It’s a hard problem, and I’m not a geometer, but I think they may agree. What are the best dynamical geometrical approaches to employ, ideate, and discover for the model of nature as a density of immutable unit potential point charges at various energies floating and flying around and creating repeating stuctures at various scales in R4. Oh, and the only thing discrete is the unit potentials themselves. Everything else, including the emitting spherical Dirac potential fields along their path, is continuous as modeled with R4. Even h-bar is a digital solution with an analog implementation in nature.
Then consider that the assemblies that form into repeating stable patterns are traversing a space time aether sea of smaller particles with very low apparent energy. From the perspective of tiny permeating aether particles, the unit potentials in standard matter are many orders of magnitude away. The energy density of Earth surface matter is noise compared to the energy density of inner dipoles of a Noether core.
It’s kind of overwhelming to think that each unit potential is interacting with every other unit potential or itself, and possibly on multiple potential field fronts. Still, don’t get too caught up in that on large scales because despite these effects we know that assembly structures form in certain conditions with a certain stability. Some structures appear to be quite stable. Therefore we realize that the assembly dynamics combined with the swirling 1/r potential fields and gradients tend to locally isolate the emergent structures to a large degree.
That means that models can differentiate and approximate the foreground and background potential fields and their complexity. It may be variously perturbative but must not be reactive in cases of stability. Long story short, pure geometrical models of standard model particles as assemblies of swirling unit potentials are highly desirable and we can learn a lot from them.
I think the concept of complimentarity, that to understand some object or domain properly may require different perspectives that are almost or actually mutually incomprehensible is a kind of wisdom that illuminates many questions and also encourages tolerance and mind expansion.Frank Wilczek – Riddles of Reality: From Quarks to the Cosmos : World Science Festival
This is a great quote from Frank Wilczek and perhaps the strongest evidence I have in support is the complimentarity of unit potential point charges where there velocity v is not limited by their field speed @. When the unit potential speed matches its field speed, at v = @, that is the main symmetry breaking point in nature. When v > @ we find ourselves in an unexplored world of unit potential self action. This symmetry breaking point and the unexplored behaviour beyond it is currently incomprehensible to scientists.
Yet another related field of study is about reactions and how they work including the provenance of each and every unit potential and all energy. This will be an amazingly lucrative area because we will find aspects of nature that enable us to safely gather energy as well as transmute elements. The pace of technology will be amazing with the source code to nature in hand.
Let’s zoom back to a basic thought experiment of two equal and opposite Dirac delta unit potentials in a Euclidean void of time and space and isolated from any other influences. Let’s begin our thought experiment with unit potential velocity magnitude less than potential field speed, i.e., where self action does not occur. What does each unit potential sense or receive from the other? It’s potential field of course. The emitter’s potential field is a Dirac sphere stream defined by the emitter’s path history (t,x,y,z). Of course this is a two way street. Each of our two point charges is both an emitter and a receiver. Each unit potential responds, or is acted upon, by the gradients of the potential. It is as if each unit potential is a perfect marble on that incoming wave with a velocity v (dx/dt, dy/dt, dz/dt) defining its own path history.
Is it straightforward to define this as a simple two body problem for velocity less than field speed? Does it make sense to abstract away from electrodyamics of classical point charges, while employing Maxwell’s equations as a reference model? Perhaps we should rebase on a geometry of path histories and Dirac sphere potentials?
The key equation is the action on the unit potential based on the Dirac sphere potential stream of it’s partner. The partner’s velocity at emission time factors in because that modulates the potential gradients at the receiver. Likewise the velocity of receiver point charge is also a factor in the action equation.
Aside : Note that there is feedback going back and forth between the unit potentials in our thought experiment. The action one causes on the other reflect back with a delay.
The scenarios when one or both unit potentials achieve a velocity greater than field speed along their path are quite rich and complex. The dynamical geometry of NPQG must cover the basic orbital patterns that are observed in nature. Of course this opens up a whole new territory of exotic scenarios as well. Perhaps some new technologies will emerge henceforth.
In essence we seek to discover the dynamical geometry of Dirac delta unit potentials emitting Dirac sphere potential wave streams along their path which is in turn acted upon by incoming potential wave streams from all other unit potentials and sometimes themselves. The speed of the Dirac sphere potential wave is the universal constant @. The speed c of the photon assembly varies and approaches @ in the limit of the coldest aether. The magnitude of the velocity v of any unit potential is not limited except by natural causes and there is an unexplored rich area of dynamical physical geometry when v > @.
I presume that many answers to questions about nature will be found by exploring the dyamical geometry of v > @. I’ve been leading up to this conjecture for quite some time.
It’s really a question for the best dynamical geometers of our era to explore the methods of modeling this implementation of nature. In the meantime, let’s forge ahead.