Saturday, December 14, 2002

Finally



(danger: contains rambling about theoretical physics)

After thinking and working about the problem for YEARS, I think I've finally discovered what spinor fields are and where they come from. The trick is to use a fairly new formulation called BRST (after the initials of the inventors) that deals with the gauge degrees of freedom in classical and quantum systems. It turns out that applying this BRST formulation to the system of gravity as described by the curvature of a Clifford algebra fibre bundle leads directly to the appearance and dynamics of anti-commuting spinor fields. It's perfect. And it explains, well, everything. OK, maybe it doesn't explain love, or why women derive such pleasure from painting their toenails, but everything below that. Or at least it will when I couple it with Kaluza-Klein theory.

I put the paper up on the physics archive a couple of days ago. There is only one guy in the world I expected to understand it right away, and he wrote back and seemed quite excited--a good sign. But, other than that, there's been no response at all, which is kind of disappointing. But I suppose not too surprising, as I'm not exactly a famous dude, nor is my research in the main stream. But that's just because the main stream is whacked.

So now I've got a great new toy to play with. It's really cool. The path I took to finding it was, of course, completely absurd. I started out, in grad school, by finding a soliton in the standard spinor equations. But no one, including me, knew quite what to make of it. So, in order to figure out an interpretation, I had to figure out what spinors were. And, much to my disgust, there really was NO good reasons for spinors to exist and be what they were. They just had properties cooked up to make them describe particles, and had no geometric justification. So I had to backtrack, in typical INTP fashion, all the way to the beginning and find it myself. And now I have. And with this good foundation I can finally move forward. After YEARS! Anyway, like I said, it's pretty cool. It will be really funny if my original solitons make sense in the new context, but I haven't even gotten around to thinking about that, and the foundation I've built is good regardless and opens up many earth shattering possibilities. Well, if you're one of the .0000001% of the population excited by that sort of thing.

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