Saturday, February 18, 2017


The TRUE Quantum Unit and the Third Form
By Edward R. Close

In this paper, focusing on the four most basic elementary particles: photons, electrons, up-quarks and down-quarks, a system of mathematical logic operating on quantum mass-energy-volumetric equivalence units is introduced. The Triadic Rotational Unit of Equivalence (TRUE, or True unit, for short) quantum equivalence unit is derived from the basic principles of quantum mechanics, relativity and particle-wave complementarity. 

The calculus of Newton and Leibniz is shown to be inappropriate for application to quantum phenomena. Introduction of quantum equivalence units enables us to revise the calculus of Newton and Leibniz and produce a calculus that is more appropriate for application to the phenomena of relativistic quantum reality.

Applying this new calculus to elementary particles and combinations of elementary particles, we obtain a clearer understanding of sub-atomic and atomic structure, and of the interchange of mass, energy and a third form of reality that we call “gimmel”. 

Gimmel is not directly measurable as mass or energy, but is necessary for atomic stability. The discovery of this third form of reality opens the door to a deeper understanding of the nature of reality. The use of the quantized system of mathematical logic clears up some of the “quantum weirdness”, yields new information about the multi-dimensional nature of reality, and makes the scientific description and analysis of quantum phenomena much more comprehensible. Some experimental data and observations that have puzzled scientists for decades, and that are inexplicable within the standard model of the current paradigm, are explained.

The Calculus of Distinctions, operating with Gimmel and Triadic Rotational Units of Equivalence (TRUE units) provides the missing link between consciousness and physical reality.

Scroll down to the Saturday, Feb. 11 for a brief summary of the paper.

If you want to review the paper, private message me on Facebook or email: 

Friday, February 17, 2017


We find ourselves at a point in time where most of us, like Alice, are looking from our familiar world, through a mirror into a strange and disturbing world. But things have changed since Alice’s time: roughly half of the people are on opposite sides of the mirror, and most of those on each side blame the people on the other side for everything that has gone wrong, and the looking glass has become a wall, no longer a door into a magical kingdom. Both sides believe there is something horribly wrong, but neither can, or is willing to step through the glass into the others’ world. It doesn’t take a rocket scientist to realize that this is a very dangerous situation.

A very wise man once said: if you find that the world is wrong, you must change yourself. That’s hard to do, but it’s easier and more productive than trying to change those of opposite persuasion.

Pogo, a once popular cartoon character, created by man named Walt Kelly, (some of us are old enough to remember) said: “We has met the enemy, and they is us!
If the world is in crises, it is we who are to blame. Humanity seems to have lost its moral compass. Love and compassion, the wellspring of inner peace, taught by the spiritual geniuses of the past was replaced as soon as the spiritual masters were gone by religious dogma designed to control the thinking of the masses… for their own good, of course! As education began to be made available to more people, dogmatic beliefs were replaced by science, as new discoveries proved dogmatic religious beliefs wrong, time after time.

So we thanked God for science! We thought reason would prevail. Scientists speak the universal language of mathematics and logic. They can discover what’s real, what’s true and what’s false, and work across national, religious, cultural, and ideological lines. If scientific discoveries can be used for positive and constructive purposes, knowledge can set us free from the tyrannies of dogma and political mind control. But sadly, that has not happened to the extent that it seemed it would.

It appears that the leaders of academia have fallen into the same trap that ensnared the religious leaders of the past: Overly impressed with their own understanding, they begin to believe that they, by virtue of their intellect and education, have the exclusive right to truth, and that it is their mission to enlighten the uneducated masses. So-called mainstream science is in great danger of becoming the new priesthood. We see evidence of this as many mainstream scientists declare that the universe, and especially the living beings inhabiting it, are nothing more than accidental consequences of a series of random events.

Mainstream science has thrown the baby of spiritual growth out with the proverbial bath water. By espousing personal beliefs rather than science, mainstream academia is in serious danger of devolving into another institutionalized suppression of the human spirit, indoctrinating rather than educating. Tenured professors tend to discourage thinking outside the box of “mainstream” thought. In all too many cases, materialistic indoctrination is confused with instruction, even in the sciences. We see evidence of this when we hear professors and their students saying things like: “I am a scientist, so of course I am an atheist!”

Atheism, if not a mental illness, is an extremely closed-minded belief, just as unscientific, if not more so, than a belief in fairies. Atheism, or even the belief that the universe could exist as it does with or without conscious beings, is simply not a scientific hypothesis. It cannot be tested. No one can observe a universe without consciousness. A real scientist cannot say “I am an atheist". A real scientist can say “I am an agnostic” because a real scientist should be skeptical. An intellectual person who has never had a spiritual experience, or has chosen to ignore anything that can’t be explained by materialism, can justify being agnostic, but there is no logical argument that infers real legitimacy on atheism.

When a whole class of intellectuals largely profess atheism, and unwisely voice their opinions that the universe and life are meaningless accidents, they do a serious disservice to humanity. When such opinions trickle down to the general population, hedonism and violence are just some of the unintended results. If you have a materialistic belief system to start with, no one should be at all surprised when your model finds no purpose or meaning to consciousness, life and the universe.

You can, of course, believe whatever you want to believe. But that does not make it true,--in any universe. At some point, your belief system must be tested against reality, just like theoretical physics, otherwise, you will miss an opportunity to grow intellectually, and more importantly, spiritually. Is the world in crisis? Being in crisis is not necessarily a bad thing. It means that the conditions are right for intellectual and spiritual growth.

Contrary to what mainstream science is telling you, the universe was created, and continues to be created for the sole purpose of manifesting the infinitely conscious substrate that underlies physical reality. That pervasive Primary Consciousness is forever flowing into the physical universe to promote organic sentient life moving toward conscious spiritual awakening. Every electron, quark and atom is pre-programmed in Primary Consciousness to support organic life that is capable of becoming self-aware. The pathway from Primary Consciousness to the individualized consciousness that is you and me, is elucidated through the mathematical logic of Multi-Dimensional Extrapolation, the Calculus of Distinctions, and the Diophantine Conveyance Equations. And it is for the purpose of spiritual evolution.

This view of reality is articulated in the work of Neppe and Close, the Unified Monism of the Triadic Rotational Vortical Paradigm (TDVP). But, is it just another multi-dimensional theory like string theory, that can’t be proved or disproved? No. What is unique about TDVP is that it is not just another philosophical or scientific theory. Its validity has been mathematically proved and verified by a number of theoretical mathematical predictions that are in exact agreement with real-world empirical data.

The importance of the following two points cannot be over emphasized: 

(1.) Proof of TDVP depends on mathematical theorems, not theory, and (2.) TDVP provides quantified predictions that are validated by real world data.

For those who might not know the difference between a theory and a theorem, let me explain again how very different they are: A theory is a hypothesis that has not been proved, or is only partially proved. A theorem, on the other hand, has been proved. So, while the two terms sound similar, the meanings are almost exactly opposite. The power of a mathematical theorem lies in the fact that once it has been proved, it is true in all circumstances, in all possible universes. It is globally and universally true.

Two theorems are critical in the proof of the TDVP paradigm: The Pythagorean Theorem and Fermat’s Last Theorem. The Pythagorean Theorem is a central part of Dimensional Extrapolation, and Fermat’s Last Theorem is applied in the Calculus of Distinctions to prove the existence of a third form of reality, beyond mass and energy. These theorems are reflections of the logical nature of reality, which is a reflection of Primary Consciousness. And gimmel, the third form of reality, proved to exist by the mathematics of the TDVP paradigm, is the door between science and spirituality. the way through the looking glass.

Tuesday, February 14, 2017


Did you know that the author of Alice in Wonderland and Through the Looking Glass was a mathematician? Lewis Carrol was a pen name for Charles L. Dodgson, a lecturer in mathematics, at Christ Church, England.

Remember Alice in Through the Looking Glass? When Alice states that she is seven and one-half years old, the White Queen says she is a hundred and one, five months and a day.

“I can’t believe that!” said Alice.

“Can’t you?” the queen said in a pitying tone, “Try again; draw a long breath and shut your eyes.”
            Alice laughed. "There's no use trying," she said: "one can't believe impossible things."

"I daresay you haven't had much practice," said the Queen. "When I was your age, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast."

Are there impossible things? How about impossible questions? Mathematician Kurt Gӧdel proved that within any logical system there are logical questions that cannot be answered.

Are the following impossible questions?

Who would you be, if your mother had never met your father?
Would you exist- - at all?
What if one of your eight great-grandparents took a wrong turn and never met any of your other great-grandparents, who would you be?
How many seemingly minor, unimportant events are there in the history of your ancestry that, if changed in any way, would radically change the DNA of the person you are today?

When I was about six or seven, a terrible, horrible thing happened in my mother’s family. In the heat of a domestic argument, my mother’s oldest sister’s husband rushed out of the house in a rage, jumped into his truck and backed over their toddler son who was playing in the driveway. He was killed instantly. The marriage was destroyed, and the lives of my aunt, and three young female cousins were negatively impacted and changed forever. But what about that poor little boy? For days I had vivid images of his fear and pain as the wheels of that truck crushed the life out of him. What happened to him after that? For the rest of my life, I’ve emphasized with the pain and suffering of all living beings.

Several life-changing events happened to me around the age of 12 to 14. Perhaps most importantly, I discovered that I had a gift for mathematics, found Albert Einstein’s wonderful work, and had a stunning experience of consciousness expansion. I also gave up hunting, even though I lived in a remote part of the country where hunting and fishing were dominant interests of most boys my age. I loved being in the woods with my dog, Rover, a smart little border collie. We would stalk deer, wild turkey and occasionally an owl or an eagle. I carried a rifle, but rarely shot at anything living. 

One day I did shoot a squirrel. My uncles and cousins hunted, killed and ate rabbits, squirrels, quail, and deer on a regular basis. The squirrel fell from the top of a large white oak, hitting the ground with a thud. As I approached the little animal, he regained consciousness and struggled to climb back up the trunk of the tree. But he was mortally wounded. He clung to the bark of the tree momentarily, within my reach, and then fell back to the ground. Just before he lost his grip, he uttered a terrible cry that pierced my heart. For a moment that seemed like an eternity, I felt his pain, fear and terror as acutely as if it were my own. I knew, beyond any doubt in that moment, that he was a vital, living being, with a warm beating heart and a quick brain. He was enjoying the prime of his life, and I had ended it. I had cut short all his earthly desires, all his future, and his future progeny. And I could not reverse it. He was gone; and with him, any desire I might have had to hunt for pleasure melted away like frost in the bright morning sun. I never carried a rifle in the woods again.

My empathy with living things has never faded. If anything, it has intensified. One consequence of this is that wild animals do not fear me. Even venomous insects do not attack me. I taught a high school algebra class for most of an hour once with a red wasp sitting on top of my head. I think that class paid more attention that hour than any class I’ve taught before or since! Domestic animals treat me like a long-lost friend. I love every cat and dog, every tree frog, ant and blade of grass.

So here is an ‘impossible’ question: Does consciousness exist outside the physical brain? It’s not answerable within most logical systems of scientific thought prevalent today. If you haven't experienced it, any answer you may have is nothing more than a hypothesis. Once you’ve experienced it, you operate in a different logical system, and within that system, the answer is clear.

Saturday, February 11, 2017


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

The TRUE Quantum Unit and the Third Form of Reality
© Edward R. Close 2/11/17

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

E = mc2 applied to the electron
Matter/energy Equivalence and the Masses of the Elementary Particles


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. 
 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.

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 (X1)m + (X2)m = Zm  has no integer solutions when m > 2, while (X1)3 + (X2)3 + (X3)3 = Z3 does have solutions. This is why elementary particles like quarks cannot combine in pairs, but do combine in triples.

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.

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.

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.

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.

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,  1905.
3. Broglie, L: Recherches sur la théorie des quanta (Researches on the quantum theory), Thesis, Paris,   1924, Ann. de Physique (10) 3, 22
4. Baron, Margaret E: The Origins of the Infinitesimal Calculus, Courier Corporation, 1969 
5. Einstein A: Relativity, the special and the general theory 15 Edition. New York: Crown Publishers,       1952.
6. Minkowski, Hermann: "Raum und Zeit", 80. Versammlung Deutscher Naturforscher (Köln,             1908). Physikalische Zeitschrift 10 104-111 (1909) and Jahresbericht der Deutschen             Mathematiker-Vereinigung 18 75-88 (1909). For an English translation, see Lorentz et al. (1952)
7. Planck, M: Max Planck:  Scientific Autobiography and Other Papers. New York: Harper 1949.
8. Einstein, A: Note to the Fifteenth Edition, Relativity, the special and the general theory 15 Edition .            New York: Crown Publishers, p. vi, 1952.
9. Einstein, A: "Zur Elektrodynamik bewegter Körper" , Annalen der Physik, 322 (10): 891–921, 1905
10. Fetter, A.L. &  Walecka, D.J: Theoretical Mechanics of Particles and Continua, Courier             Corporation, Dec 16, 2003
11. Cotton, A.F., and Wilkinson, G.: Advance Inorganic Chemistry (5th ed., John Wiley 1988)             p.1381 ISBN 0-471-84997-9
12. Brown, G. S.: Laws of Form, New York: Julian Press, 1977
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,, 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.
19., “Proton lifetime is longer than 1034 years", 25 November 2009
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
22. Cho, Adrian (April 2010). "Mass of the Common Quark Finally Nailed Down". Science Magazine April 2012
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

Saturday, January 14, 2017


This is the abstract for a paper I'm preparing for a mathematical physics journal. Obviously it is a technical and mathematical paper, but I plan to post it here after it has been published. 

By Edward R. Close, PhD, DSPE
Arguably the most important scientific discovery in modern times is the revelation that we exist in a quantized reality governed by the laws of general relativity. By far the most successful mathematical procedure used by scientists to analyze physical reality is the calculus of Newton and Leibniz. But, mainly because of its successes, the fact that Newtonian calculus is mathematically inappropriate for application to the quantum phenomena revealed by Planck and Einstein discoveries has been largely overlooked. It is the theme of this paper that this oversight causes much of the co-called “quantum weirdness” that physicists often talk about, and that the proper analysis of a quantized reality requires an appropriately quantized system of mathematical logic.

In this paper, focusing on the four most basic elementary particles: photons, electrons, up-quarks and down-quarks, a system of mathematical logic operating on quantum mass-energy-volumetric equivalence units is introduced. The Triadic Rotational Unit of Equivalence (TRUE) quantum equivalence unit is derived from the basic principles of quantum mechanics, relativity and particle-wave complementarity. Introduction of quantum equivalence units enables us to revise the calculus of Newton and Leibniz to produce a calculus that is more appropriate for application to the phenomena of relativistic quantum reality.

Applying this new calculus to elementary particles and combinations of elementary particles, we obtain a clearer understanding of the sub-atomic, atomic and molecular structure of reality. The use of this system of quantized mathematical logic clears up much of the “quantum weirdness”, yields new information about the multi-dimensional nature of reality, and makes the scientific description and analysis of quantum phenomena much more comprehensible and complete. As a result, experimental data that seemed irrelevant become meaningful, and some observations that are inexplicable in the current paradigm, are explained.

Monday, January 2, 2017



It is my hope that each and every one, who has the desire to know the truth and become everything that human beings are meant to be, is blessed with the greatest success possible in the New Year. My earnest prayer for Humankind is that 2017 is the year that, as beings of infinite potential, we experience a mass awakening from the destructive delusion of materialism, the blinding, unsustainable belief system that has dominated mainstream science for far too long. Today we stand on the threshold of the doorway to a new era of enlightenment made possible by the discovery of a third form of reality. The existence of this third form proves that reality is much more than matter and energy interacting in space and time. This discovery is easy to understand, and its proof is based on real data and mathematics reproducible by anyone who cares to try.

The mistaken idea that human consciousness is an accident emerging from random physical processes is a pernicious intellectual distraction from the real purpose and goal of existence, which is spiritual growth, enlightenment, and eventually Cosmic Consciousness. The simplistic lie of materialism, that there is nothing beyond matter and energy, is the root cause of the frightening spiral of modern society into despair and violence. The tyrannies of religious dogmas have been replaced by the tyranny of scientific materialism, specifically enforced by public education, commercialism and government. But both tyrannies are based on the same lie: the lie that you must believe what you are told, and behave as those in power dictate.  This lie has at last run its course. Even though strongly supported by the mainstream media and academia, the falsehood of materialism will melt away and the truth will shine through: We are spiritual beings temporarily inhabiting material bodies.

Thursday, December 22, 2016


©Edward R. Close, December 22, 2016

A very important fundament fact of nature was uncovered in the year 1900 when German physicist Max Planck discovered that nature metes out energy only in whole numbers of an extremely small amount called a quantum of energy. Within a few years, scientists realized that as a rule, all aspects of physical reality are quantized, and quantum physics was born.

Albert Einstein noted that mass is converted to energy by certain physical processes and energy is converted to mass by other processes. In 1905, Einstein showed that the exact mathematical equivalence of mass and energy is expressed by the equation E = mc2. In other words, he discovered that mass and energy are two different forms of the same thing.

In a paper entitled Does the inertia of a body depend on its energy content?Einstein concluded:

“It follows directly that: If a body gives off the energy L in the form of radiation, its mass diminishes by L/c². The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that the mass of a body is a measure of its energy-content.”

In addition, based on the discoveries of general relativity, Einstein declared that there is no such thing as empty space or eventless time. The space-time continuum has meaning only in relation to mass and energy, which are quantized. In Appendix V of the 15th Edition of his popular book on Relativity, Einstein says:
“It is characteristic of Newtonian physics that it has to ascribe independent and real existence to space and time as well as to matter, for in Newton’s law of motion the idea of acceleration appears. But in this theory, acceleration can only denote ‘acceleration with respect to space’. Newton’s space must thus be thought of as “at rest’, or at least as “unaccelerated”, in order that one can consider the acceleration, which appears in the law of motion, as being a magnitude with any meaning. Much the same holds with time, which of course likewise enters into the concept of acceleration. Newton himself and his most critical contemporaries felt it to be disturbing that one had to ascribe physical reality to space itself as well as to its state of motion; but there was at that time no other alternative, if one wished to ascribe to mechanics a clear meaning.
Further on in Appendix V, after discussing several historical theoretical concepts of space, Einstein makes the following startling statement concerning “… how far the transition to the general theory of relativity modifies the concept of space”:
There is no such thing as an empty space, i.e. a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field.
The idea that space and time do not exist without the presence of the mass and energy of physical objects is counter-intuitive for us because the everyday picture provided by the neurological processing of pulses of energy entering our consciousness through the functioning of our physical senses seduces us into thinking of space and time, or space-time, as a changeless background within which matter and energy interact to form objects and events. But we now know that this is not true. The illusion of space-time is created by the extension of the substance of physical objects in the form of gravitational and magnetic fields. There is no space-time to be distorted, it is the instruments of measurement (Einstein’s clocks and rods of his thought experiment) that are distorted by motion, not space-time as often depicted by popular presentations by leading mainstream physicists. A simple example will help clarify this point:
A steel ball, rolling across a table in a magnetic field created by the presence of a strong magnet placed under the table, will follow the curvature of the lines of force of the magnetic field. A non-metallic ball, however, unaffected by the magnetic field, will roll straight across the table. With this simple experiment we can see that the idea that the space above the table is warped by the magnet’s field is false. This, of course, is what you would expect if there is no such thing as empty space. In Einstein’s reasoning quoted above, this understanding is extended to space-time.
This shift in our understanding of space and time, made necessary by general relativity, (which, by the way, has been proved correct and accurate by very many, extremely detailed experiments and tests) tells us that there is no space-time independent of mass-and-energy objects and events, which are quantized. This means that the division of space and time, or space-time, into smaller increments than those occupied by a quantum of mass or energy, while theoretically conceivable, has no basis in reality. Thus for any valid mathematical analysis, space-time must be considered as quantized as is mass and energy, and it should not come as a  surprise that ignoring this requirement has resulted in erroneous conclusions about quantum reality and contributed to the perceived “weirdness” of quantum physics.
Newtonian Calculus and Quantum Mathematics
The calculus of Newton and Leibniz, known simply as “the calculus” for more than 300 years, is based on the assumption that the variables measuring objects and events may be divided indefinitely into smaller and smaller “infinitesimal” increments, approaching zero as closely as we please. However, in the real, quantized world of the physical universe, this cannot be done. As pointed out above, Planck’s discovery that energy is quantized, Einstein’s demonstration of the equivalence of mass and energy, and the conclusion that space-time has no independent existence, tells us, in no uncertain terms, that the division of the variables of space-time and mass-energy in the real world cannot approach zero infinitely closely. Therefore, the calculus of Newton and Leibniz, based on the assumption that this can be done, is inappropriate for application to quantum phenomena.
A new calculus, appropriate for application to quantum phenomena, is needed, and the Calculus of Distinctions is that calculus. I am currently working on two rigorously mathematical technical papers for submittal to mathematical physics journals proving this.

1. Planck, Max (1899) “Über irreversible Strahlungsvorgänge. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin. 5: 440–480. pp. 478–80

2. Einstein, Albert (1905) “Does the inertia of a body depend on its energy content?”  Annalen der Physik, 17, 1905. Reprinted in The Principle of Relativity, Dover Pub.

3. Einstein, Albert (1962) “Relativity, the special and general theory, a clear explanation that anyone can understand”, Appendix V, pp. 135, 154 and 155, Crown Publishers, New York