Thursday, July 31, 2014

Why is Space 3D?

A friend got me thinking about this basic question, here I write ideas related to it.

There is a perception issue to begin with. If your rooms are not cubes, like most people's, from my city of birth, you may not know what 3D is. Then you have to go to a technical high school like I did, and then you learn everything about vectors, having fun with it, like I did. I still remember explaining to a friend, who was absent that day, these ideas. I was really excited. We had already studied Cartesian Geometry in a previous lesson. All the abstract frame, was in my head, by the time I was a teenager.

Now I am over sixty, and I still don't know, why it is so. I do not feel bad, because nobody does.

Now I know much more, I even  personally met one actor of this narrative. Let me start there:

Manoj Prasad, was a very young, and famous person, when I met him. He discovered, with his professor Michael Sommerfield, what we now call, the Bogomol'nyi-Prasad-Sommerfield monopole. Neat exact solution, to a Non-Abelian field. To this day nobody has seen one of these, in the real world, so far it only exists in our minds.

As it turns out, these exact solutions exist in 3D, and through the magic of the gauge field, involve time as well. We know we live in 3 huge spatial dimensions, and something inside, or prior to us, maybe the so-called strings, has been around during a huge time. To be exact 13.798±0.037 billion years, according to Wikipedia.


It gets curiouser and curiouser, as Alice in Wonderland says.

Enter Roger Penrose, unfortunately I have not met him personally, but two friends did. One was his contemporary, Jerzy Plebanski, and the other is younger than I, Gerardo Torres del Castillo.

Penrose loved complex variables, like I did. He was studying mathematics in England, and had the insight, that a set of two complex manifolds together, would make a neat mathematical representation, of the four dimensional macroscopic space, we were born in. This proposal goes by the name of Twistor Theory.

To finish this note, I link to the computer calculations done by a Japanese group, as reported a few years back.

You can read about it in Discover Magazine.

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