Many years ago, when I was a PhD candidate at Johns Hopkins University in Baltimore, as part of course work I read Thomas Kuhn's works. He made the point that science advances in two ways: Most of the time, it is by steady growth, bit by bit, as many scientists toil away digging out details. But occasionally, there is a revolution, a new sweeping insight, when one or two scientists see something no one else has noticed, something outside the box. The history of science is studded with a precious few of these revolutions: Archimedes, Pythagoras, Descartes, Newton, Leibniz, Einstein, Heisenberg and Bohr, the names of those who created such revolutions are well known. New mathematics and new theories blossomed from a few exceptional minds. But there have been no scientific revolutions since 1935 when Relativity and Quantum Mechanics came on the scene. When scientists talk about a "breakthrough" these days, most often it is just the finding of something like the Higgs Boson, an accomplishment, to be sure, but hardly a scientific revolution, just confirmation of something the Standard Model predicted; nothing really new.
Now there IS new mathematics and a new theory! In TDVP, Dr. Neppe and I have put consciousness, mind and Spirit into the equations! Here are some details:
What we know about the elements of
the Periodic Table is almost entirely based on experimental data from
investigations of just four distinct elementary entities, known as the photon,
the electron, the upquark, and the downquark. Table One lists these elementary distinctions with two measurable
parameters that characterize them: charge and mass. In addition, the charge and
mass data for the proton, composed of two upquarks and a downquark, and the
neutron, composed of one upquark and two down quarks, as basic components of
atomic structure, are included in the table.
TABLE ONE
Elementary Particle Charge
& Mass
Particle

Symbol

Charge
(Coulomb)

Mass (m)

Photon

Ɣ

0

0

electron

e

1

0.511

u

+^{2}⁄_{3}

1.5–3.3


d

−^{1}⁄_{3}

3.5–6.0


proton

P^{+}

+1

6.5 – 12.6

Neutron

N^{0}

0

8.5 – 15.3

Normalization
Except for the electron,
the data for the mass of the particles in Table
One are presented as ranges of values. The masses of elementary particles, i.e.
the up and down quarks, are indirectly determined as energy equivalents from
particle collider detector and collector data. They are noninteger decimal
fractions because the standards for the units of measurement (MeV/c^{2}) do not happen to be integer multiples of the
smallest possible mass. In the
ultimately smallest possible quantized units, the numerical values of the actual
masses of these particles must be integers,
so we are justified in normalizing the data for purposes of comparison and
calculation.
The normalized values
in Table Two are obtained by simply
taking the smallest elementary mass, that of the electron, as unitary. Then to
convert the mass of the up quark and down quark into multiples of that standard
unit, we divide the average of each particle’s range of empirical data by 0.511and
round the results to the nearest whole number. Even if the basic unit we have
derived in this way is not be the actual smallest possible unit, it will be a
multiple of the real quantum unit, and the normalized values will reflect the
relative proportionality of the actual masses of the particles. Because charge
is a product of spin, we have also normalized it to avoid fractions by simply
taking the charge of the electron as  3. This normalizes the charge of the up
quark to + 2 and the down quark to  1. Again, as with mass, we are justified
in normalizing the measure of charge because the standard unit, the Coulomb, is
not necessarily an integral multiple of the actual quantum unit of charge,
which may be either positive or negative. The balance, or zero sum of + and –
charges in the decay process (called parity)
reflects the operation of the Law of Conservation of Energy.
TABLE TWO
Normalized Units
Particle

Symbol

Charge

Mass

Photon

Ɣ

0

0

electron

e

 3

1

u

+ 2

5


d

− 1

9


proton

P^{+}

+ 3

19

Neutron

N^{0}

0

23

1. Elementary
particles are created as the result of the interaction of the three universal
processes of expansion, contraction and rotation or spin. Their cause is thus triadic.
2. Reality
exists within at least nine finite, sequentiallynested existential dimensions.
3. We
are only partially aware of five of these dimensions through our physical
senses: three of space, one of time, and one of consciousness.
4. The
processes affecting the creation and combination of elementary particles to
form meaningful structures are rooted in the dimensionometric forms of nine
finite dimensions and one or more transfinite dimensions. The mathematical
expression of this dimensionometric form is Σ^{n}_{i=1} (X_{n})^{m} = Z^{m}
(to
be explored in more detail below).
5. These
particles are triadic in nature, comprised
of a universal substance which manifests as matter, energy and consciousness
interacting in the ninedimensional domain.
The Origin of the Particles that
form the Elements of the Periodic Table
How do particles form in the first place? Consider
an elementary contraction in the substance of reality characterized as the
drawing of a distinction. Call that distinction D_{1}. We have posited
that it is comprised of mass, energy and consciousness. As demonstrated in our
discussion of intrinsic spin and the Cabibbo angle, this elementary
distinction is rapidly spinning. With no external influence, and therefore no preferred
reference frame, the distinction spins in nine dimensions, and each plane of
rotation will cause it to resist movement like a spinning gyroscope. This
resistance to movement, or inertia,
is interpreted as mass. Since energy is quantized, the spin in each of the nine
planes of rotation contributes one unit of inertia, and the particle will possess
nine units of inertia. If we accept that these units are equivalent to units of
mass, and normalized as we’ve done above, then such a particle is equivalent to
the down quark in Table Two.
Under the entropic expansive action characterized by
the Second Law of Thermodynamics, down quarks decay into up quarks, releasing a
photon and a neutrino. This process, documented in many experiments, conforms
to the Law of Conservation of Mass and Energy. Nothing is lost or destroyed in the
process; a portion of the substance of the particle of rotational inertia
simply changes from one form (mass) to another: energy. Table Three below illustrates how an elementary distinction, D_{1},
recognized as the down quark, d, in
experimental observations, decays to form other less massive particles. These
new particles formed by natural entropic decay have the exact normalized
inertial masses that are characteristic of the other two elementary particles,
the down quark and the electron, the particles that make up all of the elements
of the Periodic Table.
TABLE THREE
Natural
Decay Path of Elementary Particle Distinctions
Elementary
Distinction

Mass in Normalized
Units

Units Emitted
as Energy^{*}

New Mass in Normalized
Units

New Entity

D_{1 =} d

9

4^{}

5

u

D_{2 =} u

5

4

1

e

D_{3 =} e

1

1

0

Ɣ

^{*}
Energy emitted is in the form of photons,
Ɣ,
and
neutrinos. v_{e}_{ }, one photon plus one neutrino = 4 normalized
units. The energy of neutrinos and photons can vary, but, since energy is
quantized, their energy can only consist of integer multiples of normalized units.
There are some indications that neutrinos may have a miniscule amount of mass,
so the neutrino emitted may have 1 unit of mass and one or two units of energy.
The photon’s mass is zero, and its energy is proportional to its wave length,
so the photons emitted in the decay process may have a wave length reflecting the
energy of one or two units.
Notice that the four units emitted, identified as
mass in the down quark, are either mass or energy in the photon and
neutrino. This indicates an equivalence between normalized mass
units and energy, and more importantly, a transformation of the measurable aspect
of the universal substance from mass to energy. We know that the transformation
relationship between mass and energy is E
= mc^{2}. Since c^{2}
is a constant, we may normalize the units of energy into units equivalent with
our normalized mass units very easily as follows: The standard unit used to
measure the energy of elementary particles is the MeV(one million electron
volts) the standard unit used in measuring the mass of the particles in Table One is one million electron volts
divided by the speed of light squared (MeV/c^{2}), equivalent to 1.782662×10^{−36} kg., a
very small fraction of a kilogram. So X units of mass in our normalized units in Table Two = X ∙ Mev/c^{2}.
That occurs as a result of the Substituting
m = X ∙ Mev/c^{2}
into and E = mc^{2}, we get E = X
∙ (Mev/c^{2 })^{ }∙ c^{2}^{ }= X ∙
Mev.
Thus the units in Table Three are
normalized equivalence units measuring both mass and energy. Any given number, X, of normalized units of mass in this
table^{ } is equivalent to X normalized units of energy.
We have also posited that the substance of reality is
not just mass and energy, i.e. binary in mode, but triadic, existing in three
forms: mass, energy and consciousness. Since mass and energy are measurable in
normalized units, it is reasonable to expect that consciousness might also be.
If, e.g., like mass and energy, consciousness is quantized, and each unit of
consciousness is equivalent to a constant multiple of energy units, then
consciousness can also be also be measured in multiples of these normalized units
of equivalence, and the processes that form the elements of the Periodic Table
can be described and analyzed using them. Even though we have not yet defined
what a unit of consciousness might consist of, we may be able to define it
indirectly relative to energy and mass in terms of the equivalence units. Extending
the logic of E = mc^{2}, the
mathematical relationship between mass, energy and consciousness, C, is
probably of the form: C = E(∆t/∆
C)^{I}
where ∆t/∆ C
is the ratio of the minimum increments at the border of the T and C domains
just as c is the ratio at the border
of the S and T domains, and I is > 2. Substituting, we have: C = m^{2} (∆t/∆
C)^{I}.
Notice that no units of consciousness appear in the
decay process depicted in Table Three
because it is a natural entropic process. So why don’t all elementary
distinctions simply decay in these three quick steps into photons and neutrinos
that expand to infinity, resulting in a swift return to a state of maximum
entropy, a state where there are no distinctions in the substance of reality? Regardless
of how particles originate, something happens to counteract the action of the
Second Law of Thermodynamics. What happens to perpetuate negative entropy? The
answer lies in the conveyance of the logic of the Csubstrate (dimensions 7, 8
and 9 of the nine dimensional domain of reality) into the 3S1T domain of
observation, by the intrinsic form of
the dimensionometric domains represented mathematically by the equation Σ^{n}_{i=1} (X_{n})^{m} = Z^{m} and by the action of one
or more units of consciousness to organize mass and energy into stable
structures reflecting the logic of the conscious substrate. In order for quarks to
combine to form the stable subatomic particles we call protons and neutrons
observable in the 3S1t domain, they must meet the requirements of the
Conveyance Expression equation when m = 3 and n = 2 as integer multiples of normalized
units of mass, energy and consciousness. This is where Fermat’s Last Theorem
enters the picture.
Fermat’s Last
Theorem and the Combination of Quantum
Particles
Consider the combination of two elementary particles to
form a new particle. This may be modeled by the Conveyance Expression when n =
2 and m = 3.
With n = 2 and m = 3, the expression Σ^{n}_{i=1} (X_{n})^{m} = Z^{m} yields the equation (X_{1})^{3} + (X_{2})^{3 }= Z^{3}.
X_{1}
and X_{2} represent the
number of normalized units making up the particles, i.e. quarks, which combine to form the proton, P^{+} and the neutron, N^{0}.
(X_{1})^{3} and (X_{2})^{3 }represent
the volumes of two combining particles and
Z^{3} represents the volume of the particle formed in the
combination. In nine dimensions, at the subquark level, whether mass, energy
or consciousness, the numerical measures of the spinning entities in normalized
equivalence units are integers and dimensionometrically equivalent. They are
therefore called Triadic Rotational Units of Equivalence (TRUE).
Triadic Rotational Units of Equivalence, or TRUE
units, for short, are the Calculus of Distinction equivalents of the
infinitesimals of the Calculus of Newton and Leibniz. The difference, and it is
a very important one, is that TRUE units are finite and integral. While the
value of the differentiation variable of a function in Newtonian Calculus may
approach zero infinitely closely, the Calculus of Distinctions numerical values
of both content and extent variables of the finite distinctions of mass, energy
and consciousness are quantized and thus cannot be smaller than one TRUE unit.
Thus the TRUE unit is the bottom, or limit of infinite descent for all
variables. Because elementary particles are rotating extremely rapidly,
regardless of the probabilistic distribution of density (such as that demonstrated
in our analysis of the electron)^{6},
a TRUE unit occupies a perfectly symmetrical, or spherical volume.
Using the axioms presented above, and TRUE units, we
will proceed to describe the processes that lead to the formation of the
Hydrogen atom and the other elements of the Periodic Table. The values of the
mass of the elementary entities, in multiples of the TRUE unit, are determined
by normalization of experimental data as described above; the values of the
energy of the entities, also in multiples of the TRUE unit, are calculated
using the established mathematical relationship between mass and energy (E =
mc^{2}); and the values of the measures of the consciousness of
the elementary entities in multiples of the TRUE units are determined by application
of the Conveyance Equation and the assumption that a mathematical relationship,
analogous to E = mc^{2} exists between energy and consciousness.
At the quantum level, to be stable
quantum particles, existing as finite threedimensional distinctions, each of these
volumes must be equivalent to either the volume of a TRUE unit, or multiples of
the volume of the TRUE unit. This means that X_{1}, Y_{2}
and Z must be integers.
Fermat’s Last Theorem tells us
there are no integer solutions for this equation, which means that no two
particles consisting of TRUE units, or integral multiples of TRUE units, can
combine to form a new symmetrical
entity. Such asymmetrical combinations of rapidly spinning entities will tumble
or spiral, especially under the influence any external force, and will thus be far
less stable than symmetric forms.
However, when n = m =3, the expression yields the
equation
(X_{1})^{3} + (X_{2})^{3 }+ (X_{3})^{3}=
Z^{3},
which does have integer solutions. The first one (with
the smallest integers) is
3^{3} + 4^{3 }+ 5^{3 }= 6^{3}
It is important to recognize that the equations produced
by Σ^{n}_{i=1} (X_{n})^{m}
= Z^{m} when n and m, and the X_{i}
and Z are integers are exact expressions of the form of the logical structure of the Csubstrate as it is conveyed
to the 3S1t domain. For this reason, we will call this expression the Conveyance
Expression. This expression, generalizing the summation of n finite mdimensional
distinctions, and the equations it generates when all variables are integers,
including the equations of the Pythagorean Theorem and Fermat’s Last Theorem,
prove to be indispensably useful in the mathematical analysis of the
combination of elementary particles.
The simplest symmetric form in threedimensional space is the sphere, and as noted above, we can assume that the TRUE unit of substance is spherical. If the particles are also spherical, their volumes are 4/3 π r_{1}^{3}, 4/3 π r_{2}^{3}, and 4/3 π r_{3}^{3}, where r_{1}, r_{2} and r_{3} are the radii of the particles. But, since the volumes of the particles are integral multiples of the TRUE unit, r_{1}, r_{2} and r_{3} must be integer multiples of the radius of the TRUE unit. So let r_{1}= X_{1}R_{T}, r_{2 }= X_{2}R_{T}, and r_{3 }= X_{3}R_{T} where X_{1}, X_{2 }and X_{3} are integers and R_{T} is the radius of the TRUE unit. The Conveyance Equation representation of the combination of the three particles becomes:
4/3
π (X_{1}R_{T}) ^{3} + 4/3 π (X_{2} R_{T})
^{3} + 4/3 π (X_{3}R_{T}) ^{3}
The newly
combined particle is also spherical, represented by the expression 4/3
π (ZR_{T}) ^{3}, where, Z is necessarily an integer, and we have:
4/3 π (X_{1}R_{T}) ^{3} + 4/3 π (X_{2}
R_{T}) ^{3} + 4/3 π (X_{3}R_{T}) ^{3} =
4/3 π (ZR_{T}) ^{3}
Dividing both
sides of the equation by all of the common constant factors: 4/3,
π and
(R_{T})^{3},
we have:
(X_{1})^{3}
+ (X_{2})^{3 }+ (X_{3})^{3}= Z^{3}, where the X_{i}
and Z are integers representing
the number of elementary particles in each term.
Since spinning elementary particles
are symmetric, and multiples of TRUE units, which are also symmetric, the fact
that this equation has integer solutions, while the equation (X_{1})^{3} + (X_{2})^{3
}= Z^{3} does not, tells us that for the elementary particles in
Table Three to combine to form the most
stable, symmetric compound distinctions, three particles, not two, must
combine.
Note that this
conclusion is independent of the actual shape of the combining particles and is
even independent of the size and substance of the TRUE unit. As long as the particles
have the same symmetrical form, the shape factor, in this case, 4/3 π (R_{T} )^{3},
cancels out. They could, e.g., be any of the regular polyhedrons like
tetrahedrons, with four equilateral triangular sides, hexahedrons (better known
as cubes), with six square sides, octahedrons, etc.
Just as the intrinsic structure of dimensional domains of
three or more dimensions causes the combination of two elementary particles to
be asymmetric, it allows the combination of three particles to be symmetric and
very stable.
We will limit the scope of the remainder of this
mathematical description to the five particles that make up the elements of the
Periodic Table, namely the electron, the up quark, the down quark, and the two
composite particles, the proton and the neutron. This set of particles form a
finite physical system in the four dimensional domain of spacetime. This means
that these elementary particles are subject to the Second Law of Thermodynamics,
which is expressed through the process of universal expansion toward maximum
entropy; but this tendency toward maximum entropy is opposed by the processes
of contraction of the substance of reality into finite distinctions and
highvelocity rotation and spin. We postulate that this substance of reality is
triadic in nature, composed of mass, energy and consciousness. With the
introduction of the TRUE unit as the
Calculus of Distinctions basic unitary distinction, and ninedimensional spin
as the dynamic nature of distinctions of
matter and energy supporting the logic of consciousness, we are
reintegrating our understanding of physical reality with the awareness of the
conscious substrate as the mathematically logical matrix from which physical
reality originates.
Albert Einstein and Hermann Minkowski began this
reintegration of the scientific description of reality with consciousness by
recognizing the geometric nature of space and time as dimensional, establishing
the concept of spacetime^{4}, and the nature of matter and energy as
two different forms of the same substance. We are extending this integration to
include the five additional finite dimensions indicated by the mathematics of
Dimensional Extrapolation, and including consciousness as the third
aspect of the substance of reality. Even though Einstein coined the new term “spacetime”
describing the new concept of a fourdimensional geometric domain, and
established the mathematical equivalence of matter and energy with E =
mc^{2}, he introduced no new terminology for the generic
substance of reality. We will use the terms “essential substance” or “essence”
to indicate the substance of reality manifesting triadically as matter, energy
and consciousness.
Consistent with decay from the strange quark,
stabilization through the Conveyance Equation and the participation of TRUE
units of consciousness, the following tables describe the electron, up quarks,
down quarks, protons, and neutrons. The elements of the Periodic Table, derived from these tables tell us a lot about how the elements are formed, how consciousness is involved, and how living, conscious entities are an integral part of the reality we experience.
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