Atoms & Space-Time
Summary Introduction:
The following verbal summary is a self-consistent analysis that is consistent also with the most fundamental
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.

Introductory Note:
From the diagram of System 3 it can be seen that each Frame is made up of a Universal Term interacting with
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

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.

System 3, Atoms from the Outside and Aristotelian Identity in Space-time:
In the diagram of System 3 one can associate Centers 1, 2, & 3 with the photon, electron, and proton,
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.)   

Inner Space and Outer Space:
By way of introduction then we can say that Centers 1, 2, 3 correspond to photon, electron, proton
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.    

Triadic Identities Inside the Atom:
Let us look more closely within one atom represented on the space frame side (bottom part of the System 3
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.

Electronic Charge in Stable Orbits:
By looking at the Universal Set it can be seen that there is a subjective to objective energy imbalance  
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

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

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.

Electron Orbits in Relation to the Proton and Photon:
The universal Form of the electron P2 is identified by its relationship with the photon P1 (and U1 inside it). But
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.

Significance of the Triadic Identity:
The proton is classified as a baryon in the family of hadrons and is thought to consist of two ”up” quarks and a
“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

The Quantum Frame:
System 3 involves the synchronous transformation back and forth between space frames and quantum
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.

Transformation from Space Frame to Quantum Frame:
In the transformation from the space frame side of System 3 to the quantum frame side (top part of the
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.

The Transformation of the Particular Set to the Quantum Frame:
Let us examine the particular set first. On the space frame side the three centers of one particular set P1, P2,
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

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.

The Transformation of the Universal Set to the Quantum Frame:
In the space frame the universal set is confined within the particular centers of the particular set. U1 is inside
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.  

The Transformation of the Universal Set Back to the Space Frame:
There is a time-like significance to the way that the universal set works in the quantum frame even though the
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
are U1. They are the form of the physical universe as a potential idea. They are
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
Idea ->Routine ->Form, although it works in a manner orthogonal
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.)

Recurrent Transformations between Space and Quantum Frames:
It is the universal set that regulates the transformations back and forth between quantum and space frames.
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

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
“I consider it quite possible that physics cannot be based on the field concept, that is,
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:
A decade after general relativity was introduced Louis de Broglie came up with another main cornerstone of
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 “
p” of the particle is equal to the quantum of action h divided by the wavelength “L”. This de  
Broglie equation
p=h/L complements Planck’s equation E=hf as a basis to quantum mechanics. (Where E is
the energy of electromagnetic transmission and
f is its frequency.)

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 =
hf = mc^2. There is a clear correspondence to System 3 here.

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
dx (for its displacement along the X axis) divided by L (L for
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

For the variation of the interval of time
dt of the internal phase of the moving particle he used the
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
vdt for dx in the expression for the moving wave. The derivatives of time  
dt cancel out and the expressions of rest energy (rest mass m x c^2 ) vanish. The expression remaining  
states that the relativistic momentum of the moving particle is equal to Planck’s constant
h divided by the

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

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 Vantage Point of the Observer:
Depending on circumstances things with respect to the particle may not change very much. If we exchange  
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  

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.

Atomic Structure and the Primary Interval of Time:
When Niels Bohr, working with Rutherford, proposed his theory of the atom he hypothesized that some of the
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
h/2pi. (This indicates that h corresponds in some sense to the radius of a
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.)

Coulomb Force & Centripetal Force:
It is curious that the angular momentum must be a whole number multiple of h/2pi. This implies, in some   
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
h that is also related to centripetal force. The
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.  

Other Observations of System 3:
There are a variety of additional observations that may be made about System 3, a couple of which are
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

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

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

Conjugate Identities:
Some evidence has been pointed out above for what may be called conjugate identities. In general it may be
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
LT for simplicity in observations that

The transformation formula for the internal frequency of a clock in motion is given by its rest frequency times
LT. This is a direct measure of relative space frames not skipped between clock and observer, since the
observer can read the clock only as a result of synchronous frames not skipped. However the relative mass of
a moving particle = rest mass/
LT. The inverse transformation is used because it is the space frames of the
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
same primary interval of
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.

System 3 provides an accurate ontological model of the atom accounting for electronic charge and mass as
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
System 3
Gravity & Historic Coordinates