PUTTING CONSCIOUSNESS INTO THE EQUATIONS OF SCIENCE, TRUE
QUANTUM UNITS AND THE THIRD FORM OF REALITY
Edward
R. Close with Vernon M. Neppe
©Edward R. Close October 15, 2016
INTRODUCTION
In this paper, we demonstrate the empirical necessity of a third form
of the substance of reality that is not directly measurable as mass or energy.
This third form of reality has not been previously defined. We have called this
third form “gimmel”: We Show that no subatomic particle can long exist without
gimmel even though gimmel is not measurable using known techniques of measuring
mass and energy. Mathematically and geometrically, atoms composed of quanta,
and compounds composed of atoms, cannot be stable without gimmel. This third
substance is necessary to maintain the symmetric stability of subatomic
particles, atoms, elements, and molecules.
Based on Fermat’s Last
Theorem for cubes: X^{3} + Y^{3}≠ Z^{3} there
cannot be any cubic volumetric combination with two components that are stable.
This means that a nucleus alone, plus electrons without gimmel cannot combine
geometrically and mathematically to form atoms.
Therefore, there have to be three components (mass, energy and
something else—the third substance “gimmel”. This is brought about when
applying a specific derivative Diophantine equation Σ^{n}_{i=1}
(X_{n})^{m} = Z^{m} we call the “Conveyance equation”, which is (X_{1})^{3} + (X_{2})^{3
}+ (X_{3})^{3}= Z^{3 }for triplet combinations.
Moreover, these Diophantine calculations only work based on applying
a 9dimensional model. The 9dimensional requirement is not surprising because
elsewhere the authors have demonstrated mathematically that our finite reality
has to consist specifically of 9 dimensions. Moreover, these dimensions must be
spinning relativistically, not folding as in string theory. We have shown this
with the derivation of a Cabibbolike mixing angle, of intrinsic electron spin
and angular momentum, of the shape of the electron which in 3S1t is
symmetrical but nonspherical, of the disappearing electron cloud and of a 9D
mathematical Cabibbo thought experiment plus with weak universality. This
validation of the 9dimensional finite spin model was specifically proposed as
a key aspect of a metaparadigm model developed by the authors called the
NeppeClose Triadic Dimensional Distinction Vortical Paradigm (TDVP).
New Concepts:
1. Traditionally,
we have applied NewtonianLeibnizian infinitesimal calculus as a mathematical
convenience. But this approximation of infinitesimals is incorrect in quantized
reality. Given the Planckian quantum units, which are integral, it is integers
that are critical in measuring finite reality as everything is quantized.
2. This
is why we must convert massenergy to unitary equivalents. This is why
we apply combinatorial Diophantine equations, with three terms on the left side
because three symmetric cubes can combine symmetrically and may be very stable
if the cube root of the result on the right is an integer. This specifically
involves using the Conveyance equation in a 9dimensional Diophantine model.
Nine dimensions are specifically indicated by dimensional extrapolation, pure
number theory and, importantly, a new Calculus, the Calculus of Dimensional
Distinctions (CoDD). The CoDD defines all mathematical operations in terms of
distinctions that are integral, to accommodate the finite components of
quantized reality.
3. Atomic
materialism is refuted by this approach because protons plus neutrons plus
electrons alone, or quarks plus electrons alone cannot form the stable integral
combinations that we call atoms and molecules. There has to be a third
substance. Without extra TRUE units of “gimmel” atoms cannot exist as stable
combinations of integer multiples of TRUE units. Effectively, this means that
our current perception of any atom or element without a massless, energyless
third substance linked with consciousness, will not provide an atom that can
exist for any length of time, which is
why the pure Standard Model of reductionistic materialist Physics has to be
incorrect.
4. Pertinently,
valence incorporates both the number
of open spaces and electrons in the
outer shell of an atom, and the figure applied depends upon which is the
smaller. These number of spaces available and electrons in outer shell give
indications of reactivity and will affect the abundance or lack thereof of
elements and their reactivity properties.
5. The
concept of integral equivalents is unique and linked with expanding our
experiential 3S1t to an existing finite 9D spin reality.
6. In
another study, the ratio of Gimmel to TRUE units was the same as the volumetric
measures of dark matter with dark energy to the proportion of the cosmos.
Indications needing confirmation:
1.
Geometrically, the shells in atoms reflect
volume and correspond to energy
levels.
2. These
concepts are not limited to elemental atoms and apply at every level to compound
entities.
3. Molecules
are not just specific sums of atoms. The combined equivalence of atoms in
molecules can be calculated based on gimmel, massenergy equivalences and TRUE.
For example, using just the presence of the atoms and taking into account the
covalent bonding of water and hydrogen sulfide, they could superficially have
the same activity and similar applications. But empirically we know this not to
be so. This is demonstrated by the more appropriate calculation of
Hydrogenhydroxide (HOH) (=water) compared with HH=S (H_{2}S)
(=hydrogen sulfide): H_{2}S calculates out at a lower gimmel /TRUE
ratio and is not a cube root, indicating that it is asymmetric.
4. We
postulate that gimmel is strongly linked with meaning: A meaningful
consciousness that is tethered with the mass/ energy in the 9dimensional domain.
Consciousness is a strong gimmel candidate because there appears none other.
Additional Concepts:
1. The
whole is more than sum of the parts because gimmel contributes to stability,
yet cannot be directly observed or measured.
2. This
new way of analyzing particles suggests that all compound structures, however
complex, and whatever their size, are quantum systems. Historically, John Von
Neumann demonstrated in his seminal 1932 work “Mathematical Foundations of Quantum Mechanics” with the Dirac–von Neumann axioms that there is
a rigid mathematical framework for quantum mechanics and that extends to the
macroworld.
3. It’s
possible that gimmel is what particle physicists have hypothesized as “gluons”,
the “glue” holding atoms together.
4.
There is something rather than nothing: Missing
from the current paradigms is another third substance/ process (gimmel).
Consciousness appears to be the common aspect, and we regard “gimmel” as
predominantly reflecting meaningful consciousness even at that subatomic level.
Towards a “theory of everything”
Many physicists, including Einstein, Pauli and Hawking have
dreamt of a ‘theory of everything’. But to this point, their dreams have not
been fulfilled. The reason is simple. You
can’t have a theory of everything if you doggedly exclude a major part of
Reality from your theory. That major part of Reality excluded by
contemporary reductionist science has two components, consciousness and
infinity.
In this paper, we focus on the first concept, consciousness, in
the context of that component of reality that we call the “finite” because that
involves discrete quantized integral components that can be analyzed according
to the principles of dimensionality and mathematical logic.
Based on Large Hadron Collider (LHC) data and mathematical
applications, our work extends Theoretical Physics to a 9dimensional spin
models not just the 3 dimensions of space in a moment in time (3S1t) which is
the basis of most current physical theory. Whereas 3S1t can explain a great
deal, our work has shown there are problems in 3S1t that can only be solved by
applying a 9dimensional spin model. We call this Dimensional Biopsychophysics.
For many years, we have insisted that the dream of a theory of
everything is never going to be realized until we find a way to put consciousness
into the equations of science. Close found the way to do thisusing a new
mathematical tool called the Calculus of Distinctions. The inspiration came to
Close in a dream in 1986, and he published it in 1990 in a book entitled
“Infinite Continuity”. But then, and even today, most people aren’t willing to
invest the time and considerable effort it takes to learn a whole new system of
mathematical logic, leaving much of our work inaccessible to the majority of
scientists.
Historical basis of TDVP:
Since 1989, we have been determined to find a better way to
explain putting the fundamental reality of Consciousness into the equations of
science. In 1996, Close published the book “Transcendental Physics”, an effort
to make his 1990 work more accessible. It reached a few more people, but still
only a relative handful of scientists and others interested in the merging of
science and spirituality. One who shared Close’s vision, and became his
research partner for the past seven years, was the neuroscientist Fellow of the
Royal Society (SAf), Dr. Vernon Neppe, MD, PhD. Together Drs. Close and Neppe
developed a comprehensive framework, a paradigm for the science of the future.
We call it the Triadic Dimensional Distinction Vortical Paradigm (TDVP). It was
first published as “Reality Begins with
Consciousness” in 2012, and has been reviewed by more than 200 scientists
and philosophers worldwide. We’ve also published a number of technical papers,
and recently, we’ve found a way to explain the revelations of the Calculus of
Distinctions of 1989, 1996 and 2011, in a more accessible way.
The fundamental questions:
This
paper provides the answer to two important questions:
1.
Why is there something rather than nothing? And:
2.
What is missing from the current scientific
paradigm?
The answer to both questions can be summed up in one word:
Consciousness. Without consciousness there could be no physical universe; and
yet, there is no place in the current paradigm for consciousness. The clues
that consciousness is the answer to the first question are plain in relativity
and quantum physics, but most mainstream scientists, trained in reductionist
materialism, are blind to those clues, and their belief – which is not a valid
scientific hypothesis – that the universe could exist without some primary form
of the consciousness manifest in sentient life, is stubbornly maintained and
the clues are ignored.
Many of the key scientists of the past were deeply spiritual (for
example, Georg Cantor, Albert Einstein, Isaac Newton, Wolfgang Pauli and Max
Planck) but they did not dare to introduce consciousness into the equations of
science because they would have been ostracized from professional science and
mathematics. The current authors, Vernon Neppe and Edward Close whose model of
TDVP unifies science and spirituality, clearly bridges this
sciencespirituality dichotomy. But the materialistic belief system widely
taught in our educational institutions today brings otherwise rational people
to openly ridicule, any mention of any form of intelligence superior to their
own. This egotistical position of mainstream scientists is justified in their
minds by the successes of materialistic science. But those successes lie almost
entirely in the realm of explaining superficial physical mechanisms. Deeper and
ultimately much more important questions about the meaning and purpose of
manifest physical reality, life and conscious awareness, are beyond their
reach. Those questions, of paramount importance to humanity, are within reach
of meaningful analysis when consciousness is included in the equations of
science. The purpose of this paper is to show how this is done.
The bottom line is that, in this world of human experience, we
will never truly understand the Nature of Reality until our searches for
scientific and spiritual knowledge are merged into one serious, combined
effort. Once this happens on a global scale, we maintain that humanity will
experience an explosion of new knowledge and understanding far beyond anything
experienced so far in the current era of recorded history. In this paper, we
show how consciousness is describable in the equations of quantum physics and
relativity, and a few of the explanatory revelations produced as a result. And
we believe this is only the tip of the iceberg!
MOVING beyond the current UNDERSTANDING OF reality
In 1714, the German polymath Gottfried Wilhelm Leibniz stated
that the most important question of all is: “Why is there something rather than nothing?” Science proceeds from
the assumption that there is
something, something that we perceive as the physical universe. In order to
investigate this something that we
appear to be immersed in, we go about trying to weigh and measure the
substances it is made of and look for consistent structures and patterns in it
that can be described mathematically. We call such mathematical descriptions
“Laws of Nature”.
A new system of units of measurement
To find the laws governing the relationships between different
features of physical reality, we have to define a system of units with which to
weigh and measure those features. Historically, units of measurement have been
chosen somewhat arbitrarily. For example, the units of the socalled English
Imperial System were based on the practice of measuring things with what one
always had at hand: parts of the human body. A horse was so many “hands” high;
one could measure rope or cloth by “inching” along its length with a joint of
one’s thumb or finger. Short horizontal distances were measured in multiples of
the length of one’s foot, or the distance from the tip of one’s nose to one’s
thumb on a laterally extended arm, and a mile was 1000 paces, when a pace
consisted of two steps. Since not all people are the same size, measurements
obtained this way are somewhat variably inaccurate. Consequently, units were
eventually standardized so that the measurements of a given object, carefully
obtained by anyone, should always be the same. But, even though units of
measurement were standardized in many countries, the basic unit was not
necessarily the same from one country to the next.
As physical science advanced, the need for international
standards grew, and the international system of units (SI) based on invariant
physical constants occurring in nature, with larger units being multiples of
ten times the smallest unit, was developed. The number base of 10 was chosen
because it was already used almost worldwide. It was a natural outcome of
counting on one’s fingers, and starting over after every count of ten. Science
generally uses SI units now for two reasons:
1. All
but three countries of the 196 countries on the planet (the US, Liberia and
Burma) use the SI metric system as their primary system of measurement. This is
significant, even though the UK still uses a mixture of the two systems, as
does the US and a few other countries to a lesser extent.
2. Computations
are simplified when all units are related by multiples or factors of 10,
eliminating the odd fractions relating inches, feet and miles, ounces and
pounds, pints quarts and gallons, etc. in the English system.
Consciousness, dimensions, TDVP, distinctions and reality
There is a need now to define a new unit of measurement based on
discoveries of quantum physics, relativity and the Calculus of Distinctions.
One purpose of this paper is to explain why a new basic unit is needed and how
it is derived. It may seem to come as a surprise, that in the process, we
provide an answer for Leibniz’s “most
important question”, and introduce a new comprehensive scientific paradigm
for the first time since 1935.
Beyond seeking practical applications that improve the quality of
life, the motivation behind our efforts in science, religion and philosophy is
the desire to know and understand the true nature of reality. Science, as we
know it, is the science developed during the past 800 years. This is a very
short time compared to the length of time life has existed on this planet: less
than two tenmillionths of the apparent age of the Earth. This science seeks to
understand the reality experienced through the physical senses in terms of the
measurable parameters of matter, energy, space, and time. It is only in the
past century that, based on a number of clues from relativity and quantum
physics, we have recognized that science is incomplete. And it is only during
the past decade, that we have identified an urgent need to include the
conscious actions of the observer in the equations of science. Consciousness is
truly the missing link in the current scientific paradigm.
In a universe where consciousness is an integral part of reality,
meaningful structure is no accident. Conscious entities are able to recognize
meaningful order and patterns in the reality they experience and interact with
certain aspects of it to enhance and perpetuate existing patterns and structures
that are beneficial to their existence and growth, creating negative entropy in
the process. Could it be that consciousness is and always has been present in some form, even in the very most basic
structure of reality, as quantum experiments seem to indicate? If so, we have
the answer Leibniz’s question. If consciousness is an integral part of reality,
continually creating meaningful structure at the quantum level, there must be a
way to include it in our scientific paradigm and the mathematics that describes
it.
The NeppeClose TDVP model, and particularly Close’s Calculus of
Distinctions and his Dimensional Extrapolation, plus the reapplication of
critically important largely ignored principles of number theory including
Diophantine Equations and with Close’s Conveyance Expression, constitute an upgrade
of the mathematics of the physical sciences to include the direct involvement
of consciousness. If successful, there is reason to believe that this new
paradigm will provide a comprehensive framework within which all the branches
of science can be expanded to include phenomena heretofore excluded from
scientific investigation.
The Role of Mathematics in investigating the Nature of Reality
Mathematical Platonism:
Some scientists, when thinking about the nature of reality, make
a distinction between the Platonic and Aristotelian worldviews: The Platonic
view is that the universe is the physical manifestation of a partly hidden,
deeply mathematical reality; while the Aristotelian view is that mathematics is
simply an invention of the human mind, developed as a tool used to process
direct observations and measurements of the material universe. Michael
RowanRobinson, Professor of Astrophysics at Imperial College, London, has
articulately expressed his belief in the Aristotelian view in his wellwritten
presentation of current observational cosmology, “The Nine Numbers of the Cosmos”:
[The] “Platonic view, that the universe is a manifestation of some kind
of ideal, mathematical form, is very fashionable today. Some of its proponents
are so astounded by this insight that they are driven to a mystical
interpretation. This deep mathematical structure is God, or the mind of God, or
is evidence for a creator. But, why isn’t this insight, that the universe is
deeply mathematical, sufficient in itself? The additional mystical
interpretation doesn’t seem to add anything. There is, anyway, an alternative
to this Platonic view, namely that we should think of mathematics as simply an
invention of the human mind, which we use as a tool to model our limited
perceptions of the universe… This Aristotelian view, which I share, sees the
universe as something we try to characterize, measure, describe.”
Mathematical Platonism, on the other hand,
incorporates three theses: The
existence, abstractness and independence of mathematical objects. This
means that had there not been any intelligent agents, or had their language,
thought, or practices been different, there would still be archetypal mathematical
objects.
Our revision of the
Platonic world view is distinguished from the view of Plato in history.
‘Platonism’ inspired by Plato's famous theory of abstract and eternal Forms and
CloseNeppe Platonism are quite different: Our Platonism has developed quite independently
of its original historical inspiration. The Mathematical Platonism we describe
is broader than purely metaphysical ‘Platonism’ because we incorporate the
underlying mathematical logic directly into scientific application recognizing
that we can apply it not only empirically, but use the equations to reflect consciousness
as an integral part of the model.
We postulate that reality
extends far beyond the 3S1t physical world and includes objects which aren't
part of the causal and spatiotemporal order studied by the physical sciences.
With respect, the mathematics we present below are far beyond naturalistic
mathematics, extending to empirical particle physics and beyond. We demonstrate
below that our revision of Mathematical Platonism is very powerful.
As proponents of the Triadic Rotational Vortical Distinction
Paradigm (TDVP), Drs. Vernon Neppe and Edward Close differ markedly from
RowanRobinson. TDVP aligns to some extent with the Platonic worldview, except
that is applied not only philosophically, but mainly based on empirical
inductive and deductive reasoning and applying feasibility as a viable method
of the Philosophy of Science. We are not therefore ‘astounded’ that the
universe is deeply mathematical,  we expected it. And we are not ‘driven’ to
‘mystical interpretation’; we see it as natural, satisfying, and more to the
point, explanatory. It explains many things that the materialistic Aristotelian
worldview cannot. The insight is ‘sufficient in itself’, only if we choose not
to look any farther. It ‘doesn’t seem to add anything’ only if you are content
to ignore the clues in relativity and quantum physics that cry out for
explanation. It doesn’t occur to materialistic scientists trained in Cartesian
dualism that if there were not some kind of (Platonic, if you must) deeper
reality, their mathematical descriptions would not work. The challenge to
science is to explore that deeper reality. Reality
is ‘mystical’ only if you don’t seek to understand it.
Mathematics is not just an abstract human artifact. Far from it,
the deep logic of mathematics is invariant because it actually reflects the
true underlying logical structure of reality. The basic axioms and theorems of
mathematics remain unchanged when dimensional transformations are applied. Thus
the logic of mathematics is a prime example of invariance in its most general
form.
The only thing that is an artifact of the human mind is the
notation developed to convey the mathematic and dimensional logic underlying
reality. While it seems that we may invent whatever mathematical procedures we
wish, the same invariant mathematical laws would ultimately be discoverable by
any sentient being. They would then be expressed in whatever culturally fashioned
symbolic language that had been developed by those specific sentient beings.
All mathematical reasoning and description is based on the
conscious drawing of distinctions, starting with the distinction of self from
other, which then allows the drawing of three types of distinctions in the
“other”: distinctions of extent, content and impact, which are measurable,
contain meaning and purpose, and impact on other objects. This reflects the
very basic form of mathematical logic which Close developed and we’ve now
amplified, i.e., the Calculus of Distinctions. It is combined with Euclidean
and hyperdimensional geometry, requiring a ninedimensional reality containing
the basic “stuff” of the universe, and provides the framework for describing
the elementary particles that appear to be the building blocks of the physical
universe. This is the logical extension of very important work started by Wolfgang
Pauli, Hermann Minkowski, Albert Einstein, Georg Cantor, Theodor Kaluza, Oskar
Klein, and others, who made significant progress explaining physical phenomena
in the framework of multidimensional geometry.
The Third Form
Based on the natural structure of pure integral number theory and
mathematical invariants relating to dimensional domains, we have developed TDVP
as a paradigm that describes reality as consisting of the substances of mass
and energy interacting within nine finite dimensions embedded within infinite
domains containing a potentially infinite number of finite logical patterns.
Based on clues from relativity and quantum physics, these domains contain the
logical organizing structures that guide the evolution of a stable universe
capable of supporting conscious life forms. We hypothesize that the infinite
substrate may constitute consciousness itself, with space and time embedded
within it, and mass energy and a third form, which we call “gimmel”, also being
contained within this infinitely continuous conscious domain.
The brilliant physicist Wolfgang Pauli worked on developing five
and sixdimensional models until 1953, but didn’t publish his findings because
he was bothered by the appearance of what he called “…rather unphysical shadow particles.” Since Pauli’s time,
science has discovered that just over 95% of the substance of reality consists
of some sort of shadowy stuff, presently called “dark energy” and “dark matter”,
not directly detectable through the physical senses or extensions of them.
The mathematics and
dimensionometry of TDVP indicate that a third form of the “stuff” of reality is
actually necessary in the subatomic structure of reality for there to be any
stable elements in the physical universe; i.e. in order for there to be
something rather than nothing.
The logic of TDVP also suggests that this third form of substance
may be imbued with the qualities we associate with consciousness. It is interesting
to note that late in his life, Pauli, who was regarded as the most brilliant
mind of his day by many physicists, including no less brilliant minds than
Albert Einstein and Max Born, dreamt of “unifying matter and spirit within the
world of physics.”
TDVP
Guided by the mathematical structure of number theory, Euclidean
and nonEuclidean geometry, particle physics data, and new mathematical tools
created for the purpose of including the direct interaction of conscious
entities with objective reality at the quantum level, we have developed TDVP, a
model of reality that includes spinning elementary distinctions existing in
nine finite dimensions embedded in a conscious substrate that contains all of
the logical patterns, reflected and/or potentially reflected in the structure
of the physical universe. Within the theoretical framework of TDVP, we are able
to explain a number of phenomena that have remained inexplicable in the
standard model of particle physics for decades, including the stability of the
triadic combination of quarks^{, }the intrinsic spin of Fermions, the
Cabibbo quark mixing angle, and the stepbystep development of the structures
of the Elements of the Periodic Table.
TDVP is a paradigm shift that explains why there is something
rather than nothing. And, it expands the “Standard Model” of physics to include
a new theoretical basis for the biological, psychological and life sciences, as
well as for littleunderstood and rare phenomena like remote viewing,
outofbody experiences (OBEs) and other socalled paranormal or psi phenomena. It even provides the
basis for a better understanding of spiritual experiences that have been
occasionally documented to impinge upon physical reality under certain
conditions.
Not surprisingly, TDVP, like paradigm shifts before it, also
requires a significant expansion of our understanding of mathematics in
general. In 1986, Close realized that George Spencer Brown’s Calculus of
Indications, presented in “Laws of Form”, reuniting for the first time,
imaginary numbers with symbolic logic, and thus realigning the algebras of
logic with mathematics, was the first step toward integrating number theory,
geometry and mathematical physics into a comprehensive logical framework
capable of describing and explaining physical, chemical, biological,
neurological, psychological, and even spiritual phenomena.
Close adapted Brown’s Laws of Form, creating the Calculus of
Distinctions (CoD), a comprehensive logical tool for dealing with the functions
of consciousness, and applied it to some longstanding cosmological puzzles.
Some of the results were published in “Infinite Continuity, a Theory Unifying
Relativity and Quantum Physics”^{ }in 1990, and in “Transcendental
Physics, Integrating the search for Truth”. By introducing appropriate
additional notational structure, the Calculus of Distinctions was refined by
Close and Neppe to become the Calculus of Dimensional Distinctions (CoDD) in
2003. From 2008 to the present, we amplified this mathematical tool, recognized
as the logical basis integrating all mathematics and applications to physical
and spiritual reality has been systematically applied to develop the
mathematical basis of TDVP.
THE Illusion of Material Reality
Clues from relativity and quantum physics suggest that the
timehonored idea that matter, energy, space, and time exist separately is
incorrect. It appears that the macroscopic forms of matter, space and time we
perceive through our physical senses are subtle illusions, although, as
Einstein said about reality, "Reality
is merely an illusion, albeit a very persistent one.” TDVP is built
upon, and an extension of, the monumental works of a number of intellectual
giants like Pythagoras, Fermat, Leibniz, Poincare, Cantor, Gödel, and
Minkowski; but most especially, it is built upon on the deep insights of Max
Planck and Albert Einstein.
Max Planck said: "As a
man who has devoted his whole life to the most clearheaded science, to the
study of matter, I can tell you as the result of my research about atoms this
much: There is no matter as such! All
matter originates and exists only by virtue of a force. We must assume behind
this force the existence of a conscious and intelligent Mind. This Mind is the
matrix of all matter."^{ }
And, Albert Einstein said: “Space
time is not necessarily something to which one can ascribe a separate existence.”^{
}And “I want to know how God created this world. I am not
interested in this or that phenomenon, in the spectrum of this or that element.
I want to know his thoughts. The rest are details.”
These statements, from two of the most brilliant scientists who
spent their entire lives studying physical reality, reveal the important
conclusion that the common perceptions of matter, energy, space, and time,
conveyed to our brains by the physical senses, are subtle illusions! And both
of them conclude that the reality behind these subtle illusions is a conscious,
intelligent linkage.
It has long been known that the appearance of solid matter is an illusion, in the
sense that there appears to be far more empty space than substance in an atom.
But now we learn that the matter of subatomic particles and the “empty” space
around them are also illusory. This is, however, consistent with quantum
physics experiments that bear out the conclusion resulting from the resolution
of the EPR paradox^{ }^{50} with the empirical
demonstration of John Bell’s inequality by experimental physicist Alain Aspect
and many others that the particles and/or waves of the objective physical
reality perceived through our senses cannot be said to exist as localized
objects until they impact irreversibly on a series of receptors constituting a
distinct observation or measurement by a conscious entity.
We must be clear, however, that the linkage to consciousness does
not validate subjective solipsist theories like that of Bishop Berkeley as one
might think; rather, it reveals a deeper, multidimensional reality, only
partially revealed by the physical senses. It suggests that reality is like a fathomless, dynamic ocean
that we can’t see except for the white caps. The difference is that the
particles and waves, analogous to the white caps, only appear in response to
our conscious interaction with the ocean of the deeper reality.
As noted above, Albert Einstein is quoted as saying: “Ich will Gottes Gedanken zu wissen, alles
anderes ist nur Einselheit.” (I want to know God’s thoughts, the rest is
just detail.) And he also said “Rafinert
ist der Herr Gott, aber Bohaft ist er nicht!” (The Lord God is clever, but
he is not malicious.) Taken together, these two statements reveal that
Einstein’s science was rooted in a deeply spiritual understanding of reality.
It appears that he believed that the universe, as a manifestation of God’s thoughts,
is very complex, but ultimately understandable.
Agreeing with Einstein, TDVP seeks to reveal that all things are,
in fact connected to, and part of that deeper ocean of reality, only
momentarily appearing to be separated from it. This apparent separation,
perpetuated by the conscious drawing of the distinction of ‘self’ from ‘other’
and the drawing of distinctions in self and other, allows us to interact with
and draw distinctions in the ‘other’. TDVP posits that, although ostensibly
separate in the 3S1t world of our physical perceptions (three dimensions of
space in one moment [the present] in time), we are never truly separated from
the whole of reality, but remain connected at deeply embedded multidimensional
levels.
There are some in the current mainstream of science who do see the universe as deeply
mathematical, but even those scientists seem to shy away from including
consciousness in their equations. The Swedish physicist, Max Tegmark, concludes
that the ultimate nature of reality is mathematical
structure. In reaching this conclusion, however, he strips mathematical
description of any intent or purpose: “A
mathematical structure is an abstract set of entities with relations between
them. The entities have no ‘baggage’: they have no properties whatsoever except
these relations.”^{ }In other words, he still does what most
mainstream materialistic scientists do: he throws the baby out with the bath
water.
It is critically important to separate science from fantasy and
wishful thinking, but consciousness is an extremely important part of reality
and should not be excluded from the equations of science just because it
complicates the picture.
The role of TDVP
From the broader viewpoint of TDVP, it is not surprising that
mainstream science, focused, as it is, on the limiting philosophy of
reductionist materialism, has lost touch its metaphysical roots, and thus
cannot explain how it is that a large part of reality is not available to us
for direct observation, but makes its existence known only indirectly through
quantum phenomena like nonlocality and quantum entanglement, as well as the
near lightspeed vortical spin of fermions, and the effects of socalled dark
matter and dark energy in the rotation of spiral galaxies.
TDVP also answers the real need to explain why we sometimes catch
glimpses of a broader reality in rare extracorporeal (outofbody) experiences
and other documented psi phenomena.
The current mainstream scientific paradigm cannot explain socalled anomalous
phenomena and the “missing” portions of reality because there is no place in
its formulation for phenomena that may involve more than matter and energy
interacting in threedimensions of space and one dimension of time. TDVP, on
the other hand, reveals a multidimensional reality and the need to recognize a
third form of reality, not measurable as mass or energy, in the equations of
science. As we shall see, TDVP provides a theoretical basis for a much deeper
understanding of reality, as well as providing the appropriate tools for
exploring it.
DO WE LIVE IN AN ACCIDENTAL UNIVERSE OF RANDOM COINCIDENCES?
Dividing the world of our experiences into the internal or
subjective and the external, assumed to be completely independent of any form
of consciousness as the current scientific paradigm does, alienates
consciousness from the ‘real’ world of the physical universe and leads to an
endless chain of unresolvable paradoxes. Consciousness remains left out of the
equations of mathematics and physics.
Alternate realities
The prevalence of this attitude among scientists is expressed
very well by MIT physicist and science writer Alan Lightman in his 2014 book “The Accidental Universe”. We know that
if any one of a number of cosmological parameters were only a minimally
different, there would be no chance for life as we know it. In talking about
the apparent ‘finetuning’ of the physical universe, Lightman points out that “Intelligent Design is an answer to
finetuning that does not appeal to most scientists.” (p. 12) ^{63}^{r }However,
when confronted with the observerrelated nonlocality of Bohr’s solution to
the EPR paradox ^{64}, many scientists
have preferred the “multiverse theory”, devised to preserve the ostensible
Cartesian duality of a separate mind and body, except that the “mind” for them
does not have relevance or exist, and the preference is to keep consciousness
completely out of the picture of ‘scientific objectivity’.
The “multiverse” has also been called the "alternate
universes", metauniverse and parallel universes. Technically, with some
linguistic and descriptive variations, they usually refer to as hypothetical
sets of infinite or finite possible universes including our current 3S1t human
living experiences.
In the multiverse theory, there are many, many parallel universes.
Just how many there are is unknown and unknowable, because your consciousness
only exists in this one, and unfortunately you cannot experience any of the
other universes. Thus, just like the spate of string theories, there is no hope
of proving or disproving such a theory. Even though these scientists pride
themselves in being ‘hardnosed’ objective scientists (read: materialists), it doesn’t seem to bother
them that string theory and the multiverse theory cannot be tested.
These models together
comprise everything that exists relating to the entirety of space, time and
matter and energy, plus the laws and constants in physics and biology that
describe them. These constants likely vary with each “world”, and amongst the
variations are describing probabilities. These superficially appear theoretical
models that sound possibly feasible but they have their difficulties.
At best, these models can only be internally consistent
(reflecting ostensibly feasible possibilities) and thus applying Popperian falsifiability
do not even qualify as scientific hypotheses. Variations occur for example, in
Tegmark’s model, the limitations are set mathematically.
LFAF
These models could qualify scientifically using the NeppeClose
model of Lower Dimensional Feasibility,
Absent Falsification” (LFAF). if they were feasible, but there are some
problems, such as lack of dimensional definitions, category errors, internal
contradictions of knowledge that are not taken into account, and definitions of
the finite and infinite. We must be careful not to throw the baby out with the
bath water and LFAF is directly involved with the study of multiple dimensions
beyond the 3S1t domain of the world revealed by our physical senses.
The difficulty with these
models is not so much what is conceptualized as what is ignored and left out;
and what is ignored are aspects that we regard as key features of reality,
namely additional dimensions, including dimensions of time and consciousness.
The most basic axioms and theorems of pure number theory, confirmed by the
calculus of dimensional distinctions, point to the existence of at least nine finite dimensional domains,
sequentially embedded in groups of three. There is compelling evidence from
relativity and quantum experimental data that the dimensions of each of these
additional triadic dimensional domains, encompassing the 3S1t domain, have
progressively much more complex qualities than the dimensions of the domain
available to us through the physical senses.
The current standard model
theories appear to make the categorical error of equating space and time, on
the other hand, the TDVP model of a reality of at least ninedimensions has
clarified phenomena not explained by the current standard model, promises to
explain more, and even more importantly, promises to unify all of our
understanding of reality under one consistent paradigm. We make these comments
not as pure speculations but as important pieces of the jigsaw puzzle of
science. It does this by applying the Calculus of Distinctions (CoD) to clarify
the relationship of dimensional measures to mass and energy, which in CoD
reflect content.
Therefore, although the
current standard model paradigm might be feasible scientifically applying LFAF,
it is difficult to fit their jigsaw pieces together when, at least in most
varieties of the standard model, there are contradictions of category errors,
and infinity is not incorporated in them. Therefore, just because the
theoretical concepts are feasible, the models have to show internal consistency
and take into account all pieces of the jigsaw puzzle of reality. We believe
that not only are many pieces missing because they take into account only
3S1t, if the remaining further dimensions (e. g. our demonstrated 9dimensional
spin model) are ignored, some of those jigsaw puzzle pieces would simply not
fit together.
To generalize is difficult,
because each model is sometimes slightly or sometimes grossly different.
However, a legitimate theory must be internally consistent taking everything
into account as required. We maintain that the limitation to the current models
of physics and perceptions of multiple 3S1t existences involves incomplete
knowledge because such factors as psi, nonlocality, and altered states of
consciousness are not properly taken into account, and in many cases, not taken
into account at all.
SUPPORTING A 9DIMENSIONAL SPIN FINITE REALITY MODEL
The validity and predictive power of a 9dimensional spin finite
reality model is now wellestablished by the previous work of Close and Neppe.
This predominantly relates to the first major discovery associated with the
NeppeClose Triadic Dimensional Vortical Paradigm (TDVP): derivation of the exact value of the Cabibbo angle from
9dimensional spin model principles, but is also substantiated by additional
supporting discoveries and data. The 9D model is also necessary and important
in the derivation of TRUE (Triadic Rotational Units of Equivalence) units and
the third substance, gimmel.
Consequently, it is appropriate to discuss briefly the support
for the 9dimensional finite spin model here. The Cabibbo mixing angle is an
empirically derived theoretical mixing angle in particle Physics that could not
be derived from the prevalent current Standard Model of Particle Physics.
Consequently, the reason why the strange empirical Cabibbo angle value of
around 13.04 degrees perplexed scientists for 50 years might have been because apparently, noone
had tested a 9D spin hypothesis before. Our work in 2012 provided a
solution.
Close and Neppe applied welldefined physics, with well
substantiated empirical data, including welldefined constants such as the Bohr
radius (radius of the hydrogen atom), speed of light, Planck’s constant, rest
mass of the electron, its radius and charge, the Coulomb constant, π and added
welldefined equations and principles, such as the Lorentz correction, the
principle of conservation of angular momentum, kinetic energy equation, De
Broglie’s wave equation, Coulomb’s equation, the centrifugal force equation,
the wave length of a rotating body and calculations of magnetic moment. These
applications allowed for a detailed mathematical derivation of the mixing angle
of elementary particle fermions, exemplified by a Cabibbolike mixing angle in
elementary particles, with the empirical calculation in quarks already having
been found to have been the 13.04 degrees±0.05 and our derived figure being
13.032 degrees. ^{2} Furthermore, a
thought experiment replication that we did found the figure to be 13.0392
degrees.
The authors also applied
these principles to fermion rotation and intrinsic spin utilizing the basic
concepts of a unified spacetimeconsciousness theory of finite reality from
the NeppeClose Triadic Dimensional distinction Vortical Paradigm (TDdVP) ^{23}. This included applying two new mathematical
techniques that we have developed as part of this TDVP model, namely
dimensional extrapolation across rotating dimensions, and the principles of the
calculus of distinctions.
We have shown how only a 9dimensional vortical (spin) model
produces a legitimate derivation. These results can easily be replicated by
applying the relatively simple mathematics to the dynamic rotation of
elementary particles as ninedimensional objects.
However, both the Standard Model of Particle Physics and the
various String Theories with folding
dimensions and none of which involve 9dimensional spin, fail. This result can only be derived by applying the dynamic
rotation of elementary particles as ninedimensional objects: Results using any
other dimensional models with any number of dimensions besides 9 are falsified,
while exponents of 9 (e.g. 81 dimensions) are not directly falsified.
Deriving the Cabibbo mixing angle mathematically supports a
component of the broader TDVP hypothesis, namely that finite reality consists
of a 9dimensional vortical (spinning) model. As sentient beings, we may be able to distinguish only part of our
finite reality, reflecting only our subjective 3S1t experience of three
spatial dimensions, in the present part of one time dimension. Nevertheless,
those 4 dimensions could reflect part of the feasibility of the larger 9dimensional
spin (vortical) unified finite reality
of the essential substrates, including mass/energy measurement of subatomic
particles. This may produce results that are incomplete, based on the overt
experiencing of three dimensions of space within a moment of time. Yet, some
dimensions may be hidden from us in our restricted 3S1t subjective reality and
we might get a more complete picture from mathematical analysis of particles
spinning in 9D.
Our 9D spin findings,
because of their breadth, have generated several novel ideas for testing and
application. The authors have proposed
that the essential substance of finite reality manifests as various
dimensionally related combinations of matter, energy and consciousness in 9
finite dimensions. Ongoing research includes analyzing the third
substance of reality we have called “gimmel”. We propose that this third
massless, energyless substance is most likely related to consciousness, and
that it is appropriate to examine this hypothesis in this paper. Although the TDVP hypothesis of a 9
dimensional finite reality is strongly supported by our findings, the relevant
mathematical derivations do not explicitly reveal the nature of specific
qualities of the dimensional substrates of Space, Time and gimmel as the postulated
substance of consciousness.
The TDVP model versus the multiverse
Our TDVP model of
“lifetracks” has some superficial similarities to the multiverse because it
recognizes that in the continuous infinite different experiential realities may
exist. The universes are not parallel or alternate. They are very real in that
they are dynamically existing, but they are covert and in the physical reality
are limited to single individual choices. Effectively, Consciousness is
part of the equation of the measurable extent of reality just as space and time
are. These make up numerous quantized finite dimensions, and these in turn, are
embedded in an infinite continuity. Moreover, the content of Consciousness is
as legitimate as mass and energy, not something to be excluded.
Therefore, the major difference in TDVP compared with the more
classical broad ideas of parallel existences, is the critical inclusion of
consciousness as part of that objective reality. The jigsaw feasibility puzzle
here is producing testable results and explaining observations that the current
materialistic paradigm cannot explain. Individual consciousness and a
unification of realities (what we call Unified Monism) allow for the
development of events that could change because of freedom of choice creating
branches of a tree that may register in 3S1t reality. These trees are tiny
components of an infinite forest. So these do not reflect everything that
exists. What exists is a reality that is molded and exhibits an infinite
continuity and is dynamic and modifiable. In the classical multiverse, this is
a finite series of events that happen, or parallel worlds, or transfinite
realities. Infinity is not perceived as an infinite continuity as in the TDVP.
In this paper, we take the
time to explain exactly how we put consciousness into the equations as part of
objective reality, and show how doing so explains many things inexplicable in
the current materialistic paradigm.
Unifying Quantum Physics and Relativity
The full unification of quantum physics and relativity is brought
about in TDVP by applying the tools of CoDD and Dimensional Extrapolation to
the mathematical expressions of three wellestablished features of reality,
recognized in the current scientific paradigm:
1. quantization
of mass and energy as two forms of the same essential substance of reality;
2. introduction
of time as a fourth dimension; and
3. the
limitation of the velocity of rotational acceleration to light speed, c.
In these processes, the need for a more basic unit of
quantization is identified, and when it is defined, the reason there is
something rather than nothing becomes clear.
Einstein recognized that mass and energy are interchangeable
forms of the physical substance of the universe, and discovered that their
mathematical equivalence is expressed by the equation E=mc^{2}.
Applying TDVP:
In TDVP, accepting the relativistic relationship of mass and
energy at the quantum level, we proceed, based on Planck’s discovery of quanta,
to describe quantized mass and energy as the content of quantized dimensional
distinctions of extent. This allows us to apply the CoDD to quantum phenomena
as quantum distinctions and describe
reality at the quantum level as integer multiples of minimal equivalence units.
This replaces the assumption of conventional mathematical physics that mass and
energy can exist as dimensionless points analogous to mathematical
singularities.
The assumption of dimensionless physical objects works for most
calculations in practical applications because our units of measurement are so
extremely large, compared to the actual size of elementary quanta. Therefore,
the quanta appear to be existing as
mathematical singularities, i.e. dimensionless points: The electron mass, e.g.,
is about 1x10^{30 }kg, with a radius of about 3x10^{15 }meter.
Point masses and point charges, etc., are simply convenient fictions for
macroscale calculations. The calculus of Leibniz and Newton works beautifully
for this as a convenient fiction because Newtonian calculus incorporates the
fiction mathematically: It assumes that the numerical value of a function
describing the volume of a physical feature of reality, like a photon or an
electron, can become a specific discrete finite entity. This occurs as the
value of a real variable, like the measure of distance or time, approaches zero
asymptotically (i.e. infinitely closely). This is a mathematical description of
a nonquantized reality. But we exist in a quantized
reality, so such a description is a fiction.
Planck discovered that the
reality we exist in is actually a quantized reality. This means that there
is a “bottom” to physical reality; it is not infinitely divisible, and thus the calculus of Newton and Leibniz does not
apply at the quantum level. This might be one reason scientists applying
Newtonian calculus to quantum mechanics declare that quantum reality is
‘weird’. The appropriate mathematical description of physical reality at the
quantum level is provided by the calculus of distinctions. In CoD, the relationships
between the measurable minimum finite distinctions of elementary particles are
defined by integral solutions of the appropriate Diophantine equations. The mathematics of quanta is the mathematics
of integers because quanta cannot be subdivided, they are by definition, whole numbers.
In TDVP we find that, for quantized phenomena, existing in a
multidimensional domain consisting of space and time, embedded in one or more
additional dimensional domains, the fiction of dimensionless objects, a convenient
mathematical expedient when we did not know that physical phenomena are
quantized, is no longer appropriate. We can proceed with a new form of
mathematical analysis, the calculus of
dimensional distinctions (CoDD), and treat all phenomena as finite,
nonzero distinctions. Replacing the
dimensionless points of conventional mathematical physics with distinctions of
finite unitary volume, we can equate these unitary volumes of the elementary
particles of the physical universe with integers. We can then relate the
integers of quantum reality to the integers of number theory and explore the
deep relationship between mathematics and reality.
In TDVP, we have also developed the procedure of Dimensional
Extrapolation using dimensional invariants to move beyond three dimensions of
space and one of time. Within the multidimensional domains defined in this
way, mass and energy are measures of distinctions of content. If there are
other dimensions beyond the three of space and one of time that are available
to our physical senses, how are they different, and do they contain additional
distinctions of content? If so, how is such content different from mass and
energy? We know that mass and energy are two forms of the same thing. If there
are other forms, what is the basic “stuff” that makes up the universe? Is it
necessarily a combination of mass and energy, or is it something else? For the
sake of parsimony, let’s begin by assuming that the substance of reality,
whatever it is, is multidimensional and uniform at the quantum level, and that
mass and energy are the most easily measurable forms of it in the 3S1t domain.
This allows us to relate the unitary
measure of inertial mass and its energy equivalent to a unitary volume, and
provides a multidimensional framework to explore the possibility that the
“stuff” of reality may exist in more than two forms.
Of spin and symmetry
The smallest distinct objects making up the portion of reality
apprehended by the physical senses in 3S1t, that which we call “physical reality”,
are spinning because of asymmetry and the force of the natural universal
expansion that occurs as long as there is no external resistance.
If there were no additional dimensions and/or features to restore
symmetry, and no limit to the acceleration of rotational velocity, physical
particles would contract to nothingness, any finite universe would expand
instantly to maximum entropy as predicted by the second law of thermodynamics
for finite systems. But, due to the relativistic limit of light speed on the
accelerated rotational velocity of elementary particles in 3S1t, the quantized
content of the most elementary particle must
conform to the smallest possible symmetric volume, because contraction to a
smaller volume would accelerate the rotational velocity of the localized
particle to light speed in 3S1t, making its mass (inertial resistance)
infinite. That minimal volume occupied by the most elementary of particles is
the finite quantum distinction replacing the infinitesimal of Newton/Leibniz
calculus, and it provides the logical volumetric equivalence unit upon which to
base all measurements of the substance of reality.
We can define this minimal volume as the unitary volume of
spatial extent, and its content as the unitary quantity of mass and energy. The
mass/energy relationship (E=mc^{2})
is linear, since in the 3S1t context, c^{2}
is a constant, allowing us to define unitary mass and unitary energy as the
quantity of each that can occupy the finite rotational unitary volume. This
fits nicely with what we know about elementary particles: All elementary
particles behave in the same way prior to impacting on a receptor when
encountering restricting physical structures like apertures or slits.
Combining unitary volumes:
A particle of unitary mass occupying a unitary volume could be an
electron, and a particle of unitary
energy occupying a unitary volume before expansion as radiant energy, could be
a photon. Einstein explained this
equivalence between electrons and photons and Planck’s constant in a paper published
in 1905.
This brings us to a very interesting problem: What happens when
we combine multiples of the unitary volumes of mass/energy to form more complex
particles? How do we obtain protons and neutrons to form the stable elemental
structures of the physical universe?
When we view the spinning elementary particles of the 3S1t
physical universe from the perspective of a ninedimensional reality, we can
begin to understand how Planck was quite correct when he said “there is no matter as such”. What we
call matter, measured as mass, is not really “material” at the quantum level.
What is it then that we are measuring when we weigh a physical object? The real
measurement of mass is not weight, which varies with relative velocity and
location and can be zero without any loss of substance; it is inertia, the resistance to motion. The illusion of solid matter arises from the
fact that elementary particles resist accelerating forces due to the fact that
they are spinning like tiny gyroscopes, and they resist any force acting to
move them out of their planes of rotation. An elementary particle spinning
symmetrically in three, six, or nine orthogonal planes of rotation resists
lateral movement equally in all directions, and the measurement of that resistance
is interpreted as mass.
In theory, an asymmetrically spinning dimensional domain, i.e. an
object spinning in any number of orthogonal planes other than three, or a
multiple of three, should result in the conversion of angular momentum into
lateral movement in the direction of least inertial resistance. Some have
claimed experimental evidence that an object affected by asymmetrical inertial
spinning in two different planes will move laterally because of this
transformation of angular momentum into linear motion. We have not
substantiated these claims, but in theory, a symmetrical object spinning in
four dimensions will move laterally because of the asymmetry of the spinning
dimensional domain.
Elementary quanta of mass and energy, the two known forms of the
substance of the physical universe, embedded in a ninedimensional domain, form
stable structures only under precisely symmetric dimensionometric spin
conditions because the angular momenta of elementary quanta spinning
asymmetrically are converted into strong divergent linear forces causing the
rapid decay of vortical structure and patterns. Without symmetric spinning conditions, no physical universe could exist
because of the second law of thermodynamics^{, }which dictates that any
finite physical system always decays toward maximum entropy, i. e. total
disorder, lacking structure of any kind.
If our universe were composed of random debris from an explosion
originating from a mathematical singularity, because of the continuous
operation of the second law of thermodynamics in an expanding debris field,
simple particles accidentally formed by random mass/energy encounter, would
decay before a new random encounter could occur and form a more complex
combination. The number of random encounters would decrease as the debris field
expands because there would be increasingly less debris in any given volume of
space. If our physical universe is embedded in the ninedimensional reality
described by TDVP, it should, in theory, escape this fate of dissolution. While
it may change and evolve, its form, and even the way it evolves, it will always
reflect the intrinsic logical order and patterns of the substrate of reality
within which it is embedded, TDVP is based on the hypothesis that logical
structure is the natural state of reality, not chaos. This hypothesis is
supported by the fact that there is order and logic in the universe in spite of
the second law of thermodynamics. If this is correct, we have the answer to the question Leibniz
regarded as the first and most important metaphysical question of all: We can explain why there is something
instead of nothing.
Unifying RELATIVITY, Particle Physics and TDVP
Quantum physics, especially the resolution of the EinsteinPodolskyRosen (EPR) paradox,
tells us that reality at the quantum level is like an allencompassing
interwoven multidimensional tapestry. However, because of the extreme
smallness of the quantized structure—far smaller than we are able to see
directly, even with the best technological extensions of our physical senses—we
are directly aware only of the broadbrush features that seem to exist as
separate objects.
We have tried repeatedly, over the history of modern science, to
identify the most basic building blocks of physical reality, starting with
large structures like cells, molecules and atoms, proceeding to smaller and
smaller objects, only to have them slip through the finer and finerscale net
of our search. Relativity and quantum physics tell us, however, that there is
an end to this, a limit to this infinite descent of spinning particles, a
bottom to our search: the smallest possible particle, the minimum quantum equivalence unit.
Applying TDVP:
TDVP suggests that the forms of physical reality are reflections
of the intrinsic logical patterns existing behind the reality perceived through
our physical senses in 3S1t. The form of this logical structure, much like the
conceptualized blueprint of a building in the mind of an architect, is conveyed
to the 3S1T domain of the physical universe through the dimensionometric
structure of a spinning ninedimensional finite universe, in the form of the
“conveyance equations”. The force causing spinning motions in the finite
distinctions of physical reality is the continuous force of universal
expansion. The fact that expansion is uniform and continuing, perhaps even
accelerating, indicates that there is nothing outside the universe to impede or
alter uniform expansion. It has been demonstrated in numerous experiments since
Einstein proposed the speed of light as the limit to acceleration, that, in the
observable 3S1t physical universe, the maximum expansion velocity between two
farthermost separated points in a quantized 3S1T reality is light speed, a
speed determined by the mass/energy ratio in the observable universe: c = √(E/m).
The mathematical expression of the conveyance of logical
structure can be derived by application of the CoDD and Dimensional
Extrapolation (DE). These mathematical logical techniques (CoDD, DE) would be
applied to the elementary distinctions of extent and content revealed by the
empirical data obtained in particle colliders, under the integer requirement of
quantization. Particle collider data provides us with an indirect glimpse of
the origin of the elementary structures that makes up the limited portion of
reality observable in 3S1t. Using particle collider data and the mathematical
principles of quantum physics and relativity, we now derive the equations
describing the combination of elementary particles to form stable subatomic structures.
Because we exist in a quantized reality, these equations will be Diophantine
equations, i.e. equations with integer solutions. We call the general
mathematical expression summarizing these equations the Conveyance Expression because it contains within it the
mathematical relationships that convey and limit the logical structure of the
substrate of reality through the sequentially embedded ninedimensional domains
of finite distinction to the 3S1t domain of physical observation and
measurement.
Within the framework of the current Standard Model of particle
physics, the basic concepts of quantum physics and relativity are applied to
the particle collider data to yield numerical values of the physical
characteristics of the subatomic particles perceived to be the building blocks
of the observable universe, including photons, electrons, neutrons and protons,
in units of MeV/c^{2}. Analysis of these data in the framework of the
mathematics and geometry of TDVP in 3S1t provides us with a way to find the
true quantum unit of measurement. The empirically measured and statistically
determined inertial masses of the three most basic elementary entities believed
to make up what we perceive in 3S1t as matter, i.e. electrons, upquarks and
downquarks, are approximately 0.51, 2.4 and 4.8 MeV/c^{2},
respectively. The values for up and down quarks are derived statistically from
millions of terabytes of data obtained from highenergy particle collisions
engineered in speciallybuilt colliders.
It is obvious from these data that the conventional unit: MeV/c^{2}
is not the basic quantum unit, because the data expressed in these units
contain fractions of MeV/c^{2} units. Max Planck discovered that energy
and matter occur only in integer multiples of a specific finite unit of quantum
action, not fractions of units. Therefore, the masses of the electron, upquark
and downquark should be integer multiples of the basic quantum unit of
mass/energy equivalence. Since the masses are fractional in MeV/c^{2}
units, one MeV/c^{2} must be a multiple of a yet smaller truly quantum unit.
Except for the electron, the data
for the mass/energy of the elementary particles, up and down quarks, in Table 1 below, are presented as ranges of
values because the mass/energy values of elementary particles are statistically
determined as statistical moments from particle collider detector and collector
data. The quantum mass/energy values are derived from raw data using
statistical methods, so the ranges thus represent the quantum values with
approximate confidence limits. Quantum particles detected in highenergy
colliders are classified either as bosons, with Bose–Einstein statistical
distribution, or fermions, obeying the Pauli Exclusion Principle with Fermi–Dirac statistical distribution^{ }in
collider data. Both of these quantum distributions approach the Maxwell–Boltzmann
statistical distribution in the limit of high temperature and low particle
density.
In this discussion, we are
primarily concerned with the basic building blocks of the physical universe,
the up and downquarks, which are
fermions, and photons, which are
bosons.
There is always some measurement
error in experimental data, and even with the advances in technological
precision from the first “atom smasher”, the CockcroftWalton particle accelerator
in 1932, to the Large Hadron Collider (LHC) today, some measurement error is still unavoidable due to the extreme
smallness of the phenomena and the indirect and delicate methods of measurement
required in the interpretation of the data. The electron mass is considered
to be one of the most fundamental constants of physics, and because of its
importance in physical chemistry and electronics, great effort has been spent
to determine its inertial mass very accurately at 0. 511 MeV/c^{2}.
It is important to note that our model is based on physics data relative
to 3S1t, because 9dimensional spin data should generate different theoretical
models. Thus Einstein’s cosmological constant and his later expression of
dismay about his error might, indeed, have been correct if it was stated
relative to a fourdimensional domain embedded in a fivedimensional domain. The
existence of 9D spin might imply that fundamental equations such as E=Mc^{2
}are relative only to 3S1t, but if there were, for example, multidimensional
Time, a speculation with strong supporting evidence, the speed of light, c, would have to be expressed
relatively. The presence of gimmel, may allow an extension of this correct
relativistic 3S1t equation to include the third substance within the
fundamental theory of everything.
Empirical eVIDENCE of gimmel in Particle Physics
The integer values in Table 1 are
obtained by noting that the electron has the least mass of any elementary
particle. The photon, which behaves like a boson, is not listed here because it
only exists within subatomic structure in a transitory manner, and we are
primarily interested here in the stable building blocks of atomic structure.
Normalizing the electron’s mass to unity and determining the average masses of
the up and downquarks as multiples of that unit, we have the normalized
masses of the electron, up and downquarks.
Using the latest available
collider data, the mass/energy averages for the up and down quarks are 2. 01
MeV/c^{2} and 4. 79 MeV/c^{2} respectively. Dividing by 0. 511
and rounding the nearest integer value, we have the normalized mass/energy
equivalence for the electron, up and down quarks, as 1, 4 and 9 respectively.
Using these normalized values, we can investigate how the finite distinctions
they represent can combine to form protons, neutrons and the progressively more
complex physical structures that make up the Elements of the Periodic Table.
The fact that the detected mass of the proton is more than 100
times the combined mass of two upquarks and one downquark is postulated in
the Standard Model to be explained, in part, by the assumed presence of other
subatomic particles such as gluons and / or bosons in the space around the
quarks, although they are not detectable until “teased” into existence by
highenergy collisions.
In TDVP, we see this as evidence of
the underlying logical structure of reality and speculate that it might be
paralleled by the socalled “dark matter” and “dark energy” detected on the
macro scale of galaxies that make up about 95% of the observable universe,
because preliminary calculations indicate a connection between this unknown
dark matter and energy and the stability of the atomic structure of the
universe.
TABLE 1:
Fermions
The Most
Common Subatomic Particles comprising the physical universe
Particle

Symbol

Spin

Charge

Mass
(Raw Data
In MeV/c^{2})

Mass/Volume

Electron

E

1/2

1

0.
511

1

Up
quark

U

3/2

+^{2}⁄_{3
}

1.
87 – 2. 15

4

Down
Quark

D

3/2

−^{1}⁄_{3}

4.
63 – 4. 95

9

Proton

P^{+}

1/2

+1

740
 1140^{}

1836

Note that 2 x 2/3=
4/3 for two up quarks 1/3 for down quarks = +1 = proton charge. Similarly, 2/3
for one up quark – 2/3 for two down quarks = 0 = neutron charge.
The smallest finite unit of volume is the smallest possible
distinction of extent that can be occupied by an accelerated spinning vortical
object. This distinction of extent has a finite value because of the limit
placed on the rotational velocity of any object possessing inertial mass by the
lightspeed limit of relativity.
As our basic unit volume, we will assign it the numerical value
of 1. We can also define the minimal quantal unit of measurement for mass and
energy by setting its value at the limiting volume equal to 1 (unity), thus
avoiding fractional results in measurements of quark mass, energy and volume.
We need to do this because the value of massenergy equivalence in the
currently used MeV/c^{2} units is based on SI units chosen
for convenience: SI units are arbitrarily based on easily measureable distances
and quantities. What we are establishing is a truly quantum unit. Our quantum unit is somewhat similar to the ‘natural’
units sometimes used in quantum physics and cosmology, that are based on setting
the speed of light, c, equal to 1,
and ћ (called hbar) the reduced Planck’s constant equal to 1. These ‘natural’
units were developed for ease in working with extremely large and extremely
small numbers in the same equations, not to define the smallest possible
quantum unit as we are doing.
[1] Normalizing the average mass to the
nearest integer value is justified on the grounds that the actual values must
be integer multiples of the basic unit of quantized mass.
Does this mean that there are actually particles below the
spatial size or subatomic level of quarks? Not necessarily. It only means that
the mass/energy and volumes of quarks are multiples of the unitary mass/energy
and volume of the smallest finite distinction. Additionally, these results do
not necessarily reflect spatial finite location; they could speculatively even
reflect a continuity that is found in the infinite, not a discreteness in
location. We could refer to this as part of the “subquantum” but the location
in space and time might be different relative to different dimensional domains.
Therefore, we’re using “subatomic” descriptively not for the definite level of
the location. In order to understand how this works, we take a closer look at
what happens when two or more subatomic particles combine.
In the 3S1T domain of the physical universe, while we may
conceptualize space, time, matter, and energy as separate aspects of reality, we never find one of them existing alone
without the others. As Einstein stated, space has no meaning without
matter, matter and energy are just two forms of the same thing, and time is
meaningful only in relation to the dynamic interaction of spatially extended
matter and energy. Clearly, if the goal is to gain an understanding of the true
nature of reality, the usefulness of any observation or measurement is
maximized and will be most meaningful if it includes all of the known
parameters of reality. The minimal quantized distinction described above, from
which we define new quantum units of observation and measurement, should
therefore include not just space and mass, but space, time, mass, and energy.
In the extended mathematical framework of TDVP, we have determined mathematically
that it should include nine finite dimensions of extent and three forms of
content. The dimensionometric mathematics of TDVP indicates that reality
consists of three kinds of dimensions (extent) and three kinds of substance
(content). The three kinds of dimensions are spacelike, timelike and (we
suggest) consciousnesslike, while
the three kinds of substance are matter, energy and another form of the stuff
of reality, heretofore unrecognized by science, an essential conscious
organizing aspect of reality, a primary form of consciousness.
For the present discussion and derivation of true quantum units,
it is not necessary to identify the third kind of dimensional extent as
consciousnesslike, or the third form of content as consciousness itself.
However, the likelihood that this is true is proposed here as a feasible
hypothesis. TDVP was developed based on the hypothesis that consciousness is an
integral part of reality and should be included in the equations of physics.
Also, TDVP is a comprehensive paradigm shift primarily because of the inclusion
of consciousness, and if the third form is neither mass nor energy, a quantized
form of the conscious substrate is the logical candidate. But many scientists
regard this as very controversial, so it is for this reason that we
emphasize the fact that what follows does not depend upon the hypothesis that
consciousness is the third form of the stuff of reality, but primarily upon
empirical data and mathematical logic.
ELEMENTARY PARTICLES AND UNITS OF MEASUREMENT: APPLYING THE CONVEYANCE
EQUATION
In order to see how the minimal quantum extent and content of our
smallest possible elementary distinction relates to known elementary particles,
we develop equations that can be used to describe the combination of up and
downquarks to form the proton and neutron of the Hydrogen atom.
We choose the Hydrogen atom to start
with because it is the simplest, most stable, and most abundant natural element
in the universe. If all forms of substance are quantized, then in order for
quarks to combine in stable structures, they must satisfy certain integer
equations reflecting the quantization of matter and energy. We call those
Diophantine (integer) equations the equations of Dimensional Extrapolation,
because they convey the logical structure of reality into the spacetime domain
of our 3S1t experience. We will show why stability depends on the integer
equation representing the combination of two or more particles to form a third
particle. This family of Diophantine equations is represented mathematically by
the expression
Σ^{n}_{i=1} (X_{n})^{m}
= Z^{m}.
The Pythagorean Theorem equation, the
Fermat’s Last Theorem equation and other important equations are contained
within this general expression. We mention this fact here because these
theorems play key roles in the geometry and mathematics of Dimensional
Extrapolation and the combination of elementary particles to form stable
physical structures. Because the various forms of this expression as m varies from 3 to 9 conveys the geometry
of 9dimensional reality to our observational domain of 3S1t, we call this
expression the “Conveyance Expression”, and individual equations of the
expression “Conveyance Equations”.
When n
= m = 2, the expression yields the equation
(X_{1})^{2}
+ (X_{2})^{2 }= Z^{2}
which, when related to areas,
describes the addition of two square areas, A_{1 }and A_{2}
with sides equal to X_{1 }and X_{2 }respectively, to form a
third area, A_{3}, with sides equal to Z. When these squares are
arranged in a plane with two corners of each square coinciding with corners of
the other squares to form a right triangle, as shown below, we have a geometric
representation of the familiar Pythagorean Theorem demonstrating that the sum
of the squares of the sides of any right triangle is equal to the square of the
third side (the hypotenuse) of that triangle.
The Pythagorean Theorem
(AB)^{2} + (BC)^{2} =
(AC)^{2}
We use this simple equation in Dimensional Extrapolation ^{1} to define the
rotation and orthogonal projection from one dimensional domain into another, in
the plane of the projection. There are an infinite number of solutions for this
equation, one for every conceivable right triangle, but in a quantized reality,
we are only concerned with the integer solutions. Considering the Pythagorean
equation as a Diophantine equation, we find that there exists an infinite
subset of solutions with AB = X_{1}, BC = X_{2 }and AC = Z
equal to integers. Members of this subset, e.g. (3, 4, 5), (5, 12, 13), (8, 15,
17), etc. i.e., (3^{2} + 4^{2} = 5^{2}, 5^{2} +
12^{2} = 13^{2}, 8^{2} + 15^{2} = 17^{2},
…) are called “Pythagorean triplets”.
When n = 2 and m = 3, the expression
becomes the equation
(X_{1})^{3}
+ (X_{2})^{3 }= Z^{3}.
When we define X_{1}, X_{2}
and Z as measures of volumes, just
as we defined them as measures of areas when n = m = 2, we can apply this equation to quantal volumes in a
threedimensional domain. Using the minimal quantal volume as the unit of
measurement, and setting it equal to one, we have a Diophantine equation
related to our hypothetical elementary particle with minimal spinning volume
containing uniform substance: if it is spherical, we can set its radius equal
to r_{1}, and if there is a
second uniform spinning particle rotating at maximum velocity, with radius r_{2}, we can describe the
combination of the two particles by the expression 4/3π(r_{1})^{3} + 4/3π(r_{2})^{3}.
If this combination produces a third spinning spherical object we have:
4/3π(r_{1})^{3}
+ 4/3π(r_{2})^{3} = 4/3π(r_{3})^{3},
where r_{3} is the radius of the new particle. Dividing through
by 4/3π, we have:
(r_{1})^{3}
+ (r_{2})^{3} = (r_{3})^{3}, which is a Diophantine equation of the form of the
Fermat equation,
X^{m}
+ Y^{m} = Z^{m} when m =3.
Notice that the factor, 4/3π cancels out, indicating that this
equation is obtained regardless of the shape of the particles, as long as the
shape and substance is the same for all three particles. (This is an important
fact because we found in investigating the Cabibbo angle^{ }that the
electron, while symmetrical, is not necessarily spherical.) Note also, that the
maximum rotational velocity and angular momentum will be different for
particles with different radii, because the inertial mass of each particle will
depend upon its total volume. In a quantized reality, the radii must be integer
multiples of the minimum quantum length. Since this equation is of the same
form as Fermat’s equation, Fermat’s Last
Theorem tells us that if r_{1}
and r_{2} are integers, r_{3} cannot be an integer.
This means that the righthand side of this equation, representing the
combination of two quantum particles, cannot be a symmetric quantum particle.
But, because Planck’s principle of quantized energy and mass tells us that no
particle can contain fractions of mass and/or energy units, the righthand side
of the equation represents an unstable asymmetric spinning particle. The
combined highvelocity angular momentum of the new particle will cause it to
spiral wildly and fly apart. This may lead us to wonder how it is that there
are stable particles in the universe, and why there is any physical universe at
all. Again,
we are faced with Leibniz’s most important question: why is there something
instead of nothing?
The answer turns out to be relatively
simple, but is hidden from us by the limitations of our methods of thinking and
observation if we allow them to be wholly dependent upon our physical sense
organs. For example, we think of a sphere as the most perfect symmetrical
object; but this is an illusion. Spherical objects can exist in a
NewtonLeibniz world, but we actually exist in a PlanckEinstein world. In the
real world, revealed by Planck and Einstein, the most perfectly spherical
object in three dimensions is a convex regular polyhedron. (polyhedron =
multisided threedimensional form; regular; all sides are of equal length.)
The most easily visualized is the cube, which is most precisely defined
geometrically as a sixsided regular polyhedron. In the NewtonLeibniz world, the number of sides of a regular
polynomial could increase indefinitely. If we imagine the number of sides
increasing without limit while the total volume approaches a finite limit, the
object appears to become a sphere. But in the quantized world of Planck and Einstein,
the number of sides possible is limited, because of the finite size of the
smallest possible unit of measurement (which we are defining here) is relative
to the size of the object. And because the “shape” factor cancels in the
Conveyance Equation for n = 3, Fermat’s Last Theorem tells us that, regardless
of the number of sides, no two regular
polyhedrons composed of unitary quantum volumes can combine to form a third
regular polyhedron composed of unitary quantum volumes.
To help understand the physical
implications of this, suppose our true quantum unit exists in the shape of a
cube. Using it as a literal building block, we can maintain particle symmetry
by constructing larger cubes, combining our basic building blocks as follows: a
cube with two blocks on each side contains 8 blocks; a cube with three blocks
on each side contains 27 blocks; a cube with four blocks on each side contains
64 blocks, each being the cubic exponent of the number of blocks on each side.
Fermat’s Last Theorem tells us that if we stack the blocks of any two such
symmetric forms together, attempting to keep the number of blocks on all sides
the same, the resulting stack of blocks will always be at least one block
short, or one or more blocks over the number needed to form a perfect cube. Recall that if these blocks are elementary
particles, they are spinning with very high rates of angular velocity, and the
spinning object resulting from combining two symmetric objects composed of
unitary quantum volumes will be asymmetric, causing its increasing angular
momentum to throw off any extra blocks until it reaches a stable, symmetrically
spinning form.
This requirement of symmetry for
physical stability creates the intrinsic dimensionometric structure of reality
that is reflected in the threedimensional Conveyance Expression. We are
interested in the 3D conveyance equation because experimental observation and
measurements are limited to quantum time slices (t = 1) in three dimensions,
indicating no movement in time. It turns out that there can be stable structures, because when n = m =3, the Conveyance Expression yields the equation:
(X_{1})^{3}
+ (X_{2})^{3 }+ (X_{3})^{3}= Z^{3},
which has integer solutions. The first one (with the smallest integer
values) is:
3^{3}
+ 4^{3 }+ 5^{3}= 6^{3}
It is important to recognize the implications of Σ^{n}_{i=1} (X_{n})^{m} = Z^{m}.
When n, m, the X_{i} and
Z are integers, an exact Diophantine expression of the form of the logical structure of the
substrate of reality as it is communicated to the 3S1t domain. For this
reason, we call it the Conveyance Expression. It should be
clear that the Diophantine equations yielded by this expression are appropriate
for the mathematical analysis of the combination of unitary quantum particles.
When the Diophantine expressions it yields are equations with integer solutions, they represent stable
combinations of quantum equivalence units, and when they do not have integer
solutions, the expressions are inequalities
representing asymmetric, and therefore, unstable
spinning structures.
In the quantized ninedimensional
domains of TDVP, the variables of the Conveyance Equations are necessarily
integers, making them Diophantine equations, because only the integer solutions
represent quantized combinations. When n
= m = 2, we have the Pythagorean Theorem equation for which the integer
solutions are the “Pythagorean Triples”. When n = 3 and m = 2, the
Conveyance Equation yields the inequality of Fermat’s Last Theorem, excluding
binomial combinations from the stable structures that elementary particles may
form. On the other hand, the Diophantine Conveyance Expression when n = m = 3, integer solutions produce in
some instances trinomial combinations of elementary particles that will form stable structures. This explains why there is something rather
than nothing, and why quarks are only found in combinations of three.
Mathematically, we find that embedded within multiple
hyperdimensional domains (more than three dimensions) are three dimensions of
space and three dimensions of time that are not detected in 3S1t observations,
and condensed into the distinctions of spinning energy (energy vortices) that
form the structure of what we perceive as the physical universe. In the humanly
observable domain of 3S1t, this spectrum ranges from the photon, which is
perceived as pure energy, to the electron, with a tiny amount of inertial mass
(0. 51 MeV/c^{2} ≈ 1 x10^{47} kg.) to quarks ranging from the
“up” quark at about 2. 4 MeV/c^{2}, to the “top” quark at about 1. 7
x10^{5 }MeV/c^{2, }to the Hydrogen atom at about 1x10^{9}
MeV/c^{2} (1. 67 x10^{27}kg.), to the heaviest known element,
Copernicum (named after Nicolaus Copernicus) at 1. 86 x10^{24 }kg ^{[1]}. So
the heaviest atom has about 10^{23} times, that is, about 100, 000,
000, 000, 000, 000, 000, 000 times heavier than the inertial mass of the
lightest particle, the electron.
All of the Elements of the Periodic Table are made up of stable
vortical distinctions that are known as fermions, “particles” with an intrinsic
angular spin of 1/2, or they are made up of combinations of fermions. Table 1, above, lists the fermions that make up
the Hydrogen atom and their parameters of spin, charge and mass based on
experimental data. The top and bottom quarks and the charm and strange quarks
are ephemeral unstable particles so are not part of the calculations, and nor
are neutrinos or any “antiparticles”. Our focus here is on stable particles
that make up the observable universe.
Niels Bohr’s solution of the EPR paradox following Bell’s
theorem, validated by the Aspect experiment and many subsequent experiments
refined to rule out other possible explanations, tells us that newly formed
fermions do not exist as localized particles until they impact irreversibly on
a receiver constituting an observation or measurement. In the TDVP unified view
of reality, every stable elementary particle, every distinct entity in the
whole range of fermions and composite particles composed of fermions, is drawn
from the discrete transfinite embedded within the continuous infinity of
reality when it is registered as a finite distinction in an observation or
measurement. Our limitations of observation and measurement and the dimensional
structure of reality result in our perception of fermions as separate objects
with different combinations of inertial mass and energy.
What determines the unique mix that
makes up each type of observed particle? To answer this question, we must
continue our investigation of the rotation of the minimum quantal units across
the four dimensions of space, time and the additional dimensions revealed by
the mathematics of TDVP.
One of the most important invariant
relationships between dimensional domains is the fact that each ndimensional domain
is embedded in an n+1 dimensional
domain. This means that all distinctions of extent, from the
ninthdimensional domain down, and the distinctions of content within them, are
inextricably linked by virtue of being sequentially embedded. Because of this
intrinsic linkage, the structure of any distinction with finite extent and
content, from the smallest particle to the largest object in the universe,
reflects patterns existing in the logical structure of the substrate of
reality. Such a distinct object will always have in its content, combinations of
the forms reflecting those patterns. In a quantized reality, the
dimensionometric forms of such objects will be symmetric and a multiple of the
smallest unit of measurement.
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 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 rotational
plane, these objects are best conceived of as closed vortical solitons.
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 atoms, the elements of the
Periodic Table. 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, the true quantal unit. The
substance of all particles is then measureable in wholenumber multiples of
this unit.
THE TRUE UNIT: TRIADIC ROTATIONAL UNITS OF EQUIVALENCE (TRUE) AND THE THIRD
FORM OF REALITY: GIMMEL OBTAINED BY APPLYING THE 3D DIOPHANTINE CONVEYANCE
EQUATION
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 measureable 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
lightspeed angular velocities in the mathematically required nine dimensional
domain of quantized reality.
The quantization of the electron is
measured as one single true quantum unit of mass/energy equivalence in the
3S1t dimensional domain of observable reality, but as we shall see, the
electron is not identical with one true quantum unit. We will show below that
it must be much more to exist as part of a stable atom. All other stable
nonradiating subatomic entities are measureable in multiples of these
subquantal units. These are units of measurement, not subquantal entities
existing as independent phenomena. Until impacting on a receptor in an
irreversible way, mass, energy and gimmel, the massless, energyless third
substance required for stable atomic and subatomic structural stability, are
absorbed in the primary substrate. As shown by validations of the Aspect
experiment, they become manifest only after impact, and their mass, energy,
gimmel mix is determined by the mathematical logic of the Conveyance Equation.
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 timelike dimensional planes manifests as energy because
time is nonexistent 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, as demonstrated below, specific volumes
of gimmel, the 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. [2]
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 3S1t
measurement, can be determined by a symmetric threedimensional conveyance
equation: We found above that the smallest set of integer values that satisfies
the threedimensional form of the conveyance equation is the set 3, 4, 5 and 6.
So the Diophantine equation 3^{3}
+ 4^{3 }+ 5^{3}= 6^{3} 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 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, the conveyance equation with 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 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 = mc^{2}) we know that the substance of the
universe is quantized. With the appropriate integer
values for X_{1}, X_{2},
X_{3}, and Z, in TRUE units, the threedimensional
conveyance equation (X_{1})^{3}
+ (X_{2})^{3 }+ (X_{3})^{3}= Z^{3} 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 ^{89}.
Applying mathematics empirically
Our approach is empirical mathematical testing: We start with the
smallest integer solution of this Conveyance Equation, 3^{3} + 4^{3 }+ 5^{3}= 6^{3}, 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 3D conveyance
equation solution of 3^{3} + 4^{3
}+ 5^{3}= 6^{3}. If this equation doesn’t fit the
empirical data, we need to establish what does work.
When we use the smallest integer solution, 3^{3} + 4^{3 }+ 5^{3}= 6^{3}, to
the 3D conveyance equation to attempt 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.
They cannot be allowed because a negative number of total ג units would produce an entity with fewer total observable TRUE
units in 3S1t 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 1P1, we attempt to use the smallest integer solution of
the conveyance equation to describe the combination of two upquarks and one
downquarks in a proton, but some of
the quarks have negative ג units.
In Table 1N1, we attempt 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. Negative gimmel units are
unacceptable for mathematical reasons: Thirdorder
Diophantine equations with negative terms cannot describe triadic combinations
because they are reducible to nontriadic equations.
This means the representations of mass, energy and gimmel in
Table 1P1 and 1N1 for the proton and neutron are empirically incorrect.
Therefore, we must look for nonnegative solutions of the Conveyance Equation.
Table 1P1: Trial Combination of Two UpQuarks and One
DownQuark, i.e.
The Proton, applying minimal TRUE Units
Particle

Charge^{*}

Mass/Energy

ג

Total TRUE
Units

MREV^{**}[3]^{}

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}

[2]
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.
[3]
Minimum Rotational Equivalent Volume (MREV):
This is a term we apply so we can reflect cubes as required in quantal volumes.
And the neutron:
Table 1N1:
Trial Combination of One UpQuark and Two DownQuarks in TRUE Units as in the
neutron (N^{0})
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 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. We propose that this is only possible if all TRUE units are undetectable in
3S1t, 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 3S1t
forms. In this way, the encompassing substrate, the additional five 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 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 3S1t 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 as quarks 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 1^{3} + 6^{3 }+ 8^{3}= 9^{3}, 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 6^{3} + 8^{3 }+ 10^{3}= 12^{3}.
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.
Table 2P2 : The Proton (P^{+}) Solution
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}

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 total 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 tried to use
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 in Table 3.
Table 3: The
First 36 Conveyance Equation Integer Solutions for n=m=3.
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,
consistent with 3S1t observation, 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.
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
subatomic 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 subatomic
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 6^{3} + 8^{3 }+ 10^{3}= 12^{3}, the
next attempt to find the TRUE unit configuration of the neutron is shown below:
Table 2N2 : Triadic Quark Combinations for the
Neutron (N^{0})
Trial
Combination
of One UpQuark and Two DownQuarks in TRUE Units using a multiple of the
minimum integer solution of the Conveyance Equation
Particle

Charge

Mass/Energy

ג

Total TRUE Units

MREV

u_{1}

+ 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 }
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 2N3 Neutron (N^{0}) trial Solution.
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}

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 4^{3} + 24^{3} + 32^{3}
= 36^{3}, 18^{3} + 24^{3} + 30^{3} = 36^{3},
or some other combination of the integers 24 and 36. For example: looking at
the TRUEunits analysis of Helium, with protons consisting of 24 TRUE units and
neutrons consisting of 36 TRUE units, we have:
Table 4H1: 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}

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, 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. Returning to Table 3, we try the next
primitive solution: 3^{3} + 10^{3}
+ 18^{3 }= 19^{3}, but it produces an unacceptable negative
gimmel value for u_{3}:
Table 2N4: 2^{nd} trial solution for Quark Combinations
for the Neutron ^{ }
Particle

Charge

Mass/Energy

ג

Total TRUE Units

MREV

u_{3}

+ 2

4

1

3

27

d_{2}

 1

9

1

10

1,000

d_{3}

 1

9

9

18

5, 832

Totals

0

22

9

31

6859^{}

Because of the unacceptable negative
gimmel value, we move on to the next primitive 3D solution of the Conveyance
Equation: 7^{3} + 14^{3} + 17^{3
}= 20^{3}
Table 2N4: The solution that works for 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
these values for P^{+} and N^{0}, the first integer
solution of the conveyance equation containing the values X_{1 }= 24 and X_{2
}= 38, or multiples of them, 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}.
Note that we have different kinds of quarks with different ratios
of mass/energy to gimmel: There are three different kinds of upquarks u_{1},
u_{2}, u_{3} with u_{3} in the neutron being different
from the u_{1} and u_{2} in the proton. Similarly, d_{1}
in the down quark of the proton, is different from the d_{2} and d_{3}
in the neutron. But because gimmel is not detectable as mass or energy, all of
the up and down quarks making up the proton and neutron are detectable in
collider data exactly the same as all other up and down quarks. Each up quark
and each down quark is triadic, combining in threes satisfying the integer
solutions of the conveyance equation.
With the TRUE units determined for protons and neutrons, we find
that the Helium atom is stable only if the total number of TRUE units for the
electron is 106. See the table below:
Table 4H2: 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 = (2x108)^{3} ^{}

Besides the TRUE units that appear as mass/energy in given
elementary particles, because of the embedded nature 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. 106^{3}+24^{3}+38^{3}=108^{3}
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 5: 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

N^{0}

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 righthand column in these tables
contains cubed integer amounts
representing the Minimum Relative
Equivalence Volume (MREV) for each particle making up the combination of
subatomic 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 downquarks 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 H_{1}, Deuterium H_{2} and Tritium H_{3}, as
shown below.
Atoms are semistable
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 H_{2}O, 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.
The Elements of the Periodic Table
The Hydrogen atom is unique among the natural elements in that it
has only two mass/energy components, the electron and proton. Thus, because
Fermat’s Last Theorem prohibits the symmetrical combination of two symmetrical
particles; they cannot combine to form stable structures like the combination
of quarks to form the proton and neutron. The electron, with a small fraction
of the mass of the proton, is drawn by electric charge to whirl around the
proton, seeking stability. This means
that the Hydrogen atom, the elemental building block of the universe, composed
only of the mass and energy of an electron and a proton, is inherently
unstable. So why is it that we have any stable structures at all; why is
there a universe? As Leibniz queried: “why
is there something rather than nothing”?
One of the X_{n}
integers must be 24 to represent the TRUE unit value of the proton, and one
must be 38 to represent the TRUE unit value of the neutron. Among the integer
solutions of the m = n = 3
conveyance equation listed above there are no primitive solutions with 24 and
38 as solution integers. But we can multiply the primitive solution 12^{3} + 19^{3} + 53^{3}
= 54^{3} by 2 to get 24^{3} + 38^{3} + 106^{3}
= 108^{3}. Since there are no smaller integer solutions with 24 and
38 as terms in the left side of the equation, we can try the solution that provided
a stable Helium atom: 24^{3} +
38^{3} + 106^{3} = 108^{3}.
Since the Proton required 17 mass/energy units and 7 ג units, adding up to 24 Total TRUE
units, to achieve triadic stability (see Tables describing the Proton), to
achieve the same level of stability as the proton and neutron, the Hydrogen
atom must have a third component. This satisfies the conveyance equation and
produces a stable Hydrogen atom with a total volume of 108^{3}.
Using these calculations to represent the Hydrogen atom, we have:
TABLE 6 TRUEUnit Analysis for Hydrogen 1 (Protium), Valence =
1*
Particle

Charge

Mass/Energy

ג

Total TRUE
Units

Volumetric
Equivalence

e

 3

1

105

106

1, 191, 016

P^{+}

+ 3

17

7

24

13, 824

ד

0

0

38

38

54, 872

Totals

0

18

150

168^{}

1, 259,
712=108^{3}

*By definition, the valence and the number of
valence electrons is the same number for Hydrogen.
At this point, we are uncertain if this is the same third
substance we have called gimmel, or could it be yet a fourth substance which we
might call daled that is substituting for the TRUE units of the electron. We
therefore provisionally call it Daledד the fourth letter of the Hebrew alphabet,. We could postulate
that this is just Gimmel ג again in addition, C_{ג}, consisting of 38 ג
units, the third form of the ‘stuff’ of reality, not measurable as mass or
energy in substitute in the form of gimmel or daled, as this way, the fact that
Hydrogen is stable and ubiquitous in the universe is explained and Hydrogen
goes from an unstable combination of quarks to a stable combination of quarks with
the most gimmel/daled of all the elements.
The third and fourth (or further third) substance completes the
mathematical logic of the Conveyance Equation so that elemental hydrogen should
be the major component in our cosmos in regard to something as opposed to
nothing. And, as we know, Hydrogen is by far the most abundant and by far the
most reactive element in the cosmos.
Yet, without the ג units
needed by Hydrogen to achieve stability, the universe as we experience it could
not exist. The TRUE units of the two symmetrically stable entities found in the
Hydrogen atom, the electron and proton, could not combine to form a third
symmetrically stable entity (due to the inescapable mathematics of Fermat’s
Last Theorem). Because they could not combine symmetrically, they would spiral,
fly apart and/or be easily separated by any external force. Even if they could
adhere to other particles, the resulting universe would be very boring. All
multiples of such a building block would have the same chemical
characteristics. With the input of the appropriate number of ג units, however, Hydrogen exists as a
basic building block of symmetrically stable forms in the 3S–1t observable
domain of the physical universe we experience.
In 3S1t, TRUE units can manifest as mass, energy or ג,
in order to form symmetrically stable particles and the 168 total TRUE units of
the Hydrogen 1 atom may be arranged in another stable structural form, observed
as the simple combination of one electron, one proton and one neutron, known as
Deuterium, an isotope of Hydrogen (an
atom with the same chemical properties).
Hydrogen 2 (H2) (also called Heavy Hydrogen) is held together by
electrical charge and 128 ג units,
22 less than the H1 atom. This means that H2 is not as stable as H1. But it
still means that satisfying the conveyance equation we should be dealing with a
somewhat stable element even if it is an isotope.
TABLE 7: TRUEUnit Analysis for Hydrogen 2 (Deuterium), Valence
= 1^{* }
Particle

Charge

Mass/
Energy

ג

Total TRUE Units

Volume

e

 3

1

105

106

1, 191, 016

P^{+}

+ 3

17

7

24

13, 824

N^{0}

0

22

16

38

54, 872

Totals

0

40

128

168

(108)^{3}

What about other isotopes of H1? Is it possible that the TRUE
units of a Hydrogen atom or a Deuterium atom can combine with one or more
additional neutrons to form stable isotopes? Hydrogen 3 (H3), known as Tritium,
is a second isotope of Hydrogen. Its form in TRUE units is represented below.
We see that H3 is an asymmetric structure. One electron, one
proton and two neutrons, brought together by attractive forces, cannot combine
volumetrically to form a symmetrically stable structure, and as a result, it is
unstable and there are very few H3 atoms.
TABLE 8: TRUEUnit Analysis for Hydrogen 3 (Tritium), Valence =
1^{* }
Valence = 1 + 2 = 1
Particle

Charge

Mass/
Energy

ג

Total TRUE Units

Volume

e

 3

1

105

106

1, 191, 016

P^{+ }

+ 3

17

7

24

13, 824

2N^{0}

0

44

32

76

438, 976

Totals

0

62

144

206

(118.
018…)^{3 *}

^{*}
Looking at the TRUE unit structure for H1, H2 and H3, we see that
all three are bonded by electrical charge, but H1 has volumetric stability and
150 ג units holding it together; H2
has volumetric stability, more mass/energy units and fewer ג units than H1; and H3 has more mass/energy units and ג units, but
no volumetric stability.
This explains why H1 is the most abundant, H2 less
abundant, and H3 correspondingly less stable. The atomic weights of the
elements of the periodic table, in “amu” (atomic mass units), are
actually the mean values of atomic masses calculated from a great number of
samples. The accepted mean atomic weight for Hydrogen to four significant
figures is 1. 008. This includes H1 and all isotopes of Hydrogen. If all
hydrogen atoms were H1 atoms, this number would be exactly 1. H1 is by far the
most stable, and therefore, most abundant, of the Hydrogen family, making up
more than 99. 99% of all Hydrogen in the universe. Other H isotopes make up the
remaining 0. 01%, mostly H2, with H3 and other isotopes heavier than H2
occurring only rarely in trace amounts.
Table 4 is repeated here only so that the reader will
not have to return to it to see the sequential pattern of the elements of the
Periodic Table.
Table 9: 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 = (2x108)^{3} ^{}

Why is this not called “quadrium”, a third isotope of Hydrogen?
It is considered to be a new element because it has two electrons filling its
outer (and only) shell, so that it is not, like Hydrogen, easily attached to
other atoms, making it unreactive and a very different atomic element.
Importantly we’re already seeing a pattern: a multiple of 108 cubed
for the total volumetric equivalent of Helium. We can hypothesize that
empirically all stable atoms of life and inert gases that are distributed in
the 3S1t cosmos, should be a multiple of the 108 cubed: 108 is 3 cubed (=27),
reflecting 3D volume, multiplied by four (=two squared), reflecting the 2D
nature of the planes of rotation. In this paper, we show that the empirical
analysis confirms this hypothesis which makes sense as well based on our
hypothesis that mathematics does not occur just for calculation but as an
intimate and integral part of life and cosmological existence. Moreover, we see
that when the cube root of the volumetric equivalence score is not an integer,
such atoms, molecules and compounds are less stable and less symmetrical.
New elements arise when a unique new combination of TRUE units,
constructed using multiples of the basic building blocks of electrons, protons
and neutrons is formed. The next element is the combination of the inert atom,
Helium, with the asymmetric atom, H3 to form Lithium.
Table 10: LITHIUM, Valence Electrons = 3  2 = 1
Particle

Charge

Mass/Energy

ג

Total TRUE
Units

Volume

3e

 9

3

315

318

32, 157, 432

3P^{+ }

+ 9

51

21

72

373, 248

4N^{0}

0

88

64

152

3, 511, 808

Totals

0

142

400

542

(330. 32…)^{3 *}

Since the total volume is not an integer cubed, Lithium, like
Tritium, is volumetrically asymmetric. It has a stronger electrical bond than
H3 and more ג units connecting it with the multidimensional substrate for
added stability, but it is less stable because it is asymmetric. Theoretically,
Lithium should crave an atom like Hydrogen 1. This would produce a stable
bonding Lithium hydride if the bonding were covalent. However, such bonding is
ionic, not directly mechanically related to spin, and therefore this is why we
do not see much lithium hydride in the cosmos and as a useful compound in
living organisms.
Therefore, analyses of molecules involve TRUE stability
tendencies but these must be calculated anew applying each TRUE calculations
for each chemical radical (like –OH, or H^{+}). These compounds must exhibit stability to
remain viable for long periods and this stability can be calculated based on
their gimmel contents and shells along with their chemical bonding. Molecules exhibit different levels of
stability just as there are with the elements themselves.
The next natural element after Lithium is Beryllium. Since it is
asymmetric and has two valence electrons, it is much less stable than Hydrogen
and Helium.
TABLE 11: Beryllium, Valence = 10  4 = 6
Particle

Charge

Mass/
Energy

ג

Total TRUE
Units

MREV

4e

 12

4

420

424

76, 225, 024

4P^{+ }

+ 12

68

28

96

884, 736

5N^{0}

0

110

80

190

6, 859, 000

Totals

0

182

528

710

(437. 8976…)^{3}

We continue by examining Boron, as the next in the sequence of
increasingly complex elements.
Table 12: BORON, Valence = 10  5 = 5
Particle

Charge

Mass/
Energy

ג

Total TRUE Units

MREV

5e

 15

5

525

530

148, 877, 000

5P^{+ }

+ 15

85

35

120

1, 728, 000

6N^{0}

0

132

96

228

11, 852, 352

Totals

0

222

656

878

162, 457,352=
(545. 648…)^{3}

We see that Boron is also asymmetric with valence electrons and
is therefore not as stable as Hydrogen or Helium; but the next element, Carbon,
is more stable, being volumetrically symmetric. Carbon and the next two atoms,
Nitrogen and Oxygen are the most stable and abundant elements after Hydrogen
and Helium, and since they are not electronshell stable, they readily combine
with Hydrogen to form natural organic compounds. This establishes Hydrogen,
Carbon, Nitrogen and Oxygen as the main building blocks of life, making up between
92% and 96% of living matter.
As we proceed with the TRUE unit analysis, we note that the other
elements and compounds necessary for life and the manifestation of
consciousness in sentient beings are produced in abundance by the organizing
action of the third form as ג
units, and the conveyance equation.
Carbon C, Nitrogen N and Oxygen O are listed next.
Similarly, we could include Sulfur S, Phosphorus P, Magnesium Mg,
and Calcium Ca as fundamental elements of life. All score the same
proportionate number of TRUE relative to their mass / energy and other than
Hydrogen which is unique, they exhibit the highest proportion of gimmel.
Moreover, the cube root of their volumetric MREV score (making it
linear to more easily analyze) are all multiples of 108.
Table 13: CARBON, Valence = 10  6 = 4
Particle

Charge

Mass/
Energy

ג

Total TRUE Units

MREV

6e

 18

6

630

636

257, 259, 456

6P^{+ }

+ 18

102

42

144

2, 985, 984

6N^{0}

0

132

96

228

11, 852, 352

Totals

0

140

768

1, 008

272, 097, 792
= (6x108)^{3}

Table 14: NITROGEN, Valence = 10  7 = 3
Particle

Charge

Energy/Mass

ג

Total TRUE Units

MREV

7e

 21

7

735

742

408, 518, 488

7P^{+}

+ 21

119

49

168

4, 741, 632

7N^{0}

0

154

112

266

18, 821, 096

Totals

0

280

896

1, 176

432, 081, 216
= (7x108)^{3}

Table 15: OXYGEN, Valence = 10  8 = 2
Particle

Charge

Mass/Energy

ג

Total TRUE Units

MREV

8e

 24

8

840

848

609, 800, 192

8P^{+ }

+ 24

136

56

192

7, 077, 888

8N^{0}

0

176

128

304

28, 094, 464

Totals

0

320

1, 024

1, 344

644, 972, 544 =(8x108)^{3}

We now look at a very volatile element, Fluorine, and we find it
to be volumetrically asymmetric and thus very reactive.
Table 16: FLUORINE, Valence Electrons = 10  9 = 1
Particle

Charge

Mass/Energy

ג

Total TRUE Units

MREV

9e

 27

9

945

954

868, 250, 664

9P^{+ }

+ 27

153

63

216

10, 077, 696

10N^{0}

0

220

160

380

54, 872, 000

Totals

0

382

1, 168

1, 550

933,200,360 =
(977. 218…)^{3}

And we analyze Neon, as another example of an inert gas, stable,
symmetric and inert because there are no openings in its electron shells.
Table 17: NEON, Valence = 10  10 = 0 (Inert)
Particle

Charge

Mass/Energy

ג

Total TRUE Units

Volume

10e

 30

10

1050

1060

1,
191, 016, 000

10P^{+ }

+ 30

170

70

240

13, 824, 000

10N^{0}

0

220

160

380

54, 872, 000

Totals

0

400

1, 280

1, 680

1, 259, 712, 000 = (10x108)^{3}

Hydrogen, Carbon, Nitrogen, and Oxygen, the basic elements of
organic life thanks to the presence of ג
in their atomic structure  are volumetrically symmetric and have available
valence electrons. Similarly, Calcium and Magnesium exhibit these properties as
well as, as indicated, Sulfur and Phosphorus.
Yet Helium and Neon are also symmetric, but are not among the
basic elements of organic life because they are inert and therefore unable to
readily combine with Hydrogen.
All of the other elements analyzed so far, are asymmetric and
less abundant in nature, except for Silicon (Si) below.
It is no accident that the
reactive, volumetrically symmetric elements are important building blocks of
natural organic compounds, and that complex combinations of them manifest life
and consciousness.
Sodium is very reactive, but asymmetric with more neutrons than
protons.
Table 18: SODIUM, Valence =  10 +11 = 1
Particle

Charge

Mass/
Energy

ג

Total TRUE Units

Volume

11e

 33

11

1, 155

1, 166

1, 585, 242, 296

11P^{+ }

+ 33

187

77

264

18, 399, 744

12N^{0}

0

264

192

456

94, 818, 816

Totals

0

462

1, 424

1, 886

(1, 193. 12…)^{3}

Contrast Sodium with 11 electrons and protons, but 12 neutrons
with Magnesium which is what we call “superstable”: Magnesium is an element of
life with equal protons, neutrons and electrons, and a larger amount of gimmel
than sodium.
Table 19: MAGNESIUM, Valence = – 10 +12 = 2
Particle

Charge

Mass/Energy

ג

Total TRUE Units

Volume

12e

 36

12

1, 260

1, 272

2, 058, 075, 648

12P^{+}

+ 36

204

84

288

23, 887, 872

12N^{0}

0

264

192

456

94, 818, 816

Totals

0

480

1, 536

2, 016

(12X108)^{3}

Aluminum is next with 13 electrons, and asymmetric. It is
prevalent certainly but it does not appear to be necessary to support life.
Table 20: ALUMINIUM^{*}, Valence = – 10 + 13 = 3
Particle

Charge

Mass/Energy

ג

Total TRUE Units

Volume

13e

 39

13

1, 365

1, 378

2, 616, 662, 152

13P^{+}

+ 39

221

91

312

30, 371, 328

14N^{0}

0

308

224

532

150, 568, 768

Totals

0

542

1, 680

2, 222

(1, 409. 057…)^{3}

The element Silicon by all
its properties should be an element of life based on its proton, electron and
neutron contents and the equivalent amounts of Gimmel to TRUE as there are with
the other life sustaining superstable elements. A testable hypothesis is that Silicon should be a lifesustaining
fundamental element!
Table 21: SILICON, Valence = 10 +14 = 4
Particle

Charge

Mass/
Energy

ג

Total TRUE Units

Volume

14e

 42

14

1, 470

1, 484

3, 268, 147, 904

14P^{+}

+ 42

238

98

336

37, 933, 056

14N^{0}

0

308

224

532

150, 568, 768

Totals

0

560

1, 792

2, 352

1, 512^{3}=(14x108)^{3}

Table 22: PHOSPHORUS, Valence = 10 + 15 = 5
Particle

Charge

Mass/
Energy

ג

Total TRUE Units

Volume

15e

 45

15

1,575

1, 590

4,019,670,000

15P^{+}

+ 42

255

105

360

46,656,000

16N^{0}

0

352

256

608

224,755,712

Totals

0

622

1, 936

2, 558

4,291,081,712 =
(1625.008…)^{3}

Table 23: SULFUR, Valence = 10 + 16 = 6
Particle

Charge

Mass/
Energy

ג

Total TRUE Units

Volume

16e

 48

16

1, 680

1, 696

4,878,401,536

16P^{+}

+ 48

272

112

384

56,623,104

16N^{0}

0

352

256

608

224,755,712

Totals

0

640

2, 048

2, 688

5,159,780,352 =
16x(108)^{3}

We will close by summarizing the TRUE analyses presented so far.
The table below summarizes the TRUEunit properties of elements
of the Periodic Table from Hydrogen through Sulfur.
Table 25: SUMMARY
OF TRUE UNIT ANALYSES OF THE ELEMENTS
Element

ג Units

Total TRUE

Percent ג Units

Valence

TRUE Volume

Abundance Rank

Hydrogen

150

168

89%

1

108^{3}

1

Deuterium

128

168

76%

1

108^{3}


Tritium

144

206

70%

1

(118. 02)^{3}


Helium

256=
2x128

336

76%

0

(2x108)^{3}

2

Gap





(3x108)^{3}


Lithium

512 =
4x128

672

76%

+1

(330. 32)^{3}


Gap





(4x108)^{3}


Beryllium

528

710

74.4%

+2

(437. 89)^{3}


Gap





(5x108)^{3}


Boron

656

878

74.7%

+3

(545. 65)^{3}


Carbon

768=
6x128

1,008

76. 2%

+4

(6x108)^{3}

4

Nitrogen

896=
7x128

1,176

76. 2%

+3

(7x108)^{3}

6

Oxygen

1, 024=
8x128

1, 344

76. 2%

+2

(8x108)^{3}

3

Gap





(9x108)^{3}


Fluorine

1, 168

1, 550

75. 4%

+1

(977. 22)^{3}


Neon

1, 280=
10x128

1, 680

76. 2%

0

(10x108)^{3}

3

Gap





(11x108)^{3}


Sodium

1, 424

1, 886

75. 5%

+1

(1,193. 12)^{3}


Magnesium

1, 536=
12x128

2, 016

76. 2%

+2

(12x108)^{3}

9

Gap





(13x108)^{3}


Aluminium

1, 680

2, 222

75. 6%

+3

(1, 409. 06)^{3}


Silicon

1, 792=
14x128

2, 352

76. 2%

+4

(14x108)^{3}

8

Gap





(15x108)^{3}


Phosphorus

1,936

2,558

75.7%

+5

(1625.008...)^{3}


Sulfur

2,048=
16x128

2,688

76.2%

+6

(16x108)^{3}


Inspection of this table reveals that the elements that have
volumetric symmetry all have three things in common with regard to TRUE and
gimmel.
1. The
number of ג units it takes to give
them volumetric stability is the number of electrons they possess times 128,
the number of ג units of Deuterium;
2. the
percentage of TRUE units is exactly the same, 76.19…;
3. their
total TRUE volume is the cube of the value of their number of electrons times
108, the number of the TRUE units of Hydrogen and Deuterium.
These three features of the elements that are symmetric in TRUE
units underline the role of ג units
and the Neutron in the formation of a stable universe.
Notice that the sequence of multiples of 108 cubed has gaps not
filled by the elements. Because the symmetrically stable elements that fill
most of the other multiples of 108 TRUE units cubed are life supporting, it
will be interesting to see if the gaps are filled by compounds somehow
essential to life.
Inspection of Table 25 also reveals that there are no elements to
fill the 3x108, 4x108, 5x108, 9x108, 11x108, and 13x108 positions in the table.
But these gaps can be filled if we expand our definition of the Periodic Table.
If we think of the TRUE units of mass, energy and ג as the primary building blocks of the universe, electrons,
protons and neutrons as the secondary level of building blocks, and molecules
as the tertiary level of building blocks, this table becomes a list of all of
the building blocks of the universe, not just elements.
The first clue to identifying the symmetric entity that fills a
given gap in the sequence of TRUEunit volumetric symmetry is its location
relative to the other symmetric forms in the table. The compound that fills a
given gap can only be formed from combinations of symmetric atoms and/or
compounds that are smaller than it.
For example, the (3x108)^{3} gap can only be filled by a
compound entity composed of components of Helium [TRUE volume = (2x108)^{3}]
and Hydrogen or Deuterium [TRUE volume = (1x108)^{3}]. A table with symmetrical
molecular entities that fill the gaps will complete the Periodic Table of
Building Blocks of Reality. Filling these gaps is a subject for additional
research.
It is interesting to note that the 10x108 cubed slot filled by
Neon, could also be filled by H_{2}O, a compound of considerable
importance to the support and continuation of life on this planet. This leads
to an interesting hypothesis that replacing the inert and/or unstable elements
and filling the symmetry gaps with lifesupporting compounds might produce a
complete Periodic Table of the Building Blocks of Reality essential to life as vehicles
of consciousness.