Vladimir,
There are a lot of Vladimirs in this contest:-)
This is an interesting essay. You present many novel ideas, perhaps even too many for a single essay. I suspect you could go into greater detail and make 3 or 4 essays from this subject matter. This is not a bad thing. It simply means you are very enthusiastic about your work.
Some of your ideas I am agreeable with. Some of the ideas I am less clear about.
The third paragraph of the Introduction clearly states the many difficulties that plague Physics in its present form.
I too am a believer that the vacuum is some type of medium ... I'm simply less clear regarding what its properties must be. I do think there is a scalar term present such as h/(2*pi) that accounts for vacuum energy and the lowest energy level of the electron.
You mention photons travelling for billions of years and suggest that they lose energy to the vacuum. This idea is frequently refered to as "tired light" ... i.e., the light is tired because it has lost energy due to the distance and time it has traveled. I'm less clear regarding this since I know of no evidence that the vacuum has any kind of viscosity. Even if the argument is made that there is a small amount of hydrogen present in interstellar and intergalactic space, it would not result in viscosity. It would behave like an extremely rarefied gas. Aerospace engineers have to deal with this type of analysis for airplanes that fly very high ... also for spacecraft in the upper atmosphere.
I like your idea of resonance and vortices. If you watch a fire, you will see lots of tiny spinning vortices in the flames. They flitter in an out pretty fast but sometimes they are stable. I think that nature prefers structures that are stable and this is one such possibility.
I am not familiar with the Mathieu Equation. You reference it several times.
A soliton is a very stable wave that does not interact with other waves. It does not act like a heat pump or any such analogy. Trust me on this. I'm a chemical engineer and we know heat pumps.
There is a way of eliminating some of the mathematical singularities that you mention. Milo Wolff did so in his Wave Structure of Matter theory. The essence is that the wave-function is a solution to the spherical wave equation and that solution is of the form (1/r)*sin(r). At r = 0, the value is one.
I like your analogy between gravity and the Lorentz Force. I have thought along that line of reasoning myself although I attribute it to a blend of absolute motion and relative motion. For me, the sun's motion through space creates the gravitation that keeps the planets and such in their orbits. This is what I mean by so many ideas .... just the idea of Lorentz type gravity could be a whole essay:-)
I have never thought about the speed of gravity as you describe. I do not think gravity propagates at light speed as is required by General Relativity. This is supported by the fact that orbit calculations are performed using the actual position of objects rather than the apparent position based upon light speed.
I've already written a lengthy response to your essay and I could easily go one. Let me simply close by stating that you have many novel and useful ideas that can be further developed. Just remember Occam's Razor ... The simplest idea is the best idea, but it must explain all that is observed. Well done!!
Best Regards and Good Luck,
Gary Simpson