The Mathematical Foundation of NPQG

Imagine that nature emerges from ample pairs of immutable Planck radius spherical particles, the electrino and the positrino, which are equal yet oppositely charged. These are the only carriers of energy, in electromagnetic and kinetic form. The are located in an infinite 3D Euclidean space (non curvy) and observe classical mechanics and Maxwell’s equations. 𝗡𝗣𝗤𝗚 explores this recipe for nature and how it emerges as a narrative and theory that is compatible with GR and QM, yet far superior in ability to explain the universe and resolve open problems.
For 𝗡𝗣𝗤𝗚 basics see: Idealized Neoclassical Model and the NPQG Glossary.

As I continue my physics and cosmology research I am learning more of the academic terminology. In this post I will apply that learning to the definition of the mathematical foundation of the theory and mathematical model of NPQG.

The Foundational Elements of Nature and the Universe

  1. The universe foundation includes one and only one real 3D volume, called space, and it has a Euclidean geometry.
  2. Space extends beyond the observable universe and possibly to infinity in all directions.
  3. There are only two types of fundamental physical objects, called Planck spheres, and they have the following properties:
    • they are equal and opposite.
    • they are immutable.
    • they are spherically symmetrical around the center of the sphere.
    • they have a Planck radius.
    • they carry a charge.
    • they may carry energy in relative kinetic form.
    • they may transfer energy in any positive real amount and this transfer is mediated by electromagnetic forces (not photons) between Planck spheres.
  4. The Planck spheres are termed the electrino and the positrino, and have the following hypothesized metrics.
    • The number of electrinos and positrinos found naturally in any given volume of the universe is expected to be statistically equal as the scale of the volume grows.
    • There is no limitation on the number of electrinos and/or positrinos in a structure other than as determined by the limits that arise from energy density. The highest density is the Planck core, which is hypothesized as an HCP/FCC lattice structure.
    • a charge of -1/6th e for the electrino.
    • a charge of +1/6th e for the positrino.
    • The electric field of the charge will be presumed to emanate from the center of the sphere as if it were a point particle.
    • Likewise, the magnetic field of a moving Planck sphere will be determined by Maxwell's equations with a moving point charge.
  5. Planck spheres may react to form composite structures.
    • Some composite structure forms are capable of exchanging quanta of energy while maintaining overall stability of the structure.
    • The canonical example is a composite shell of neutral electrino/positrino pairs that may or may not contain a payload of other electrinos and positrinos.
  6. One form of composite structure is a superfluid spacetime gas particle.
    • A spacetime gas particle is a shell with no payload.
    • Spacetime gas particles permeate the observable universe.
    • Spacetime gas particle size changes with energy.
      • Increased energy causes the spacetime gas particle to shrink in volume.
      • Decreased energy cause the spacetime gas particle to inflate or expand in volume.
    • At certain scales, spacetime gas behaves as if it has a Riemannian geometry and at those scales it implements the geometrical spacetime in Einstein's theories of relativity.
  7. Time
    • Planck spheres do not experience time.
    • Every composite particle with a shell experiences time as a function of the energy of the Planck spheres in its shell.
  8. Planck spheres obey the physics of classical mechanics and electromagnetism, in particular Maxwell's equations.
    • There are aspects of these sciences which are emergent behaviour of composite particles and do not apply directly to the fundamental electrino and positrino.
  9. Planck spheres and the composites they form are the sole inputs and outputs of interactions and reactions.
    • An interaction is defined by changes in motion of the inputs caused by other inputs without changes in their composite structures.
    • A reaction is defined by change in the composite structure of the inputs.
  10. The photon is a composite particle with a shell and no payload.
  11. The proton, neutron, and electron are composite particles with a shell and a payload.
  12. The neutrinos are hypothesized to be composite particles with a payload and no shell. The electron neutrino (three electrino/positrino dipoles) and muon neutrino (two electrino/positrino dipoles) payloads are loosely bound.

Planck spheres have no defined origination and no defined implementation. At the beginning of the NPQG era it is difficult to imagine a level of nature more fundamental than NPQG with its Euclidean space and energy carrying Planck spheres. However, as they say jokingly, never say never and it could be turtles all the way down.

The immutability property of the electrino and positrino leads to fascinating mathematical properties that are essential to the universe and emergence. First, there are no mathematical infinities caused by fundamental distances approaching zero in classical mechanics and electromagnetism due to use of point particles. This means there is no singularity in black holes and instead the ultimate density is a core of Planck spheres at the Planck energy. Second, there is no friction or heating of the Planck spheres themselves. An isolated electrino-positrino pair or dipole could orbit each other while touching with no loss of energy.

Note: I expect that there is more to add here in terms of foundational definition. The goal here is to define the minimum set of foundational elements, their properties, and physical laws that enable nature and the universe to emerge. I also hope to improve the mathematical specification.

J Mark Morris : San Diego : California : May 22, 2020 : v1

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