This is an elegant solution, the cause of low energy nuclear reaction (LENR) is the force F of m space itself. It has to be modelled to be positive in order to overcome the strong nuclear force that binds the protons and neutrons together. In the words of Bob Dylan, “The times they are a changin'”. I agree that the masses of the elementary particles are given by the geometrical structure of m (r). In the last analysis F (the m force) is given by the spin connection and gamma connection in Eq. (17) of Note 431(1). Elementary particle mass is also determined by this geometry. The proton for example, is made up of two up quarks and one down quark in the standard model. If quarks indeed exist, as claimed, then their mass is also given by Cartan geometry, which can also explain why there are up quarks and down quarks. However the quark model is full of strange concepts and quantum chromodynamics is also plagued with renormalization and regularization, asymptotic freedom and so on. It is better to start an entirely new theory of nuclear physics, m theory. All the products of a heavy hadron collision are described in UFT247 and UFT248, so these products become manifestations of Cartan geometry. Low energy nuclear reaction is also a manifestation of Cartan geometry. In getting a low energy nuclear reaction to take place, the experimenter effectively modifies F by trial and error. The theory could give guidelines as to how to maximize the probability of LENR taking place. Conventional fission and fusion are also described in terms of F. The basic advance is that LENR is understood as taking energy from m space itself. The force due to m space on the classical level has been demonstrated to be the same in Euler Lagrange and Hamilton dynamics.This leads to Eqs. (24) and (25) of Note 431(1). The m theory could also be applied to explain why there are hadrons, leptons, gluons, colour and so on. It may turn out that these concepts can be entirely replaced by m theory.

Note 431(1) : Masses of the Elementary Particles and LENR

PS: I extended the m(r) model function to negative values within the nuclear radius which is 1.6e-5 a_0 for the proton. Then the force is positive within the radius, there is a pole at the radius (see last figure of the protocol). This pole could represent a natural boundary which is overcome in LENR processes.

Horst

Am 06.02.2019 um 13:06 schrieb Horst Eckardt:

This is a highly interesting note. It uses the ECE wave equation to determine expressions for the particle mass. This is an idea I wanted to discuss with you at any time, now the time is has come 🙂

In eq.(13) there seems to be a typo, it should read -R instead of +R according to the earlier ECE papers. The values of m1 should be constants, therefore probaly an integration over the particle radius is required to obtain m1 from (33) for example.

There is another problem with the sign of F. With our standard modeling functions of m(r), F is always negative because ofr dm(r)/dr < 2m(r)

and

dm(r)/dr > 0.I am preparing some graphs to show this. It may be required to set up a more sophistiated modeling function which behaves different within the particle radius. This is a parametrized solution but may be a first step to a obtain positive LENR energies. Of course we should develop some ideas of the mechanism because most nuclei are stable with the same m(r) function in all undisturbed cases.

Horst

Am 06.02.2019 um 11:22 schrieb Myron Evans:

Note 431(1) : Masses of the Elementary Particles and LENR

This note shows that the masses of the elementary particles can be understood by Eq. (12), each particle is defined by its individual m ( r ) function. LENR is understood straightforwardly in terms of the Casimir force (24) of m space discussed in the immediately preceding paper UFT430. Under the condition (28) this force due to m space can easily become greater than the strong nuclear force binding protons and neutrons, so the nucleus splits apart, emitting the energy (32), and causing transmutation.This process is observed as heat. The process has been shown to be reproducible and repeatable many times, and is part of mainstream science. It was discovered in the University of Utah as is well known. There are industrial and military LENR plants, and it is hoped that domestic LENR heaters are just around the corner. The problem has been controlling the heat, so the container does not melt. It is blazingly obvious, to coin an awful pun, that the heat is there. LENR is vastly more efficient than conventional sources of power and heat. The heat can be used to drive turbines and produce electricity. In making a LENR device, the experimenter has effectively tuned to condition (28), discussed in great detail by Horst Eckardt in UFT417 and UFT430. The m(r) function is linked to the R function of the ECE wave equation in Eq. (17). So m(r) has been described self consistently in terns of Cartan geometry.