"Not A Pilot-wave"
Hi Alan,
I support you in the argument to take off the blinders. Although I was never told to shut up and just accept the math, I was told that maybe I couldn't understand it. Fair enough, but I remember staying up all night throwing forks and spoons up in the air and pretending I was in an elevator so that I could understand the equation that I knew would be on the exam next day. I passed and Jimmy Haight my best physics teacher allowed me on the ski team where I learned more about gravity.
I agree that as you say "a more natural way out of this dilemma is to dispense with the point particle entirely, and obtain the discrete particle nature from purely wave phenomena".
That is what I did when I considered there might be a model of matter that explains both relativity and quantum mechanics. It is a rotating wave similar to your "helically rotating electric field vector corresponding to a circularly polarized (CP) electromagnetic wave". I have attached the general picture with the planar wave fronts arrayed around the axis of rotation which is in the forward (translational) motion of the rotating wave.
Note how the planar wave fronts incline in accordance with EM (wave front and electric + magnetic fields must be perpendicular to motion of wave). That exhibits phenomenae described in the Special Theory of Relativity (Lorentz invariance) and furthermore when accelerated exhibits phenomenae described in the General Theory of Relativity.
Of course when one considers the rotating wave (or field), then it logically explains gravity with required binding energy plus expansion of the universe and slowing of time. There is no need for the cosmological constant. I'm pretty sure I got the math right now on the Gkl derivation from the rotating wave.
The inclined planar wave fronts of the rotating wave (or field) look similar to a propeller (or vanes of a jet engine). If you fly a plane in a tight circle and the propeller spins only ½ the way, then it looks upside down. It will take the plane two trips around to get the spinor propeller back into the original state. I suspect that is a valid reinterpretation of the "Balinese Dance" or "Feynman Plate Trick" and the helical rotation would thus be an inherent requirement.
Good math makes good physics. I get a thrill of ah ha when the equation suggests a physical model and the physical models speaks back. The whole is greater than the sum of its parts. If one can dream up many dimensions, then one can look at alternative models, but certainly through the eyes of trained physics and math. My suggestion is to develop a special forum on the classically rotating wave (or field). It would be a work in progress with various specialists examining various attributes. There is also the technical application as well. I think there is already a patent application on the EM Propellor.
I got to go for my jog and think. That "mysterious angular momentum of spin" and "dark energy / dark matter" are beckoning. I'd love to one day run past Einstein's house in Princeton and then maybe go on to Greece. I bet Dirac would enjoy your article.
Bill ChristieAttachment #1: Rotating_Wave_picture_close_up.pdf