Scientists, skeptics, and critics often ask me “*where’s the math?*” when I describe Neoclassical Physics and Quantum Gravity (đť—ˇđť—Łđť—¤đť—š). It turns out that is a complex and nuanced question to answer.

First, I’ll list some of the blog posts that have at least a modicum of mathematical concepts.

- A Vulnerability in the Mathematics of Physics
- The Mathematical Foundation of NPQG
- Freeman Dyson: Is a Graviton Detectable?
- Planck Core Energy
- Nature and Math
- A Tale of Two Geometries

Objectively, we can state unequivocally that general relativity (GR) and quantum mechanics (QM) are incorrect because they do not offer a physical model. Neither GR nor QM theories account for point charges (electrino and positrino) nor spacetime Ă¦ther nor the recycling universe in their models. However, we also know that the math of general relativity (GR) and quantum mechanics (QM) effectively matches observation for a reasonably large set of conditions and that those theories make many predictions that match the real world. *How can this be? *

Let’s imagine that you are researching a large collection of X-rays and magnetic resonance images (MRI’s) of human hands in different positions, and you also have a well fitting glove for each hand studied. With these, you could develop a model for how a human hand works, without ever actually seeing or touching a human hand. Your model might actually be quite sophisticated and accurate. Still the fact would remain, that you had **never** observed a human hand directly. This is like GR and QM. GR is like the glove and QM is like the X-rays and MRI’s. The hand is the đť—ˇđť—Łđť—¤đť—š electrinos, positrinos, and spacetime Ă¦ther and how they behave in reality.

GR and QM math do not describe a classical foundation of the universe. Yet NPQG is a classical model. GR is based on a Riemannian spacetime geometry, yet the space in our universe is 3D and Euclidean. A spacetime Ă¦ther overlays the Euclidean space and implements a Riemannian spacetime. It would be a poor approach to adapt GR and QM math for a classical foundation. It is far better to approach GR and QM from fundamentals and first principles. Eventually this will lead to the ability to reproduce GR and QM math in their ranges and scales of applicability. I focus on the narratives and interpretations and the hierarchy of scaffolding built by the GR-QM era scientists. In doing so, I pick up on the “poker tell” when the theoretical or observational foundation or the narrative interpretation is weak, illogical, or contrary to my reasoning, logic, and intuition about nature. Understanding these weaknesses has provided many clues on where to examine closely for insight into đť—ˇđť—Łđť—¤đť—š. Those insights have led to hypotheses that, if proven, will create a firm foundation for ongoing science.

Consider scale. The electrinos and positrinos are point charges. An orbiting dipole has maximum curvature at a radius around . Assemblies of these point charges make everything – spacetime Ă¦ther particles, photons, neutrinos, protons, neutrons, electrons and all the other exotic particles of the Standard Model and Particle Data Guide. However, the most sensitive equipment in particle colliders can only detect particles of order . That is a sixteen order of magnitude gap. So when folks ask for the math, I sometimes think “**You can’t handle the scale!**” because nothing would be directly testable in the next decade at the scales I am imagining. Even so, given that NPQG is a classical theory, it may be possible to eventually develop math for the Planck scale that when scaled up would reproduce GR-QM era math.

As much as we would like to have easy math, we need to remember that everything is not rainbows and rosemary. Nature makes all math possible (in myriad ways), but nature itself may be modeled at different levels of complex reality vs. accuracy vs. precision vs. cost vs. response time vs. other application specific metrics. Similarly, while đť—ˇđť—Łđť—¤đť—š may be the basis for a theory of everything, we will always need a wide variety of application specific models. This raises the interesting question of which math to develop first.

Which math is a priority? Shall we start with the classical math of harmonic series? How does đť—ˇđť—Łđť—¤đť—š math map to GR or QM? Is the thermodynamic version of general relativity relevant to NPQG? What is the math associated with a Planck core and the conditions under which it will emit as a jet or rupture? At the most detailed model of reality, we need to think about the geometrical structure of the spacetime Ă¦ther. Does its geometrical structure change as a function of Ă¦ther energy? Is the Ă¦ther a foam? Is it a lattice? Does it tend to arrange in a face centered cubic (FCC) structure over some or all temperatures? Are there multiple geometrical lattice arrangements of spacetime Ă¦ther particles under different conditions? How does each form of standard matter-energy move through the Ă¦ther? What about faults, rips, tears, and holes in the spacetime Ă¦ther geometry? What about turbulence? What level of math is needed for the application? What math is required for simulation of various aspects of đť—ˇđť—Łđť—¤đť—š? These are **all** great maths to pursue at the appropriate time and it will require a large effort by many people to sort all this out and get it done.

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 universe foundation includes one and only one real 3D volume, called`

**space**, and it has a Euclidean geometry.**Space**extends beyond the observable universe and possibly to infinity in all directions.`There are only two types of fundamental physical objects, called point charges, and they have the following properties:`

`they are equal and opposite.they are immutable.they emit spherically expanding potential fields.they have a radius of immutability near the Planck length.`

`they carry a charge.`

`they may carry energy in kinetic form.`

`they may transfer energy in any real amount and this transfer is mediated by electromagnetic forces (not photons) between point charges.`

`The point charges 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.`

`The scalar and vector potentials caused by a point charge act upon any point charges they encounter.`

`Point charges may form assemblies.`

`Some assemblies are capable of exchanging quanta of energy while maintaining overall stability of the assembly.`

`One form of assembly is a spacetime Ă¦ther particle.`

`A spacetime Ă¦ther assemblies, aka Higgs, are made of from pro and anti Noether cores. Some of these may come from ultimately redshifted photons and neutrinos.`

`Spacetime Ă¦ther assemblies permeate the observable universe.`

`Spacetime Ă¦ther assembly size changes with energy.`

`Increased energy causes the spacetime Ă¦ther assembly to shrink in volume.`

`Decreased energy cause the spacetime Ă¦ther assembly to inflate or expand in volume.`

`At certain scales, spacetime Ă¦ther behaves as if it has a Riemannian geometry and at those scales it implements the geometrical spacetime in Einstein's theories of relativity.`

`Time`

`Immutable point charges do not experience time.`

`Time has its origin in the universal constant field speed @ of emitted potential.`

`Immutable point charges obey the physics of neoclassical`

electrodynamics`, in particular Maxwell's equations augmented for the full behaviour of point charges.`

`There are aspects of these sciences which are emergent behaviour of assemblies and do not apply directly to the fundamental electrino and positrino.`

s`Immutable point charge`

`and the assemblies they form are the sole inputs and outputs of interactions and reactions.`

`An interaction is defined by changes in`

potential and kinetic energy`without major structural change to their assembly.`

`A reaction is defined by change in the assembly of the inputs.`

`In its most concentrated form, energy in a motionless core of`

`immutable point charges,`

there is ~100% electromagnetic potential energy, ~0% kinetic energy, and ~0 entropy.

Immutable point charges 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 point charges. 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 immutable point charges at the Planck energy.** Second, there is no friction or heating of the point charges themselves. An isolated electrino-positrino pair or dipole could orbit at the closest possible point of approach with no loss of energy.

From the foundational elements of NPQG, structured assemblies emerge. Each emergent structure may be described in one or more mathematical languages of equations each based upon hypothetical mathematical foundations. In GR-QM-Î›CDM physics the mathematical foundation is often based upon the Riemannian spacetime of Einstein. However, in NPQG we know that the absolute foundation is Euclidean space and absolute time. We also hypothesize structure for each particle of spacetime as well as each particle of the standard model. The photon is a composite particle with a shell and no payload. The proton, neutron, and electron are composite particles with a shell and a payload. 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.

*Note: I expect that there is more to add in terms of foundational definition. The goal 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.*

*I am thinking in the absolute frame of 3D Euclidean space, instead of in the Riemannian spacetime of GR. Even then I haven’t quite figured out how to handle a Planck core in an SMBH. If the SMBH is spinning then it would seem the Planck core might be spinning too, relative again to absolute space. I can’t really see why the Planck core would be stationary in absolute space. So, it may be the Planck cores only approach Planck energy and density and zero entropy and cannot quite get there because of the spin. This will probably be an area of some intense math if NPQG gains liftoff. My intuition says that as a point charge state nears joining the Planck core, that its angular momentum around the core must match the core, so if its angular momentum is greater than the Planck core, it must steal angular momentum from the layers outside the core. If it’s angular momentum is greater than the Planck core then it must shed angular momentum to the layers outside the core. Since intense spin of SMBH seems to be what we think is happening in AGNs, I am leaning towards the latter.*

*When it comes to the gravitational potential energy there is a bit of a challenge, because it needs to be decomposed into both kinetic energy and electromagnetic potential energy. Once I determine how to do that then I can address the Lagrangian : Action = S = integral (KE – PE) dt.*

**J Mark Morris : San Diego : California**

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