TRUE UNITS AND THE THIRD FORM OF REALITY

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 tinker-toy 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 sub-atomic 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 three-dimensional Conveyance Equation, they do not simply stick together - they combine to form a new, dimensionally stable, symmetrically-spinning 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 down-quarks, 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 symmetrically-spinning objects formed by the combining of smaller vortical objects form closed vortices in 3S-1t 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 sub-quark 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 time-like 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 Phoenician-Aramaic-Hebrew 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 sub-quark 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 3S-1t measurement, will be determined by the appropriate Conveyance Equation, as demonstrated below. When n = m = 3, Σⁿ_i=1 (X_n)^m = Z^m yields:

(X₁)³ + (X₂)³ + (X₃)³= Z³

The integer solutions of this Diophantine equation in TRUE units represent the possible combinations of three symmetric vortical distinctions forming a fourth three-dimensional symmetric vortical distinction.

THE PRIMARY LEVEL OF SYMMETRIC STABILITY – QUARKS

With the appropriate integer values of X₁, X₂, X₃, 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 3³ + 4³ + 5³= 6³.

Trial Combination of Two Up-Quarks and One Down-Quark, i.e.

The Proton, With Minimal TRUE Units

Particle	Charge*	Mass/Energy	ג	Total TRUE Units	MREV**
u1	+ 2	4	-1	3	27
u2	+ 2	4	0	4	64
d	- 1	9	-4	5	125
Total	+ 3	17	-5	12	216=63

* 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, 3³ + 4³ + 5³= 6³, to find the appropriate values of ג for the Proton, we obtain negative values for ג for the first up-quark and the down-quark and zero for the second up-quark. 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 up-quark and two down-quarks in a neutron, all of the quarks have negative ג units. See the table below:

Trial Combination of One Up-Quark and Two Down-Quarks in TRUE Units

Particle	Charge	Mass/Energy	ג	Total TRUE Units	MREV
u	+ 2	4	-1	3	27
d1	- 1	9	-5	4	64
d2	- 1	9	-4	5	125
Totals	0	22	-10	12	216=63

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 3S-1T until a 3S-1t measurement or observation is made. This is only possible if all TRUE units are ג units, undetectable in 3S-1t, 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 3S-1t forms. In this way, the encompassing substrate, the additional six plus dimensions of the nine-dimensional structure of reality, organizes the 3S-1t 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 3S-1t 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 1³ + 6³ + 8³= 9³, 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 6³ + 8³ + 10³= 12³, using this solution we have the electrically and symmetrically stable Proton:

The Proton (P⁺)

Particle*	Charge	Mass/Energy	ג	Total TRUE Units	MREV
u1	+ 2	4	2	6	216
u2	+ 2	4	4	8	512
d1	- 1	9	1	10	1,000
Total	+ 3	17	7	24	1728=123

* u₁ and u₂ have the same number of TRUE units of mass and energy, and therefore will register as up-quarks 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 3S-1t 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: (X₁)³ + (X₂)³ + (X₃)³= Z³. If the number of TRUE units in the proton is equal to the integer X₁, the number of TRUE units in the neutron = X₂, the number of TRUE units in the electron = X₃, then the resulting compound entity, will be stable in the 3S-1T domain of physical observations.

We know that the 24 TRUE-unit 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 X₁ 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: 3³ + 4³ + 5³ = 6³ and 1³ + 6³ + 8³ = 9³. (A primitive Diophantine solution is defined as one without a common factor in all terms.) We have also used 6³ + 8³ + 10³= 12³, 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 (X₁)³ + (X₂)³ + (X₃)³ = Z³ are listed below in ascending order. Primitive solutions are in bold.

3³ + 4³ + 5³ = 6³

1³ + 6³ + 8³ = 9³

6³ + 8³ + 10³ = 12³

2³+ 12³ + 16³ = 18³

3³ + 10³ + 18³ = 19³

7³ + 14³ + 17³ = 20³

12³ + 16³ + 20³ = 24³

4³ + 17³ + 22³ = 25³

3³ + 18³ + 24³ = 27³

18³ + 19³ + 21³ = 28³

11³ + 15³ + 27³ = 29³

15³ + 20³ + 25³ = 30³

4³ + 24³ + 32³ = 36³

18³ + 24³ + 30³ = 36³

2³ + 17³ + 40³ = 41³

6³ + 32³ + 33³ = 41³

16³ + 23³ + 41³ = 44³

5³ + 30³ + 40³ = 45³

3³ + 36³ + 37³ = 46³

27³ + 30³ + 37³ = 46³

24³ + 32³ + 40³ = 48³

8³ + 34³ + 44³ = 50³

29³ + 34³ + 44³ = 53³

12³ + 19³ + 53³ = 54³

36³ + 38³ + 42³ = 56³

15³ + 42³ + 49³ = 58³

21³ + 42³ + 51³ = 60³

30³ + 40³ + 50³ = 60³

7³ + 42³ + 56³ = 63³

22³ + 51³ + 54³ = 67³

36³ + 38³ + 61³ = 69³

7³ + 54³ + 57³ = 70³

14³ + 23³ + 70³ = 71³

34³ + 39³ + 65³ = 72³

38³ + 43³ + 66³ = 75³

31³ + 33³ + 72³ = 76

The numbers appearing in the totals in the tables describing quarks, protons, neutrons and atoms are the smallest possible non-negative 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 three-dimensional 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 sub-atomic particles. The correct unique solution can be found for each triadic sub-atomic 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 6³ + 8³ + 10³= 12³, the first attempt to find the TRUE unit configuration of the neutron is shown below:

Trial Combination of One Up-Quark and Two Down-Quarks in TRUE Units

Particle	Charge	Mass/Energy	ג	Total TRUE Units	MREV
u	+ 2	4	2	6	216
d1	- 1	9	-1	8	512
d2	- 1	9	1	10	1000
Totals	0	22	2	24	1728=123

Since this solution still produces a negative value of ג for d₁, 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 9³ + 12³ + 15³= 18³

Second Trial of Quark Combinations for the Neutron

Particle	Charge	Mass/Energy	ג	Total TRUE Units	MREV
u3	+ 2	4	5	9	729
d2	- 1	9	3	12	1,728
d3	- 1	9	6	15	3,375
Totals	0	22	14	36	5,832=183 = 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 TRUE-units analysis of Helium as an example, we have:

Attempt to Construct a Helium Atom with P⁺ = 24 and N⁰ = 36

Particle	Charge	Mass/Energy	ג	Total TRUE Units	MREV
2e	- 6	2	78	80*	512,000
2P+	+ 6	34	14	48	110,592
2N0	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 7³ + 14³ + 17³ = 20³.

Third Trial of Quark Combinations for the Neutron

Particle	Charge	Mass/Energy	ג	Total TRUE Units	MREV
u3	+ 2	4	3	7	343
d2	- 1	9	5	14	2,744
d3	- 1	9	8	17	4,913
Totals	0	22	16	38	8,000=203

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 N⁰, the first integer solution of the conveyance equation containing the values X₁ = 24 and X₂ = 38 is obtained by multiplying both sides of the primitive solution 12³ + 19³ + 53³ = 54³ by 2, yielding  the integer solution 24³ + 38³ + 106³ = 108³.

Helium Atom with P⁺ = 24 and N⁰ = 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
2N0	0	44	32	76	438,976
Totals	0	80	256	336	10,077,696=2163

^*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 down-quark 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.