mathematical relationships of the atom.

It will be necessary to refer to the drawing of System 3 on the website. System 3 consists of a Space Frame

that illustrates one particular atom and a Quantum Frame that illustrates the same atom as a quantized bundle

of equivalent energy. All particular atoms synchronously appear and disappear with oscillations back and forth

between Space Frames and Quantum Frames. This defines a discontinuous universe. Since the Quantum

Frames are timeless the Space Frames close ranks to present the appearance of continuity to space and

time, called the integrated fabric of space-time.

The Quantum Frames are spatially indeterminate and collectively they constitute a timeless field of energy

quanta called the Void. The Void is also referred to as the Quantum Sensorium. It is orthogonal to space-time

and being timeless it spans and integrates history.

It is possible to intuitively perceive that the quantum frame is the inverse of the space frame in the sense that it

is orthogonal to the integrated fabric of space-time. In that special sense it does not exist in space-time even

though it is real and has real effects. It represents a periodic discontinuity in the integrated fabric of space-

time, the period being associated with a primary interval of time. This discontinuity is related to Planck’s

universal quantum of action, designated as h.

a Particular Term, the latter being representative of many of its kind. Each Term is made up of a Set of three

Centers, the Universal and Particular Sets being self-similar in character.

A Center as it relates to an atom is defined as an active interface between a common inside in light and a

common outside in darkness. Light and darkness are used in this context since they are observable

phenomena that exemplify the active and passive aspects of the creative process. Light refers to all

electromagnetic energy and its derivatives, such as virtual images that occur in the higher Systems. Because

active interfaces exhibit an active common center in light they are called Centers to simplify descriptive

language.

An active interface is not a static boundary between designated entities since the word entity itself implies a

boundary that defines it in some way. The active interface IS the entity. What we observe in phenomenal

experience is active processes across active interfaces between a common inside and a common outside. The

active energy processes occur in efflux from inside to outside. The common inside and outside are shared by

all phenomena. This is a primary condition for there to be such a thing as Universal Wholeness that can

provide for coherent meaning of diverse phenomena. The nature of the common inside and outside becomes

progressively elaborated upon by the higher Systems.

Centers can actively relate to one another in a variety of ways through the efflux and reflux of light energy as

illustrated in the diagrams and as described below. The System explores and meaningfully integrates all

possible ways that Centers can relate to one another with respect to a common inside and outside. In System

3 there are four possible ways that three Centers can relate to one another, each way being called a Term.

They interact in pairs to define the Space Frame alternating with the Quantum Frame.

The System is therefore inherently all embracing. It does not make a priori assumptions about the nature of

space and time, the characteristics of which emerge with the synchronous projection of atoms in the

explanations that follow.

It is in the nature of the System that it must find confirmation in phenomenal experience of some kind. In a

scientific context empirical evidence is essential to intuitively understanding it, and vice versa. This is implicit in

the methodology of the System. The System is not a logical construction erected as a superstructure on

axiomatic principles and yet it is logically self-consistent. Not only can it find confirmation in the public domain

but also in personal experience that can transcend reason and the discursive intellect.

respectively in a single primary atom of hydrogen. The relationship between the three Particular Centers of

each Particular Set is intimate in a cosmic sense, since it is prescribed by a single archetypal Universal Set

common to all hydrogen atoms. The Universal Set cannot exist separately in the integrated fabric of space-

time. It is confined within the three Particular Centers of each atom, similar to quarks, intimately linking the

Particular Centers up in pairs. Because the Universal Set is self-similar to all Particular Sets all atoms of

hydrogen are identical. The identity of each is defined by its relationship to the common archetypal energy

pattern. All atoms are indistinguishable energy quanta in the unified field of the Void, and they are separate

physical things that define material existence in the integrated fabric of space-time.

Each hydrogen atom thus exists as an intimately bound unit that is spatially distinct and separate from other

identical atoms on the space frame side of the diagram. On this side of the System 3 diagram one hydrogen

atom is separate from but identical in character to every other. Since our ordinary spatial perceptions are

confined to this side of the diagram we can equate one hydrogen atom to another in the traditional Aristotelian

way, that is, A=A.

In a more comprehensive sense Centers 1, 2 and 3 can be associated with Idea, Routine and Form

respectively. These three words take on the broadest possible meaning in a general context and they become

focused differently according to the circumstances in which they are applied. Nevertheless, there is a common

significance to the words that prevails across a broad spectrum of circumstance.

For example an Idea entertained in the human mind gives direction to Routines of muscular action that result

in a specific Form consistent with the Idea. One may have an Idea to draw a picture using a pencil and paper.

The Routines that one employs result in a Form to the picture that is consistent with the Idea. We expend

energy (derived from the sun) in drawing the picture (which will be called efflux designating an outflow of

energy originating from the Idea) and that energy becomes invested through our Routines in the Form of the

picture. We also get visual feedback (called reflux designating an inflow of light energy back from the picture

on the page). The reflux recreates the Idea in the “inner space” of our minds in a way that is self-consistent

with the Idea originally conceived. All conscious human activity conforms to this archetypal pattern, in which

there is a unique universal set of Centers 1, 2 & 3 that intimately binds the three particular Centers into a

common result. If we draw two pictures the same we can equate one to the other and say A=A.

We are each like human atoms, mutually distinct and different, yet also the same, since we each

independently relate to our common humanity. The biological organization of all living creatures conforms to

the same pattern (A general description of how it works in biology is given in Fisherman’s Guide.). In this

context we can equate one ape or one elephant to another ape or elephant. All particular creatures of a

species are identified by their common relationship to the universality of their species. That is how we identify

a particular human or individual animal. Nothing that exists in space-time is unique unless it is the last living

member of a dying species. Implicit in the identity A=A is a fundamental ontological relationship between the

universal and particular aspects of all being. This is prescribed as a fundamental relativity principle by System

2 which transcends and subsumes System 3. (The relationship of universals and particulars has been a

philosophical issue throughout the history of human thought.)

respectively and that they also correspond in universal ways to Idea, Routine, and Form. In what follows it will

prove advantageous to think of a primary atom of hydrogen in this way. The hydrogen atom will be considered

as primary to the physical creation.

Electrons and protons can be independently identified when they become removed from the “inner space” in

which they are intimately bound together within the atom. They derive from the atom, not vice versa.

Theoretically there are an infinite number of energy levels or orbits that the electron can occupy in relation to

the proton inside the atom. Each higher energy level diminishes quickly in relative magnitude approaching

zero at infinity. Since the energy level in the first orbit is -13.6 electron volts, this amount of photonic energy

absorbed by the atom becomes the energy of ionization beyond which the electron and proton become free

from their mutually bound state within the atom. They escape the inner space of the atom and become free to

move independently in the external space between atoms.

The energy of ionization is the amount of photonic energy that defines the maximum “inner space” of the

atom. The spatial projection of a whole atom is quantized in each Primary Interval of Time defined by the

successive recurrence of each space frame. When electron and proton exist independently beyond this limit,

they remain linked by photonic energy. They are still intimately coalesced as photonic energy that is integral

with the photonic energy interface C1 of the Universal Set within each Quantum Frame. (System 3) This

means that the Universal Set now has to span one or more primary intervals of time to link up electron and

proton. In this way light, expressed as the energy of ionization, defines the inner spherical space of the atom.

Light also defines the outer linear space that interconnects all physical matter in the integrated fabric of

space-time. Where there is no light there is no space. There is a black hole.

Linear electromagnetic waves are generated by electron quantum jumps in successive space frames from

excited orbits within the inner space of the atom back to lower energy orbits. No particulate motion is allowed

within one Space Frame so the jump occurs from one space frame to a succeeding frame. The energy emitted

lights up and interconnects the external universe by defining external space that is generally flat, but with

curvatures conditioned by high relative motions and concentrations of high density matter.

High relative motions introduce relative space frame skipping accounting for relativistic effects between

different inertial systems. High density matter consists of fused atoms that concentrate space by occupying

less space than un-fused atoms. One atom of helium defines less than half the space of two atoms of

hydrogen. Atoms thus have an independent relationship to the light that defines space. That is why the speed

of light is universal. Relative patterns of angular motion together with the related fusion of atoms have the

effect of introducing relativistic curvatures in the integrated fabric of space-time.

Electromagnetic fields are generated by the photonic energy that must span a succession of space frames to

link free electrons to their proton partners, since they are beyond the reach of light in a single frame that

defines a primary interval of time. Nevertheless the electron, proton and photon remain intimately bound in the

timeless quantum frame that spans and integrates history. The linking by the universal set is stretched out as

a polarization on the space frame side and can reach to the ends of space and time. In so doing it creates the

electromagnetic field.

diagram). The three particular centers, which we can designate P1, P2, P3, are spatially closed and are thus

identifiable by experiment in the right circumstances as separate three dimensional things with independent

but mutually related qualities. Within the atom each has a separate but intimate relationship with the other two,

since they are linked up in pairs by the single but open set of universal centers, which we can designate as

U1, U2, U3. Open Centers are archetypal and do not exist as separate entities in space-time. They are

confined within closed Particular Centers which have separate spatial identities in space-time. (Closed

particular Centers always occur as an intimately bound triad and this can happen in a variety of ways in the

higher Systems that relate to living biological systems.)

The universal set is an archetypal energy pattern that is common to all hydrogen atoms (similar to a

genotype). These open centers transcend the limitations of the integrated fabric of space-time since they

influence its very nature without existing as separate space-time entities. Although they transcend space-time

in this sense, they can also have explicit space-time influences. For example they account for quantum

correlation and electromagnetic fields.

If we look closely at the space frame side of the System 3 diagram we see that P1, P2, P3 are separate and

distinct, while U1, U2, U3 are not. U1 is inside U2 and it represents a common center within each of P1, P2,

P3. U1 relates out through U2 from within each of P1, P2, and P3, and in doing so defines a subjective aspect

residing within each Particular Center. At the same time U3 is perceptually transposed (facing in the opposite

direction) with respect to U1 and U2 and it is also confined within each of P1, P2, P3. But it relates back in the

opposite countercurrent direction across the “inner space” within the atom between P1, P2, P3. In this way it

defines an objective external aspect to each closed Particular Center even while it binds them intimately

together in the inner space of the atom. Together this intimate relationship constitutes a single spatially distinct

atom that acts like an indivisible particle of matter.

The countercurrent relationships defined by U1, U2, and U3 between P1, P2, P3 involves a transfer of

electromagnetic energy in efflux and reflux. (It is convenient to use these common dictionary words as general

indicators of all processes that are structurally similar but with differences in character when it comes to

biological systems.) Energy flows from U1 through U2 to leave each particular center (efflux) only to enter U3

in the adjacent particular center across the inner spaces between P1, P2, P3. There is reflux back in the

countercurrent direction between each pair of particular centers. These countercurrent relationships must

follow pair by pair in the same direction, since no particular center can have two universal centers within it. The

universal set is unique. The way the space frame side of the System 3 diagram is drawn this linking up is

shown in a counterclockwise direction in relation to efflux.

The subjective to objective identities of the Universal Term in the Space Frame defines each Particular Center

as spatially distinct with a closed energy interface. The electron, proton and photon thus assume separate

physical identities by being intimately linked up in pairs by the Universal Term. These three mutually

reinforcing identities in pairs is called a Triadic Identity.

Spatially distinct and therefore closed Centers only occur as Triadic Identities. No other combination of

Centers than three can produce spatially distinct material things that we can be identified in space-time. The

higher systems delineate more elaborate ways that this can work in living organisms, however.

between U1 and U3 across U2, since U2 is an active interface between them that objectively faces U3 outside

it and has U1 within it. Another look at the diagram will show that the objective relationship between U2 and

U3 coincides with the same objective relationship between the electron P2 and the proton P3, but not between

P1 and P2, or between P3 and P1. U2 is aligned with P2 and U3 with P3 only across the inner space between

electron and proton. This indicates that the subjective to objective energy imbalance imposed by the

Universal Set across U2 and thus between electron P2 and proton P3 is directly associated with the electronic

charge between the electron and the proton as mediated by photonic energy.

The attraction between electron and proton does not result in electromagnetic radiation within the inner space

of the atom because no particulate motion takes place within a single space frame. All relative motion can only

occur between space frames as sudden jumps in position. The electron can not lose energy and fall into the

proton.

The System 3 diagram also indicates that the photon Center P1, with U1 inside it, is uniquely defined as

having a universal center consistent with itself. Although the electron P2 and proton P3 also have U1 within

them they have reciprocal relationships to the particular photon P1 with which they are intimately bound. As

pointed out above, the particular and universal Centers 1, 2 and 3 also represent Idea, Routine and Form in a

more comprehensive sense that applies to biological organization and human behavior, as well as to atomic

structure.

So we can see that within one atom, the photon P1, with U1 inside it, relates in efflux to the electron P2

through the universal Routine interface U2 of P1. At the same time the universal Form interface U3 within the

electron P2 relates back in reflux to the photon P1. In this way it is photonic energy that determines the Form

of electronic Routines that predominate within the atom. Photon energy becomes invested in the orbital

mechanics of the electron from space frame to space frame. In doing so the electron must relate to the “inner

space” of the atom defined by photonic energy.

We know of course that the spectral lines of hydrogen are directly related to the allowable orbits of the

electron and their energy levels, but now we can begin to see an ontological reason for it that can further

clarify why. There must be a whole number of quantum jumps in electron position around each orbit that

encloses the inner space of the atom as defined by the photon. There is no such thing as half a jump. The

quantum jumps in position thus correspond to the de Broglie wave length of the electron in each orbit. The

wave motion of the electron is the jumps back and forth between frames.

the electron also has universal photonic energy U1 within it. This photonic content of the electron must be

associated with its mass and it relates in efflux through its Routines toward the Form of the proton P3. So its

successive quantum jumps in position must orbit the recurrent position of the proton from space frame to

space frame. The latter must remain essentially at the center of the inner space defined by photonic energy in

each space frame. The Proton in turn relates in efflux to the Photon to establish this. As a result its mass is

much greater than that of the electron, 1836 times greater according to empirical measurements.

The electron P2 is also the closed Routine interface of the particular set, the proton being the closed Form

interface of the particular set. This indicates that the Routines within the atom are focused predominantly in

the electron while the mass is focused predominantly in the Form of the proton. The illustration of the space

frame side of System 3 does not provide a physical picture of the atom directly but it does indicate how the

atom must be organized as an ontological unit since System 3 exhausts all possible relationships between

three centers as an elaboration of System 2 consistent with experience and the empirical evidence.

We can also see that the proton, P3 with U1 inside it, relates in efflux through the universal Routine interface

U2 within it to the universal Form interface U3 of the photon P1. The photon relates back to the proton in reflux

through its universal Form interface U3. In this way the Form of the photon interface P1 is specified as a

closed energy shell with respect to the Routine interface of the proton. The proton is at its center, consistent

with the way electron orbital Routines relate to the proton.

The photon P1 which is uniquely defined by photonic energy U1 within it, consistent with itself, thus prescribes

the inner space of the atom and the orbital routines of the electron around the proton. The ontological

organization of this triadic identity is thus reinforced by the countercurrent relationships taken in pairs between

photon, electron and proton, consistent with the empirical evidence.

The inverse relationship of the photon to the electron as compared to the proton is also consistent with their

opposite charges. While the electron and proton are invested with mass the photon is uniquely defined by a

universal center the same as itself and displays no mass. In this respect photonic energy, in itself,

characteristically defines space, not mass. This is the Idea that becomes invested in the Form of the atom as a

unit of matter through these organizational Routines.

“down” quark confined within it. This begs a correspondence to the Universal Centers. U1 and U2 relate in

efflux (up) to the photon and U3 relates in reflux (down) back to the electron. (Although the electron has the

same universal centers within, it does not relate in efflux to the photon, but vice versa.)

The only other long lived particles known in the universe are the neutron and the neutrino. Descriptions of how

they may relate to the fusion and decay of heavier atoms are given in Science & Cosmic Order. All other

particles are highly transient homologues of System 3, and higher systems. There is no conclusive evidence,

and to my mind no convincing evidence, that they are in any way fundamental to the creation of the universe.

An origin to the universe is an inherent contradiction when space-time is defined by its material content.

It can be seen that the triadic identity is a complex of interacting processes that on the one hand define

photon, electron, and proton in the inner space of the atom and on the other hand define the whole atom as

an indivisible unit in the external space. External space is also defined in relation to the inner space of the

atom. Light comes to us as the efflux of electromagnetic energy from quantum jumps of excited electrons back

to lower orbits that define the active energy interface of individual atoms as indivisible particles of matter.

Since light can only travel a discrete distance in a primary interval of time, this defines space in relation to

each atom.

Moreover the triadic identity applies to biological processes and the synchronous integration of human activity.

While the language used to describe these other processes takes on different nuances of meaning according

to the particular circumstances it nevertheless retains a universal significance.

These characteristics of the triadic identity render it difficult to access with mathematical language although

some aspects of the identity allow mathematical expression, as in quantum chromodynamics. In my view

however an accurate and comprehensive mathematical generalization of the complete identity is not possible.

There are other flies in the ointment. The triadic identity described defines only the space frame side of

System 3, not the quantum side. System 3 also subsumes all higher systems and is itself subsumed by the

lower systems. Since the System itself defines the nature of space and time, and the meaning implicit in

language, mathematics cannot assume a more fundamental embrace sufficient to express it. Mathematical

identities derive from the System as an expression of the cosmic order, not vice versa.

The System can nevertheless give ontological significance to quantitative measurements and direction to

mathematical predictions in appropriate circumstances. In this way it can offer valuable direction to research

efforts that is not otherwise available at present. Later we will see how the mathematics that is most

fundamental to the structure of the atom fits the way the System works and how it can offer new avenues to

explore.

frames. Space frames consist of atoms, atomic particles, and electromagnetic fields all integrated into a

coherent and apparently seamless fabric of space-time by electromagnetic waves emitted from excited atoms,

primarily in suns. Light links everything up by defining the external space between particles of matter. It does

not travel through an a priori concept of space or a spacetime continuum as a thing in itself. Light defines

external space by its action relative to the primary projection of atoms and their inner space. Since its

transmission relates to the primary projection of each individual atom, the speed of light is universal with

respect to each atom irrespective of their relative motion with respect to one another. Electromagnetic

radiation is omnipresent in the universe except in black holes. Space itself is an intimate mix of light and

darkness. It appears as darkness except where light interacts with itself as particulate matter to generate

space frames in a holographic cosmic movie.

Between each integrated space frame in which all atoms are linked by light there is a timeless quantum frame

in which each physical atom becomes a packaged bundle of photonic energy that is spatially indeterminate.

Each photonic bundle is the formless energy equivalent of an atom. It is a potential atom, the Idea potential of

an atom if you like, and it can not be specifically identified. Because the quantum frames are timeless,

successive space frames close ranks to present the impression of spatial and temporal continuity to the

physical universe. Although the universe gives the appearance of being seamless there are synchronous

discontinuities in it that quantize the transmission of light and all particulate matter. Space and time are

themselves quantized so that we can not speak in this context of a spacetime continuum, only of the

integrated fabric of space-time. (The hyphen is used in the latter expression to distinguish it from the former.)

The wave-particle duality of quantum mechanics derives from the transformations back and forth between

space frames, (with a limited duration defined by the action of light), and timeless quantum frames. There is

no particulate motion within one space frame. There is only the electromagnetic activity that projects it.

Relative motion results from a series of quantum jumps in position through a succession of still frames. The

projection of space-time is thus analogous to a holographic cosmic movie.

The integrated spatially indeterminate field of quantum frames is referred to as the Void. It may also be called

the quantum sensorium since it operates like a master memory bank that can span space and time, and from

which successive space frames are recalled into Form through a recurrent Routine of transformation back and

forth from emptiness to form. The Void is a field of quantized energies that exists orthogonal to the integrated

fabric of space-time. In rare instances it can be experienced directly by humans. There are references to it in

all spiritual traditions especially in the East (not all of them are authentic). It can also be subject to

misinterpretation after the fact, because there is nothing specific in the pure “Being Experience” of the Void,

awe inspiring though it is. It embraces all in a state of formless being. We will focus however on the scientific

aspects as it relates to System 3.

diagram) several things happen to both the Particular and Universal Centers. The changes that occur in the

particular set P1, P2, P3 are generally the inverse of those that occur to the universal set U1, U2, U3. This is

understandable since the universal set is confined within all particular sets on the space frame side whereas it

is integral with all particular sets on the quantum frame side. In this integral sense all particular sets are

contained within the unique universal set in the quantum frame. The quantum frame is unity. This includes all

the atoms in the universe. Although we will be looking at just one atom, the pattern of transformation is

synchronously the same for all atoms in relation to the single universal set that spans the whole of space and

time. As we shall see later the universal set integrates history.

P3 are spatially closed and intimately bound by the universal set confined within them. In transforming to the

quantum frame the spatially closed photon center, P1, makes what is called a perceptual transposition. It turns

around or inverts with respect to P2 and P3. In the space frame P2 and P3 are outside P1, all three being

closed centers separate from one another within the atom. When P1 perceptually transposes it becomes an

open center that now contains P2 and P3 that also become open centers without spatial form. P2 and P3 still

face one another but close the inner space between them like a face to face union that is called coalescence.

They are married in an intimately bound state in mutual efflux through to the inside of one another that is

mutually shared as the inside of P1 that now relates in efflux to a universal outside.

The universal outside is not space. It is outer darkness. Outer darkness is indefinable except in its passive

relationship to the action of light in efflux through an active interface between them. In phenomenal experience

we see neither the universal inside nor the universal outside, but only active energy processes across an

active interface between them. (Note: Perceptual transpositions work in a variety of different ways in the higher

systems.)

In contrast with the quantum frame, the space frame of one atom relates P1, P2, P3 in efflux to one another

within the inner space that is implicitly defined for the atom by photonic energy. In their mutually bound state

they do not relate directly to the external space between atoms. There is no universal outside on the space

frame side. Space is defined by photonic energy as internal space distinct from external space.

In the quantum frame the efflux out through P1 derives from the coalescence of the combined efflux from P2

and P3 that close together face to face. Efflux from each relates directly to the inside of the other, such that

they share a common inside. Their mutual inside becomes the inside of the open photon interface P1 that now

relates in efflux to a universal outside. (The organization of this open particular set can be seen in the top part

of the System 3 diagram.) The atom thus becomes a coalesced unit of photonic energy. It becomes the

quantum energy equivalent of one whole atom. The inside and outside of all three particular centers is

simultaneously realized. It is a timeless relationship.

In other words the internal and external aspects of an atom become an eternal bundle of energy. The inside

and outside of things no longer exists in space or time. The origins or ends of space and time lose all

significance. Space and time as we experience them in the integrated fabric of space-time are suspended in

the Void. There is only a limitless timeless field of pure being that is spatially indeterminate. The pure

experience of the Void is truly awesome.

U2 and both are within each particular center in turn, relating in efflux to U3 within the adjacent particular

center such that it relates back in reflux. The universal centers thus relate in efflux from P1 to P2 to P3, in that

order, and in reflux back in reverse order. (If the order of efflux and reflux is reversed it results in degenerate

anti-matter as described in Science & Cosmic Order.) (see System 3)

U1 is inside U2 which faces U3 on the space frame side. The three universal centers are confined within the

particular centers of each atom. The open Idea interface U1 is subjective to the Routine interface U2 which

objectively faces the Form interface U3. The particular centers are linked up in this way across the inner space

of the atom. It is this universal relationship that defines a subject aspect relative to an objective aspect for

each particular center. Subjective and objective are not assumed as given axioms or a priori qualities.

Whereas the transformation of the particular set to the quantum mode involves the perceptual transposition of

the Idea (photon) interface P1, the transformation of the universal set involves the perceptual transposition of

the Form interface U3. The Form interface U3 that specifies a form to each of the particular centers in the

space frame turns around to contain U1 and U2 in the quantum mode. It turns outside in, so to speak, not

inside out. It contains all particular sets in the quantum frame whereas it was contained by them in the space

frame mode.

In the quantum frame efflux through the universal centers proceeds from U1 which is a universal center of

light, progressively out through Routine U2 and Form U3 to a universal outside in darkness. The three

universal centers assume their universal significance as Idea, Routine and Form, in that order. This is the

same order in which the particular centers P1, P2, P3 are linked up in the space frame. In the quantum frame

the universal set thus relates to each particular set in a symmetrically inverse manner to the way that it relates

to each particular set in the space frame.

Void itself is timeless. Efflux from the universal inside U1 proceeds through U2 thence through U3 to the

universal outside. We already know this. Ideas become translated into explicit Forms via Routines. When we

make anything the idea comes first. We can not say precisely what the idea consists of, or precisely where it

comes from. We wonder about something and the idea comes. It comes from the Void as an energy complex

that directs subsequent action, that is, the routine of making it. Then along comes the form of the finished

article as a result of exercising the routine. In this time-like sense the Idea of a drawing a picture comes first. It

gives direction to the Routines involved in the process of drawing. Those Routines give direction to the Form

of the finished drawing. The sequence is universal as it relates to the potential Idea. We know we will always

have to exercise a routine of some kind to achieve the form. In the special case of the physical universe the

universal set embraces all physical being.

The Void is the quantized energies of all atoms as formless bundles of photonic energy P1 coalesced with

P2=P3 inside. Collectively all the coalesced bundles of photonic energy associated with all the atoms of the

universe constitute U1. They

the universal inside of the universe as it relates to a universal outside.

So the time-like progression of the universal set in the quantum frame side of the System 3 diagram relates to

the progressive translation of the Idea center U1 that constitutes the pure being of the Void through a

universal Routine, into a universal Form. The universal Form is the integrated fabric of space-time on the

space frame side. It is the integrated Form of the whole universe. This integrated Form of the universe is

recalled from the formless Idea implicit in the Void (or the quantum sensorium) via the Routine of

transformation from the Void back to Form. Thus even the process of translation from the quantum frame

back to the space frame follows the pattern

to space-time.

Energy exchanges that involve relative accelerations occur via this Routine of transformation from the Void

back to Form. This is developed in S&CO and involves a relative increase in the skipping of atomic space

frames with respect to a frame of reference. Relative motions introduce synchronous distortions in the

integrated fabric of space-time in a variety of ways with a variety of physical effects. Some of these effects

relate to well known phenomena that otherwise have no convincing or generally accepted explanation.

The transformation back to the quantum frame occurs when light has exhausted its external transmission

capacity that defines external space with respect to the inner space of each atom within each integrated space

frame. There must be external spatial continuity or we would see it full of black holes. This external

transmission capacity is related to the inner space of each atom where a primary interval of time is defined.

(Keep in mind that each integrated space frame is a 3D still picture without particulate motion. Only

electromagnetic activity occurs in each frame. It is quantum jumps between successive frames that generate

relative motions.)

Although the space frames close ranks there is a discontinuity between them where the quantum frame

timelessly intrudes. Although space has every appearance of being continuous in three dimensions it is

everywhere full of irrational holes. In addition electromagnetic radiation that defines three dimensional space is

likewise discontinuous where quantum frames timelessly intrude. The electromagnetic spectrum is sliced

across its entire breadth once every primary interval of time. Even though the EM spectrum consists of a

continuous range of frequencies, the EM radiation is transmitted as a series of quantized pulses that we call

photonic energy, space frame by space frame.

Max Planck’s disturbing “act of desperation” quantitatively expressed this discontinuity with his universal

constant, the quantum of action h. The photonic energy of radiation E is equal to h times the frequency. The

higher the frequency the higher the electromagnetic photonic energy in each primary interval of time and each

primary interval of time is universally constant. A century ago it would have seemed ludicrous to suppose that

the whole universe might be discontinuous and synchronous, but that is what Planck’s constant directly

indicates. There was simply no self-consistent and credible ontological paradigm that could justify such a

supposition, so both relativity theory and quantum theory developed side by side on mutually contradictory

foundations.

Einstein proposed the special theory of relativity to resolve apparent contradictions that arise in Maxwell’s

equations between different moving frames of reference, and the measured universality of the speed of light

observed in the experiments of Michelson and Morley. He later devised the general theory to show that gravity

could be explained by curvatures introduced by concentrations of mass in a presumed spacetime continuum.

Even though Einstein made important contributions to the early beginnings of quantum mechanics, it was not

recognized that the discontinuity indicated by Planck’s constant is inconsistent with the presumption of an a

priori spacetime continuum. Einstein strongly objected to the direction that quantum mechanics later took, a

position he maintained until the end of his life. A quote in a letter to a friend the year before he died is

noteworthy:

on continuous structures. Then nothing remains of my entire castle in the sky, including the theory

of gravitation, but also nothing of the rest of modern physics.”

The de Broglie Equation:

quantum mechanics. In developing his insight of a particle as “a little clock in motion in phase with its wave,”

he employed the Lorentz transformations of special relativity. He explicitly equated the transformation formula

for the retardation of clocks in motion to the transformation formula for the frequency of a wave, also adding a

term to the latter for the displacement of the wave along the direction of travel. This led to the result that the

momentum “

Broglie equation

the energy of electromagnetic transmission and

Louis de Broglie said he was “greatly smitten” by the fact that the Lorentz transformation formula for a wave is

the inverse of that for a clock. In view of the above description of System 3 we can see an ontological reason

why one Lorentz formula is inverted relative to the other. The particle is transforming back and forth between

space and quantum frames, the latter being orthogonal to the former. In each space frame the inner space of

the atom is also distinct from external space. The cyclic transformation back and forth between atom and

energy quantum is associated with the internal frequency of the particle along with all the particles in the

universe, like synchronous clocks. Louis de Broglie began by defining an internal rest frequency of the particle

connected with energy as E =

The particle is moving with respect to an external stationary frame of reference, however, defined by

stationary atoms. System 3 tells us that all particulate motion only occurs as quantum jumps in position from

space frame to space frame, and all motion is relative. So de Broglie expressed the external variation in

wavelength of the moving particle as a ratio

wavelength) and used this in his expression for the change in external phase of the moving wave. This ratio

however assumes that the wavelength of the stationary particle is the same as the wavelength of the

stationary frame of reference. In his expression for the variation of the external phase of the wave de Broglie

thus included a term for the displacement of the wave along the X axis relative to the wavelength of the

stationary particle and observer. The overall expression included the Lorentz transformation for the change

in frequency of a wave moving with speed v relative to a stationary frame of reference, such as a measuring

apparatus.

For the variation of the interval of time

transformation formula for a clock in motion, which is the inverse of that for a wave in motion. He included no

term for an internal wavelength (which would lack meaning) focusing instead on the change in the internal

interval of time associated with the frequency of the particle as it moves in relation to a stationary external

frame of reference.

He then equated the variation in the external phase of the moving wave with the change in the internal phase

of the moving clock, and substituted

states that the relativistic momentum of the moving particle is equal to Planck’s constant

wavelength.

What wavelength? Is it the wavelength of the moving particle or the wavelength of the stationary observer? Or

does it matter, since the wavelength is relative to the relationship between a moving particle and observer? If

the particle is not in relative motion the particle would have no momentum and the equation could not be

derived.

There must be some ontological significance behind the equation since it is consistent with experiment and

has become a foundation stone of quantum mechanics. According to System 3 relative motions introduce

space frame skipping between particle and observer. They get out of synch with the primary projection of the

universe because light cannot fully bridge the quantum jumps in positions of the moving particle relative to the

observer. Little black holes tend to open in the trajectory of the moving particle so the observer’s space

frames tend to get swallowed in them at intervals relative to the particle. Relative to the observer the particle

appears to move in ever shorter quantum jumps the faster it goes, since more and more of the observer’s

space frames are being skipped relative to it. The faster it goes the more the primary intervals of observer’s

time that are skipped. So the observer’s time is compressed relative to the particle, while the relative space of

the moving particle is being contracted in the direction of travel with respect to the observer. There is a

corresponding accumulation of timeless quantum frames of the moving particle that do not actualize with

respect to the observer. They become an accumulation of energy associated with the moving particle that

results in an increase in its relativistic momentum. There is thus a clear ontological reason for why the de

Broglie equation works and de Broglie himself glimpsed something of it when he derived his equation. His

derivation is given in his own words (fifty years later), describing the ideas that led him, in Chapter IV of

Science & Cosmic Order. (In later developments de Broglie's "pilot wave" inspired David Bohm's Quantum

Potential associated with Schroedinger's wave equation.)

the particle for a space ship with people aboard who are able to observe the stationary observer arbitrarily

situated on a platform in space, the inverse changes may be apparent to those in the ship, since external

space is defined by light in relation to the inner space of the atom. In such a circumstance there may be no

way to assign a preferred reference frame to either the space ship or the platform of the observer.

The vantage point of the observer is not necessarily an arbitrary matter as when there is no preferred frame

of reference, however. Experience is not normally presented to us in this way. The physical universe exhibits

a preponderance of synchronicity in its organization into galaxies, star systems, planets and moons. A pattern

of relative rotational motions predominates involving a relative skipping of space frames at their centers with

respect to their peripheries that must be reconciled with the synchronous projection of the universe as a

whole.

This can involve a variety of effects mediated through the quantum mode on all scales and in extreme cases it

results in black holes such as at the centers of galaxies. (Some of these effects are yet to be recognized and

this avenue of explanation can be applied to understand others that are known, such as the differential

rotation of the sun and the observed inverse distribution of momentum in the solar system, the missing mass

needed to account for celestial mechanics generally, and other effects.) There are patterns within patterns

within patterns on a cosmic scale that no one can change. Mach’s principle is associated with this

preponderance of synchronicity that is universally regulated on a cosmic scale.

The concept of simultaneous events also takes on different implications according to System 3. While there

remains no way to make measurements of simultaneous events in the integrated fabric of space-time, as

relativity theory maintains, this does not mean that simultaneous events do not occur. In a synchronously

projected universe its atomic constituents are simultaneous within each primary interval of time with respect to

any observer, while taking into account the relativistic skipping of frames in the integrated fabric of space-time.

Space-time spans and integrates the history of space frame skipping accounting for space-time curvatures

associated with relative motions and the condensation of matter into the heavier elements in the centers of

suns. The sun is still projected synchronously with the observer on Earth, even though it takes eight minutes

for the light to reach the observer. The universe shares a common “present” in the timeless quantum frame

from which each space frame is recalled to form. (There is much more to this than can be expressed in a very

general way in one paragraph.)

As de Broglie’s derivation indicates there are inverse relationships that are apparent on a cosmic scale and

that involve synchronous transformations back and forth between space and quantum frames. In itself this

does not lead to inverse identities in a meaningful way that has practical application for us on the space frame

side. However they do become meaningful when there are relative changes spanning a succession of frames

and when we seek to historically integrate processes of change in significant ways by applying universal laws

and equations.

well established laws of physics do not apply within the atom. This is a remarkable assertion. He followed it up

with several precepts for which he had no explanation. He stated that electrons could only exist in certain

stationary orbits within the atom and that in this condition they do not radiate away energy which would cause

them to slow down and fall into the nucleus. In addition he stated that the angular momentum of the electron

must be a whole number multiple of

circle, in this case the cyclic recurrence of each space frame.) He also maintained that the centripetal force

that holds the electron in orbit is the Coulomb force of attraction between electron and nuclear proton. He

further stated that energy emissions from the atom corresponding to discrete frequencies of spectral lines

occur as quantum jumps from higher to lower orbits. He insisted that it must be a jump. The electron cannot

exist between orbits.

Bohr was forced to make these ontological assumptions in order to fit the evidence and Rydberg’s

mathematical relationships together into a coherent theory. Later Louis de Broglie showed that his particle

waves could explain why only certain orbits are allowed. There must be an integral number of electron

wavelengths around each orbit to avoid interference. As pointed out above de Broglie waves are quantum

jumps in position of the electron and there is no such thing as part of a jump.

These premises of Niels Bohr are generally consistent with System 3. There is no electron motion with respect

to the nucleus within each space frame of the atom, not even orbital motion. Both electron and proton are

synchronously transforming back and forth between space and quantum frames. With the recurrence of each

space frame the electron makes a quantum jump in position via the quantum frame. It can jump from orbit to

orbit according to discrete energy exchanges with external space without traversing the space between orbits.

It also jumps in position through successive space frames in order to orbit the proton nucleus. These

successive jumps in position correspond to the de Broglie wave length. Since there is no relative motion in the

inner space of the atom within each space frame no energy is radiated away. The inner space of the atom is

distinct from the outer space.

It is known empirically that the angular momentum of the electron in the first orbit of the hydrogen atom must

be zero. This clearly indicates that there is no relative motion of the electron from space frame to space frame

and yet its recurrent position in the same place must be equivalent to one revolution of the first orbit in order

to generate a centripetal force equal to the Coulomb force with the nucleus. The time that would be required

for one such revolution thus defines one primary interval of time. The revolution, however, takes place as a

transformation through the Void and back again. The Bohr radius of the first orbit of the hydrogen atom is

5.29 x 10^-11 meters and the primary interval of time works out to be 1.519 x 10^-16 seconds. This also

means that EM (light) transmission is limited to 4.554 x 10^-8 meters in each primary interval of time. Time

and space are thus quantized. (Note: The symbol ^ preceding a number indicates an index. For example 2^3

indicates 2 cubed or 2x2x2=8. Or 10^-4= 1/10x10x10x10=1/10,000.)

sense alien to our minds so conditioned with space-time continuity, that the electron in relation to the proton

follows a pseudo circular or cyclic path of circumference 2pi

Coulomb force cannot result in action within one space frame since particulate motion cannot occur within one

space frame, so it must act via transformation from the quantum mode. Since electron momentum is a

function of the de Broglie wavelength and thus with each primary interval of time, this cyclic recurrence can

be considered to take place via a complex field orthogonal to the space defined both inside and outside the

atom. The complex conjugate of the Schroedinger Wave Equation directly indicates this.

Given that electron and proton have no characteristics that can relate their relative position to one another in

the inner space of the hydrogen atom, there is no way to determine relative motion of one with respect to the

other inside the atom through a succession of frames without some external frame of reference. The

momentum in the first orbit must be zero in a primary hydrogen atom.

The second orbit is different. A discrete quantum of energy must have entered the atom from some direction

outside to excite the atom and jump the electron into the second orbit in a succeeding frame. An external

reference is provided for quantum jumps to either higher or lower orbits, since the jumps must span and

integrate two or more space frames and they relate to external space.

The radii of orbits increase with respect to the radius of the first orbit as the square of the principal quantum

number, which is the number of the orbit. The radius of the second orbit is 4 times the radius of the first and so

on. But the number of quantum jumps in position around the orbit varies as the cube of the principal quantum

number. (See S&CO Pg. 76) There are eight de Broglie wave lengths around the second orbit and it takes

eight primary intervals of time for the electron to go around. In the third orbit there are 27, in the fourth 64, and

so on.

relevant to purposes here.

It is apparent that there is a minimum limit to the increment of the differential in the calculus, since space and

time are not infinitely divisible, a convenient solution to Zeno’s paradox. This places limitations on

mathematical methods that may be applied to very small scale quantum events. The principle of indeterminacy

is related since exact relative position is determined in a single space frame, whereas momentum by its nature

can only be measured over a succession of space frames. Momentum and position do not commute for this

reason.

Another important feature is a fundamental distinction between the nature of electromagnetic radiation and

fields and the nature of gravity. While there are analogies between EM fields and gravity, they derive from the

primary projection of space-time in very different ways. Electromagnetic radiation and electromagnetic fields

both derive from the intimate processes within each atom, the former defining external space and the latter

spanning a succession of space frames. On the other hand System 3 indicates that gravity derives from the

integral unity of all matter as quantized energy in the Void, and is thus directly associated with the

synchronous projection of the universe from the timeless Void. Since gravitational effects can only be detected

through the integrated fabric of space-time, detection methods are dependent on the speed of light. This

implicitly means that there is no experimental way to determine whether gravitational effects are instantaneous

via the timeless quantum mode or not, since determination of the effects can not exceed the speed of light that

itself derives from the synchronous projection of space-time. Experimental access to the Void is implicitly

denied.

Nevertheless gravity is not a force that is transmitted through space-time faster than light. System 3 indicates

that it is not transmitted through space-time at all. In the absence of the spacetime continuum presumed by

general relativity, System 3 indicates that gravitational effects observed in the integrated fabric of space-time

are universally implemented via transformations from the quantum frame to the space frame side in the

cosmic projection of matter. Gravitational effects must still take place by relative quantum jumps in position,

space frame by space frame and these cannot exceed the speed of light. The universal law of gravitation can

be seen to derive from conjugate identities and historic integration as described below, in a manner

analogous to Coulomb’s Law but for different reasons.

There are a variety of other phenomena that also indicate a family of quantum forces and effects hitherto

unrecognized that are operative via the Void to preserve synchronicity on a cosmic scale. These include the

differential rotation of the sun, magnetic pole reversals, the missing mass associated with celestial

mechanics, and the apparent prolific energies of distant quasars integrated across a span of billions of years

of historic reflux. In telescope images of distant galaxies their history of change must be reconciled with the

timeless Void. We share a common synchronous "present" that must integrate the history between then and

now.

said that conjugate identities derive from the inverse equivalence between space and quantum frames taken

over a succession of recurrent space frames and involving relative motions. Conjugate identities thus involve

the historic integration of linear processes in space-time, but taking into account relative quantum effects that

are orthogonal to the integrated fabric of space-time.

The inverse equivalence derives from the complex of relationships between particular and universal sets in

System 3 that inverts with each transformation between space and quantum frames as described above.

Unlike Aristotelian identities, conjugate identities are not a simple relationship between entities perceived in

space-time. There are qualitative differences associated with quantitative equivalences across the

transformation from space to quantum frames. The integration of this complex relationship can have a variety

of effects in the integrated fabric of space-time. Conjugate identities cannot be logically derived from

Aristotelian identities without some additional ontological or empirical indication of how to apply them.

The de Broglie equation is a case in point since its derivation involves the mass-energy relationship to the

transmission of light in special relativity. The Lorentz transformation formula for the phase change of the

external wave is equated to the transformation formula for the phase change of the internal period of a clock in

motion, the one being the inverse of the other. The wavelength is created by relative quantum jumps in

position that incur space frame skipping. Louis de Brogie took a quantum leap of faith in making the

assumptions that he did. His only justification for doing so was an idea of a particle as a little clock in motion.

Space frame skipping is a function of relative velocity (v) in space-time. If space is quantized by the distance

that light defines by its transmission in one primary interval of time, then space frame skipping is also a

function of the velocity of light. The Lorentz Transformations indicate that the proportion of space frames

skipped is a function of (v/c)^2. The transformations give the relative proportion of space frames not skipped

as the square root of the quantity 1-(v/c)^2, a quantity I will designate as

follow.

The transformation formula for the internal frequency of a clock in motion is given by its rest frequency times

observer can read the clock only as a result of synchronous frames not skipped. However the relative mass of

a moving particle = rest mass/

observer, including the stationary surroundings that are skipped relative to the moving particle. The inverse

transformation formula is also used for the frequency of a wave for the same reason.

Many observations can be made to indicate how conjugate identities can work in various circumstances. In

time a set of general guidelines can emerge that can provide direction to potentially valuable new techniques

that can be developed. For example System 3 indicates that there is a quantum energy equivalent of mass,

that we can write as E=m, where the energy equivalent of mass in the quantum frame is the inverse of mass in

the space frame. This has no practical significance in a single space frame relative to a single quantum frame,

since we live in the integrated fabric of space-time continuity. But the relation E=mc^2 does have practical

significance in conjunction with the Lorentz transformations.

This indicates that square of the speed of light c^2 is associated with the historic integration of space-time.

Space-time is determined by the integration of successive increments of space, each increment defined by the

distance light travels in a single primary interval of time. Each increment is thus like a derivative of space-time

defined by light. The historic integration raises the power of c to c^2, in an analogous manner to the way

integration in the calculus works.

Coulomb’s Law is related to historic integration. The force exerted between two point-like charges is directly

proportional to the product of their charges (a square function if the charges are equal) and inversely

proportional to the square of their distance of separation. As noted in the section above describing the

primary interval of time the Coulomb force can only act between two or more space frames, so that historic

integration is implicitly involved. Although the law was determined experimentally by Coulomb, it is apparent

that conjugate identities together with historic integration are both involved since the relationship is

associated with the intimately bound electron and proton within the atom and their synchronous recurrence

through a succession of space frames.

The Universal Law of Gravitation is likewise related to historic integration. The whole physical universe is

integrally unified as energy in the Void. It is also separate particulate matter in the

time in each Space Frame. Over a succession of space frames Separate Masses are thus historically

integrated as indicated by their mutual product being inversely proportional to the square of their separation

as defined by light. Space, time, mass and energy as we differentiate them in phenomenal experience become

implicitly integrated historically through the medium of the Void.

As mentioned above a variety of other observations may be made concerning conjugate identities and historic

integration. Some relate to number theory. Irrational numbers, transcendental numbers, and imaginary

numbers can be seen to relate to the recurrence of space and quantum frames as these are reconstructed in

human thought and applied to geometry.

well as various symmetries implicit in atomic structure. In doing so it defines both an internal space and an

external space in relation to the projection of each atom. It explains why the speed of light is universally

constant. It defines the Void as a quantum sensorium that is orthogonal to the integrated fabric of space-time.

This presents a new theory of quantum relativity as an alternative to special and general relativity in a

discontinuous universe. A new approach to cosmology necessarily follows from the way that System 3 works.

System 3 distinguishes between three distinct kinds of identities that apply in different circumstances. In

addition to familiar Aristotelian Identities there are also Triadic Identities and Conjugate Identities. The

Coulomb force and Gravitational force can be shown to derive from conjugate identities associated with

historic integration. Electromagnetic effects are shown to derive from photonic energy spanning successive

space frames to maintain the intimate coalescence of electron and proton as elements of quantized energy in

the quantum frame (or Void). From similar considerations an analysis of Maxwell’s equations can be related

directly to atomic structure drawn out beyond the threshold of the ionization energy and thus required to span

space and time and integrate history. New approaches are indicated for better understanding a variety of

phenomena. This can expand scientific horizons and offer new directions to explore in more meaningful ways.

Atoms, Space-Time & System 3 by Robert Campbell, 2006 |