| To Infinity and
Beyond! Is the Universe Finite? Is the Universe finite in volume? This option had been discarded for a long time, until mathematicians started studying different types of geometries and manifolds. To fully understand the possibilities, let us start our discussion focusing on several possible 2-D finite worlds that we could encounter.  One
possibility is living in a 2-D world which is like the surface of a
sphere. No matter in which direction we move, as long as we move in a
straight path we will be back at the starting point.
Another interesting possibility is the following. Suppose we live in a finite rectangle, where we have identified the edges as in the following drawing (so you just have to glue the sides, a with a and b with b in such a way that we match the arrows):  Thus if you walk out
through the "a" side on the right, you come back through the "a" side
on the left. The resulting surface looks like this.
Now suppose that instead of glueing side "a" with "a" matching the arrow, we glue the sides "a" with "a" but we flip the right side first. The surface we get looks like this (we obtain the so-called Mobius strip). Notice that the Mobius strip in "non-orientable". If we glue side "a" with side "a" flipped and side "b" with side "b" (not flipped) as in the picture:  then we obtain this surface instead (the so-called Klein
bottle). Now, the challenge is to imagine these possible worlds in 3-D.
In fact, there is certain Cosmological facts that may indicate that our Universe is finite in volume. The observations (using NASA's WMAP sattellite) of the effects of the Universe's vibrations in the past show that there are certain types of vibrations which are significantly depleted, and this fact has no explanation so far. However, if the Universe is finite, then certain wave lengths would be depleted, in some sort of wave cancellation effect.  |
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