The Energy-Momentum Relation in NPQG

NEOCLASSICAL PHYSICS AND QUANTUM GRAVITY
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, QM, modified ΛCDM, yet superior in ability to explain the universe and resolve open problems.
For 𝗡𝗣𝗤𝗚 basics see: Idealized Neoclassical Model and the NPQG Glosssary.

In NPQG we understand that the speed of light (i.e., photons) through spacetime æther is determined by the the local permittivity and permeability of the spacetime æther as the light travels.

\mathbf{c^{2}=\frac{1}{\epsilon \mu }}

The local permittivity and permeability are determined by the density of electromagnetic energy in the neighborhood of each point in the spacetime æther. The higher the energy density, the slower the speed of the photon in an absolute frame. Note that when we say local density of energy, this includes the attenuated contribution from all sources in the universe that arrive at a given moment.

In this post I will discuss the energy-momentum relation and how it “relates” to NPQG. Here is the equation definition with a slight correction since we know that c is not a constant in the absolute frame.

In physics, the energy–momentum relation is the relativistic equation relating any object’s rest (intrinsic) mass, total energy, and momentum:

\mathbf{E^{2}=(pc)^{2}+\left(m_{0}c^{2}\right)^{2}}

holds for a particle having intrinsic rest mass m0, total energy E, and a momentum of magnitude p, where the constant c is the speed of light, assuming the special relativity case of flat spacetime.

Wikipedia

Momentum p is given by intrinsic mass times velocity.

\mathbf{p={m_{0}}v}

Let’s rewrite the energy-momentum relation.

\mathbf{E^{2}=({m_{0}}vc)^{2}+\left(m_{0}c^{2}\right)^{2}}

Let’s consider the intrinsic energy of a particle.

\mathbf{E_{0}=m_{0}c^{2}}

Let’s rewrite the energy-momentum relation in terms of intrinsic energy.

\mathbf{E^{2}=({m_{0}}c^{2})^{2} \frac{v^{2}}{c^{2}}+\left(m_{0}c^{2}\right)^{2}}

Simplifying.

\mathbf{E^{2}=(E_{0})^{2} \frac{v^{2}}{c^{2}}+\left(E_{0}\right)^{2}}

or

\mathbf{E^{2}=(E_{0})^{2}( \frac{v^{2}}{c^{2}}+1)}

or

\mathbf{E=E_{0}\sqrt{\frac{v^{2}}{c^{2}}+1}}

This is an absolutely fascinating equation. We can clearly see that as the velocity approaches the speed of light, that the energy will be two times E0. The kinetic energy will exactly balance the electromagnetic energy. For the velocity of a particle to approach the local speed of light, the energy density is so high that the absolute velocity of a photon is approaching zero. Thus when a particle approaches the speed of a photon this is the state that represents the slowest absolute motion which in turn is driving kinetic energy in relation to electromagnetic energy. This kinetic motion is a very slow rotation of dipoles. I expect this will correspond to H0, the Planck “constant” of angular momentum when v=c. Note that at the Planck scale, having any angular momentum at all is a really big deal and represents an immense amount of energy.

Now let’s apply our conversion to local permittivity and permeability.

\mathbf{c^{2}=\frac{1}{\epsilon \mu }}

So, let’s rewrite the energy-momentum equation with our new physical understanding.

\mathbf{E=E_{0}\sqrt{v^{2}\epsilon \mu+1}}

This is the fundamental formula that relates rest energy of a composite particle to velocity and local energy density.


At the Planck scale, as found in a Planck core of Planck spheres, the permeability and permittivity are not infinite. The speed of a photon is slow, but not zero. Therefore we need to add two new Planck constants, \mathbf{\epsilon_{P}} and \mathbf{\mu_{P}} . As we evaluate the true constants of nature we may find ways to express these in terms of other constants.

This post has illuminated the energy-momentum relation, but it has also opened the door to further insight. We still need to discuss more about the Planck constant of angular momentum. We need to understand the physical basis of potential energy. We need to understand how kinetic energy and electromagnetic energy relate as a function of spacetime æther energy. We appear to have equal kinetic and electromagnetic energy at the Planck scale and more variation in forms as we inflate/expand from Planck scale.

We also need to think on the concept of work at the Planck limit “Work transfers energy from one place to another, or one form to another.”—Wikipedia. In all of these efforts it is important to purify the physical understanding in concert with the mathematics so that everything irons out seamlessly. For example, one open issue is whether the Planck spheres in a Planck core actually come to a halt or have a minimum velocity. I am inclined to think it is a halt relative to each other with a phase change. However, even then it is somewhat confusing because presumably a Planck core would not be fixed in absolute space so it would still have kinetic energy from rotation or translation.

J Mark Morris : San Diego : California : June 20, 2020 : v1

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