Doughnut-Shaped Universe Back In the Race

SpaceAdmiral writes "The once-popular idea that the universe could be small and finite is making a comeback. Many researchers thought that a 'wraparound' universe would mean that distant objects would be seen multiple times in the sky, but new research suggests that a '3-torus' (or 'doughnut universe'), as well as other shapes, could fit our actual observations, particularly the WMAP data."

Comments

That's silly.

[ivanmarsh]

Though it's possible, how many other things in the universe are naturally doughnut shaped?

Re:That's silly.

[wass]

It's primarily the boundary conditions that are leading to the 3-torus idea.

A torus gives periodic boundary conditions in two dimensions. Periodic boundarty conditions for one axis can be thought of as curling a piece of paper around to make a cylinder. For someone on this paper, picture running on a soccer field, and if you run out of bounds on the left side you pop back in in the right side, aka pacman's tunnel. To make a torus, you'd need to wrap the top exposed circular edge to the bottom circular edge, in a donut way. You'd need to bend the paper to do this, so you'd really need something like a rubber membrane. But once you connect this, then you have a soccer field where when you kick a ball behind your opponent's goal, it comes out from behind your goal. That is 2-D boundary conditions. The simplest shape that can manifest these boundary conditions of a two-dimensional system is a torus, which exists in 3-D.

Now extend this one step further. Take a 3-D space, and add periodic boundary conditions for left/right, back/front, and also top/down. This is the 3-torus that is discussed in the article. Someone confined to this 3-D surface has a full three independent degrees of freedom for movement, but the manifestation of this shape would look more complicated in four or five dimensions. But that is what is being talked about here.

Of course in quantum cosmology there are other dimensions, such as the warped 5th dimension of the Randall-Sundrum model , which may or may not be periodic, and add to very peculiar topologies of the universe.

Re:That's silly.

[mikael]

You mean we're trapped inside a giant Asteroids-3D screen level?

Re:That's silly.

[exp(pi*sqrt(163))]

Yes. There's no need for these long-winded explanations. Asteroids is played on a 2-torus and if it were a 3D game where going off the 'front' brought you on at the 'back' then it'd be played on a 3-torus. Interestingly, asteroids played on a circular screen where going off one side brought you back on the other would be on a completely different topological space, the cross cap. But if you think about it there's an interesting issue with that: going off one side would bring you back on the other side reflected. There would be some pretty weird consequences if our universe were like that.

Obligatory Simpsons quote

[CrazyJim1]

"Your theory of a donut-shaped universe is intriguing, Homer. I may have to steal it."

Re:Obligatory Simpsons quote

[pak9rabid]

Hehe..another favorite Hawking quote (from Futurama):

Nichelle Nichols: "It's about that rip in space-time that you saw!"
Stephen Hawking: "I call it a Hawking Hole."
Fry: "No fair! I saw it first!"
Stephen Hawking: "Who is the Journal of Quantum Physics going to believe?"

Pay for the article?

[NecroBones]

I'd love to read it, but... what's with all these pay-to-read links lately?

$8 for an article? Most magazines cost less.

Re:Pay for the article?

[SpaceAdmiral]

Ha! When I submitted it it was available for free. They must have changed it when they noticed all the /. traffic.

Re:Pay for the article?

[LurkerXXX]

One of my old mentors was the editor of a journal. He had a secretary who was paid by the journal because there is a boatload of work to do in managing submissions, finding reviewers, sending copies of submitted articles out to them, bugging them to get in their reviews, sending out critiques to submitters, checking rewrites, resending out answers to criticisms,etc, etc, etc. Editors also get pay, because it sucks up a LOT of time. Much more than reviewer time, which can already be a lot for some folks.

So there are defiantly costs involved. There's also the salary for the folks working the presses making the dead-tree copies. Magic faeries also rarely run the journals website. I know I'd want to be paid for running it. Wouldn't you? So there are lots of costs involved. The publishing companies also want to make a profit on top of that. Now I won't argue with you about how much profit the publishing companies should make off it. Just wanted to point out that there are very real expenses involved in making a journal, even with free reviews.

your theory has a hole in it!

[peter303]

Right in the very middle.

suggestion /. stop advertisementing for pay sites

[frovingslosh]

To read this story in full you will need to login or make a payment

So what's the point in running this if we have to pay to RTFA? Supposedly anyone already paying is likely to read it anyway, so the only ones this posting is for is for those who do not already subscribe to the site. In a world where information wants to be free, I hardly see it as appropriate for Slashdot to hype up a pay site. Were there no interesting articles on any free sites today? Or did Slashdot get a payment for posting this advertisement for this pay site? Did paid subscribers to /. also see this ad sneakily disguised as an article (if so I bet they resent it even more than I do).

Re:Questions.

[esampson]

...Or is the idea of an edge just not valid? ...

It isn't valid because a 3-torus is a 4 dimensional shape. To be more accurate it is valid, but not in a way you can conceive of.

Think of it in these terms; you are a two dimensional creature. Your world is defined solely by X and Y coordinates and is of a finite size. Take two opposite sides and bring them together and now your world is a tube. The only edges you can perceive are the ends of the tube. Take the two ends of the tube and bring them together. You are now living on a standard torus (not a 3-torus). As far as you are concerned there is no "edge" to the torus. Roam as much as you want to but you will never reach an edge. The only way for you to experience an "edge" would be if you stepped up one dimension and became three dimensional.

A 3-torus is a similar construct but instead of being a two dimensional world with the X edges and the Y edges brought together it is a three dimensional world in which the X edges, Y edges, and Z edges have all been brought together. From your three dimensional perspective there is no "edge" and the only way to perceive one is to step up a dimension and become a four dimensional entity.

Re:suggestion /. stop advertisementing for pay sit

[Anonymous Coward]

FWIW, here's the preprint.

Re:Scientists

[grahamd0]

Bagels aren't mathematically delicious enough to fit the equations.

Here it is!

[spun]

I just looked it up and you are correct. Here's what I found:

"There is no way of taking a man and moving him about in space, as ordinary people understand space, that will result in our changing his sides. Whatever you do, his right is still his right, his left his left. You can do that with a perfectly thin and flat thing, of course. If you were to cut a figure out of paper, any figure with a right and left side, you could change its sides simply by lifting it up and turning it over. But with a solid it is different. Mathematical theorists tell us that the only way in which the right and left sides of a solid body can be changed is by taking that body clean out of space as we know it,--taking it out of ordinary existence, that is, and turning it somewhere outside space. This is a little abstruse, no doubt, but any one with any knowledge of mathematical theory will assure the reader of its truth. To put the thing in technical language, the curious inversion of Plattner's right and left sides is proof that he has moved out of our space into what is called the Fourth Dimension, and that he has returned again to our world." The Plattner Story

That was written in 1896, putting it 12 years after Flatland which I think was the first treatment of the theme of the consequences of differing numbers of dimensions. Nothing new under the sun, eh?

Re:The Problem With Curvature

[Tangent128]

Nonsense. Look at the faces of a geodesic dome. Each face is discrete, but the structure as a whole is curved for all practical purposes.