Hi Geoffrey,
I read your article in order to 1) compare it to the Rotating Wave (soliton) which I think is the basic form of fermion (eg electron) matter and 2) to see if I could find any enlightenment on quaternions, spin and Dirac Equation relating to the Rotating Wave.
To me wave particle duality does not necessarily mean that there is a particle there guided by a piloting wave. "Wave particle duality" refers to particle like phenomenae exhibited by a wave packet. I agree that the basic form of matter is a localized wave. I think that is what Louis de Broglie suggested in the first place. Furthermore, I think physicists have for many years considered matter as possibly a purely localized wave function, but the math of Relativistic QM best describes what is happening between the observer and the observed.
Your assertion that no one has understood the real "solution" for Dirac's wave equation for the past 80 years is not quite correct. From de Broglie to Dirac in the 1920's attempts were made to made to represent the waves in ordinary 3d space. The pilot wave was an alternate. Back in 1979, I had discussions with physicists and they were quite aware of the possible full wave mechanics for particles. That is when I realized that as per Dirac, the rotating wave might be the solution. Dirac put relativity into wave mechanics and got spin. Conversely if one puts classical spin into a wave function, you get relativity. I think some physicists may have even considered that relativity like QM both came from spin.
Even Dirac knew there was something profound about the spinor matrices since they involve only constants:
"They must therefore denote some quite new dynamical variables, which may be pictured as describing some internal motion in the electron. We shall see later that they just describe the spin of the electron." - Paul A.M. Dirac
I think I understand your "in and out" wave action and that you emphasize "metaphysics" plus Occam's Raor requires the simplest action. When I was trying to see what kind of wave mechanics could create a localized wave that exhibits relativity, I first considered waves bouncing back and forth in a shell or waves just interfering in space. However it didn't exhibit spin, so then I realized it might be just a classically rotating wave which in accordance with electromagnetism appears to exhibit relativity and quantum (wave) mechanics. As the light wave is bent around the sun, perhaps it could also be brought into a full rotation by some kind of "binding energy" and maintained.
I can't see how an "in and out" wave would create rotation. I can only say that chances of a straight on collison of waves would be rare and thus a rotation would somehow follow. If that is what you are suggesting, then diagrams and math would help. Definitely, rotation seems predominant in the universe from micro to macro.
Of course one wonders what is at the base of all this aether/space stratum and what more lies underneath this stratum that we are aware of.
I understand that you say the quaternions explain the spin in QM, but I don't see how that translates into a physical description of spin within your "in and out" wave. To me the quaternions substitutes for the vector addition. Vectorially, the Rotating Wave has vectors: Cbar = Vvbar Vrbar in special relativity. Vectors have "bar" after them. Squaring you get: C2 = Vv2 Vr2. Vrbar is the rotational vector and reflects the time cycle of the rotating wave. The fact that one can get and energy from the same vector addition by simply multiplying by mass (mC2 = mVv2 mVr2; mCbar = mVvbar mVrbar), implies that these vectors are indeed at right angles to each other and thus Vrbar is indeed about rotation.
I think the binding energy that keeps the rotating wave in rotation is likely the source of dark energy. The rotation of one wave will affect another and hence gravity, expansion, and general slowing of time. In a free falling universally accelerating reference frame, the relativistic equation of a Rotating Wave then becomes: Cbar = Vvbar Vrbar Vtbar where Vtbar is a radial velocity (outward or inward). The light line where C is constant spirals outward (time slows down) or inward (time speeds up). At the macro level this stug of war with interacting waves generally gives up binding energy. Astrophysicists might well have considered that already.
I gotta get and learn Latex,
Bill Christie
