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

`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 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.`

`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.`

`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.`

`One form of composite structure is a spacetime æther particle.`

`A spacetime æther particle is a shell with no payload.`

`Spacetime æther particles permeate the observable universe.`

`Spacetime æther particle size changes with energy.`

`Increased energy causes the spacetime æther particle to shrink in volume.`

`Decreased energy cause the spacetime æther particle to inflate or expand in volume.`

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

`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.`

`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.`

`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.`

`In its most concentrated form, energy in a core of Planck spheres, there is ~100% electromagnetic potential energy, ~0% kinetic energy, and ~0 entropy. In its least concentrated form, near 0 Kelvin, there is ~100% kinetic energy and ~0% electromagnetic energy, and entropy is maximized.`

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.

From the foundational elements of NPQG, structure emerges. Each emergent structure may be described in one or more mathematical languages of equations each based upon hypothetical mathematical foundations. In GR-QM-ΛCDM 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’m still thinking about Lagrangians. I think electromagnetic potential* *energy is still a solid concept in NPQG and would include the same thing as GR-QM era physics. I made some progress on the two endpoints at near Planck temperature and near 0 Kelvin : In its most concentrated form, energy in a core of Planck spheres, there is ~100% electromagnetic potential energy, ~0% kinetic energy, and ~0 entropy. In its least concentrated form, near 0 Kelvin, there is ~100% kinetic energy and ~0% electromagnetic potential energy, and entropy is maximized. This latter state may not be possible unless there are regions of the universe where spacetime æther is very diffuse or even decayed and there are no photons and neutrinos flying through. So presumably we can only approach closely to the latter state in nature – in deep free space, possibly deep into a cosmic void.*

*I am thinking of 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 sphere 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 temperature and Planck 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 Planck sphere state nears the point of 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. My general thought here is that as a particle moves from higher gravity to lower gravity that the kinetic energy density of the Planck spheres in the particle shell increases and the electromagnetic energy density decreases.*

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