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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."
"Your theory of a donut-shaped universe is intriguing, Homer. I may have to steal it."
God spoke to me.
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.
make world, not war
Ha! When I submitted it it was available for free. They must have changed it when they noticed all the /. traffic.
You mean we're trapped inside a giant Asteroids-3D screen level?
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Right in the very middle.
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.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
Bagels aren't mathematically delicious enough to fit the equations.