|Gravity, Quantum Relativity & System 3
Robert Campbell 2008
|Note: Taken from Chapter IV of Science and Cosmic Order: A New Prospectus - Book 1 Physics
It is advisable to read Introduction to the System first.
System 3 prescribes a discontinuous universe as an alternative to the spacetime continuum assumed as the
foundation of General Relativity. Space and time are projected as a linear series of atomic space-frames alternating
with orthogonal quantum frames that are unified in the timeless Void that spans and integrates space and time.
Space and time are defined by light in each space frame, consistent with Planck’s constant. Since each space and
quantum frame together defines one primary interval of time, they can be historically integrated by the introduction
of historic coordinates. The mass-energy relationship of special relativity is defined by the world box of the
coordinate system. The Lorentz Transformations between different inertial systems are defined by the relative box
with respect to the world box. The gravitational and Coulomb forces follow similar considerations. Gravity is a force
of attraction between separate atoms in external space-frames that are united in corresponding quantum frames by
the universal set. The Coulomb force is generated by the universal countercurrent identities that intimately link
electron and proton in the inner space of the atom in each space-frame that are likewise united as photonic energy
in the quantum frame. Both forces reconcile the unity and separation between quantum and space frames in the
same interval of time. The synchronous projection of atoms everywhere at once accounts for Mach’s principle and
the distinction between inertial velocity and mass. Electromagnetic fields derive from the need for the universal set
to span successive increments of space-time to link free electrons with their proton partners, consistent with
Maxwell’s equations. The world box of the historic coordinates shows how gravitational acceleration of the entire
stellar population of galaxies requires space-frame skipping at their centers with respect to their peripheries. The
resultant contraction of the integrated fabric of space-time at their centers drives the eternal regeneration of their
stellar populations. Quantum relativity emerges naturally in a way that indicates completely new approaches to
celestial dynamics and cosmology. Three distinct kinds of identity are indicated by System 3.
In a letter to his friend Michele Besso the year before he died Einstein wrote: “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.”
This alternate possibility is the discontinuous projection of space-time, distinct from the assumed spacetime
continuum of general relativity. It requires a structural insight into the dynamics of how space and time are
generated. Space and time are concepts derived a posteriori from this physical creation and there is no real
justification for raising them to a priori status as general relativity does.
The discontinuous projection of space and time requires that mass itself must be discontinuous. It must appear as
particulate atoms separated by distance in a succession of synchronous projections, like frames in a holographic
cosmic movie in which all atoms are still projections linked up by light. Light itself defines the space between them.
If mass is discontinuous it must also synchronously disappear into timeless bundles of quantized energy, each
quantum atom thus having a photonic energy equivalent that is both timeless and spatially indeterminate. It must be
timeless so that successive still frames of spatial projection can close ranks to present the appearance of spatial
continuity. It must be spatially indeterminate because atoms are only detectable as discrete particles of mass in the
integrated fabric of space-time.
This alternate energy mode of mass constitutes a holistic boundless field that is orthogonal to the integrated fabric
of space-time. In the System it is called the Void. It is consistent with Planck’s universal quantum of action and with
Bohr’s initial assumptions in establishing an ontological model of the atom.
Certain things necessarily follow. A primary interval of time is defined by the occurrence of one space frame
together with one timeless quantum frame. The inner space of an atom is distinct from the outer space between
atoms. Space and time are quantized.
System 3 illustrates how separate particular hydrogen atoms are synchronously projected by a unique universal
set that intimately binds photon, electron and proton within each particular set everywhere at once. In each
integrated space frame all atoms are linked up by light that defines external space in relation to the inner space
defined within each atom by discrete photon energy levels. All light issues from within excited atoms and it thus has
a universal relationship to each independent atom irrespective of relative velocity.
Space frames specified by each atom alternate with timeless quantum frames that are the photon energy
equivalent of each atom. All the discrete quantized energy equivalents of all atoms in the universe are holistically
integrated as one by the unique universal set in the quantum frames. This holistically integrated energy field is
timelessly balanced and spatially indeterminate. In Systems 3 and higher it is called the Void. (1) It is a quantum
sensorium or master memory bank from which the world of form is synchronously recalled to project a succession
of integrated space frames that define space-time. The Void spans and timelessly integrates the whole of space
and time. The Void integrates history. The timeless Void is orthogonal to space and time, such that the integrated
fabric of space-time is projected with the appearance of a seamless reality.
What we accept as a seamless reality is a discontinuous projection however. The discontinuity is betrayed by
Planck’s universal constant h that tells us the light comes to us as a discontinuous series of quantized pulses such
that E=hf, where E is the photonic energy and f is the frequency of the light. This is consistent with System 3 and
with the quantization of both space and time. The primary interval of time is 1.519 x 10^-16 seconds,(2) consistent
with zero angular momentum in the first orbit of hydrogen and the hydrogen spectrum generally. The primary
interval of space is the distance that light can transmit in the primary interval of time, namely 4.554 x 10^-8 meters.
This is the circumference of the largest fully coherent atom, since photonic energy in the internal spherical space of
the atom functions orthogonal to its linear projection that defines external space between atoms. This
circumference corresponds to the 12th orbit of a primary hydrogen atom. Hydrogen is the largest atom, since the
electron orbits are contracted in heavier atoms.
Light Speed and Gravity Waves:
The speed of light is universal because it relates to each individual atom. It specifies a maximum speed of
transmission through the integrated fabric of space-time because it defines the very nature of space-time. This
does not mean, however, that atoms are completely separate entities. Physical events remain synchronously
correlated via the universal set that coheres with all particular sets at once. Neutral atoms are separate and distinct
within each successive space frame but they are also holistically integrated as an indeterminate and timeless
energy field in the Void within the same primary interval of time. A primary interval of linear time is defined by each
single recurrence of an integrated space frame in classical units of time consistent with the Planck-Einstein relation
E=hf above. Particular atoms are both distinct and indistinct at the same time. The oscillation between space and
quantum frames accounts for the wave-particle duality of matter and the uncertainty principle.
Gravitational phenomena derive from this fundamental ontological reality. Each spatially integrated frame that
projects separate atoms on the space frame side is holistically unified as a coherent energy field on the quantum
frame side. Physical matter is both One and Many, at the same time. It is one on the integrated quantum frame side
and many on the integrated space-frame side.
This means essentially that gravitational attraction derives from the unity of all physical matter via the Void. Since
the orthogonal Void spans space-time and integrates history, gravity acts through the successive projection of
space-frames. Gravity derives from the primary projection of the physical universe frame by frame, and the
attractive force between separate particulate masses is universally apparent.
Gravity is not a force transmitted through space-time faster than light. It is a quantum force of attraction that
operates timelessly via the Void. It is the primary member of a family of a hitherto unrecognized quantum forces
that operate timelessly via the Void. Since all relative motion depends on the speed of light for its detection, and
since gravity is associated with the synchronous projection of all matter, there is no measurable way to establish
that gravity is a force transmitted as a gravity wave at the speed of light through a spacetime continuum. This is
especially so in a discontinuous universe because there is no continuum. Motions due to gravity or any other force
can only be known through a succession of space frames over time and their detection depends on the speed of
The synchronous projection of successive space frames can themselves be regarded as waves associated with all
particulate matter. The wave nature of particulate matter only becomes apparent in relative motions. In this
scenario gravitational attraction is implicit in the time-like synchronous projection of space frames from the timeless
and boundless Void that is irrationally present in the orthogonal bottomless seams between frames. In other words
mass is both separate and distinct in each space frame projection and unified and boundless, at the same time.
Since electromagnetic energy E is mass in reflux through the cosmic movie consistent with E=mc^2, this means that
massive ejections of energy such as from colliding black holes can synchronously warp the integrated fabric of
space and time. The slight warp relative to the total synchronous projection of the universe should propagate at
light speed through the integrated fabric of the universe, since light itself defines space. There is no a priori space-
time continuum for a gravity wave to move through.
The current excitement over the supposed discovery of gravity waves from two colliding black holes is misplaced.
The result may be real but for a different reason. Quantum mechanics is fundamentally inconsistent with Einstein’s
General Relativity as Einstein himself maintained to the end of his life. He also insisted that singularities (black
holes) must be cut from his theory because they are not consistent with the assumptions on which the theory is
based. But this is ignored in the claim that the so-called discovery of gravity waves confirms his theory. It is a kind of
double speak. In the final appendix of his book The Meaning of Relativity 5th Ed, he maintains that General
Relativity is not a complete description of reality and that a discrete approach consistent with quantum numbers is
needed but no one knows how to establish the basis to such a theory. A coherent non-linguistic structural basis is
provided here and in related articles on the website. It defies reduction to algorithm. The meaning implicit in all
language derives from it not vice versa.
The Calculus and Historic Integration:
The method of integration in the calculus depends upon summing the differentiation of small increments that
approach zero in equations that relate to Cartesian coordinates. The method was questioned at the time it was
introduced because of the indeterminate magnitude of infinitesimal increments.(4) Are space and time infinitely
divisible? Zeno’s paradoxes indicate that this does not make rational sense. So do quantum jumps in position from
one electron orbit to another orbit via the Void without traversing the inner space between orbits. Space and time
must be generated in discrete amounts that place a minimum limit on the increment of the differential in the calculus.
Knowing that these discrete amounts exist allows a natural process of historic integration that is similar in some
general respects to integration in the calculus, but only when cosmic relationships are involved. This can find a
variety of mathematical applications in astrophysics, stellar evolution and galactic organization on the macroscopic
scale consistent with the Lorentz transformations, just as Schrödinger, de Broglie and Bohm demonstrated
applications associated with the inner space of the atom and sub-atomic interactions on the microscopic scale.
System 3 & Historic Integration:
The Lorentz Transformations derive from relative space-frame skipping in conjunction with historic integration over
a succession of space frames. Since space and time are quantized so is relative velocity, mass, and momentum as
it relates to the velocity of light. The spatial distribution of atomic matter on the space-frame side of System 3 has
reciprocal quantum counterparts in the timeless Void, since the Void constitutes an indeterminate orthogonal space
as a conjugate field associated with the organization of timelessly quantized mass as energy. (See System 3 page.)
Both the Particular and Universal Sets of System 3 invert the subjective to objective orientations of the centers that
constitute them in transformations between space and quantum frames. They also invert the manner in which they
mutually cohere together. They are mutually reciprocal. It will be said that the quantum frame is the conjugate
equivalent of the space-frame. The Void is orthogonal to the integrated fabric of space-time.
In other words the coalesced photonic energy equivalents of atomic matter have quantized spatial relationships in
the Void. The Void is a conjugate field that reflects the spatial distribution and organization of particulate matter but
not in a way that can be explicitly determined from the space frame side as a human being. The field is a boundless
and all embracing unity.(5) It is one. There is no distinction of separate phenomena in the Void. Nevertheless
energy transformations from space-frame to space-frame are effected through the orthogonal agency of the Void.
They are not transmitted through the integrated fabric of space in a single frame because there is no particulate
motion in a single space frame. Each synchronous space-frame is a still projection that defines an increment of time.
Each synchronous projection of a still space-frame is integrated by electromagnetic (EM) activity alone. EM activity
emanates as efflux from within atoms due to quantum jumps between space-frames. It is energy in a dynamic
process of efflux and reflux associated with the synchronous projection of matter.
Consistent with this view historic integration involves summing relative increments of space-time associated with the
projection of atoms, taking into account both the orthogonal conjugate field of the Void and the integrated fabric of
space-time. This is analogous to summing the differentiated area of rectangles under a curve along the x axis in
Cartesian coordinates with respect to diminishingly small increments in the value of x in the calculus. There are
major differences, however.
Introducing Relativity with Historic Coordinates:
In order to grasp the significance of historic integration we can assign historic coordinates such that the x axis
represents a mass in relative motion in three dimensions with respect to a stationary frame of reference A given by
the origin of the coordinates. The y axis represents the quantum energy equivalent associated with the moving
mass represented by the x axis.
The origin of the x and y coordinates can be assigned the value 1,1 since any point in A is relatively stationary with
respect to every other point in A and thus A is fully synchronous with itself. Every unit mass in the inertial frame of A
has a one-to-one mutual correspondence. If a second frame of reference “B” is stationary with respect to A then its
historic coordinates will also coincide. See Figure 2.
It should be noted that historic coordinates have no universal origin at a unique point in space and time. In this
respect they are generalized coordinates that can be used to designate relationships between any two inertial
It should especially be noted what the designated origin at A means by being 1 unit along the abscissa and 1 unit
along the ordinate. This defines it as an inertial frame of reference that is stationary and thus synchronous with
itself because all atoms in A are synchronously linked by light without space-frame skipping. The distance light can
travel in each space frame is c. Light defines space relative to each atom in each space frame.
This means that the unit distance along the x axis represents the distance light can transmit in each space-frame
relative to each atom, which defines a primary interval of time relative to each synchronous atom in A. This is a
universal ratio that can be translated into classical units of time and space.
Each quadrant of the historic coordinates thus represents a complete space-frame along the x axis and its
corresponding quantum frame along the y axis. For example if a particle could move at the speed of light relative to
A then each quantum jump would be one unit in a negative direction along the x axis to x=0. Each quantum jump in
position would be the distance light can travel in a primary interval of time. Since a primary interval of time is 1.519
x10^-16 seconds the corresponding unit distance that light can travel in a single space-frame is 4.554x10^-8
meters.(6) Travelling at the speed of light the unit mass would disappear relative to a stationary observer at the
origin A while its quantum energy equivalent would double. The particle would jump to position 0, 2 on the historic
The unit value of the ordinate of A along the y axis thus defines a quantum energy equivalent to atomic mass in a
space-frame together with a quantum equivalent of the distance light can transmit in a single space-frame. This
means that the quantum energy equivalent of a mass at A, represented by the ordinate y=1, is equivalent to the
designated mass at A, represented by the abscissa x=1, times the square of the speed of light. E=mc^2. The
square of the speed of light is represented by the square area of unit dimensions defined by the coordinates of A at
the origin 1, 1.
The origin at point 1, 1 represents the historically integrated mass-energy of any mass in A, over any span of
space-time, because there is no relative motion within the inertial frame of A.
Relative Motion and Relative Space Frame Skipping:
Relative motion of B with respect to A introduces relative space-frame skipping in A with respect to B. Light can not
link up all the synchronous space-frames in A with those in B because of its motion so some are skipped in A
relative to B, even though A remains fully synchronous with itself. There is a consequent displacement of B some
negative distance along the x axis relative to A. This represents a discrepancy in the number of mutually
synchronous space-frames between B and A with respect to those of A that are synchronous with itself.
The y axis represents the conjugate field of the Void. The y axis does not represent a complex plane but a
conjugate field that is spatially indeterminate and timeless. It nevertheless consists of timeless quantized energy
equivalents of atoms together with associated quantized elements of space that mirror corresponding spatial
relationships in each space-frame.
The rate of space-frame skipping represented as a change in x of B in a negative direction along the x axis thus
introduces orthogonal accumulations of the quantized energy equivalents of the atoms in B with respect to A. If the
motion is constant this accumulated energy equivalent is constant. It can be represented by a single point on the 45
degree diagonal above the negative x axis, as shown in the upper left quadrant of Figure IV-1.
Relative rates of space-frame skipping associated with relative rates of quantum jumps in position with respect to
the x axis also represents a contraction in relative linear space in B as perceived from A. This is represented by the
remaining synchronous frames that are not skipped in A relative to B.
Deriving the Lorentz Transformations:
When the inertial system B is moving at constant relative velocity v with respect to A, the proportion of space frames
observed skipped from the perspective of A on the space-frame side is proportional to the relative motion of B as a
fractional ratio to the speed of light c. Space frame skipping is directly proportional to v/c, since c has a constant
relationship to each atom in each space-frame.
The quantity v/c is thus a direct ratio of space-frames skipped in the inertial system A with respect to the inertial
system B. Light can not fully bridge the quantum jumps of B with respect to A so space frames in A are skipped to
compensate. As a result A observes a contraction in B in the direction of travel. The proportion of space frames not
skipped from the perspective of A between A and B is thus 1- v/c. This quantity is represented by a single discrete
increment in the abscissa to -x1 at B as shown in Figure IV-1
From the standpoint of A there is also a correspondingly equal relative accumulation on the quantum frame side of
B that is equivalent to 1+v/c. This quantity quantum energy is represented by a single discrete increment in the
ordinate to +y1 that is the equivalent to the increment in the abscissa.
The increment along the abscissa times the increment along the ordinate represents the historic integration of A
and B. It defines a square between the integrated fabric of space on the space-frame side of System 3 and the
corresponding orthogonal Void on the quantum frame side consistent with E=mc^2. This square relationship
represents the historic integration of A and B, since the orthogonal Void integrates the history of change that has
taken place on the space-frame side. In other words the square represents the degree of mass-energy
synchronicity between the space and quantum frames of B relative to A.
The perspective of a stationary observer in B can also be represented at the origin 1, 1. This gives a similar result
in the opposite direction along the diagonal in the lower right hand quadrant, by the shift in the relative position of A
to x2, -y2.
In either case the historic integration is represented by the area of this conjugate square. It is given by:
(1+v/c)(1-v/c) = 1-(v/c)^2.
The projection of the square onto the space frame side only of either A or B is thus given by the square root of
1-(V/C)^2 = (1-(v/c)^2)^1/2. This is so because the conjugate timeless and boundless Void is orthogonal to the
integrated fabric of space-time.
This quantity is a universal transformation factor from the inertial system of A to that of B, or vice versa. It
represents the degree of relative space frame-skipping and corresponding quantum frame accumulation as it
applies to mass, as well as to the integrated fabric of external space relative to each atom, and to relative time, in
one inertial system as compared to another.
The internal spatial relationships of electron orbits within neutral atoms are not affected since space-frames
associated with the projection of each atom are either skipped entirely or not at all. Atoms are not flattened in the
direction of travel. System 3 resolves this enigma in current relativity theory. Inner space is distinct from external
With respect to mass, the space-frames of an observer at A are skipped relative to a moving mass in B, such that
the observed mass M in B carries with it a relative accumulation of quantized energy that effectively increases its
relative instantaneous mass M according to the formula M=Mo/(1-(v/c)^2)^1/2, where Mo is the rest mass.
With respect to linear space L in the direction of motion of B with respect to A the contraction of length L
associated with skipped space-frames in A with respect to B is given by L= Lo(1-(v/c)^2)^1/2. The relative length of
a static dimension in the inertial frame of B is shortened in the direction of B’s motion because space-frames in A
are skipped relative to it. With fewer synchronous frames between them A sees B shortened.
With respect to the internal frequency of a clock associated with the degree of synchronicity remaining between A
and B the frequency of the clock ticks T in B are retarded with respect to those in A according to
These are the same as the Lorentz transformations between any two inertial systems moving with constant relative
velocity with respect to one another.(8)
Note that although there is a relative skipping of space-frames the space-frames not skipped are nevertheless
mutually synchronous. This is another inconsistency with current relativity theory. There is such a thing as
simultaneous events whether this can be determined by measurements in space-time or not. Einstein dispensed
Acceleration and Historic Coordinates:
If B is steadily accelerating in a linear direction with respect to A there will be incremental jumps in the historic
coordinates of B along a diagonal through A. The size of the incremental jumps will depend on the rate of
acceleration and each increased quantum jump in B represents a corresponding force that is the equivalent of one
or more discrete skipped frame sequences. Force, like space and time, is also quantized. Force exerted in the
integrated fabric of space-time is the conversion of mass-energy in skipped space-frame sequences into
If we take a look at Newton’s second law of motion F=ma, we see that the units of force are essentially the same as
the units of mass.(9) The discrepancy in units between the two sides of the equation is unit distance per second
per second. Given that space is quantized according to the distance that light can travel in a primary interval of
time, acceleration thus represents a progression in the rate of space-frame skipping between the body accelerated
and the stationary frame of reference. Mass is converted to energy that becomes translated as a force within the
space-time fabric of the stationary frame of reference.
For example we burn fuel to accelerate a car or a rocket ship and the combustion products weigh slightly less than
the reactants by the amount of energy needed according to E=mc^2. At normal rates of acceleration that we
experience this mass discrepancy in the frame of reference is very small. At relativistic velocities approaching the
speed of light it becomes very large. Whatever the case it represents the conversion of skipped space-frames
associated with mass into energy translated as a force of acceleration.
As B is accelerated toward light speed relative to A at the origin, it moves on a 45 degree diagonal through A,
upwards to the left. That is, it moves in a negative direction along the x axis toward a zero point, while also moving
in a positive direction along the y axis toward the value 2. The reverse is true of A from the perspective of B. This is
illustrated by lower right hand quadrant of the relative box in Figure IV-1. With acceleration the relative box
expands toward the world box. On a cosmic scale indicated by the world box there are differences indicated
between A and B as a reference frame, even though the Lorentz transformations equally apply.
In other words, as a reference atomic mass in B approaches the point of disappearing with respect to one in A
there is a corresponding doubling of quantum energy associated with the atomic mass of B in the orthogonal
quantum field of the Void, as indicated by the upper left hand quadrant of the world box. From the perspective
of A at the origin, A remains synchronous with itself and it takes infinite energy to accelerate B to light speed as A
approaches zero relative to B.
With respect to B, A effectively moves along the diagonal in the lower left hand quadrant of the world box toward
the point 0, 0. B disappears with respect to A and vice versa. But the world box indicates that with respect to B
there is only a doubling of mass-energy in the quantum field of the Void relative to A. This conservation of the total
mass-energy of B with respect to A is thus illustrated by diagonals in both left hand quadrants of the historic
While constant relative velocity is a succession of constant jumps in position that involves no energy input in a
frictionless environment, acceleration within a relatively stationary inertial frame of reference does require energy
input. A frictionless rocket ship traversing interstellar space must expend energy of some kind to accelerate. The
energy is translated via the Void to increase the magnitude of quantum jumps in position from space-frame to
space-frame as it moves along the diagonal. Like all relative particulate motion, acceleration occurs in discrete
increments however it involves an increasing degree of relative space frame skipping that involves mass in reflux as
This implicitly requires that there are fundamental differences between forced linear acceleration within the context
of a stationary inertial frame of reference and gravitational acceleration on a cosmic scale. Gravity and acceleration
are not equivalent. This is inconsistent with another cornerstone on which General Relativity theory is erected in
addition to the assumption of a spacetime continuum.
Reverse Transformations and Cosmic Coherence:
The reverse situation applies to A from the perspective of B if B is taken to remain synchronous with itself at the
origin. Then the expansion of the relative box toward the world box accelerates A along the diagonal in the lower
right quadrant of the world box toward the position 2, 0. From the standpoint of B there is a doubling of space
frames in A even though there is a relative vanishing of related quantum frames. It can appear to B that A can
accelerate unimpeded to light speed and vanish without trace in a singularity. Mass-energy conservation is
indicated in the upper right hand quadrant of the world box towards a relative doubling of both space and quantum
frames of B at point 2, 2. The right hand half of the historic coordinates is the reciprocal of the left hand half.
We thus find that different inertial systems have reciprocal relationships between them on a cosmic scale as
illustrated by the world box. In practical terms this requires that there must be a universal frame of reference
associated with a balance between the left and right sides of the Historic coordinates diagram in order for there to
be synchronicity in the universe as a whole. Since all matter in the heavens is in a perpetual state of nested
cyclical motions within cyclical motions this necessarily introduces a family of quantum forces to accommodate
relative space-frame skipping on several cyclical levels in such a way as to preserve synchronicity with the
universe as a whole. The universal set of System 3 requires universal coherence with all particulate matter. And
there must be coherence for us to observe phenomena in a coherent way.
Gravitational Force & Acceleration:
According to Newton’s formulation of gravity, two masses m1 and m2 separated by a distance d exert a mutual
force of attraction proportional to the product of their masses and inversly proportionate to the square of the
distance between them.
System 3 relates Newton’s law to the synchronous projection of atomic space-frames everywhere at once from
quantum energy equivalents of atoms that are integrated as one in the orthogonal Void. The quantum side is the
reciprocal of space-frame side. This synchronous recall of independent atoms into particulate form also generates
a reciprocal relationship between the spherical inner space of each atom and linear external space between
In this compound situation two masses m1 and m2 are both timelessly united as one and they are also spatially
separate. They are simultaneously both at once since each recall of a space-frame from the Void defines one
primary interval of linear time. The two masses will be impelled to bridge this discrepancy between union and
separation. This represents a force of mutual attraction that tends to contract the reciprocal external space
Historic integration involves integrating space frames and conjugate quantum frames. This is a square relationship
even in a single primary interval of time. The two masses are projected together from their quantum equivalents at
the same time. The space-frame of one mass exists in the same primary interval of time with the quantum frame of
the other and vice versa even while they are both one in the quantum frame and separate in the space-frame. That
is what the integration of the square means. If the two masses are two identical atomic masses the attractive force
will be proportional to m^2. If the two masses are different one will be heavier by some multiple of the other so the
square will simply be represented by the product of their masses. The attractive force will be proportionate to m1m2.
A similar but reciprocal relationship exists between their separation in external space relative to atomic inner space
and also to the conjugate quantum equivalent in the Void. The integration as it relates proportionately to the
gravitational force of attraction is the reciprocal square relationship 1/d^2. Combining these two into the integration
of a single space and quantum frame gives Newton’s universal force of gravitation F=Gxm1m2/d^2, where G is a
constant for dimensional consistency.
Gravitational force is a static force of attraction in each space frame. It does not result from the conversion of
skipped mass as energy translated into a force of linear acceleration over a succession of space frames as in
Newton’s formula F=ma. It is not the same as burning fuel to accelerate a vehicle or burning energy to accelerate
in a race. Gravitational force of acceleration is spontaneous frame projection by frame projection..
If two masses are mutually restrained as when a person is standing on firm ground the force is constant and
measured by the person’s weight. If the person falls from a cliff the person accelerates frame by frame and yet
remains synchronous with the planet Earth so far as their mass is concerned. The skipped space frames
associated with the person’s gravitational acceleration are external space-frames. They are not synchronous
atomic space-frames that define the person’s inner mass. The person is projected still space-frame by still space-
frame synchronous with the planet.
The gravitational force of attraction increases little by little in each successive frame as the person falls because
the distance of separation is being reduced. Over such a short distance the increase in gravitational force is
negligible and the person’s inertial and gravitational mass remain the same, as Einstein assumed.
On a cosmic scale gravity applies to the preponderance of synchronous mass and its spatial distribution in the
entire universe. This is distinct from relative space-frame skipping due to linear velocities and forced acceleration.
Gravitational force is the reciprocal of force generated through the physical expenditure of energy that results in
In summary it can be said that gravity is associated with the primary projection of matter by System 3. The force of
gravity derives solely from the unity of the quantum sensorium or Void and it is related to the synchronous
projection of all matter everywhere at once.
This underlines the important distinction between forced acceleration within the integrated fabric of space-time and
acceleration due to gravity. Since gravity is associated with the synchronous projection of all atomic matter
everywhere at once there is no relative skipping of space-frames associated with matter itself. The inner space of
atoms is distinct from external space. Earth atoms are not skipped relative to the centripetal acceleration of atoms
on the moon due to gravity for example. Only increments of external space defined by the transmission of light in
space frames between the earth and moon are skipped. This curves the integrated fabric of space-time between
the earth and moon sufficiently to hold the moon in its orbit. In the local environment of the solar system the inertial
mass of the moon remains consistent with the gravitational mass of the earth and vice versa. There are important
differences with respect to galactic dynamics however.
Foucault’s Pendulum and Mach’s Principle:
In 1851, the French physicist Jean Foucault suspended a 200 foot long pendulum from the dome of the Pantheon
in Paris and set it to swinging under the force of the earth’s gravity alone. It was shown that the arc of its swings
remained constant with respect to the “fixed stars,” thousands of light years distant, while the earth rotated beneath
it. This demonstrated that the inertial velocity of the earth’s rotation is something quite distinct from its gravitational
mass which is the same as its inertial mass in rotation. While motion of the pendulum is due to the gravitational
attraction between the pendulum’s bob and the earth, the arc of the pendulum’s swings is synchronous with its
spatial relationship to the universe at large and it remains unaffected by its proximity to the earth. General
Relativity can not offer an explanation as to why this is so. If gravity is caused by a local spacetime curvature as
Einstein's theory requires then the swings of the pendulum should rotate with the earth.
The reason is implicit in the discontinuous universe prescribed by System 3. Atomic mass together with associated
external space-frames are synchronously projected everywhere at once. Gravity derives from this fact. Inertial
velocity remains constant with respect to the preponderance of synchronicity in the universe as a whole in the
absence of a force to change it.
The gyro compass works on the same principle known as Mach’s Principle. It remains oriented in a fixed position
relative to the “fixed stars.” There is thus a clear distinction between gravitational mass and its inertial velocity, even
though its inertial mass may remain consistent with gravitational mass in our stellar environment.
The Coulomb Force versus Gravitational Force:
Coulomb’s law has the same form as Newton’s law of gravitation and it can be seen to follow from similar
considerations. Charge, like mass, derives from the linking up of particular centers in sets by the common
universal set of System 3. The Coulomb force, however, derives from the relationship of the three centers within
System 3 sets, whereas gravitational force derives from the relationship between separate particular sets.(10)
In each atomic space-frame, the Coulomb force is a static force like gravity. It is the force of attraction between
electron and proton that holds the electron in orbit as it moves but the orbital motion of the electron is a series of
quantum jumps in position between a succession of space-frames. There is no motion in a primary interval of time,
and thus no energy loss due to radiation.
The Coulomb force is directly associated with the countercurrent identities of the universal set as it tunnels through
the particular centers of each particular set to intimately link them as a whole atom in each space-frame. On the
quantum frame side the charge becomes coalesced as one within the quantum photon energy equivalent of the
neutral atom. There is thus a conjugate relationship between the space and quantum frames that is similar to that
So the charge is both separate and distinct between electron and proton in the space-frame, and coalesced as one
in the corresponding quantum frame in the same primary interval of time that defines the inner spherical space of
the atom. The Coulomb force is impelled to bridge this difference between union and separation. It results in a
centripetal force of acceleration between electron and proton in the internal spherical space of the atom that
counterbalances the inertial tendency of the electron as it orbits in quantum jumps around the much heavier proton.
This is structurally self-similar to the external Gravitational force between massive aggregations of separate atoms
in suns, planets and moons.
Since historic integration defines a square relationship between the space-frame and the quantum frame even in a
single primary interval of time, the Coulomb force is directly proportional to the square of the electronic charge, and
inversely proportional to the square of the radius of the electron orbit that specifies the inner distance between
electron and proton. This is the same form as Newton’s law of gravity.
Electromagnetic Fields and Maxwell’s Equations:
The inner spherical space of an atom is a function of discretely quantized photon energy shells that define the
radius of specific electron orbits. If the photon energy of the atom exceeds the ionization limit that defines the
maximum coherent radius of an atom the electron becomes ejected from the spherical inner space into the linear
external space between atoms.(11)
It becomes a free electron and the charge between it and its proton partner persists in accordance with Coulomb’s
law. The electron and its proton partner are still intimately linked by the universal set that tunnels through them,
but now the countercurrent identities R1 and R2 of universal term 2 of System 3 must span a succession of space-
frames to link them. (See System 3 page.) It must do so since proton and electron are timelessly coalesced as one
in the conjugate quantum frames.
The lines of force of electromagnetic fields are defined by this spanning of space and time between electron and
proton required by the countercurrent identities of the universal set of System 3. The active interfaces of the
universal set remain confined within the particular centers of each particular set but the particular photon energy
interface must also span the successive frames. This requires that the countercurrent identities must carry with
them specific quantized amounts of photonic energy in each space-frame consistent with the conjugate energy
equivalent in the quantum frame. This generates electromagnetic waves that transmit at the speed of light
consistent with Maxwell’s equations.
When an alternating charge is induced in a transmitting radio antenna wire an electromagnetic wave radiates
laterally away from it at the speed of light. The intensity of the wave determines its amplitude. The electric
component of the amplitude is orthogonal to the direction of travel but oscillates parallel to the alternating direction
of the electric charge in the antenna. The magnetic component of the wave oscillates perpendicular to the electric
The reciprocal relationship between space-frames and conjugate quantum frames becomes mirrored in the
orthogonal relationship between the electric and the magnetic components of the transmitted electromagnetic
wave. The two components of the waves are in phase because each primary interval of time includes the space-
frame component with the conjugate quantum component. The electric component corresponds to the space-frame
and the magnetic component to the quantum frame. The latter must be represented on the space frame side
because the universal set is required to span successive increments of space-time in linking up electron and
The two components of the wave are mutually orthogonal because the quantum and space-frames are orthogonal.
The wave represents the stretching out of the charge relationship in the spherical inner space of the atom into
linear external space. This drags with it the orthogonal magnetic component associated with related quantum
frames in spanning increments of space and time. Note that inside the atom there is no magnetic component
produced because the electron does not move with respect to the proton. The whole atom is synchronously
projected as a series of still frames and the electron only jumps between frames.
The reciprocal product of the permittivity and the permeability of free space 1/εμ is equal to the square of the
speed of light because it has a reciprocal relationship to the square defined by the historic coordinates between
each space and conjugate quantum frame in each primary interval of time. The electromagnetic wave is
superimposed on the integrated fabric of space-time which is itself defined by the transmission of light space-frame
by space-frame. The linear propagation of the wave in external space is orthogonal to the circular motion of the
electron frame by frame with respect to the proton in the inner space of the atom.
It is noteworthy that Maxwell believed that field lines represented elastic distortions of the ether that was believed at
the time to fill all space, including vacuum. In this limited respect the ether might be taken to correspond with the
boundless, timeless, and spatially indeterminate Void. The stretching of the countercurrent identities of the
universal set to span a succession of space frames might be taken to correspond to his intuitive notion of elastic
Galactic Organization and Gravity:
Galaxies involve orbital motions of their stellar populations about their centers and gravity is the force that keeps
stars from flying tangentially off into space under their own inertial momentum. A force of acceleration toward their
center must be synchronously active over time.
We thus have an effect in the relative rotation of galaxies where each star system can be represented by a point B
with respect to the galactic center at Point A on historic coordinates. The acceleration of stellar populations toward
the center contracts space toward the center with respect to the periphery.
Since the gravitational acceleration does not in itself introduce relative skipping of atomic mass space-frames, but
preferentially skips external space-frames between atomic or stellar masses, quantum forces are necessarily
introduced that account for stellar formation and migrations of stellar populations. This relative contraction of space-
time nearer the center requires matter to condense into stars that fuse space-frames of atomic mass into heavier
elements that contract space to suit the local environment of space-time. This curvature of the integrated fabric of
space-time also introduces a quantum force that results in the migration of younger stars toward the periphery and
dense old stars back toward the center.
On a cosmic scale, however, represented by the world box, space frame skipping can proceed without limit. The
continual acceleration of the whole stellar population of a galaxy toward the center moves point B for the whole
population diagonally up to the left toward the value 0 on the x axis and toward the value 2 on the y axis of the
historic coordinates with respect to A at the center. At this point the value 2 represents an energy equivalent of the
mass of the stellar population accumulated in the Void with respect to the galactic center which has ceased to exist
relative to the whole stellar population. There is a black hole at the galactic center that represents a singularity
common to all galactic centers.
The upper left hand quadrant of the historic coordinates has a complementary relationship to the lower right hand
quadrant. If we take B to represent the whole stellar population of a galaxy synchronous with itself at the origin of
the coordinates we find that old stellar masses migrating back to the center lose their quantum energy equivalents
as they approach the speed of light. B then represents the preponderance of synchronicity in the universe as a
whole and old stellar masses move into the lower right hand quadrant of the coordinate system. As they accelerate
around an accretion disc at the center they lose their associated quantum energy equivalent to the Void. There is
no directly associated accumulation of quantum energy to prevent them reaching light speed and disappearing
completely beyond an event horizon at the center. This is consistent with a growing body of empirical evidence.
This singular condition in black holes is shared by galactic centers. It is associated with the primary synchronous
projection of primary hydrogen in the universe as a whole. There is a generalized accumulation of quantized
energy in the Void associated with the reflux of old stars back to the black hole that must be periodically released
as a new generation of primary hydrogen emitted as efflux from the center. This is represented by the upper right
hand quadrant of the historic coordinates. The accumulated doubling of both space-frames and quantum frames
builds to restore the black hole to a synchronous condition with the universe as a whole. This finds expression in
the periodic emission of primary hydrogen outward into the galactic disc. The heavy elements fused in stellar
centers are regenerated back to primary hydrogen.
Each new generation of primary hydrogen is impelled to move outward from the center with star formation within it
to compensate for the spatial contraction near the center. As old stars contract space through the fusion of heavier
elements they are drawn back in toward the center to maintain synchronicity, and are eventually accreted back into
the black hole as they approach light speed. The cyclic birth, death and regeneration of stellar populations is
eternally repeated in this way.
Since the relative angular velocities of galaxies regulate stellar migration rates with respect to one another as a
whole on a cosmic scale, gravitational acceleration is regulated as well. Relative rates of stellar formation and reflux
are regulated accordingly. If reflux rates are very high this can result in highly active galactic nuclei with jets of
material being ejected axially at high velocities orthogonal to the accretion disc to compensate. This can act as a
brake over time, to preserve synchronicity with the universe as a whole.
It should be emphasized here that matter is not at the unrestrained beck and call of gravity on a cosmic scale.
Quantum forces introduced by relative angular motions moderate and regulate linear motions to preserve a
preponderance of synchronicity with the primary projection of matter in the universe as a whole. Stellar motions
tend to retain their collective spatial integrity because of the requirement for coherence with the universal set. This
places galactic stellar masses in tensional contact with one another. There is no “missing mass” but quantum
forces can qualify as “dark energy.”
From this brief overview it should be clear that System 3 necessarily implicates the regeneration of stellar
populations and a variety of other effects that are not currently recognized and that allow mathematical treatment.
In the next chapter the foundations of atomic structure and quantum mechanics are reviewed in a cosmic context,
taking into account the structural dynamics of System 3.
Three Kinds of Identity:
System 3 clearly indicates three distinct kinds of identity. They have never been formally acknowledges as distinct
even though they have been used in the most fundamental formulae of physics.
The first kind of identity will be called Aristotelian Identity. It is the identity that we are most familiar with and that
mathematics primarily depends upon. It equates separate things and numbers of things that are perceived as
identical in space and time. Ten goats are the quantitative equivalent of ten fingers. One goat is identical with
another, and so on. Rules of syllogism and algorithms develop accordingly. It may be noted that mathematics
begins with the invention of numbers. The Idea of ordinary counting depends on the Routine of adding one more to
give the Form of the succeeding number, consistent with the hierarchy of System 3. Although numbers
quantitatively equate separate things each number also has a qualitative aspect that defines it as a unified whole.
(12, 13) This is analogous to the space and quantum frames of System 3. Also the square of any number is equal
to twice the sum of all the digits up to the quantum frame that qualitatively defines the last number in the sequence,
similar to historic integration.(14) This is consistent with the second kind of identity.
The second kind of identity we have called Conjugate Identity. It is the orthogonal identity between space and
quantum frames represented by the historic coordinates. These identities creep in unnoticed to the formulation of
our most fundamental laws of physics. This will be demonstrated in the next chapter with Louis de Broglie’s
derivation of his wave equation for matter.
The third kind of identity can be called Triadic Identities. They relate to the way the countercurrent identities of the
universal set intimately link up the three particular centers of each particular set. Quark theory and quantum
chromodynamics makes use of triadic identities to some extent.
Prior to Einstein, motion was assumed to be relative to an all pervasive ether which acted as a medium for the
transmission of light. Since motion relative to the ether could not be detected, Einstein set the question aside,
simply asserting that the velocity of light was universal.(15) His Special Theory of Relativity was thus preferred over
the equivalent, but twice amended, ether theory of Lorentz-Fitzgerald and Lorentz-Larmor, to account for spatial
contraction and time dilation with respect to the ether.
In his thorough review of the matter, Adolf Grünbaum points out that the philosophical preference for Einstein’s
theory stems from the fact that it refuses to postulate a preferred ether frame of reference when there is no
physical foundation for doing so. He also points out that the General Theory of Relativity fails to incorporate
essential features of Mach’s program, that it fails to repudiate the concept of “absolute space,”(presumably
meaning the ether).(16)
Dirac also indicates that the original ether theory can play the role of the perfect vacuum of special relativity since
quantum mechanics allows the assumption that all values of the velocity of the ether are equally probable. Einstein,
however, remained adamantly opposed to the direction that quantum mechanics took until the end of his life.(18)
For Einstein, de Broglie, and others, the point of departure was Heisenberg’s principle of indeterminacy. At 23,
Heisenberg, working as Max Born’s assistant, had found a mathematical rule in quadratic arrays. Max Born writes:
... Such quadratic arrays are quite familiar to mathematicians and are called matrices, in association with a quite
definite rule of multiplication. I applied this rule to Heisenberg’s quantum condition and found that it agreed for the
diagonal elements. It was easy to guess what the remaining elements must be, namely, null; and immediately there
stood before me the strange formula:
qp-pq=ih/2pi where q represents the position of a particle and p its momentum.(19)
What does this unusual equation mean? There is a difference in the product of p and q that is dependent on their
order. Dirac saw that the dominant characteristic of Heisenberg’s theory was that it contradicted the commutative
axiom of mathematics.(20) Why?
To answer this question we may look to System 3 again. Relative position is given in each space frame, changes
in position being effected through a series of quantum jumps in position from one space frame to the next.
Momentum, by its nature, depends on changes of position between space frames. Momentum may therefore be
measured between space frames immediately prior to, or immediately following, the space frame in which position
is determined. It depends on the order in which the measurements relate to one another. The relative
indeterminacy of the two is therefore a function of the recurrence of space frames given by the universal quantum
of action in the expression ih/2pi.
Since we obviously observe that physical forms cohere as integral wholes, it must follow that the universal quantum
of action is synchronous with respect to the material content of the universe as a whole.
Now the pieces fall into place. Einstein has his way that God does not play dice with the universe, but space and
time are discontinuous, invalidating most of his relativistic assumptions. And Heisenberg has his way that position
and momentum are not simultaneously knowable, but the rules of roulette do not govern the universe.
If one wants to consider that relative motions occur with respect to an omnipresent ether, then the ether is the
quantum sensorium, the Void, and it is spatially indeterminate, not allowing of measurements of motions relative to
it. Yet the Void provides a basis of historic integration that is not reducible to a linear series of local physical
influences. The universal set as it relates to the Void is the implicitly discretionary means through which experience
is hierarchically integrated. As intelligent beings we are products of the higher systems as elaborations of Systems
2 and 3 and we are synchronous with the physical projection of the universe according to System 3. It is through
our relationship to the same universal hierarchy and its elaborations in higher Systems that gives us access to the
Void and allows us to span space and time, in this remote corner of the universe, to observe the whole of creation.
Where does this leave us from the standpoint of having pragmatic theories with which to cope intelligently? Special
Relativity remains reasonably intact, albeit with a very different interpretation attached. General Relativity does not
fare as well, nor do the cosmological models associated with it. Space and time cannot be considered an a priori
continuous field as a thing independent from the gravitational mass which conditions its curvature. There is no such
independent thing as a spacetime continuum. There are alternate explanations for the Red Shift in the spectra of
distant galaxies, and also for the cosmic background radiation, both of them consistent with the System and more
credible in the light of all the other evidence. Quantum theory remains partially intact, but with the conceptual
nature of the quantization of all experience vastly modified in such a way that a self consistent Quantum Relativity
Whatever apparent damage the System may do to existing scientific frameworks of understanding, it mends much
more than it tears, and it offers a great deal more besides. It offers us an insight into the nature of intelligent
systems, a new family of quantum forces, and completely new perspectives to explore in astrophysics and
cosmology. The higher Systems offer challenging new insights into biological systems, how they are organized and
work, with the attendant hope that we can better come to understand our place in the cosmos and how better to
organize our affairs accordingly.