Nature is both discrete and continuous. GR-QM era physics understands and models nature and “particles” as fields. Everything is a field. There are no fundamental classical particles in GR-QM era physics. In contrast, the NPQG model is based upon two fundamental particles, the electrino and positrino and the fields they emit. In NPQG, particles are discrete, and local fields are continuous. If the natural world is physical with real particles, then the pure math used in GR-QM physics is employed at a scale larger than reality, where that pure math works. However, at smaller and smaller scales the discrete nature of the fundamental electrino and positrino particles plays an important role that is not accounted for in GR-QM mathematics.
At the scales of concern in the GR-QM era, the contemporary mathematics works well because the discrete aspect of nature is at scales well below consideration. It is as if the discrete nature of particles is like the epsilon-delta that leads to calculus. The granularity is so fine, that continuous math works.
One notable exception is the case where infinities arise in GR-QM theories. In the natural world, there may be a limit where nature does not continue to infinity in some dimension. A great example is the so called singularity in a supermassive black hole. Thankfully, a singularity can not occur, because the Planck scale is the limit of size and energy of a particle. Discrete nature means that divide by zero or integrals with infinite bounds may not match reality. If nature is truly quantized then as we approach the limit of nature, nature’s math may behave differently than theoretical math. The scale and precision of the math required depends on the question.
Aren’t different scales already assumed in physics — quantum vs. classical worlds? Yes, but at a different level. Classical physics at the macroscopic level and quantum physics at the microscopic level represent the progression of science in the GR-QM era. For many applications, classical models are still quite good.
If the NPQG model is correct and there are only two fundamental particles types (electrino, positrino) that occupy Euclidean 3D space, then these fundamental particles have real absolute (3D) positions in 3D Euclidean space at all absolute times. No uncertain quantum positions, no curvy spacetime, but real and continuous positions in absolute 3D space and absolute time. Then we can add layers of emergent behaviour as groups of particles form structures of composite standard-matter particles, or as they become particles of spacetime æther, or as they are subjected to the intense energy of a supermassive black hole, or as groups of them become atoms, or molecules.
“In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.”Wikipedia
Would the NPQG system of nature qualify as dynamical? Yes. We can definitely place nature in a 3D Euclidean space. No twisting or compression or curving of 3D space. We can place each fundamental point charge in a real location in that volume. Those same point charges make everything, including Einstein’s spacetime. Spacetime coordinates becomes a transformation based on the density and energy of the low energy composite particles that make the spacetime æther.
J Mark Morris : San Diego : California