THE BASICS OF TRUE QUANTUM UNIT ANALYSIS

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: X³ + Y³≠ Z³ 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 Σⁿ_i=1 (X_n)^m = Z^m we call the “Conveyance equation”, which is (X₁)³ + (X₂)³ + (X₃)³= Z³ for triplet combinations.

Moreover, these Diophantine calculations only work based on applying a 9-dimensional model. The 9-dimensional 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 Cabibbo-like mixing angle, of intrinsic electron spin and angular momentum, of the shape of the electron which in 3S-1t is symmetrical but non-spherical, of the disappearing electron cloud and of a 9-D mathematical Cabibbo thought experiment plus with weak universality. This validation of the 9-dimensional finite spin model was specifically proposed as a key aspect of a metaparadigm model developed by the authors called the Neppe-Close Triadic Dimensional Distinction Vortical Paradigm (TDVP).

New Concepts:

1.    Traditionally, we have applied Newtonian-Leibnizian 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 mass-energy 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 9-dimensional 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 mass-less, energy-less 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 3S-1t 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, mass-energy 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 Hydrogen-hydroxide (H-OH) (=water) compared with H-H=S (H₂S) (=hydrogen sulfide): H₂S 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 9-dimensional 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 macro-world.

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 9-dimensional spin models not just the 3 dimensions of space in a moment in time (3S-1t) which is the basis of most current physical theory. Whereas 3S-1t can explain a great deal, our work has shown there are problems in 3S-1t that can only be solved by applying a 9-dimensional 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 this-using 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 science-spirituality 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 so-called 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 ten-millionths 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 Neppe-Close TDVP model, and particularly Close’s Calculus of Distinctions and his Dimensional Extrapolation, plus the re-application 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 Rowan-Robinson, Professor of Astrophysics at Imperial College, London, has articulately expressed his belief in the Aristotelian view in his well-written 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 Close-Neppe 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 3S-1t 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 Rowan-Robinson. 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 hyper-dimensional geometry, requiring a nine-dimensional 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 six-dimensional 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 sub-atomic 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 non-Euclidean 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 step-by-step 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 little-understood and rare phenomena like remote viewing, out-of-body experiences (OBEs) and other so-called 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”, re-uniting for the first time, imaginary numbers with symbolic logic, and thus re-aligning 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 long-standing 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 time-honored 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 clear-headed 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 sub-atomic 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, multi-dimensional 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 3S-1t 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 multi-dimensional 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 non-locality and quantum entanglement, as well as the near light-speed vortical spin of fermions, and the effects of so-called 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 extra-corporeal (out-of-body) experiences and other documented psi phenomena. The current mainstream scientific paradigm cannot explain so-called 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 three-dimensions of space and one dimension of time. TDVP, on the other hand, reveals a multi-dimensional 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 ‘fine-tuning’ of the physical universe, Lightman points out that “Intelligent Design is an answer to fine-tuning that does not appeal to most scientists.” (p. 12) ^63r However, when confronted with the observer-related non-locality 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", meta-universe 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 3S-1t 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 ‘hard-nosed’ 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 Neppe-Close 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 3S-1t 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 3S-1t 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 nine-dimensions 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 3S-1t, if the remaining further dimensions (e. g. our demonstrated 9-dimensional 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 3S-1t existences involves incomplete knowledge because such factors as psi, non-locality, and altered states of consciousness are not properly taken into account, and in many cases, not taken into account at all.

SUPPORTING A 9-DIMENSIONAL SPIN FINITE REALITY MODEL

The validity and predictive power of a 9-dimensional spin finite reality model is now well-established by the previous work of Close and Neppe. This predominantly relates to the first major discovery associated with the Neppe-Close Triadic Dimensional Vortical Paradigm (TDVP): derivation of the exact value of the Cabibbo angle from 9-dimensional spin model principles, but is also substantiated by additional supporting discoveries and data. The 9-D 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 9-dimensional 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, no-one had tested a 9-D spin hypothesis before. Our work in 2012 provided a solution.

Close and Neppe applied well-defined physics, with well substantiated empirical data, including well-defined 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 well-defined 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 Cabibbo-like 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 space-time-consciousness theory of finite reality from the Neppe-Close 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 9-dimensional 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 nine-dimensional objects.

However, both the Standard Model of Particle Physics and the various String Theories with folding dimensions and none of which involve 9-dimensional spin, fail. This result can only be derived by applying the dynamic rotation of elementary particles as nine-dimensional 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 9-dimensional vortical (spinning) model. As sentient beings, we may be able to distinguish only part of our finite reality, reflecting only our subjective 3S-1t 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 9-dimensional 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 3S-1t 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. On-going research includes analyzing the third substance of reality we have called “gimmel”. We propose that this third mass-less, energy-less 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 “life-tracks” 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 3S-1t 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 well-established 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=mc².

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 macro-scale 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 non-quantized 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 multi-dimensional 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, non-zero 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 multi-dimensional 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 multi-dimensional and uniform at the quantum level, and that mass and energy are the most easily measurable forms of it in the 3S-1t domain. This allows us to relate the unitary measure of inertial mass and its energy equivalent to a unitary volume, and provides a multi-dimensional 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 3S-1t, 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 3S-1t, 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 3S-1t, 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=mc²) is linear, since in the 3S-1t context, c² 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 3S-1t physical universe from the perspective of a nine-dimensional 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 nine-dimensional 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 nine-dimensional 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 Einstein-Podolsky-Rosen (EPR) paradox, tells us that reality at the quantum level is like an all-encompassing interwoven multi-dimensional 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 broad-brush 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 finer-scale 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 3S-1t. The form of this logical structure, much like the conceptualized blueprint of a building in the mind of an architect, is conveyed to the 3S-1T domain of the physical universe through the dimensionometric structure of a spinning nine-dimensional 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 3S-1t physical universe, the maximum expansion velocity between two farthermost separated points in a quantized 3S-1T 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 3S-1t. 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 sub-atomic 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 nine-dimensional domains of finite distinction to the 3S-1t 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 sub-atomic particles perceived to be the building blocks of the observable universe, including photons, electrons, neutrons and protons, in units of MeV/c². Analysis of these data in the framework of the mathematics and geometry of TDVP in 3S-1t 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 3S-1t as matter, i.e. electrons, up-quarks and down-quarks, are approximately 0.51, 2.4 and 4.8 MeV/c², respectively. The values for up and down quarks are derived statistically from millions of terabytes of data obtained from high-energy particle collisions engineered in specially-built colliders.

It is obvious from these data that the conventional unit: MeV/c² is not the basic quantum unit, because the data expressed in these units contain fractions of MeV/c² 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, up-quark and down-quark should be integer multiples of the basic quantum unit of mass/energy equivalence. Since the masses are fractional in MeV/c² units, one MeV/c² 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 high-energy 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 down-quarks, 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 Cockcroft-Walton 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/c².

It is important to note that our model is based on physics data relative to 3S-1t, because 9-dimensional 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 four-dimensional domain embedded in a five-dimensional domain. The existence of 9-D spin might imply that fundamental equations such as E=Mc² are relative only to 3S-1t, 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 3S-1t 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 sub-atomic 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 down-quarks as multiples of that unit, we have the normalized masses of the electron, up- and down-quarks.

Using the latest available collider data, the mass/energy averages for the up- and down- quarks are 2. 01 MeV/c² and 4. 79 MeV/c² 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 up-quarks and one down-quark 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 high-energy collisions.

In TDVP, we see this as evidence of the underlying logical structure of reality and speculate that it might be paralleled by the so-called “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/c2)	Mass/Volume (Normalized) [1]
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 light-speed 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 mass-energy equivalence in the currently used MeV/c² 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 h-bar) 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.

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[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 “sub-quantum” but the location in space and time might be different relative to different dimensional domains. Therefore, we’re using “sub-atomic” 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 3S-1T 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 space-like, time-like and (we suggest) consciousness-like, 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 consciousness-like, 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 down-quarks 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 space-time domain of our 3S-1t 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

Σⁿ_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 9-dimensional reality to our observational domain of 3S-1t, we call this expression the “Conveyance Expression”, and individual equations of the expression “Conveyance Equations”.

 When n = m = 2, the expression yields the equation

(X₁)² + (X₂)² = Z²

which, when related to areas, describes the addition of two square areas, A₁ and A₂ with sides equal to X₁ and X₂ respectively, to form a third area, A₃, 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 sub-set of solutions with AB = X₁, BC = X₂ and AC = Z equal to integers. Members of this subset, e.g. (3, 4, 5), (5, 12, 13), (8, 15, 17), etc. i.e., (3² + 4² = 5², 5² + 12² = 13², 8² + 15² = 17², …) are called “Pythagorean triplets”.

When n = 2 and m = 3, the expression becomes the equation

(X₁)³ + (X₂)³ = Z³.

When we define X₁, X₂ 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 three-dimensional 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 r₁, and if there is a second uniform spinning particle rotating at maximum velocity, with radius r₂, we can describe the combination of the two particles by the expression 4/3π(r₁)³ + 4/3π(r₂)³. If this combination produces a third spinning spherical object we have:

4/3π(r₁)³ + 4/3π(r₂)³ = 4/3π(r₃)³,

where r₃ is the radius of the new particle. Dividing through by 4/3π, we have:

(r₁)³ + (r₂)³ = (r₃)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 r₁ and r₂ are integers, r₃ cannot be an integer. This means that the right-hand 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 right-hand side of the equation represents an unstable asymmetric spinning particle. The combined high-velocity 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 Newton-Leibniz world, but we actually exist in a Planck-Einstein world. In the real world, revealed by Planck and Einstein, the most perfectly spherical object in three dimensions is a convex regular polyhedron. (polyhedron = multi-sided three-dimensional form; regular; all sides are of equal length.) The most easily visualized is the cube, which is most precisely defined geometrically as a six-sided regular polyhedron. In the Newton-Leibniz 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 three-dimensional Conveyance Expression. We are interested in the 3-D 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:

(X₁)³ + (X₂)³ + (X₃)³= Z³,

which has integer solutions. The first one (with the smallest integer values) is:

3³ + 4³ + 5³= 6³

It is important to recognize the implications of Σⁿ_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 3S-1t 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 nine-dimensional 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 hyper-dimensional domains (more than three dimensions) are three dimensions of space and three dimensions of time that are not detected in 3S-1t 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 3S-1t, 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/c² ≈ 1 x10^-47 kg.) to quarks ranging from the “up” quark at about 2. 4 MeV/c², to the “top” quark at about 1. 7 x10⁵ MeV/c^2, to the Hydrogen atom at about 1x10⁹ MeV/c² (1. 67 x10^-27kg.), to the heaviest known element, Copernicum (named after Nicolaus Copernicus) at 1. 86 x10^-24 kg ^[1]. So the heaviest atom has about 10²³ 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 “anti-particles”. 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 n-dimensional domain is embedded in an n+1 dimensional domain. This means that all distinctions of extent, from the ninth-dimensional 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 tinker-toy fashion with plastic or wooden spherical objects connected by single or double cylindrical spokes. This is helpful for visualizing molecular compounds in terms of their constituents prior to combining, but that is not what actually happens.

Inside a stable organic molecule, volumetrically symmetric atoms are not simply attached; their sub-atomic spinning vortical “particles” combine, forming a new vortical object. Elementary particles are rapidly spinning symmetric vortical objects and when three of them combine in proportions that satisfy the three-dimensional Conveyance Equation, they do not simply stick together - they combine to form a new, dimensionally stable, symmetrically-spinning object. Because they are spinning in more than one rotational plane, these objects are best conceived of as closed vortical solitons.

The triadic combinations of elementary vortical objects, like up- and down-quarks, form new vortical objects called protons and neutrons, the combinations of electrons, protons and neutrons form new vortical objects called 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 symmetrically-spinning objects formed by the combining of smaller vortical objects form closed vortices in 3S-1t with new physical and chemical characteristics, depending upon both their internal and external structure.

We will take the volume of the smallest possible quantized vortical object as the basic unit of measurement, the true quantal unit. The substance of all particles is then measureable in whole-number multiples of this unit.

THE TRUE UNIT: TRIADIC ROTATIONAL UNITS OF EQUIVALENCE (TRUE) AND THE THIRD FORM OF REALITY: GIMMEL OBTAINED BY APPLYING THE 3-D 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 light-speed 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 3S-1t 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 non-radiating sub-atomic entities are measureable in multiples of these sub-quantal units. These are units of measurement, not sub-quantal entities existing as independent phenomena. Until impacting on a receptor in an irreversible way, mass, energy and gimmel, the mass-less, energy-less third substance required for stable atomic and sub-atomic 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 time-like dimensional planes manifests as energy because time is non-existent without movement, and any movement of mass relative to an observer is measured by that observer as kinetic energy. Spinning in the additional planes of reality containing the space and time domains, requires, 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 3S-1t measurement, can be determined by a symmetric three-dimensional conveyance equation: We found above that the smallest set of integer values that satisfies the three-dimensional form of the conveyance equation is the set 3, 4, 5 and 6. So the Diophantine equation 3³ + 4³ + 5³= 6³ describes the addition of three volumes with integer radii 3, 4, and 5 to form a symmetric volume with the integer radius r = 6.

When n = m = 3, the Conveyance Equation Σⁿ_i=1 (X_n)^m = Z^m yields:

(X₁)³ + (X₂)³ + (X₃)³= Z³

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

The primary level of symmetric stability – quarks and the conveyance equation

Because of Planck’s discovery that energy only occurs in integer multiples of a very small quantum, and Einstein’s discovery of the equivalence of matter and energy, (E = mc²) we know that the substance of the universe is quantized. With the appropriate integer values for X₁, X₂, X₃, and Z, in TRUE units, the three-dimensional conveyance equation (X₁)³ + (X₂)³ + (X₃)³= Z³ represents the stable combination of three quarks to form a Proton or Neutron. There are many integer solutions for this equation and historically, methods for solving it were first developed by Leonhard Euler ⁸⁹.

Applying mathematics empirically

Our approach is empirical mathematical testing: We start with the smallest integer solution of this Conveyance Equation, 3³ + 4³ + 5³= 6³, and see if it can describe the combination of mass/energy and gimmel consistent with particle collider data.

In order to test the mathematical hypothesis that the combination of the volume and content of three quarks to form protons and neutrons can be adequately described using the Diophantine conveyance equations, we can start by using the simplest 3-D conveyance equation solution of 3³ + 4³ + 5³= 6³. If this equation doesn’t fit the empirical data, we need to establish what does work.

When we use the smallest integer solution, 3³ + 4³ + 5³= 6³, to the 3-D conveyance equation to attempt to find the appropriate values of ג for the Proton, we obtain negative values for ג for the first up-quark and the down-quark and zero for the second up-quark. It is conceivable that some quarks may contain no ג units, but negative values are a problem. They cannot be allowed because a negative number of total ג units would produce an entity with fewer total observable TRUE units in 3S-1t than the sum of mass/energy units of that entity, violating the conservation of mass and energy, destroying the particle’s equilibrium and identity.

We now compare two tables showing hypothesized TRUE and gimmel in the proton and then the neutron. We apply a trial and error approach, knowing that we need positive integers and ultimately quantal volumetric figures, where the cube roots are integral. For consistency in a quantized reality, charge has also been normalized in these tables.

In Table 1P1, we attempt to use the smallest integer solution of the conveyance equation to describe the combination of two up-quarks and one down-quarks in a proton, but some of the quarks have negative ג units.

In Table 1N1, we attempt to use the smallest integer solution of the conveyance equation to describe the combination of one up-quark and two down-quarks in a neutron, all of the quarks have negative ג units. Negative gimmel units are unacceptable for mathematical reasons: Third-order Diophantine equations with negative terms cannot describe triadic combinations because they are reducible to non-triadic 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 non-negative solutions of the Conveyance Equation.

Table 1P1: Trial Combination of Two Up-Quarks and One Down-Quark, i.e.

The Proton, applying minimal TRUE Units

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

---

[1] Cn and atomic number 112 was created in 1996. It is an extremely radioactive synthetic element that can only be created in a laboratory. The most stable known isotope is copernicium-285 ⁸⁷.

[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 Up-Quark and Two Down-Quarks in TRUE Units as in the neutron (N⁰)

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

In conformance with Bohr’s solution of the EPR paradox (the Copenhagen interpretation of quantum mechanics), newly formed elementary entities do not exist as localized particles in 3S-1t until a 3S-1t measurement or observation is made. We propose that this is only possible if all TRUE units are undetectable in 3S-1t, before observation and measurement. This means that they exist in the substrate underlying all dimensional domains and will manifest as either mass/energy, or ג units, to exhibit the logical patterns of the substrate in observable symmetrically stable 3S-1t forms. In this way, the encompassing substrate, the additional five plus dimensions of the nine-dimensional structure of reality, organizes the 3S-1t world that we experience through the physical senses and their extensions into discrete forms.

The mathematical distribution of TRUE units cannot result in the appearance of negative ג units in the internal structure of an entity. A triadic entity with negative total ג units is not possible because a negative number of total ג units would violate the conservation of mass and energy, destroying the particle’s equilibrium and identity. Why? Because analogous to the axiom ‘nature abhors a vacuum’, a result of the second law of thermodynamics, just as the electrons of an incomplete shell rush around the entire volume of the shell trying to fill it, negative ג units would cause TRUE units of the mass/energy of the particle to fill the void and the measurable mass/energy of the particle would no longer be that of a proton or neutron, and conservation of mass/energy in 3S-1t would be violated because the measured mass/energy equivalence would be changed and the proton or neutron would become unstable.

Attempting to use the smallest integer solution, (3, 4, 5, 6) of the Conveyance Equation to find the appropriate values of ג for both the proton and neutron, we obtain negative total ג unit values. This would change the particle’s measurable mass/energy identity 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 1³ + 6³ + 8³= 9³, but, using it also results in negative values of gimmel.

Therefore, the smallest integer solution of the conveyance equation that produces no negative values of ג and also no zeroes for the Proton is 6³ + 8³ + 10³= 12³.

Using this solution, we have the electrically and symmetrically stable Proton. This would mean if we adequate figures for the Neutron (and the Electron) then our calculations would be viable for symmetrical, stable particles.

Table 2P2 : The Proton (P⁺) Solution

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

  

Nature, reflecting the patterns of the dimensional substrate, does not have to rely upon random particle encounters to build complex structural forms. Compound structures are formed within the mathematical organization of the Conveyance Equation, and useful building blocks have a significant level of stability in 3S-1t for protons to combine with other compound particles and create structures sufficiently complex to support life. To see how other structures arise from quarks, protons and electrons, we need to know how protons, neutrons and electrons relate to the Conveyance Equation: (X₁)³ + (X₂)³ + (X₃)³= Z³. If the total number of TRUE units in the proton is equal to the integer X₁, the number of TRUE units in the neutron = X₂, the number of TRUE units in the electron = X₃, then the resulting compound entity, will be stable in the 3S-1T domain of physical observations.

We know that the 24 TRUE-unit Proton must combine with an electron to form a Hydrogen atom, and with other protons, electrons and neutrons to form the other elements. In order to find the smallest solution of the conveyance equation that can include the 24 TRUE units of the proton, we may start by trying the solutions we’ve used so far.

24 is a multiple of 2, 3, 4, 6, and 8, any one of which can be a factor of X₁ in the conveyance equation solutions we’ve used so far. Up to this point we’ve only used the first two of the smallest primitive integer solutions of the equation: 3³ + 4³ + 5³ = 6³ and 1³ + 6³ + 8³ = 9³. (A primitive Diophantine solution is defined as one without a common factor in all terms.) We have also tried to use 6³ + 8³ + 10³= 12³, an integer solution obtained by multiplying all of the terms of the smallest primitive solution by 2. The first 36 integer solutions of the conveyance equation (X₁)³ + (X₂)³ + (X₃)³ = Z³ are listed below in ascending order. Primitive solutions are in bold in Table 3.

Table 3: The First 36 Conveyance Equation Integer Solutions for n=m=3.

33 + 43 + 53 = 63	13 + 63 + 83 = 93	63 + 83 + 103 = 123
23+ 123 + 163 = 183	33 + 103 + 183 = 193	73 + 143 + 173 = 203
123 + 163 + 203 = 243	43 + 173 + 223 = 253	33 + 183 + 243 = 273
183 + 193 + 213 = 283	113 + 153 + 273 = 293	153 + 203 + 253 = 303
43 + 243 + 323 = 363	183 + 243 + 303 = 363	23 + 173 + 403 = 413
63 + 323 + 333 = 413	163 + 233 + 413 = 443	53 + 303 + 403 = 453
33 + 363 + 373 = 463	273 + 303 + 373 = 463	243 + 323 + 403 = 483
83 + 343 + 443 = 503	293 + 343 + 443 = 533	123 + 193 + 533 = 543
363 + 383 + 423 = 563	153 + 423 + 493 = 583	213 + 423 + 513 = 603
303 + 403 + 503 = 603	73 + 423 + 563 = 633	223 + 513 + 543 = 673
363 + 383 + 613 = 693	73 + 543 + 573 = 703	143 + 233 + 703 = 713
343 + 393 + 653 = 723	383 + 433 + 663 = 753	313 + 333 + 723 = 76

The numbers appearing in the totals in the tables describing quarks, protons, neutrons and atoms are the smallest possible non-negative integers consistent with the empirical data and the requirement for symmetry that the sum of the three totals cubed must equal an integer cubed. Thus, we can calculate the number of ג units involved, and the totals of TRUE units required by the conveyance equation to yield results consistent with empirical particle collider data. Note that the TRUE units in these tables, consistent with 3S-1t observation, are measurements of three-dimensional objects in multiples of the unitary linear measure of their volumes, and their minimal rotational equivalence volumes (MREV), listed in the last column are equal to the TRUE unit values cubed.

As indicated, negative values for ג cannot occur because of the conservation of mass and energy as negatives would destroy the mass/energy/ ג balance and turn the quarks into unstable combinations which would decay quickly. Note that unstable quarks, e.g. top, charm or bottom quarks, will likely fall into specific unstable series of conveyance Diophantine equations. But this is a subject for further research. For now, we must find the smallest unique conveyance equation solution for each combination of sub-atomic particles. Nature is parsimonious, and we must never make a mathematical description or demonstration any more complicated than it has to be. The correct unique solution can be found for each triadic sub-atomic particle by starting with the smallest integer solution of the conveyance equation and moving up the integer scale by trial and error, until no negative values are obtained. Also, a solution with the total for any term equal to zero cannot be allowed, because, in that case, there would be no solution as the resulting Diophantine equation and the Fermat inequality would apply. Using the solution 6³ + 8³ + 10³= 12³, the next attempt to find the TRUE unit configuration of the neutron is shown below:

Table 2N2 :  Triadic Quark Combinations for the Neutron (N⁰)

Trial Combination of One Up-Quark and Two Down-Quarks in TRUE Units using a multiple of the minimum integer solution of the Conveyance Equation

Particle	Charge	Mass/Energy	ג	Total TRUE Units	MREV
u1	+ 2	4	2	6	216
d1	- 1	9	-1	8	512
d2	- 1	9	1	10	1000
Totals	0	22	2	24	1728=123

Since this solution still produces a negative value of ג for d₁, we must move to the next larger solution to represent the Neutron. The smallest unique Conveyance Equation solution with no negative or zero values of ג for the stable Neutron is 9³ + 12³ + 15³= 18³

These TRUE unit numbers give us a stable neutron; but now we have another problem: None of the solutions with a term equal to 24 have a second term equal to 36. Nor do any of the solutions listed have two terms with the ratio 24/36 =2/3. This is a problem because it means that atoms with equal numbers of protons and neutrons could not be stable because they would not satisfy any of the solutions of the conveyance equation, and we know that the element Helium, and other elements are stable combinations with equal numbers of protons and neutrons.

Table 2N3 Neutron (N⁰) trial Solution.

Quark Combinations for the Neutron

Particle	Charge	Mass/Energy	ג	Total TRUE Units	MREV
u3	+ 2	4	5	9	729
d2	- 1	9	3	12	1, 728
d3	- 1	9	6	15	3, 375
Totals	0	22	14	36	5, 832=183

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

Table 4H1: Attempt to Construct a Helium Atom with P⁺ = 24 and N⁰ = 36

Particle	Charge	Mass/Energy	ג	Total TRUE Units	MREV
2e	- 6	2	78	80	512, 000
2P+	+ 6	34	14	48	110, 592
2N0	0	44	28	72	373, 248
Totals	0	80	120	200	995, 840=(99. 861…)3

The number of TRUE units making up the electron is unknown at this point. This value was chosen because it is the integer value that produced a total MREV nearest to a cube, as it must be for a stable Helium atom. So these figures for protons or neutrons or electrons must be incorrect, 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: 3³ + 10³ + 18³ = 19³, but it produces an unacceptable negative gimmel value for u₃:

Table 2N4: 2^nd trial solution for Quark Combinations for the Neutron  

Particle	Charge	Mass/Energy	ג	Total TRUE Units	MREV
u3	+ 2	4	-1	3	27
d2	- 1	9	1	10	1,000
d3	- 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 3-D solution of the Conveyance Equation: 7³ + 14³ + 17³ = 20³

Table 2N4: The solution that works for Quark Combinations for the Neutron  

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

Next, we need to see if this quark combination for the neutron combined with protons and electrons will yield stable atomic structures. Using these values for P⁺ and N⁰, the first integer solution of the conveyance equation containing the values X₁ = 24 and X₂ = 38, or multiples of them, is obtained by multiplying both sides of the primitive solution 12³ + 19³ + 53³ = 54³ by 2, yielding the integer solution 24³ + 38³ + 106³ = 108³.

Note that we have different kinds of quarks with different ratios of mass/energy to gimmel: There are three different kinds of up-quarks u₁, u₂, u₃ with u₃ in the neutron being different from the u₁ and u₂ in the proton. Similarly, d₁ in the down quark of the proton, is different from the d₂ and d₃ in the neutron. 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 N⁰ = 38

Particle	Charge	Mass/Energy	ג	Total TRUE Units	MREV
2e	- 6	2	210	212*	9, 528, 128
2P+	+ 6	34	14	48	110, 592
2N0	0	44	32	76	438, 976
Totals	0	80	256	336	10, 077, 696 = (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 down-quark decay from the strange quark, the stabilization requirement of an integer solution for the conveyance equation, and the additional TRUE units of ג needed for particle stability, the following table describes the electron, proton and neutron in TRUE units, with up quarks composed of a total of 24 TRUE units, down quarks composed of a total of 38 TRUE units and electrons composed of a total of 106 TRUE units. 106³+24³+38³=108³

It therefore represents the normalized mass/energy, minimum ג and total volumes for stable electrons, protons and neutrons, the building blocks of the physical universe.

Whether mass, energy or gimmel (ג), upon measurement, each TRUE unit of the substance of reality occupies the same volume, i.e. the minimal volume for an elementary particle as a spinning object, as required by relativity and defined in TDVP as the basic unit of volume is consistently the same for any electrons (106 with 105 gimmel), protons (24 with 7 gimmel) and neutrons (38 with 16 gimmel).

Each TRUE unit is capable of contributing to the structure of physical reality as m, E or ג to form a stable particle, according to the logical pattern in the substrate reflected in the Conveyance Equation, and the relative volume of each particle (in the three dimensions of space) is equal to the total number of TRUE units cubed times the shape factor.

Table 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
N0	0	22	16	38	54, 872

As noted before, the shape factor of any regular form always cancels out of the conveyance equation. (As demonstrated above for the sphere, the shape factor, 4/3π, occurs in all terms of the equation, and thus can be cancelled by dividing both sides of the equation by 4/3π.) Thus the same equation is obtained regardless of the shape of the particles, as long as the shape and substance is the same for all three particles). For this reason, the right-hand column in these tables contains cubed integer amounts representing the Minimum Relative Equivalence Volume (MREV) for each particle making up the combination of sub-atomic particles.

The TRUE unit values for these elementary particles are uniquely determined by conditions necessary for the existence of a stable universe. The values for up- and down-quarks are the necessary values for the proton and neutron, as determined above, and the number of ג units and the total TRUE units for the electron are determined by calculating the ג units necessary to form stable atoms like the Helium atom. They also determine the smallest possible stable atoms, Hydrogen H₁, Deuterium H₂ and Tritium H₃, as shown below.

Atoms are semi-stable structures composed of electrons, protons and neutrons. They are not as stable as protons and neutrons, but they are generally more stable than molecules. Some molecules, like H₂O, are more stable than others ostensibly because of higher gimmel content, but all of the factors that contribute to stability must be considered, especially symmetry.

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 12³ + 19³ + 53³ = 54³ by 2 to get 24³ + 38³ + 106³ = 108³. 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: 24³ + 38³ + 106³ = 108³.

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 108³.

Using these calculations to represent the Hydrogen atom, we have:

TABLE 6 TRUE-Unit 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=1083

*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 3S-1t, 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: TRUE-Unit 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
N0	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: TRUE-Unit 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
2N0	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 N⁰ = 38

Particle	Charge	Mass/Energy	ג	Total TRUE Units	MREV
2e	- 6	2	210	212*	9, 528, 128
2P+	+ 6	34	14	48	110, 592
2N0	0	44	32	76	438, 976
Totals	0	80	256	336	10, 077, 696 = (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 3S-1t 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
4N0	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 multi-dimensional 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
5N0	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
6N0	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 electron-shell 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
6N0	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
7N0	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
8N0	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
10N0	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
10N0	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
12N0	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
12N0	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
14N0	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 life-sustaining 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
14N0	0	308	224	532	150, 568, 768
Totals	0	560	1, 792	2, 352	1, 5123=(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
16N0	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
16N0	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 TRUE-unit 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	1083	1
Deuterium	128	168	76%	-1	1083
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 TRUE-unit 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 H₂O, 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 life-supporting compounds might produce a complete Periodic Table of the Building Blocks of Reality essential to life as vehicles of consciousness.