Gravity, Quantum Relativity & System 3
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| Gravity, Quantum Relativity & System 3 Robert Campbell 2008 |
Note: Taken from Chapter IV of Science and Cosmic Order: A New Prospectus
It is advisable to read Unified Theories, Fantasy, & Cosmic Order first.
Abstract:
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.
Preamble:
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.
Introduction:
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. 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 light.
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.
While wave-like distortions or perturbations in the local fabric of space-time may be detectable in the
immediate vicinity of rapidly rotating super-dense neutron stars, due to localized intense levels of non-
synchronous space-frame skipping, there is no related mechanism that will allow such effects to propagate
endlessly throughout the integrated fabric of space-time even if they can occur. There is no such independent
thing as a spacetime continuum for a superimposed wave effect to propagate through. Experiments to detect
gravity waves in the normal synchronous environment of our solar system are unlikely to turn up any
convincing evidence that they exist.(3)
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. This is outlined in
Chapter III.
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 IV-1.
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
systems.
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 1.519x10^-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 coordinates.
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.
Figure IV-1
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 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 space.(7)
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=M0/(1-(v/c)^2)1/2, where M0 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= L0(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
T=T0(1-(v/c)^2)1/2.
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 with simultaneity.
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
acceleration.
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 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 coordinates.
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 a progressive degree of relative space frame skipping.
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 contradicts 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. An event horizon swallows A in a
singularity from the standpoint of B. But mass-energy conservation requires that B effectively moves along the
diagonal in the upper right hand quadrant of the world box towards a relative doubling of both space and
quantum frames at 2, 2. The right hand half of the historic coordinates is thus the reciprocal of the left hand
half.
We thus find that although the Lorentz transformations apply equally between different inertial systems,
there can be 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
preponderance of synchronicity in the universe as a whole. Since all matter in the heavens is in a perpetual
state of 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 inversely 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 separate atoms.
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 between them.
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/d2. 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 car. Gravitational force is
spontaneous.
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.
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 linear acceleration.
In summary it can be said that gravity is associated with the primary projection of matter. 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.
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. 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 centers within 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 of gravity.
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 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. 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 component.
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 proton.
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/ε0μ0 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 roughly
correspond to his intuitive notion of elastic distortions.
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 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.
Concluding Observations:
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:(19)
...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.
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 emerges naturally.(21)
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.
Notes and References:
1. The Void is directly accessible in human experience. As human beings we too are required to span and integrate history
in order to cope in a practical way with phenomenal experience. The Void is associated with our conscious intensions. We recall
and re-assimilate elements of past experience in order to formulate plans that anticipate a future result.
2. This will be shown in the next chapter.
3. At least five methods have been proposed to detect gravitational waves: resonant bar detectors on Earth, laser
interferometers on Earth, space microwave interferometers, laser interferometers in space, and Doppler tracking in space.
Ciufolini and Wheeler, Gravitation and Inertia, Princeton University Press, 1995.
4. The calculus assumes that space and time are continuous, allowing of infinitesimal increments. It is noteworthy that
George Berkely refuted Newton’s theory of fluxions over this issue in the Analayst, 1734. Luce, A. A., and Jessop, T. E., Eds., The
Works of George Berkeley, Bishop of Cloyne, 9 Vols., London and New York, 1948-1957.
5. In is interesting that the concept of the boundless was expressed by the Milesian philosopher Anaximander as the
source of the world in the sixth century BC. The First Philosophers, translated by Robin Waterfield, Oxford University Press, NY,
2000.
6. This will be shown in Chapter V.
7. In developing his initial theory of the atom when working with Rutherford, Neils Bohr arbitrarily stated that some of the
classical laws of physics do no apply within the atom. This remarkable statement requires that the inner space of the atom is
distinct from external space. We will return to this in the next chapter.
8. The arguments advanced by Lorentz (and independently by Fitzgerald), that the phase differences of light to be expected
in the famous experiments of Michelson and Morley can be compensated by changes in the relative dimensions of the arms of
the interferometer apparatus, is similar to but not identical to a relative skipping of space frames between the two orthogonal
arms. Michelson and Morley, American Journal of Sciences, 34, 1887, p. 333; Phil. Mag., 24, 1887, p. 449. Lorentz, Arch, Néerl.,
2, 1887, pp. 168-176. Lorentz H.A., Michelson’s Interference Experiment, also Einstein A., On the Electrodynamics of Moving
Bodies, both in The Principle of Relativity, A Collection of Original Memoirs on the Special and General Theory of Relativity,
Methuen, London, 1924. Also Planck, M., Eighth Lecture (General Dynamics, Principle of Relativity.) Eight Lectures on
Theoretical Physics, Colombia University Press, 1915.
9. They were identical before the Newton was introduced to mask the difference in units.
10. Dimensionless relationships between the atom and the universe at large have been suggested many times in the
past, together with various other dimensionless numbers. Sir Arthur Eddington was one of the earliest enthusiasts, pointing out
that the coulomb force and the gravitational force between the electron and proton in the hydrogen atom differ in order of
magnitude by a factor of about 1039 and this is approximately the square root of the assumed number of particles in the
universe. Sir Arthur Eddington, The Expanding Universe, Cambridge University Press, 1933.
11. As pointed out previously, the duration of the primary interval of time, has a value of 1.519 x 10-16 seconds. This is also
the time required for light to circumscribe the 12th shell of the hydrogen atom, the shells being largest in hydrogen and the 12th
being at an energy level close the limit of the ionization continuum. Hänsch T.W., Schawlow A.L., Series G.W., The Spectrum of
Atomic Hydrogen, The Laureates’ Anthology, Vol. II, Scientific American, 1991. The primary interval of time is derived in Chapter
V, where it is shown to be related to the red shift of distant galaxies and also to the cosmic background microwave radiation.
12. Bertrand Russell attempts to define number in, Introduction to Mathematical Philosophy, Touchstone Books, NY, 1971.
After some discussion of “primitive” concepts and classes, he defines number as follows:
The number of a class is the class of all those classes that are similar to it.
...In other words, a number (in general) is any collection which is the number of one of its members; or more simply still:
A number is anything which is the number of some class.
Such a definition has a verbal appearance of being circular, but in fact it is not... This kind of procedure is very common and it is
important to recognize that it is legitimate and even often necessary.
The difficulty which Russell has in defining number stems from the recurrent character of the primary activity, alternately
representing number as a particular quantity and then as a universal quality. By the word ‘class’ he clearly intends a unifying
quality which defines the quantitative number.
13. Dirk J. Struik points out: “Greek mathematicians made a distinction between ‘arithmetica’ or science of numbers
(arithmoi ) and ‘logistics’ or practical computation. The term arithmos expressed only a natural number, a ‘quantity composed of
units’ (Euclid, Book VII, Def. 2; this also meant that ‘one’ was not considered a number)... This lasted until the Renaissance.
Stevin, in his arithmétique of 1585, pleads passionately for the recognition of ‘one’ as a number like other integers.” Dirk J.
Struik, A Concise History of Mathematics, 4th Ed., NY, Dover, 1987, p. 60.
14. In 1888 Richard Dedekind writes: “...it appears as something self-evident and not new that every theorem of algebra and
higher analysis, no matter how remote, can be expressed as a theorem about natural numbers,—a declaration I have heard
repeatedly from the lips of Dirichlet. But I see nothing meritorious—and this was just as far from Dirichlet’s thought—in actually
performing this wearisome circumlocation and insisting on the use and recognition of no other than rational numbers.”
Dedekind R., The Nature and Meaning of Numbers, Essays on the Theory of Numbers, English translation first published by
The Open Court Publishing Company (1901), NY, Dover, 1963.
15. Einstein, A., On the Electrodynamics of Moving Bodies. Ibid.
16. Grünbaum, A., Philosophical Problems of Space and Time, NY., 1963; Grünbaum, A., The Bearing of Philosophy on the
History of Science, Science, 143, 1406, 1964; Grünbaum, A., Relativity Theory, Philosophical Significance of, The Encyclopedia
of Philosophy, Vol. 7, NY., Macmillan, 1967.
17. Dirac, P.A.M., Is There an Aether? Nature, 168, 906, 1951.
18. In a letter to Born in 1947, concerning Quantum Mechanics, Einstein wrote, “ I cannot seriously believe in it because the
theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a
distance.” He was convinced that the “‘old one’... is not playing at dice.” The Born-Einstein Letters, translated by Irene Born.
Walker, New York, 1971. This famous objection was formalized in a paper, A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev.
47, 777 (1935). Experiment did not substantiate his objection, thus indicating action at a distance in some sense that is better
interpreted as quantum correlation. Objections to a probability approach have been expressed by David Bohm for many years.
Bohm, D., Quantum Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1951. Albert, D.Z., Bohm’s Alternative to Quantum
Mechanics, Scientific American, May 1994, Vol 270, No 5. System 3 provides a mechanism for quantum correlation via the
universal set. In doing so, System 3 is not consistent with a blind probabilistic interpretation of reality, so that it contains
elements of both sides of the argument.
19. Mehra, J., and Rechenberg, H., The Formulation of Matrix Mechanics and its Modifications, The Historical Development
of Quantum Theory, Vol. 3, NY., Springer Verlag, 1982.
20. Dirac, P.A.M., The Development of Quantum Theory, NY., Gordon and Breach, 1971.
21. There are aspects of this that are similar to David Bohm’s conception of wholeness and the implicate order, for that
could be taken as an apt description of the System. He too is speaking of the cosmic order, although some of his views diverge
from those expressed here. Bohm, D., Wholeness and the Implicate Order, London, Routledge and Kegan Paul, 1980.
It is advisable to read Unified Theories, Fantasy, & Cosmic Order first.
Abstract:
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.
Preamble:
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.
Introduction:
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. 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 light.
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.
While wave-like distortions or perturbations in the local fabric of space-time may be detectable in the
immediate vicinity of rapidly rotating super-dense neutron stars, due to localized intense levels of non-
synchronous space-frame skipping, there is no related mechanism that will allow such effects to propagate
endlessly throughout the integrated fabric of space-time even if they can occur. There is no such independent
thing as a spacetime continuum for a superimposed wave effect to propagate through. Experiments to detect
gravity waves in the normal synchronous environment of our solar system are unlikely to turn up any
convincing evidence that they exist.(3)
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. This is outlined in
Chapter III.
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 IV-1.
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
systems.
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 1.519x10^-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 coordinates.
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.
Figure IV-1
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 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 space.(7)
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=M0/(1-(v/c)^2)1/2, where M0 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= L0(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
T=T0(1-(v/c)^2)1/2.
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 with simultaneity.
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
acceleration.
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 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 coordinates.
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 a progressive degree of relative space frame skipping.
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 contradicts 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. An event horizon swallows A in a
singularity from the standpoint of B. But mass-energy conservation requires that B effectively moves along the
diagonal in the upper right hand quadrant of the world box towards a relative doubling of both space and
quantum frames at 2, 2. The right hand half of the historic coordinates is thus the reciprocal of the left hand
half.
We thus find that although the Lorentz transformations apply equally between different inertial systems,
there can be 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
preponderance of synchronicity in the universe as a whole. Since all matter in the heavens is in a perpetual
state of 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 inversely 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 separate atoms.
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 between them.
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/d2. 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 car. Gravitational force is
spontaneous.
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.
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 linear acceleration.
In summary it can be said that gravity is associated with the primary projection of matter. 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.
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. 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 centers within 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 of gravity.
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 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. 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 component.
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 proton.
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/ε0μ0 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 roughly
correspond to his intuitive notion of elastic distortions.
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 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.
Concluding Observations:
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:(19)
...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.
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 emerges naturally.(21)
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.
Notes and References:
1. The Void is directly accessible in human experience. As human beings we too are required to span and integrate history
in order to cope in a practical way with phenomenal experience. The Void is associated with our conscious intensions. We recall
and re-assimilate elements of past experience in order to formulate plans that anticipate a future result.
2. This will be shown in the next chapter.
3. At least five methods have been proposed to detect gravitational waves: resonant bar detectors on Earth, laser
interferometers on Earth, space microwave interferometers, laser interferometers in space, and Doppler tracking in space.
Ciufolini and Wheeler, Gravitation and Inertia, Princeton University Press, 1995.
4. The calculus assumes that space and time are continuous, allowing of infinitesimal increments. It is noteworthy that
George Berkely refuted Newton’s theory of fluxions over this issue in the Analayst, 1734. Luce, A. A., and Jessop, T. E., Eds., The
Works of George Berkeley, Bishop of Cloyne, 9 Vols., London and New York, 1948-1957.
5. In is interesting that the concept of the boundless was expressed by the Milesian philosopher Anaximander as the
source of the world in the sixth century BC. The First Philosophers, translated by Robin Waterfield, Oxford University Press, NY,
2000.
6. This will be shown in Chapter V.
7. In developing his initial theory of the atom when working with Rutherford, Neils Bohr arbitrarily stated that some of the
classical laws of physics do no apply within the atom. This remarkable statement requires that the inner space of the atom is
distinct from external space. We will return to this in the next chapter.
8. The arguments advanced by Lorentz (and independently by Fitzgerald), that the phase differences of light to be expected
in the famous experiments of Michelson and Morley can be compensated by changes in the relative dimensions of the arms of
the interferometer apparatus, is similar to but not identical to a relative skipping of space frames between the two orthogonal
arms. Michelson and Morley, American Journal of Sciences, 34, 1887, p. 333; Phil. Mag., 24, 1887, p. 449. Lorentz, Arch, Néerl.,
2, 1887, pp. 168-176. Lorentz H.A., Michelson’s Interference Experiment, also Einstein A., On the Electrodynamics of Moving
Bodies, both in The Principle of Relativity, A Collection of Original Memoirs on the Special and General Theory of Relativity,
Methuen, London, 1924. Also Planck, M., Eighth Lecture (General Dynamics, Principle of Relativity.) Eight Lectures on
Theoretical Physics, Colombia University Press, 1915.
9. They were identical before the Newton was introduced to mask the difference in units.
10. Dimensionless relationships between the atom and the universe at large have been suggested many times in the
past, together with various other dimensionless numbers. Sir Arthur Eddington was one of the earliest enthusiasts, pointing out
that the coulomb force and the gravitational force between the electron and proton in the hydrogen atom differ in order of
magnitude by a factor of about 1039 and this is approximately the square root of the assumed number of particles in the
universe. Sir Arthur Eddington, The Expanding Universe, Cambridge University Press, 1933.
11. As pointed out previously, the duration of the primary interval of time, has a value of 1.519 x 10-16 seconds. This is also
the time required for light to circumscribe the 12th shell of the hydrogen atom, the shells being largest in hydrogen and the 12th
being at an energy level close the limit of the ionization continuum. Hänsch T.W., Schawlow A.L., Series G.W., The Spectrum of
Atomic Hydrogen, The Laureates’ Anthology, Vol. II, Scientific American, 1991. The primary interval of time is derived in Chapter
V, where it is shown to be related to the red shift of distant galaxies and also to the cosmic background microwave radiation.
12. Bertrand Russell attempts to define number in, Introduction to Mathematical Philosophy, Touchstone Books, NY, 1971.
After some discussion of “primitive” concepts and classes, he defines number as follows:
The number of a class is the class of all those classes that are similar to it.
...In other words, a number (in general) is any collection which is the number of one of its members; or more simply still:
A number is anything which is the number of some class.
Such a definition has a verbal appearance of being circular, but in fact it is not... This kind of procedure is very common and it is
important to recognize that it is legitimate and even often necessary.
The difficulty which Russell has in defining number stems from the recurrent character of the primary activity, alternately
representing number as a particular quantity and then as a universal quality. By the word ‘class’ he clearly intends a unifying
quality which defines the quantitative number.
13. Dirk J. Struik points out: “Greek mathematicians made a distinction between ‘arithmetica’ or science of numbers
(arithmoi ) and ‘logistics’ or practical computation. The term arithmos expressed only a natural number, a ‘quantity composed of
units’ (Euclid, Book VII, Def. 2; this also meant that ‘one’ was not considered a number)... This lasted until the Renaissance.
Stevin, in his arithmétique of 1585, pleads passionately for the recognition of ‘one’ as a number like other integers.” Dirk J.
Struik, A Concise History of Mathematics, 4th Ed., NY, Dover, 1987, p. 60.
14. In 1888 Richard Dedekind writes: “...it appears as something self-evident and not new that every theorem of algebra and
higher analysis, no matter how remote, can be expressed as a theorem about natural numbers,—a declaration I have heard
repeatedly from the lips of Dirichlet. But I see nothing meritorious—and this was just as far from Dirichlet’s thought—in actually
performing this wearisome circumlocation and insisting on the use and recognition of no other than rational numbers.”
Dedekind R., The Nature and Meaning of Numbers, Essays on the Theory of Numbers, English translation first published by
The Open Court Publishing Company (1901), NY, Dover, 1963.
15. Einstein, A., On the Electrodynamics of Moving Bodies. Ibid.
16. Grünbaum, A., Philosophical Problems of Space and Time, NY., 1963; Grünbaum, A., The Bearing of Philosophy on the
History of Science, Science, 143, 1406, 1964; Grünbaum, A., Relativity Theory, Philosophical Significance of, The Encyclopedia
of Philosophy, Vol. 7, NY., Macmillan, 1967.
17. Dirac, P.A.M., Is There an Aether? Nature, 168, 906, 1951.
18. In a letter to Born in 1947, concerning Quantum Mechanics, Einstein wrote, “ I cannot seriously believe in it because the
theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a
distance.” He was convinced that the “‘old one’... is not playing at dice.” The Born-Einstein Letters, translated by Irene Born.
Walker, New York, 1971. This famous objection was formalized in a paper, A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev.
47, 777 (1935). Experiment did not substantiate his objection, thus indicating action at a distance in some sense that is better
interpreted as quantum correlation. Objections to a probability approach have been expressed by David Bohm for many years.
Bohm, D., Quantum Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1951. Albert, D.Z., Bohm’s Alternative to Quantum
Mechanics, Scientific American, May 1994, Vol 270, No 5. System 3 provides a mechanism for quantum correlation via the
universal set. In doing so, System 3 is not consistent with a blind probabilistic interpretation of reality, so that it contains
elements of both sides of the argument.
19. Mehra, J., and Rechenberg, H., The Formulation of Matrix Mechanics and its Modifications, The Historical Development
of Quantum Theory, Vol. 3, NY., Springer Verlag, 1982.
20. Dirac, P.A.M., The Development of Quantum Theory, NY., Gordon and Breach, 1971.
21. There are aspects of this that are similar to David Bohm’s conception of wholeness and the implicate order, for that
could be taken as an apt description of the System. He too is speaking of the cosmic order, although some of his views diverge
from those expressed here. Bohm, D., Wholeness and the Implicate Order, London, Routledge and Kegan Paul, 1980.
