The prevailing notion of elementary
particles as points, or even as strings, just didn't appeal to my sense of
aesthetics. So once I saw how solitons behaved -- that a continuum theory
could have solutions that look like coherent lumps interacting with one another --
I was hooked on the idea that this had to be the way the universe works. So
before anyone could tell me that what I was trying to do was impossible, I sat
down at my trusty NeXT and found a
Solitary Wave Solution to the Maxwell-Dirac Equations. The Maxwell-Dirac
equations are the foundation of Quantum ElectroDynamics and describe the interaction
of matter and light. No one expected solitons to pop up in this theory and my ideas
are rather unconservative (even if the math is correct) so I don't go around screaming to other
physicists about my discoveries lest they send in the men in white coats. Plus, although
these solitons have many intriguing properties, it's not at all clear that they
are in any way physically relevant. Nevertheless,
I did win first prize ($5. Wooo-hooo, more toppings for my pizza.) in a contest on
sci.physics to describe the electron.
I've
spent the past few years figuring out the first sentence of that description, which
was:
Start with classical General Relativity (minimize the curvature)
and compactify some dimensions (Kaluza-Klein theory) to get GR coupled to your
Dirac and gauge fields.
I've finally developed a way of deriving what a Dirac spinor field is within the context of geometry,
and am working on using that description to complete a unified description of
Geometry, Spinors, and Quantum Field Theory. Oddly enough, it may turn out that
this soliton I found originally, which led me to this whole investigation, is irrelevant within this new framework.
I just don't know yet, but it's been an interesting journey.
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