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3    The Fundamental Field Equation

The following equation is fundamental in understanding how the four force fields interact and come together for this new unified field theory:

D = (E/cG) / Pi(sub2)

where D is the relativistic density, E is the energy of the unified field, c is the velocity of light, G is the universal gravitational constant, and the last part of the equation, / A2*, will be explained below.  D and E are tensors with eigenvalues and quantum states associated therewith.

*"A2" should read "capital Pi, sub-2"

3.1    Density Dependence, D

The density is the dependent variable; changes in the energy (energy flow in and out of a region) cause changes in the density.  For example, the energy flow to and/or away from any space-time continuum along the gravitational diallel lines determines the corresponding change in the density in that space-time continuum.  Appreciating the energy field at the particle as well as in a region is central to the understanding of this theory.  The energy can come from any of the force fields.  For example, both equations apply: E = mc2, where m is the relativistic mass and E = hv, where "h" is Planck's constant "v" is the electromagnetic frequency of the photon.

Energy can come from the other force fields as well.  Later we will see some spectacular and very important examples of this interplay of the force fields.

3.2    Parallel Component (A2)

A dimensional analysis of the above equation reveals that A2 has dimensions of length, time and mass as the four known fields interact.  The forward slash "/" denotes being parallel in the unified field theory's mass-space-time continuum. The "sub-2" on the "A" denotes that part parallel for the receiver in the space-time continuum with respect to the energy emitted by the transmitter along diallel lines in its environment or region.

Combining the energy with this term we have E/Pi2.  Hence, we see that this denotes the energy per mass, per length and per time taken in the parallel direction of the local diallel lines.  The quantity in the denominator of equation(1), cG, is the normalizing factor, so that the dependent variable, D, is the density factor taken in the parallel direction of the diallel lines.  It is the density that is the final determining factor for the force fields -- the four known fields plus a fifth.

The subscript "sub-2" denotes the receiver of the energy field.  Since the change in the source of the energy field is implied to be the initiator of the density change, it is implied as being "sub-1."  Thus, the reason for no subscript on the energy, E, and the resulting density, D.


4    Characteristics of Equation (1)

4.1    Density and Energy relationship

The dependent variable "D" can also be taken as density of matter in the usual sense: mass per unit volume.  But in general, "D" is a tensor description as the dependant variable resulting from that part of the energy tensor, "E," given by the parallel part A2, as will be described later.

This equation has application at both the particle level as well as the macroscopic level.  For example, we may conceptualize a particle placed in a quantized energy field, which field can come from any of the force fields.  A particle interacts with this combined field to determine its density (quantum state, for example).  One may think of it as an energy pressure: the greater the energy the greater the density.

The constant of proportionality is 1/cG.  The speed of light, c, is also the speed of gravitational waves.  The velocity of light squared, c2, is also the proportionality constant in the conversion of mass into energy, since E = mc2.  Of course, 1/c2 is the proportional constant in the opposite conversion of energy into mass, since m = E/c2.

The universal gravitational constant, G, logically is needed to tie the gravitational field to the other energy fields. We see that the density, D, has great significance in this new theory.

4.2    Behavior of Particles in the Unified Field Theory

4.2.1 Behavior of Electrons

A free electron, with no other outside forces, naturally spirals downward along a diallel gravitational field line toward the mass center -- reminiscent of the appearance of the DNA structure.  It spirals clockwise as one looks down along this diallel line, and while so traveling it can exist in one of several quantum states.  It will emit or absorb photons as it changes from one quantum state to another similar to what naturally happens within atoms and molecules.  One has direct evidence of this in the Aurora-Borealis with complementary spin directions of the electrons in the diallel lines and in the magnetic field of the earth, and some of the quantum states are evidenced by the multiple colors of photons emitted during this phenomenon.

In this simple model for the electron, one observes that there are two forces: 1) gravitational -- pulling the electron, as it spirals along this diallel gravitational field line, toward the mass center, and 2)the attraction keeping it in its quantum state with respect to a particular diallel line.  Its quantized-spiral energy state is determined by the energy field in which it finds itself.  This will become evident in some experimental examples -- given later.

From this new theory, we learn that when an electron reaches the mass origin (such as the center of the earth, for example), its energy typically contributes to core heating in different ways.  At the center of the earth, a controlled fission process is on going.  These entering electrons can contribute to a variety of nuclear reactions.  If a high energy electron combines with an available proton -- creating a neutron -- then a large quantum of photon energy is necessary to make up the mass deficit; this process is part of the cooling stabilization necessary for core equilibrium. There is a change in momentum as it reverses its direction of spiraling and starts up a diallel line. Significant heating takes place at the center of the earth, for example, as a result of this reversal because of the enormous net number of electrons that flow through the center of the earth -- maintaining the earth's magnetic field.

Since free electrons are in much greater abundance than most any other atomic particles, their behavior is of primary interest. They are the principal "food" from the sun for the earth. Since they carry a negative charge, and they are extremely light, they become a very useful tool for experimentation and verification of the theory.  We will see this in the experimental section.

Because electrons repel other electrons, the earth has a significant shell of high electron density at the surface of the earth. This is like the surface tension for water; this shell creates a barrier, but is penetrable.  After an electron enters the earth along a diallel line with a sufficient velocity to penetrate the electrostatic force at the shell, it will continue along a diallel line to the center of the earth and out on the opposite side with no net effect from the electron shell, if it does not interact with the fission process at the core, or if it is not reflected by the core.

For a homogeneous sphere, these diallel lines are along diameters and are straight in a non-rotating frame of reference.  In a rotating frame, they will appear curved as do light beams.  This must be accounted for in experiments using the rotating earth as the platform.

4.2.2    Behavior of Protons

Since protons are usually bound in atoms and/or molecules, their abundance is much less than that of electrons.  In nuclear reactions, free protons are emitted, as they are from the sun, in great abundance.  Since they are about 2,000 times more massive than an electron and they have a positive charge, their behavior is significantly different, but similar in important details.

A free proton interacting with a diallel gravitational field line will also naturally spiral downward toward the mass origin of the diallel line.  It, however, will spiral counter-clock-wise and also in a quantized state. Similar to the electron, it will interact with the particles at the origin -- providing energy and affecting their density -- also according to equation 1. The proton will also reverse its spiral direction at the mass center.  Given its much larger cross section, its probability of arriving at the center of the earth is greatly reduced.  If protons are emitted from the core, they continue to spiral in the opposite direction of that of the electrons (counter-clockwise as viewed from above).

For the earth, the penetration depth of a proton is negligibly small, because basically all it sees is electrons -- to which it is immediately attracted -- making hydrogen, which then joins with another hydrogen atom to make a hydrogen molecule or implodes with oxygen to make water.  The fact that we don't see a large amount of this activity indicates that the number of free protons at the surface of the earth is small.  Because of these reasons, protons do not typically continue with significant probability to the center of the earth.  They are, however, very important in nuclear reactions and in the effects on our atmosphere as they are projected from the sun along diallel lines.

4.2.3    Behavior of Neutrons

Neutrons travel down the center of the diallel gravitational field lines -- somewhat like they reside at the nucleus of an atom.  They exist in quantum states and their velocities are a function of local density parallel to their movement per equation (1).  Remember, this density can come from any of the force fields and includes the local mass.  Neutrons don't spiral like electrons and protons, but due to their mass, they contribute to the local density and move along a diallel line toward the mass origin of the gravitational field.  They change quantum states as they interact with local conditions.

Even though there are a very small percentage of neutrons penetrating the crust of the earth as compared with electrons, they still play a very important role at the core of the earth.  They can also be generated at the core, which provides important core cooling -- stabilizing the core heating from the balanced continuous fission process on going there, and which is fed by the very large number of electrons, which arrive at the core from the sun.

Generally, in this unified field theory, the neutron is a key player because it helps to  maintain balance.  The neutron could be called the converter as it converts energy from one form into another as it is either created or as it splits.  It, of course, can be split in a nuclear reaction into an electron and a proton with also the emission of a high energy photon. 

In a typical atomic bomb explosion, large amounts of electrons, protons, neutrons and high energy photons are emitted -- along with other atomic particles.  The amount of each depends on the kind of nuclear reaction. Neutron bombs have been designed to emit large amounts of neutrons.  These are much harder to shield against because the neutron has no charge, and the neutrons are high energy.  The principle designed attribute of the neutron bomb is that it will penetrate structures without destroying them, and reach and kill people from the intensity of the radiation. 

4.2.4    Behavior of Photons

Like a light-pipe, when emitted along a diallel path, photons will transmit their energy at the speed of light along that path until reaching a reflecting or refracting boundary or absorbing material.  Photons also contribute to core heating of the earth and the sun.  They also contribute energy in the above equation causing increased density as they travel along diallel lines.

It is well known how photons bend at some boundary according to the change in the index of refraction at that boundary.  The path taken can be exactly calculated according to Fermat's principle (the principle of least action). In other words, nature likes to be most efficient.  This is very analogous in this new unified field theory.  The bending of the diallel gravitational field lines is a function of the density (like the index of refraction) as driven by the energy flow parallel to the diallel lines.  Hence, like light, diallel gravitational field lines can be refracted (focused or defocused), reflected or absorbed.  A black hole is an example of absorption.  In the experimental section, we will see examples of refraction.

Under certain conditions, photon energy can continue through the earth and be reflected as in Tesla's experiment.  He was able to bounce a radio signal off of the other side of the earth and build up the energy density.  His experiment was a very good example of the diallel gravitational field lines working for him as conduits of the RF energy generated.  This is discussed more in the experimental section.

There are some very important experiments to be done in this regard.  It is of particular interest that whales can communicate using ULF frequencies over very large distances utilizing the resonance frequencies of the earth. A frequency of 23.56 Hz has a wave length of one earth diameter.

4.3    Quantum-mechanical Concepts and Diallel Gravitational Field Lines

Although we have not obtained an analytic expression for the new force field on an electron or proton traveling along a diallel gravitational field line, the particle will exist in a quantum state that may be described as a density distribution in a manner analogous to that arising in atomic and molecular physics and leading to so-called electron orbitals. It may be helpful in envisioning the diallel quantum states to consider other physical systems with cylindrical symmetry and having eigenfunction solutions. One such example is the set of modes defining the electromagnetic fields propagating along a circular-cylindrical waveguide. Of special interest are the modal distributions in the case of highly-overmoded waveguides, a situation that may occur when the free-space wavelength of the electromagnetic field is much less than the diameter of the waveguide. Solving the electromagnetic wave equation subject to the appropriate boundary conditions and assuming a waveguide of infinite length yields field expressions given in terms of Bessel functions of the first kind. These functions provide an orthogonal set with which to describe the waveguide modes. The eigenvalues are related to the zeroes of the Bessel functions. The particle density distributions in a diallel-quantum state would be described in terms of a similar set of orthogonal functions. Although a great many electrons could propagate along a diallel line by occupying a multiplicity of quantum states, Fermi-Dirac statistics would limit the number of electrons in each state to two electrons. In addition, just as the electromagnetic field can be circularly polarized (the macroscopic manifestation of the spin quantum number of the associated photons) leading to a spiraling of the field vectors in the circular waveguide, the density distribution of a particle in a diallel-quantum state may also be described as spiraling.

In addition, the force field equations need to be developed for neutrons, photons as well as the other fundamental particles.  Clearly, there is a great amount of work and insight yet to be gained as we press forward in these areas.  Here, we hope our colleagues will bring forth their insights, wisdom and expertise.

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