The Big Donut

Written by on November 18, 2010 in Commentary with 0 Comments

“Can we visualize a universe that is both finite and unbounded?” – Albert Einstein.

It wasn’t all that long ago (relatively speaking) that mankind regarded the Earth as flat. Of course these days we know different but imagine going back to those times and explaining that the earth is round and it’s simply impossible to fall off the edge. You would surely get laughed at, or even worse, jailed by the church.

To an observer on the ground, the earth’s spherical surface behaves like an infinite space, allowing movement in any direction, forever. Take any timid sailor who feared falling into oblivion, up in a spacecraft to see the shape of the planet, and besides soiling his breeches, he would certainly see how this was true.

But what if the universe was infinite in a similar way with respect to extra-dimensions?

What if we too could travel out into these extra-dimensions look back and see the shape of our universe and realize it is also infinite with respect to a certain topology. What could that topology be exactly?

We are 3 dimensional beings living a 3 dimensional existence (actually 3+1 dimensions if you include time). We can move up+down, left+right, backwards+forwards, all the while our clocks tick as we move forward in time. If you were to take all this, our entire physical reality and squash it down into a flat plane with no thickness, only width and height, and put this into an empty higher dimensional space, how could you make our plane of existance infinite?

You could bring all the edges of the fabric together and produce a sphere, like what the earth is, but I don’t think that’s good enough. What I had in mind was a donut (or torus), for it too has closed surface like a sphere or ball but it has something more, a quality that I think is an important factor and crucial in how the universe evolves and could go on forever.

To explain what I mean, let’s start off with a Big Bang. The Big Bang theory has it that the birth of the universe came from an infinitely dense point called a singularity that suddenly expanded, cooled and created everything while it did. In fact it is thought to be still expanding today. There is so much supportive evidence of this fact that the Big Bang theory is universally accepted. And because of this, it should probably play a key role in determining what sort of hyper-dimensional shape our universe could be.

The very fact that the universe is expanding rules out any spherical shape because a sphere’s surface is uniform in every direction, is has no natural form to which matter could migrate from one place to another. Its like taking a toboggan out onto a farmer’s field, there’s no potential for movement!

However, a donut has more functional possibilities because its composed of a compacted central region that expands outward to a bulging peripheral boundary. In essence, we have a source of compression in the centre and a relief of it on the outer margins.

As an added bonus, because a donut’s surface is infinite like a sphere’s, the movement could be cyclical in nature. Expanding outward from the ‘donut hole’ to the outer boundary, then looping around the bottom side, returning back into contraction as it approached the centre. Hence a ‘Big Crunch’ and thus the completion of one full cycle.

An important thing to remember here is that I am reffering to the donut’s surface and not its ‘volume’.

As matter traverses the narrow part of the donut hole, it collapses into a singularity and gets squeezed out the far side as hot plasma. This creates yet another Big Bang Event. Behold, the carousel of existence!

The Good Word:

So, could the universe really be something as unsophisticated as a donut? No, of course not. The donut does not exist. It’s an idea, a concept to visualize the infinite properties of the cosmos from a vantage point in the ‘n’th dimension, similar to how Albert Einstein imagined the fabric of spacetime – ask yourself if spacetime actually exists? Or is it too a manufactured framework for the mind’s consumption, a place for the inconceivable to be given some degree of meaning.

If you don’t fancy donuts, I understand but I hope you can appreciate mankind’s remarkable ability to wonder about this grand universe. We don’t have all the answers yet and I suppose we never will. But in the interim let’s keep our eyes and minds open, and watch as this grand mystery unfold before us.

CJ

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