks like a bumpy sphere with dimples. It is a huge golf ball with the dimples in migration on the surface due to orbits of centers.

[I_Pwn_Crackpots]

No, it doesn't mean that at all.

[mooeypoo]

Dr. Pamela Gay in one of her goodies: explaining (trying to) what the possible shape of the universe might be and why we guess it so.

 

http://www.astronomycast.com/astronomy/ep-81-questions-on-the-shape-size-and-centre-of-the-universe/

 

Astronomy Cast is brilliant, btw, very recommended.

 

BTW: OMGOMGOMG, Capn Refsmmat asked a question! Dude! I thought you know everything.

[npts2020]

Knowing the shape of the visible universe should help our understanding of the mechanisms involved in cosmic expansion, plus it may give clues about what lies beyond

[bob000555]

If I’m not mistaken “A Brief History of Time” explains singularity as such: before the big bang the universe was of infinite density and temperature, thus it would be a 0-point singularity. The only logical way a 0-point figure could expand uniformly would be a sphere and assuming expansion has been uniform since the big bang he universe is still spherical; though that’s a rather big assumption.

[Pradeepkumar]

Maybe it is elliptical like our earth for it may also rotate something(just an imagination)

[Realitycheck]

If I’m not mistaken “A Brief History of Time” explains singularity as such: before the big bang the universe was of infinite density and temperature, thus it would be a 0-point singularity. The only logical way a 0-point figure could expand uniformly would be a sphere and assuming expansion has been uniform since the big bang he universe is still spherical; though that’s a rather big assumption.

 

What guarantees that the universe expands equally in every single direction for 14 billion years? Stars explode, matter accumulates, slowing things down as it runs into each other, fusion occurs again, while other areas race outward. It is shaped like a giant fuzzy wuzzy.

 

This picture should give you a good idea. Got the whole universe in my hand.

 

Edited October 12, 2008 by agentchange

[Martin]

Everyone wants to know the shape of the universe. It's a rather interesting question. But: is there a practical application of the knowledge?...

 

A better understanding of physical laws has oftentimes led to practical benefits. Understanding electricity and magnetism gets you things like electric motors and radio. Understanding quantum mechanics eventually gets you lasers and computer chips.

 

So a deeper understanding of physical law, well, it often leads to the discovery of new laws, and eventually often brings about things that you can't anticipate at the time.

 

The question you are raising, as a cosmologist would look at it, is whether or not the universe is spatially finite

 

The "shape" would follow trivially from the uniformity (to one part in 100,000) of the CMB, and indications that any overall curvature is non-negative. We can see from the CMB map that the expansion has been very very close to uniform in all directions.

 

the key question is Is space finite? If so then the shape is almost certainly the bumpy 3sphere that one or more posters have mentioned.

 

Evidence is building up that space is, in fact, finite. But it hasn't reached the tipping point. Infinite still provides a good fit to the data---it could go either way. But the 2009 launch of the Planck observatory will help decide. We should have more certainty on this score within 5 to 10 years.

 

If space turns out to be finite this could impact our understanding of the origin of presentday physical laws, in particular the Standard Model governing the behavior of particles---the microscopic interaction of matter fields and the vacuum. One can reasonably guess that deeper understanding may even suggest new laws----more fundamental than what we already have.

 

As I said earlier, an increased understanding of basic laws of physics (what they are and why they are what they are) has in the past produced a great richness of practical results. But it is likely to be impossible to see what they are likely to be. Faraday playing with coils and magnets would not have foreseen Radar, nor might Maxwell though he would have come closer. Trying to guess specifics is likely to be a waste of time. What you can be fairly sure about, however, is that there will be practical life-changing consequences of some sort.

[Dr. Jekyll]

Evidence is building up that space is, in fact, finite. But it hasn't reached the tipping point.

Have there been any new discoveries/data regarding this? Got the impression from the latest WMAP articles, and statements from cosmologists regarding WMAP, that they seem "more confident" that universe is flat/infinite.

[Martin]

Have there been any new discoveries/data regarding this? Got the impression from the latest WMAP articles,...

 

I think the last time you and I discussed this was in this thread

http://www.scienceforums.net/forum/showthread.php?p=394357#post394357

 

That was when the 5th year WMAP data came out---the WMAP5 report "cosmological interpretations" in particular. Let's examine that again.

 

BTW as far as authoritative WMAP stuff, I don't have anything more recent than that! That was around March 2008. If you have something more recent please post a link!

 

Here is the link to the latest authoritative paper I know of:

http://arxiv.org/abs/0803.0547

Two of the co-authors of this one are Ned Wright and Joanna Dunkley. I listen to what they say on the flat versus "nearly flat" issue with special attention. Both have warned against assuming flat in analyzing the data. I think it may be because of their vigilance that the report gives a lower bound for the radius of curvature. (Something that I think was new this time, I don't remember any earlier WMAP report doing that.)

Edited October 16, 2008 by Martin

[Realitycheck]

We can see from the CMB map that the expansion has been very very close to uniform in all directions.

 

How can you base your predictions of further expansion and uniformity thereof on the CMB, when it was only 380,000 years old? How does it have any effect on further expansion, especially when matter was so dense at that stage of the universe's "life".

[Martin]

Agent thanks, you caught some logical sloppiness/gaps on my part. Must have written that when either tired or in a hurry. I have to re-do the argument. Here is what I was saying, with a phrase added to make the intent clear:

 

...

The question you are raising, as a cosmologist would look at it, is whether or not the universe is spatially finite

 

[if it is spatially finite, then] The "shape" would follow trivially from the uniformity (to one part in 100,000) of the CMB, and indications that any overall curvature is non-negative. We can see from the CMB map that the expansion has been very very close to uniform in all directions.

 

the key question is Is space finite? If so then the shape is almost certainly the bumpy 3sphere that one or more posters have mentioned.

...

 

It probably was not clear what point I was trying to make. I will try to say it better. The point is that shape is not the important thing, the important issue is finiteness.

 

Keep in mind that for various reasons cosmologists assume a kind of uniformity or sameness---they assume the universe is approximately homogeneous and isotropic: that is, about the same in whatever direction you look and from the standpoint of any other contemporary observer. And it certainly looks that way! *points to the CMB.*

 

You are probably familiar with this, it is called the cosmological principle.

 

In brief form my point is, it's not the shape that matters, it's the finiteness. This is based on two things, one is that excluding some cases of funny topology: space finite implies it's a 3-sphere. The other is that practically speaking the only way we would know it's finite would be to find out it has positive curvature, and positive curvature implies it's a 3-sphere.

 

Now I am not a cosmologist, I'm just a retired mathematician who loves the stuff--I watch the field and follow new developments. As it happens I haven't myself gone over the argument, I see that the pros take this for granted and it seems obvious to me. But let's scrutinize it critically.

 

Keep in mind we don't know whether or not space is finite.

 

If it is finite, though, then the shape is just a consequence---it would come out as a kind of footnote to the finiteness.

 

Or, since the only way we are likely to ever be able to prove finiteness is by measuring positive curvature, you could say that shape would be a footnote to the discovery of positive curvature.

 

Now I haven't given an airtight mathematical proof of this! So I will have to think about it and get back to you on it. Before I regretably just waved my hands and alluded to the cosmological principle---the Great Sameness in the face that nature shows us. This handwaving is admittedly not satisfactory, so I will see what else I can come up with.

 

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Interesting issue. Here's some related stuff from Wikipedia

http://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture

". The claim concerns a space that locally looks like ordinary three dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold). The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point then it is just a three-dimensional sphere."

 

The business of being able to shrink any loop down to a point excludes funny topologies, like the donut (or worse). Toroidal topologies have been excluded, out to a certain large size limit, by surveys of the CMB that look for repetition and don't find it (hall-of-mirrors effects that aren't seen). Funny topologies somehow don't seem very likely.

 

Poincaré conjecture is another bit of evidence that it is finiteness that matters. Shape would just be a footnote. But again I don't have a completely airtight argument, at least not yet.

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A propos of positive curvature. The latest WMAP report gave a 95 percent confidence interval for the main curvature number Omega_k.

 

By historical accident, somebody's equation years ago, having this number turn out negative means that curvature is positive. Don't ask why, just the convention. The interval is:

 

-0.063 < Omega_k < 0.017

 

The point is that it is lopsided, three or four times more on the downside than on the upside.

Some people are betting that this confidence interval is saying that Omega_k is really exactly zero which would mean space is infinite with no largescale average curvature.

That turns out to be simple to work with mathematically and a lot of people would prefer that.

 

On the other hand if it is not exactly zero, then since the interval is lopsided it makes it seem plausible that Omega_k is negative, which is the positive curvature case.

 

The total Omega that people often mention is by convention equal to 1 - Omega_k. So, for example, if Omega_k = - 0.063,

then Omega = 1.063.

 

that would be a nice spatial finite positive curved case.

 

The relevant WMAP report is

http://arxiv.org/abs/0803.0547

this 95% errorbar would be page 4, Table 2, if I remember correctly. also in the conclusions section at the end.

Edited October 21, 2008 by Martin
multiple post merged

[DrP]

But: is there a practical application of the knowledge? If I find out that space is a sphere, what does that allow me to do besides change our textbooks?

 

 

If you DID find the answer you could make and market universe shaped doughnuts or jelly sweets in universe shapes. People would buy them for sure! You could charge a few pence/cents more than ordinary shaped sweets just because of your funky universe shapes! Every kid would want them!

[Realitycheck]

I'll say it again. Infinity does not compute when applied to the physical universe. Infinity is a mathematical term defined as an impossibly large, unknown quantity and that's all it is ... a mathematical term, meant to be used in equations. Realistically though, logically, it has no meaning. It's just a way to get around saying, "Well, we really don't know the answer, so we'll just call it "the symbol formerly known as x."

[Martin]

I'll say it again. Infinity does not compute when applied to the physical universe...

 

Go ahead, say it again---with rising passion. I only wish you were making sense. I would be delighted to know for certain that space is finite.

 

Unfortunately you and I are just slightly evolved monkeys. Our logic does not govern the universe (or didn't the last time I checked.)

 

All I get from your words is that something or other does not compute for you.

 

If you DID find the answer you could make and market universe shaped doughnuts!

 

This is helpful DrP,

it establishes for us the baseline mentality of someone who is unable to see why it might be of practical significance to know whether or not the universe is finite.

 

It's actually a fairly steep intellectual challenge. I feel a fair amount of uncertainty on my part. I suspect that it would be of enormous practical importance (besides being interesting in its own right) if we could know the universe to be spatially finite.

 

And I mean know on scientific grounds, not because somebody says the alternative doesn't compute for him