TRUE UNITS & THE THIRD FORM
STABLE VORTICAL FORMS AND TRUE QUANTAL
UNITS
Chemists trained in the current
paradigm think of the combination of elementary particles and elements as forming
atoms and molecules by the physical bonding of their structures, and model
these combinations in tinkertoy fashion with plastic or wooden spherical
objects connected by single or double cylindrical spokes. This is helpful for
visualizing molecular compounds in terms of their constituents prior to
combining, but that is not necessarily what actually happens. Inside a stable
organic molecule, volumetrically symmetric atoms are not simply attached; their
subatomic spinning vortical “particles” combine, forming a new vortical
object. Elementary particles are rapidly spinning symmetric vortical objects
and when three of them combine in proportions that satisfy the threedimensional
Conveyance Equation, they do not simply stick together  they combine to form a
new, dimensionally stable, symmetricallyspinning object. Because they are
spinning in more than one plane, these objects are best conceived of as closed
vortical solitions.
The
triadic combinations of elementary vortical objects, like up and downquarks,
form new vortical objects called protons and neutrons; the combinations of
electrons, protons and neutrons form new vortical objects called elements; and
the triadic combinations of volumetrically symmetric elements form new vortical
objects called organic molecules. Thus, the dimensional forms of
symmetricallyspinning objects formed by the combining of smaller vortical
objects form closed vortices in 3S1t with new physical and chemical
characteristics, depending upon both their internal and external structure. We
will take the volume of the smallest possible quantized vortical object as the
basic unit of measurement as the true quantal unit.
THE TRUE UNIT, THE CONVEYANCE EQUATION
AND THE THIRD FORM OF REALITY
Conceptually,
the true quantum unit in TDVP is therefore a subquark unitary extent/content entity
spinning in the mathematically required nine dimensions of quantized reality.
When we choose to measure the substance of a quantum distinction, the effects
of its spinning in the three planes of space register as inertia or mass, spin
in the timelike dimensional planes manifests as energy, and spinning in the additional
planes of reality containing the space
and time domains, requires a third form of the stuff of reality, in addition
to, but not registering as either mass or energy, to complete the minimum
quantum volume required for the stability of that distinct object. Because this
third form of the stuff of reality is unknown in current science, we need an
appropriate symbol to represent it. Every letter in the English and Greek
alphabets has been used as a symbol for something in math and science, so we have
gone to the historically earlier PhoenicianAramaicHebrew alphabet. We will
represent that potential third form of reality here with the third letter of
the Aramaic alphabet, ג (Gimmel), and we will call the subquark unitary
measure of the three forms of reality the Triadic
Rotational Unit of Equivalence,
or TRUE Unit.
The
mix of the three forms, m, E and ג, needed
to maintain symmetric stability, present in any given 3S1t measurement,
will be determined by the appropriate Conveyance Equation, as demonstrated
below. When n = m = 3, Σ^{n}_{i=1} (X_{n})^{m}
= Z^{m} yields:
(X_{1})^{3} + (X_{2})^{3
}+ (X_{3})^{3}= Z^{3}
The integer solutions of this
Diophantine equation in TRUE units represent the possible combinations of three
symmetric vortical distinctions forming a fourth threedimensional symmetric
vortical distinction.
THE PRIMARY LEVEL OF SYMMETRIC STABILITY – QUARKS
With the appropriate integer values of X_{1},^{ }X_{2}, X_{3}, and Z, in TRUE units, this equation represents the stable combination of three
quarks to form a Proton or Neutron. There are many integer solutions for this
equation and historically, methods for solving it were first developed by Leonhard
Euler ^{ref}. The smallest integer solution
of this Conveyance Equation is 3^{3}
+ 4^{3 }+ 5^{3}= 6^{3}.
Trial Combination of Two UpQuarks and One DownQuark, i.e.
The Proton, With Minimal TRUE Units
Particle

Charge^{*}^{}

Mass/Energy

ג

Total
TRUE Units

MREV^{**}

u_{1}

+ 2

4

1

3

27

u_{2}

+ 2

4

0

4

64

d

 1

9

4

5

125

Total

+ 3

17

5

12

216=6^{3}

* For consistency in a quantized reality,
charge has also been normalized in these tables.
^{** }Minimum Rotational Equivalent Volume (MREV)
If we attempt to use the smallest integer solution,
3^{3} + 4^{3 }+ 5^{3}=
6^{3}, to find the appropriate values of ג
for the Proton, we obtain negative values for ג
for the first upquark and the downquark and zero for the second upquark. It
is conceivable that some quarks may contain no ג
units, but negative values are a problem, because a negative number of total ג units would produce an entity with
fewer total TRUE units than the sum of mass/energy units of that entity,
violating the conservation of mass and energy, destroying the particle’s
equilibrium and identity. When we try to use the smallest integer solution of
the conveyance equation to describe the combination of one upquark and two downquarks
in a neutron, all of the quarks have negative ג units. See the table below:
Trial Combination of One UpQuark and Two DownQuarks in TRUE Units
Particle

Charge

Mass/Energy

ג

Total
TRUE
Units

MREV

u

+ 2

4

1

3

27

d_{1}

 1

9

5

4

64

d_{2}

 1

9

4

5

125

Totals

0

22

10

12

216=6^{3}

In conformance with the Bohr’s solution of the EPR
paradox (the Copenhagen interpretation of quantum mechanics), newly formed elementary
entities do not exist as localized particles in 3S1T until a 3S1t measurement
or observation is made. This is only possible if all TRUE units are ג
units, undetectable in 3S1t, before observation and measurement. This means
that they exist in the dimensional substrate and will manifest as either
mass/energy, or ג units, to manifest
the logical patterns of the substrate in observable symmetrically stable 3S1t
forms. In this way, the encompassing substrate, the additional six plus
dimensions of the ninedimensional structure of reality, organizes the 3S1t
world that we experience through the physical senses and their extensions into
discrete forms.
The redistribution of TRUE units cannot result in
the appearance of negative ג units
in the internal structure of an entity. A triadic entity with negative total ג units is not possible because a negative
number of total ג units would
violate the conservation of mass and energy, destroying the particle’s
equilibrium and identity. Analogous to the axiom ‘nature abhors a vacuum’, a
result of the second law of thermodynamics, just as the electrons of an
incomplete shell rush around the entire volume of the shell trying to fill it, negative
ג units would pull a TRUE units out
of the mass/energy of the particle to fill the void and the measurable mass/energy
of the particle would no longer be that of a proton or neutron and conservation
of mass/energy in 3S1t would be violated.
Attempting to use the smallest integer solution, (3,
4, 5, 6) of the Conveyance Equation to find the appropriate values of ג for the proton and neutron, we obtain
negative total ג unit values. This
solution would change the particle’s measurable mass/energy identity and
violate conservation of mass and energy, so we continue to look for an
appropriate solution. The next numerically smallest integer solution for the
Conveyance Equation is 1^{3} + 6^{3
}+ 8^{3}= 9^{3}, but, using it also results in negative
values. The smallest
integer solution of the Conveyance Equation that produces no negative values of
ג for the Proton is 6^{3} + 8^{3 }+ 10^{3}=
12^{3}, using this solution we have the electrically and
symmetrically stable Proton:
The Proton (P^{+})
Particle*

Charge

Mass/Energy

ג

Total
TRUE Units

MREV

u_{1}

+ 2

4

2

6

216

u_{2}

+ 2

4

4

8

512

d_{1}

 1

9

1

10

1,000

Total

+ 3

17

7

24

1728=12^{3}

* u_{1 }and u_{2} have the same number of TRUE units of mass and energy, and
therefore will register as upquarks in the collider data, but have different
numbers of TRUE units of equivalent volume participating as ג
to produce the volumetrically
symmetric, and therefore stable, Proton.
Nature, reflecting the patterns
of the dimensional substrate, does not have to rely upon random particle
encounters to build complex structural forms. Compound structures are formed
within the mathematical organization of the Conveyance Equation, and useful
building blocks have a significant level of stability in 3S1t for protons to combine
with other compound particles and create structures sufficiently complex to
support life. To see how other structures arise from quarks, protons and
electrons, we need to know how protons, neutrons and electrons relate to the
Conveyance Equation: (X_{1})^{3} + (X_{2})^{3 }+
(X_{3})^{3}= Z^{3}. If the number of TRUE
units in the proton is equal to the integer X_{1}, the number of TRUE units in the neutron = X_{2}, the number of TRUE units
in the electron = X_{3}, then
the resulting compound entity, will be stable in the 3S1T domain of physical
observations.
We know that the 24 TRUEunit Proton
must combine with an electron to form a Hydrogen atom, and with other protons, electrons
and neutrons to form the other elements. In order to find the smallest solution
of the conveyance equation that can include the 24 TRUE units of the proton, we
may start by trying the solutions we’ve used so far. 24 is a multiple of 2, 3,
4, 6, and 8, any one of which can be a factor of X_{1} in the conveyance equation solutions we’ve used so
far. Up to this point we’ve only used the first two of the smallest primitive
integer solutions of the equation: 3^{3}
+ 4^{3 }+ 5^{3 }= 6^{3} and 1^{3} + 6^{3 }+ 8^{3 }= 9^{3}. (A
primitive Diophantine solution is defined as one without a common factor in all
terms.) We have also used 6^{3}
+ 8^{3 }+ 10^{3}= 12^{3}, an integer solution
obtained by multiplying all of the terms of the smallest primitive solution by
2. The first 36 integer solutions of the conveyance equation (X_{1})^{3}
+ (X_{2})^{3 }+ (X_{3})^{3 }= Z^{3} are listed below in ascending order. Primitive
solutions are in bold.
3^{3}
+ 4^{3} + 5^{3} = 6^{3}
1^{3}
+ 6^{3} + 8^{3 }= 9^{3}
6^{3} + 8^{3}
+ 10^{3} = 12^{3}
2^{3}+ 12^{3}
+ 16^{3} = 18^{3}
3^{3}
+ 10^{3} + 18^{3 }= 19^{3}
7^{3}
+ 14^{3} + 17^{3 }= 20^{3}
12^{3} + 16^{3}
+ 20^{3 }= 24^{3}
4^{3}
+ 17^{3} + 22^{3} = 25^{3}
3^{3}
+ 18^{3} + 24^{3 }= 27^{3}
18^{3}
+ 19^{3} + 21^{3 }= 28^{3}
11^{3}
+ 15^{3} + 27^{3} = 29^{3}
15^{3} + 20^{3}
+ 25^{3} = 30^{3}
4^{3} +
24^{3} + 32^{3} = 36^{3}
18^{3} +
24^{3} + 30^{3} = 36^{3}
2^{3}
+ 17^{3} + 40^{3} = 41^{3}
6^{3}
+ 32^{3} + 33^{3} = 41^{3}
16^{3}
+ 23^{3} + 41^{3} = 44^{3}
5^{3} + 30^{3}
+ 40^{3} = 45^{3}
3^{3} + 36^{3}
+ 37^{3} = 46^{3}
27^{3} + 30^{3}
+ 37^{3} = 46^{3}
24^{3} +
32^{3} + 40^{3} = 48^{3}
8^{3} + 34^{3}
+ 44^{3} = 50^{3}
29^{3}
+ 34^{3} + 44^{3} = 53^{3}
12^{3}
+ 19^{3} + 53^{3} = 54^{3}
36^{3}
+ 38^{3} + 42^{3} = 56^{3}
15^{3} + 42^{3}
+ 49^{3} = 58^{3}
21^{3} + 42^{3}
+ 51^{3 }= 60^{3}
30^{3} + 40^{3}
+ 50^{3} = 60^{3}
7^{3} + 42^{3}
+ 56^{3} = 63^{3}
22^{3}
+ 51^{3} + 54^{3} = 67^{3}
36^{3}
+ 38^{3} + 61^{3} = 69^{3}
7^{3}
+ 54^{3} + 57^{3} = 70^{3}
14^{3}
+ 23^{3} + 70^{3} = 71^{3}
34^{3} + 39^{3}
+ 65^{3} = 72^{3}
38^{3} + 43^{3}
+ 66^{3} = 75^{3}
31^{3} + 33^{3}
+ 72^{3} = 76^{}
The
numbers appearing in the totals in the tables describing quarks, protons,
neutrons and atoms are the smallest possible nonnegative integers consistent
with the empirical data and the requirement for symmetry that the sum of the
three totals cubed must equal an integer cubed. Thus, we can calculate the
number of ג units involved, and the totals of TRUE
units required by the conveyance equation to yield results consistent with
empirical particle collider data. Note that the TRUE units in these tables are
measurements of threedimensional objects in multiples of the unitary linear
measure of their volumes, and their minimal rotational equivalence volumes
(MREV), listed in the last column, are equal to the TRUE unit values cubed.
Negative values for ג cannot occur
because of the conservation of mass and energy. Negatives would destroy the
mass/energy/ ג balance and turn
the quarks into unstable combinations which would decay quickly. So we must
find the smallest unique conveyance equation
solution for each combination of subatomic particles. The correct unique
solution can be found for each triadic subatomic particle by starting with the
smallest integer solution of the conveyance equation and moving up the scale
until no negative values are obtained. Using the solution 6^{3} + 8^{3 }+ 10^{3}= 12^{3}, the first
attempt to find the TRUE unit configuration of the neutron is shown below:
Trial Combination of One UpQuark and Two DownQuarks in
TRUE Units
Particle

Charge

Mass/Energy

ג

Total
TRUE
Units

MREV

u

+ 2

4

2

6

216

d_{1}

 1

9

1

8

512

d_{2}

 1

9

1

10

1000

Totals

0

22

2

24

1728=12^{3}

Since this solution still produces a
negative value of ג for d_{1}, we must move to the
next larger solution to represent the Neutron. The smallest unique Conveyance
Equation solution with no negative or zero values of ג for the stable Neutron is 9^{3}
+ 12^{3 }+ 15^{3}= 18^{3 }
Second Trial of
Quark Combinations for the Neutron
Particle

Charge

Mass/Energy

ג

Total
TRUE
Units

MREV

u_{3}

+ 2

4

5

9

729

d_{2}

 1

9

3

12

1,728

d_{3}

 1

9

6

15

3,375

Totals

0

22

14

36

5,832=18^{3}
^{= 54x108} 
These TRUE unit numbers give us a
stable neutron; but we have another problem: None of the solutions with a term
equal to 24 have a second term equal to 36. Nor do any of the solutions listed
have two terms with the ratio 24/36 =2/3. This is a problem because it means
that combinations with equal numbers of protons and neutrons could not be
stable, and we know that Hydrogen, the element Helium, and other elements are
stable combinations with equal numbers of protons and neutrons. Looking at the
TRUEunits analysis of Helium as an example, we have:
Attempt to Construct a Helium Atom with P^{+ }= 24
and N^{0} = 36
Particle

Charge

Mass/Energy

ג

Total
TRUE
Units

MREV

2e

 6

2

78

80^{*}^{}

512,000

2P^{+ }

+ 6

34

14

48

110,592

2N^{0}

0

44

28

72

373,248

Totals

0

80

120

200

995,840=(99.861…)^{3}

*Note: The number of TRUE units
making up the electron is unknown at this point. This value was chosen because
it is the integer value that produced a total MREV nearest to a cube, as it must
be for a stable Helium atom. The smallest integer value in TRUE units for the
proton is 24.
Since a neutron of 36 TRUE units
produces an unstable Helium atom, contradicting the empirical fact that stable
Helium atoms exist, we have to seek another integer solution of the conveyance
equation for the neutron.
Going back to the list of conveyance
equation solutions, we see that the next smallest solution that does not generate
negatives for the neutron is the primitive solution 7^{3} + 14^{3}
+ 17^{3 }= 20^{3}.
Third Trial of
Quark Combinations for the Neutron
Particle

Charge

Mass/Energy

ג

Total
TRUE
Units

MREV

u_{3}

+ 2

4

3

7

343

d_{2}

 1

9

5

14

2,744

d_{3}

 1

9

8

17

4,913

Totals

0

22

16

38

8,000=20^{3}

Next, we need to see if this quark
combination for the neutron combined with protons and electrons will yield
stable atomic structures. Using the values we derived for P^{+} and N^{0},
the first integer solution of the conveyance equation containing the values X_{1 }= 24 and X_{2 }= 38 is obtained by
multiplying both sides of the primitive solution 12^{3} + 19^{3}
+ 53^{3} = 54^{3}
by 2, yielding the integer solution 24^{3}
+ 38^{3} + 106^{3} = 108^{3}.
Helium Atom with P^{+ }= 24 and N^{0} = 38
Particle

Charge

Mass/Energy

ג

Total
TRUE
Units

MREV

2e

 6

2

210

212^{*}^{}

9,528,128

2P^{+ }

+ 6

34

14

48

110,592

2N^{0}

0

44

32

76

438,976

Totals

0

80

256

336

10,077,696=216^{3}
^{}

^{*}With the TRUE
units determined for protons and neutrons, the Helium atom is stable only if
the total number of TRUE units for the electron is 106.
Besides the TRUE units that appear
as mass/energy in given elementary particles, because of the embedded nature
(dimensional tethering) of dimensional domains in TDVP, there must be a minimum
number of ג units associated with each particle for stability. Consistent with up
and downquark decay from the strange quark, the stabilization requirement of
an integer solution for the conveyance equation, and the additional TRUE units of
ג
needed for particle stability, the following
table describes the electron, proton and neutron in TRUE units, with up quarks
composed of a total of 24 TRUE units, down quarks composed of a total of 38
TRUE units and electrons composed of a total of 106 TRUE units. It therefore represents the normalized
mass/energy, minimum ג and total volumes for stable electrons, protons and neutrons, the
building blocks of the physical universe.
NEXT: The Elements of the Periodic Table and the Three levels of Stability.
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