Tuesday, December 29, 2015

PUTTING CONSCIOUSNESS INTO THE EQUATIONS PART 12


THE TRUE UNIT: TRIADIC ROTATIONAL UNITS OF EQUIVALENCE (TRUE) AND THE THIRD FORM OF REALITY: GIMMEL; APPLYING THE CONVEYANCE EQUATION (PART 12)

The true quantum unit of mass/energy, as defined above, is very useful in dimensional extrapolation processes and as the basic measurement unit of phenomenological distinctions in the calculus of distinctions. It is the smallest possible measurable discrete quantity of the universal substance of reality. Every elementary particle is therefore composed of a whole number of these true quantum units of the universal substance. Quantum mechanical phenomena that defy explanation in terms of classical physics concepts, are explicable if they are symmetrical vortical structures spinning at near light-speed angular velocities in the mathematically required nine dimensional domain of quantized reality.
The electron is measurable as one single true quantum unit of mass/energy equivalence in the 3S-1t dimensional domain of observable reality, but as we shall see, the electron is not identical with one true quantum unit. We have found that it must be much more to exist as part of a stable atom. All other stable non-radiating sub-atomic entities are measurable in multiples of these sub-quantal units also. These are units of measurement, not sub-quantal entities existing as independent phenomena. Until impacting on a receptor in an irreversible way, gimmel, the substance of these units, is a mass-less, energy-less third substance which is required for stable atomic and sub-atomic structure.
When we choose to measure the substance of a quantum distinction, the effects of spinning in the three planes of space register as inertia or mass, and spin in the time-like dimensional planes manifests as energy because time is non-existent without movement, and any movement of mass relative to an observer is measured by that observer as kinetic energy. 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, some for multiple subjects, as a symbol for something in math and science, so we have gone to possibly the historically oldest maintained alphabet, Hebrew, at an estimated 3100 years, but likely older. [1] We have represented that potential third form of reality here with the third letter of the Hebrew alphabet, ג (Gimmel), and we will call this unitary measure of the three forms of reality the Triadic Rotational Unit of Equivalence, or TRUE Unit.
The mix of the three equivalent forms of the substance of reality, (mass, energy, and gimmel) needed to maintain symmetric stability, present in any given 3S-1t measurement, can be determined by a symmetric three-dimensional conveyance equation: We found above that the smallest set of integer values that satisfies the three-dimensional form of the conveyance equation is the set 3, 4, 5 and 6. So the Diophantine equation 33 + 43 + 53= 63 describes the addition of three volumes with integer radii 3, 4, and 5 to form a symmetric volume with the integer radius r = 6.
When n = m = 3, the Conveyance Equation Σni=1 (Xn)m = Zm yields:
(X1)3 + (X2)3 + (X3)3= Z3
The integer solutions of this Diophantine equation, the conveyance equation with 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 and the conveyance equation

Because of Planck’s discovery that energy only occurs in integer multiples of a very small quantum, and Einstein’s discovery of the equivalence of matter and energy, (E = mc2) we know that the substance of the universe is quantized. With the appropriate integer values for X1, X2, X3, and Z, in TRUE units, the three-dimensional conveyance equation (X1)3 + (X2)3 + (X3)3= Z3 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 99.

Applying mathematics empirically

Our approach is empirical mathematical testing: We start with the smallest integer solution of this Conveyance Equation, 33 + 43 + 53= 63, and see if it can describe the combination of mass/energy and gimmel consistent with particle collider data.
In order to test the mathematical hypothesis that the combination of the volume and content of three quarks to form protons and neutrons can be adequately described using the Diophantine conveyance equations, we can start by using the simplest 3-D conveyance equation solution of 33 + 43 + 53= 63. If this equation doesn’t fit the empirical data, we need to establish what does work.
When we use the smallest integer solution, 33 + 43 + 53= 63, to the 3-D conveyance equation to attempt 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. They cannot be allowed because a negative number of total ג units would produce an entity with fewer total observable TRUE units in 3S-1t than the sum of mass/energy units of that entity, violating the conservation of mass and energy, destroying the particle’s equilibrium and identity.
We now compare two tables showing hypothesized TRUE and gimmel in the proton and then the neutron. We apply a trial and error approach, knowing that we need positive integers and ultimately quantal volumetric figures, where the cube roots are integral. For consistency in a quantized reality, charge has also been normalized in these tables.
In Table 2P1, we attempt to use the smallest integer solution of the conveyance equation to describe the combination of two up-quarks and one down-quarks in a proton, but some of the quarks have negative ג units.
In Table 2N1, we attempt 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.
This means the data in Table 2P1 and 2N1 for the proton and neutron are empirically incorrect: This is impossible.
The table numbering is complex here [2]

Table 12A-P1: Trial Combination of Two Up-Quarks and One Down-Quark, i.e. The Proton, applying minimal TRUE Units
Particle
Charge*
Mass/Energy
ג
Total TRUE Units
MREV**[3]
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
                     
And the neutron:
Table 12B-N1: Trial Combination of One Up-Quark and Two Down-Quarks in TRUE Units as in the neutron (N0)
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 Bohr’s solution of the EPR paradox (the Copenhagen interpretation of quantum mechanics 100), newly formed elementary entities do not exist as localized particles in 3S-1t until a 3S-1t measurement or observation is made. We propose that this is only possible if all TRUE units are undetectable in 3S-1t, before observation and measurement. This means that they exist in the substrate underlying all dimensional domains and will manifest as either mass/energy, or ג units, to exhibit the logical patterns of the substrate in observable symmetrically stable 3S-1t forms. In this way, the encompassing substrate, the additional five 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 mathematical distribution 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. Why? Because 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 cause TRUE units 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 because the measured mass/energy equivalence would be changed and the proton or neutron would become unstable.
Attempting to use the smallest integer solution, (3, 4, 5, 6) of the Conveyance Equation to find the appropriate values of ג for both the proton and neutron, we obtain negative total ג unit values. This would change the particle’s measurable mass/energy identity and violate conservation of mass and energy, so this solution of the conveyance equation will not work and 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 of gimmel.
Therefore, the smallest integer solution of the conveyance equation that produces no negative values of ג and also no zeroes for the Proton is 63 + 83 + 103= 123.
Using this solution, we have the electrically and symmetrically stable Proton. This would mean if we adequate figures for the Neutron (and the Electron) then our calculations would be viable for symmetrical, stable particles. [4]
Table 12A-P2: The Proton (P+) Solution
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

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 total 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 tried to use 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 in Table 3.
Table 12C: The First 36 Conveyance Equation Integer Solutions for n=m=3.
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 = 763

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, consistent with 3S-1t observation, 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.
As indicated, negative values for ג cannot occur because of the conservation of mass and energy as negatives would destroy the mass/energy/ ג balance and turn the quarks into unstable combinations which would decay quickly. Note that unstable quarks, e.g. top, charm or bottom quarks, will likely fall into specific unstable series of conveyance Diophantine equations. But this is a subject for further research. For now, we must find the smallest unique conveyance equation solution for each combination of sub-atomic particles. Nature is parsimonious, and we must never make a mathematical description or demonstration any more complicated than it has to be. 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 integer scale by trial and error, until no negative values are obtained. Also, a solution with the total for any term equal to zero cannot be allowed, because, in that case, there would be no solution as the resulting Diophantine equation and the Fermat inequality would apply. Using the solution 63 + 83 + 103= 123, the first attempt to find the TRUE unit configuration of the neutron is shown below:
Table 12B-N2: The Neutron (N0) Solution
Trial Combination of One Up-Quark and Two Down-Quarks in TRUE Units
Particle
Charge
Mass/Energy
ג
Total TRUE Units
MREV
u1
+ 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
These TRUE unit numbers give us a stable neutron; but now 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 atoms with equal numbers of protons and neutrons could not be stable because they would not satisfy any of the solutions of the conveyance equation, and we know that the element Helium, and other elements are stable combinations with equal numbers of protons and neutrons.
Table 12B-N3 Trial of Quark Combinations for the Neutron (N0)
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

We now apply the stable proton and neutron to the smallest element with both neutrons (hydrogen does not have a neutron) and protons. To describe a stable neutron, proton, electron combination, the conveyance equation solution would have to be either 43 + 243 + 323 = 363, 183 + 243 + 303 = 363, or some other combination of the integers 24 and 36. For example: looking at the TRUE-units analysis of Helium, with protons consisting of 24 TRUE units and neutrons consisting of 36 TRUE units, we have:
Table 12D-He1: 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

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. So these figures for protons or neutrons or electrons must be incorrect with us applying the derived figures: We have found that the smallest integer value in TRUE units that can satisfy the conveyance equation to produce a stable proton is 24, and the smallest integer value in TRUE units that can produce a stable neutron is 36. But, if the proton consists of 24 TRUE units and the neutron consists of 36 TRUE units, or multiples of these integers, atoms with equal numbers of protons and neutrons, like Helium, cannot combine to satisfy the conveyance equation. This would contradict the empirical fact that stable Helium atoms do exist, so, following the law of parsimony, i.e. using the smallest possible integers, we have to seek another integer solution of the conveyance equation for the neutron.

Table 12B-N4 The trial that works of Quark Combinations for the Neutron N0
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 these values for P+ and N0, the first integer solution of the conveyance equation containing the values X1 = 24 and X2 = 38, or multiples of them, is obtained by multiplying both sides of the primitive solution 123 + 193 + 533 = 543 by 2, yielding the integer solution 243 + 383 + 1063 = 1083.
Note that we have different kinds of quarks with different ratios of mass/energy to gimmel: There are three different kinds (or colors) of up-quarks u1, u2, u3 with u3 in the neutron being different from the u1 and u2 in the proton. Similarly, d1 in the down quark of the proton, is different from the d2 and d3 in the neutron. Therefore, each up quark and each down quark is triadic. They logically come in threes fitting the integer solutions to the conveyance equation.
Table 12D-He2: 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 4A 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. 1063+243+383=1083
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.
Whether mass, energy or gimmel (ג), upon measurement, each TRUE unit of the substance of reality occupies the same volume, i.e. the minimal volume for an elementary particle as a spinning object, as required by relativity and defined in TDVP as the basic unit of volume is consistently the same for any electrons (106 with 105 gimmel), protons (24 with 7 gimmel) and neutrons (38 with 16 gimmel).
Each TRUE unit is capable of contributing to the structure of physical reality as m, E or ג to form a stable particle, according to the logical pattern in the substrate reflected in the Conveyance Equation, and the relative volume of each particle (in the three dimensions of space) is equal to the total number of TRUE units cubed times the shape factor.
Table 12E1: The Building Blocks of the Elements in TRUE Units
Particle
Charge
Mass/ Energy
ג
Total TRUE Units
Volume
e
- 3
1
105
106
1,191,016
P+
+ 3
17
7
24
13,824
N0
0
22
16
38
54,872

As noted before, the shape factor of any regular form always cancels out of the conveyance equation. (As demonstrated above for the sphere, the shape factor, 4/3π, occurs in all terms of the equation, and thus can be cancelled by dividing both sides of the equation by 4/3π.) Thus the same equation is obtained regardless of the shape of the particles, as long as the shape and substance is the same for all three particles). For this reason, the right-hand column in these tables contains cubed integer amounts representing the Minimum Relative Equivalence Volume (MREV) for each particle making up the combination of sub-atomic particles.
The TRUE unit values for these elementary particles are uniquely determined by conditions necessary for the existence of a stable universe. The values for up- and down-quarks are the necessary values for the proton and neutron, as determined above, and the number of ג units and the total TRUE units for the electron are determined by calculating the ג units necessary to form stable atoms like the Helium atom. They also determine the smallest possible stable atoms, Hydrogen H1, Deuterium H2 and Tritium H3, as shown below.
Atoms are semi-stable structures composed of electrons, protons and neutrons. They are not as stable as protons and neutrons, but they are generally more stable than molecules. Some molecules, like H2O, are more stable than others ostensibly because of higher gimmel content, but all of the factors that contribute to stability must be considered, especially symmetry.





[1] Hebrew is the oldest continuously enduring language and regarded as the “holy language”. As this third substance has a postulated possibly mystical significance, the name gimmel, as the third letter of the Hebrew alphabet, may be appropriate.
[2] The numbering here as a convenience. It involves the part e.g. Part 12 and the first table so 12A. But in the instances of testing it has a suffix. So here Table 12A – P1 has the –P1 referring to the first in the test sequence of Protons so P1. Because this might not work out, the next would be Table 12A- P2. This allows convenience for those observing the mathematical test sequence only.
[3] Minimum Rotational Equivalent Volume (MREV): This is a term we apply so we can reflect cubes as required in quantal volumes.

[4] Up-quarks are designated u, and down-quarks as d: u1 and u2 in the proton, 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, (and also vary in spin proportions of 0.5) We could refer to u1 and u2 using another method of particle description commonly employed in physics, namely distinction by color, as in chromodynamics theory (QCD). We would have little difficulty, e.g., saying that because the stable quarks in the proton come in threes and they could be referred to as ‘green’ for u1 and ‘yellow’ for u2 which have the same mass and energy in collider data but have different third substance gimmel values and are therefore different in the combination. With this scheme, it is clearly indicated that stable quarks are in fact triadic, occurring only in threes in the proton. The d1 for the down-quark could be another color, e.g., ‘orange’. The converse applies to the neutron, which is still triadic with three stable quarks but this time what is referred to as 2 down-quarks would be the d2 and d3 and the colors could be “blue” and “red” but again reflecting the mass-energy collider data of down-quarks, plus say a “purple” for u3, the third up-quark.

1 comment:

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