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

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, / A_{2}*, will be explained
below. D and E are tensors with eigenvalues and quantum states associated therewith.

*"A_{2}"
should read "capital Pi, sub-2"

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* = *m*c^{2}, where m is the relativistic
mass and *E = *h*v*, 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.

A dimensional analysis of the above equation reveals that A_{2}
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/*Pi*_{2}. 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.

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 A_{2},
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, c^{2}, is also the
proportionality constant in the conversion of mass into energy, since *E* = *m*c^{2}.
Of course, 1/c^{2} is the proportional constant in the opposite conversion of
energy into mass, since *m = *E*/*c^{2}.

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.

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.

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.

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.

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.

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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