Six Representational Modes
and the
Structure of Photons
Lawrence E. Denslow
As students of the Reciprocal System of Theory
we have become used to a somewhat different set of paradigms than those
held by all other students of the physical sciences, and by each of us
prior to our acceptance of the concepts embodied within the Reciprocal
System. The rest of the scientific community accepts without question
the primacy of the observed characteristics of this physical plane of
existence. To the community at large, mass is a fundamental characteristic
of anything to be called matter and matter is the fundamental building
block of the universe. To the establishment it is totally unthinkable
to even conjecture that motion could exist unless matter is moving. That
is the biggest stumbling block or hurdle to be overcome. Our thought patterns
are still inhibited by our previous habitual use of that paradigm, resulting
in such extreme difficulty in taking "an old set of data" for interpretation
"from a new perspective" that we do not recognize our use of those old
habits. By perspective I mean totally new set of concepts as outlined
by D.B. Larson in his presentations of the fundamental concepts for a
"Universe of Motion." Even Larson had difficulty turning loose of many
of the undeclared assumptions hidden in our observations of the physical
universe from this region of Time/Space.
Larson has outlined for us an order of complexation of units of displacement
motion and given us some of the new representational modes required for
many of the phenomena observable in a physical universe of motion; such
as two dimensional rotations. Invoking the rules of ordinary mathematics
in all regions, including the representational requirements of Euclidean
geometry and the concepts of probability relations for any representation
of the concept of motion, requires us to really understand exactly what
the rules of ordinary mathematics are and also what they imply. It is
this requirement for knowing, not only how ordinary mathematics is used,
but what its rules imply, that has led to the requirement for six possible
modes of representation at three dimensional reference points, not just
the familiar four of the Time/Space region.
In a multiple reference point Universe of Motion only the point coordinate
axes for any specific reference point combination of representations of
the concept of motion is important for that combination representation,
regardless of how complex the final representation may become. Critical
examination of the idea of a multiple reference point universe reveals
that only the individual set of coordinate axes of each and every reference
point need ever be considered with respect to any individual reference
point. Every photon, every subatomic particle, every atom, cosmic or
material, is its own reference point.
For the existence of any reference point phenomena, no other reference
point is of any importance, so far as the representation of motions or
effects of motions at that reference point are concerned. The only possible
subsequent importance any reference point may have to another comes about
when, and only when, they share the same unit of primary motion and, thereby,
become a new reference point for a different reference point phenomena.
There are at least two possibilities for this situation: atoms in chemical
orientation and photon interactional phenomena. The two interacting components
become not two phenomena at the same reference point; they become a new
phenomena at a new reference point because the new reference point phenomena
is a different combination of motions.
The resulting mathematical expression for this concept must reflect this
reality even though the new reference point effect may be measurable in
terms of each of the previous reference point phenomena. Conceptual and
mathematical consensus for any expression of the effective reality of
a reference point phenomena causes the requirement for the concepts embodied
in the algebraic expression relating magnitude and direction to be coherent
with the magnitudes of the arithmetic. A numerical sequence is required
for any expression of quantity, whether that quantity is of substance
or direction. One is followed by two and then three.
Let us now consider, "What is it that makes a unit of displacement be
a displacement? Is it its opposition to primary motion in whatever required
representation primary motion must have, or is it something else?" Since
primary motion is the very first possible motion that can be represented,
primary motion must be given the very first possible mode of representation
in the three dimensions available for its representation. That representation
is one Dimensional and one directional in any one of the three dimensions.
What must be next? Is it two Dimensional and one directional, or is it
one Dimensional and two directional? Can primary motion be directly represented
in more than one way? If it could, would there be any consistency among
subsequent combinational representation? I have played with as many possibilities
as I could think of and have always come back to one and only one possible
way of directly representing primary motion: one Dimensional, one directional
linear. Any other possibility led to so many possible second steps that
it became almost impossible to calculate a required sequence for a third
step.
In answer to these questions about displacements and primary motion,
it seems clear that since primary motion can be represented in a direct
manner only as one Dimensional one directional linear, a displacement
must first be able to oppose that kind of representation before a generalization
can be considered. With primary motion directly representable only as
one Dimensional one directional linear, and that one direction being in
either of the two directions of one dimension in any conceivable three
dimensional coordinate system, an opposition to primary motion in that
dimension has to be represented as one Dimensional two directional linear.
It can not be in just one of those directions, because primary motion
would be left free to be expressed in the other direction and nothing
would have been accomplished and nothing could be represented! That is
why the first representable displacement motion must be one Dimensional
two directional linear in one of the three dimensions, which thereby leaves
both directions of both remaining dimensions open in which to represent
primary motion. Once the direction of primary motion is selected, it is
done, and that's that, so far as that reference point is concerned. Any
effects of displacements remaining with that unit of primary motion will
seem to have straight line movement relative to any reference system of
coordinates. The first possible reference point phenomena must have a
structure represented as a combination of a one Dimensional two directional
linear displacement and a unit of primary motion in a perpendicular dimension.
We call these reference point structures photons!
The question for these photon reference points concerning now the effect
of their structure is to be expressed relative to a whole bunch of other
reference points of whatever kind must have an answer related to, or given
in terms of, the mathematics used for their representation. This requires
consideration of the meaning of directionality as it applies to the idea
of dimensional systems.
Random orientation of reference point coordinate systems with respect
to all other reference point systems requires the use of probabilities
for sameness among all such coordinate system. Use of probabilities is
limited by the arithmetical system and, thus, the question of which must
come first: substantive quantity or direction. An obvious question is:
"Is it obvious that the quantity being represented must exist before it
can be given direction?" This question is, for us, similar to the question
for most physicists of whether motion can exist without the presence of
matter; specifically, can there be direction without something (even a
concept of something) to have a direction? If so, we have a universe of
motion, not direction. This conclusion seems to be the same as that derived
by present day physicists; matter, not motion. If a quantity (e.g., the
concept of a unit of motion) must be available before directionality can
be specified, then the effect of the quantity being analyzed must be one
directional, two directional, or multidimensional. Since one directional
can be in either of two directions, the effect of a two directional
linear displacement is equally probable in either of the two directions
possible. To maintain equality of probability, two such units of displacement
must be sequentially related in order to complete the probability function
for the representation of either one of the units of displacement.
Considering all the mathematical functions capable of fulfilling the
conceptual requirements for representation of the one Dimensional one
directional linear primary motion and the one Dimensional two directional
linear displacement perpendicular to the primary motion, it is found that
only the sine and cosine functions can satisfy those conceptual requirements
in an unambiguous manner; i.e., an effect that is linearly positioned
and continuously variable and has two directions of possible effect.
By this convoluted path it has been shown that photons must be conceptually
represented as a combination of 1D2d_{L} displacements with perpendicularly
primary motion and mathematically as sine wave functions. It has been
implied that the next step of complexation must be similarly related thru
appropriate application of probabilities for the ideas of dimensionality
and directionality.
The idea of rotational representation of directionality around an axis
causes all linear directions to become partially accessed and thereby
related in the resultant effect. Possibilities for subsequent representations
require primary motion to be represented with rotational directionality.
Direct representational probability of this possibility is so small as
to be nonexistent. However, it is the augmentation of the concept of
directionality for the representation of primary motion that allows for
a displacement motion to be represented rotationally and development of
the generalization for displacement to be an opposition to primary motion
as previously questioned.
Chart 1 indicates what the six modes of representation for units of displacement
motion must be at sufficiently compound motion reference points. That
which is observable in a generalized three dimensional system is only
the effect of Notational Reference Point representations of displacement
motions other than 1D1d_{L}. Primary motion is the one dimensional
velocity observed for photons and some subatomic particles. Equivalent
primary motion is the maximum resultant one dimensional velocity for all
atomic and the remaining subatomic structural representation. The order
of complexation among the six modes of representation at individual reference
points is as shown in Chart 2, increasing complexity from the bottom up.
The final Chart shows the resultant physical universe composed of seven
principle regions in Three Sectors.
Chart 1
Equivalent Euclidean mode; (in symbols #of Dimensions #of directions _{type})
Motion Symbol # Dimensions #directions directionalityLinear
translation; 1D1d_{L} One Dimension one direction linear
Linear oscillation; 1D2d_{L} One Dimension two directions linear
Unidirectional rotation; 1D1d_{R} One Dimension one direction
rotational
2D1d_{R}
 Two Dimensions one direction rotational
Rotational Oscillation 1D2d_{R} One Dimension two directions
rotational
2D2d_{R} Two Dimensions two directions rotational

