What follows is a brief summary of a paper I'm currenntly submiting to about a dozen scientists for peer review prior to publication.

** QUANTUM MATHEMATICS FOR QUANTUM REALITY**

The TRUE Quantum Unit and the Third Form of Reality

^{©} Edward R. Close 2/11/17

PARTICLE/WAVE
EQUIVALENCE

In this section I discuss the work of Max Planck and Albert
Einstein upon whose ideas this paper builds.

THE NEED FOR
A QUANTUM MATHEMATICAL SYSTEM OF LOGIC

In this
section I explain why Newtonian calculus is inappropriate for application to
quantum phenomena, and why the application of the calculus in particle physics
gives rise to unnecessary “quantum weirdness”.

**in any meaningful
representation of the physical universe, all of the basic measurable variables:
mass, energy, space, and time, must be quantized, and therefore, Newtonian
calculus does not work for quantum phenomena. For the proper analysis of quantized
reality, a new calculus is required. This calculus must be a system of
quantized mathematical logic based on natural quantum units.**

DEFINING THE
BASICS OF QUANTUM MATHEMATICS

E = mc^{2} applied to the electron

Matter/energy Equivalence and the Masses of the Elementary
Particles

QUANTIZATION
OF SPACE-TIME

*Max Planck said;
“There is no matter as such” and Albert Einstein said: “The concept of empty
space has no meaning.”*

In
this section I calculate the velocity of the electron in orbit around the
Hydrogen atom.

QUANTIZATION
OF ANGULAR AND ELECTRON SPIN

Calculating the angular velocity (spin) of the
free electron, we find that it reaches the speed of light before its volume
shrinks to zero. This allows us to calculate the minimum volume of the particle
with minimum mass. Normalizing the speed of light allows us to define quantum equivalence units for space
and time. A complete table of natural quantum equivalence units is presented in
this section.

QUANTUM
CALCULUS: The Calculus of Dimensional Distinctions (CoDD)

In a quantized reality, the concept of a point, or
mathematical singularity, is replaced by the existential single three-dimensional
quantum.

*The quantum
equivalence unit should not be confused with a physical particle.* *The quantum equivalence units are
units of measurement, not particles. *The fact that an up-quark has the
mass of 4 electrons does *not* mean
that an up-quark *contains* 4
electrons, and the fact that an electron has one quantum equivalence unit of
mass does not mean that it does not have additional quantum equivalence units
of energy, space and time associated with it.

The CoDD system of
units is in some ways similar to some of the existing ‘natural’ units because
it sets the speed of light equal to unity (**c
= **1). But it does not directly naturalize the other ‘universal’ constants. An
important feature of this normalization of the mass of the electron and the
basic measurement units of the four directly measurable features of physical
reality: mass, energy, space and time, is that it ensures that all measurements
of quantized reality in the CoDD system will be *integers*.

HOW DO
PARTICLES COMBINE TO FORM STABLE STRUCTURES?

In this section I discuss the disparity between the
stability of the proton and other particles. For example, the proton has a
half-life decay longer than the big-bang age of the universe, while the
half-life of a free neutron is about 10 to 15 minutes.

Elementary
Particles and Fermat’s Last Theorem

Fermat’s Last Theorem
is famous among mathematicians because it was unsolved for more than 300 years.
Its importance here comes from the fact that the possibility of certain combinations of elementary particles
is eliminated by Fermat’s Last Theorem, which says that the equation (X_{1})^{m}
+ (X_{2})^{m} = Z^{m }has
no integer solutions when m > 2, while (X_{1})^{3} + (X_{2})^{3}
+ (X_{3})^{3} = Z^{3} does have solutions. This is why
elementary particles like quarks cannot combine in pairs, but do combine in triples.

THE TRUE
QUANTUM EQUIVALENCE UNIT AND THE THIRD FORM OF REALITY

In
this section I prove that there has to be a third form of reality, not
detectable as matter or energy, for there to be any life-supporting stable
atoms.

THE ORIGIN
OF MASS

In this
section, I state two hypotheses about mass and particle spin in extra dimensions:

*I. At the quantum level, mass is nothing more and nothing
less than resistance to acceleration due to the angular momentum and moments of
inertia of spinning particles.*

*II. Elementary particles have spin components in multiple
dimensional planes.*

(Acceleration is defined as
any change in motion. Angular momentum and moment of inertia are defined as in
classical mechanics and general relativity.)

I spend most
of the rest of the paper demonstrating their validity with calculations and tables
describing the origin of neutrons and the isotopes of Hydrogen and their role
in the existence of the rest of the elements of the Periodic Table.

THE
UNDERLYING PATTERN

This section presents calculations and a table showing the
pattern of creation of the natural elements from Hydrogen and its two isotopes:
Deuterium and Tritium.

WHAT IS
GIMMEL?

Gimmel is the
third form of reality, not directly measurable as mass or energy that
nevertheless completes the symmetry of the combinations of elementary
particles, making it possible for a complex physical universe with atomic and
molecular structures supportive of life to exist.

*Gimmel can manifest
as either mass or energy, as needed to maintain symmetry and stability, and
plays a role in the conservation of mass and energy.*

*The
hypotheses proposed in this paper concerning the origin of mass and the
multi-dimensional spin of elementary particles have been demonstrated to be
valid because results obtained with them are consistent with empirical experimental
data to a level of accuracy that would not be possible if they were not valid*.

With the application of the quantum
mathematics of the CoDD, the mathematical imperative of Fermat’s Last Theorem,
and the symmetry of multi-dimensional spinning elementary particles, it is
possible to explain a number of things unexplained or only vaguely explained in
the current standard model paradigm. These things include, but are not limited
to: the variable mass of combined particles, the intrinsic spin of fermions ^{30},
and the Cabibbo mixing angle of quarks ^{31}. Recognition of the
existence of a *multi-dimensional third form of reality* not directly
measureable as mass or energy provides a new avenue for investigation of
paranormal and rare event phenomena, especially if gimmel can be shown to be related
to consciousness.

**REFERENCES:**

1. Planck, M: *The Theory of Heat Radiation*. Translated by Masius, M.P.,
Blakiston’s Sons & Co, 1912.

2.
Einstein, A: Explanation of the photoelectric effect with use of the quantum
hypothesis of Planck: Concerning a heuristic point of view toward the emission
and transformation of light.__ __*Annalen
der Physik* 17: 132-148, http://einsteinpapers.press.princeton.edu/vol2-trans/100 1905.
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Ann. de Physique (10) **3**,
22

4. Baron, Margaret E: *The Origins of the Infinitesimal Calculus,* Courier Corporation, 1969

5. Einstein A: *Relativity,
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6. Minkowski, Hermann: "*Raum und Zeit*", 80. Versammlung Deutscher Naturforscher
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see Lorentz et al. (1952)
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8. Einstein, A: Note
to the Fifteenth Edition, *Relativity, the
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10. Fetter, A.L. &
Walecka, D.J: *Theoretical
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13. Close, E.R.: *Infinite
Continuity,* Paradigm Press, 1990

14. Ibid: *Transcendental
Physics*, Paradigm Press, 1997, iuniverse, 2000

15. Brandin V, Close ER: *The calculus of
dimensional distinctions: Elements of mathematical theory of intellect*, Moscow, 2003

16. Neppe, V.M., & Close, E.R.: Reality Begins With
Consciousness, BrainVoyage.com, 2016

17. Close ER, Neppe VM: The
Calculus of Distinctions: A workable mathematicologic model across dimensions
and consciousness.__ __*Dynamic
International Journal of Exceptional Creative Achievement *1210: 1210; 2387
-2397, 2012.

18. http://www.periodictable.com/Properties/A/HalfLife.html

20. Schwinger,
Julian: *The Theory of
Quantized Fields I*. *Physical
Review*. **82**.
p. 914, 1951

21. Singh, Simon: *Fermat's Enigma: The Epic Quest to Solve the World's Greatest
Mathematical Problem*, Fourth Estate, Ltd. 1997

23. Hugh G.
Gauch, *Scientific Method in
Practice, Cambridge University Press*, 2003
Occam’s razor

24. Close, ER and Neppe, VM Putting
Consciousness into the Equations of Mathematics: the third substance Gimmel and TRUE, IQNexus J 7:4;
7-‐119, 2015 v2 151221© ECAO

25. Trimble,
V. (1987). "Existence and nature of dark matter in the universe",
Annual Review of Astronomy and
Astrophysics* ***25**: 425–472.

26. Close
ER, Neppe VM: The TRUE unit: triadic rotational units of equivalence (TRUE) and
the third form of reality: gimmel; the conveyance equation (Part 12).__ __*IQNexus Journal* 7: 4; 55-65, 2015.

27. Breithaupt, J: *New Understanding Physics for Advanced Level*,
Chapter 4: Nelson Thornes, Rotational
Dynamics, p 54-65, 2000

28. Silk,
Joseph: *Horizons of Cosmology*.
Templeton Press. p. 208, 2009

29. Basdevant,
Jean-Louis; Rich, James; Spiro, Michael (2005). *Fundamentals in Nuclear Physics:
From Nuclear Structure to Cosmology*,
Chapter 4: 4.3.2, b decay of nuclei, p.202, Springer.

30. Close ER, Neppe VM: The eighth
conundrum: angular momentum and intrinsic electron spin. IQNexus Journal 7: 2; 44-45, 2015

31. Close ER, Neppe VM: The seventh
conundrum: the mathematical derivation of the Cabibbo mixing angle in fermions.
IQNexus Journal 7: 2; 41-43, 2015