## Monday, March 16, 2009

### The Infinite Universe that Started as a Point

The beginning of our universe is shrouded behind a huge paradox. Recent observations seem to indicate our universe is open. Which basically means that it has infinite volume. Yet, and here comes the paradox, it started in a single point: the Big Bang.

Sure enough there are alternative solutions to the equations. It could have a closed universe. It's much easier to convince oneself that a closed universe can start at a single point. Imagine you have lost 1 dimension, so you live on a sphere. (there is no such thing as space outside of this sphere: you have become 2-D yourself.) At the moment of the big bang the sphere come into existance and expands fast. whereever you are on the sphere, if you look around you you see other galaxies move away from you. But, since the volume of this space is finite, it's not hard to imagine that at some point in the past it was zero, which was the time of the Big Bang.

Alas, observations say we are not in a closed universe, but in an open one. Logic seems to demand that if space is infinite now, it must have been infinite when the universe got created (unless you believe there was a time after the Big Bang that it suddenly became infinite). It was filled with matter everywhere, and moreover, this matter was expanding outward. In fact, it doesn't matter who you would ask, everyone would tell the same story: the universe is exanding outwards and galaxies that are far away are expanding faster than the galaxies that are close by.

I find that paradoxical. Yet there is a way out. It is described very well here. The basic idea is this. You can switch to another frame of reference. In this view the universe has finite volume and you can visualize it as an expanding sphere again. However, galaxies are packed into this sphere in a peculiar way. Due to the so called Lorentz contraction, distances become contracted for galaxies flying away at very speeds. Since the galaxies at the outer edge of the expanding sphere fly at lightspeed, radial distances are infinitely contracted there. And so we can pack infinitely many galaxies in an infinitely thin slice of space.. In fact, because there is infinitely mass at that rim, it forms a sort of wall (a singularity) beyond which there is simply nothing. So it is not useful to think of this sphere as expanding inside something else. Spacetime is not defined outside this wall. Btw note that you can not visit this wall to peek over it, because it is receding at the speed of light. Also, there is noone really at this edge because the picture looks the same for everyone!

Ok, we have now packed infinitely many galaxies inside a finite volume. Why is space then infinite? For that we need to realize that not only does space contract at high speeds, it also slows down time. So watches on those distant galaxies are moving at a slower rate relative to your watch. Again, this situation is perfectly symmetric: people on those distant galaxies don't notice their watches going any slower (that's because their brains go slower too, so we reason) and moreover, they observe our watches going slower too. Now, we introduce a new cosmic time. This is the time where every observer in the galaxy sets their watch at 0 at the Big Bang and takes their watch with them when they fly outwards. If we now measure the volume of space defined when all these watches display some constant time space becomes infinite. This is because time is standing still at the rim (according to us) and so the infinite space contraction and the infinite time dilatation cancel.

It's head-spinning, but the conclusion is that space was created infinitely large in one point.

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