## Specific Rotation of Displacements

It has been shown that it is the presence of negative electric displacement that makes it possible to form, and thus develop representations for, individual molecules or structural units composed of a specific number of atoms of certain elements; formulas for compounds and radicals. Now that some of the possible orientations required by atoms of matter for compound formation are at least more familiar and the mathematical expressions representative of the interactive forces are recognized, the “how” of obtaining the values for the principal variable in those expressions must be considered.

The initial displacements of each type, linear and rotational, extend from unit primary motion to give rise to effects in either dimensional aspect. The direction in the generalized dimensional aspect of the effect of displacement is outward for several reasons: a displacement motion is dimensional only within the individual reference point system; clockwise vs. counter-clockwise is a matter of viewpoint; inside unit space, time is dimensional, because the spatial quantity cannot be less than unit value. Any effect in generalized space for both primary and displacement motions can be represented only in an outward direction from each reference point.

A background unit of primary motion cannot be given rotational representation, although it is the primary motion in each dimension by which to begin the sequence of counting to determine the specific rotation involved in any given orientational relationship. Orientations for subsequent “bonding” extend from the natural datum, unity, as does the gravitational force effect of the rotations, mass. Specific rotations are a* *consequence of requiring atoms and all interactional effects related to their presence to be relative to the stationary reference system. They are not additional motions or parts of atomic structure; they are merely ways of accounting for our stationary reference system.

It is only in interactions among atoms and between atoms and sub-atoms along with the need to calculate an observable result in a fixed reference system that the presence of units of photon vibration become required in the expression. Representation of extra units of vibration for a given ground state rotational displacement notation requires an adjustment in appropriate dimensions for the specific rotational displacement values.

From the viewpoint of the generalized three dimensional reference system of space, *zero *rotational displacement must be represented as unit rotation. As a result, the initial unit of speed in each rotational dimension must be counted when determining the quantitative effects of all rotational representations relative to the stationary reference frame. The *specific rotation** *of every atom is at least one unit greater in each dimension than the displacement represented by the notation given in the periodic charts for the ground state elemental configuration. This is part of the reason for choosing this type of structural notation for atomic structures in developing the consequences of the postulates for the Reciprocal System of theory.

From the initial comments in Chapter Three in the section on Representable Motions, positively displaced rotationally represented displacements added to negatively displaced 1D2d_{L} displacements may be represented in different dimensions as well as in different modes. Since all displacement representations at individual Notational Reference Points have a scalar effect relative to the motions at other reference points, the magnitude of the net effect for each atomic system is maintained by a very specific minimum effective displacement from unity. This minimum is obtained by geometric summations of all effective displacements considering dimensional and directional characteristics, as well as direction of displacement from unity.

Additional units of negatively displaced 1D2d_{L} motion are always added during the atom building process. Some photons are emitted during the process but the high energy 1D2d_{L} units of displacement remaining with the new atomic structure cause the total rotationally represented displacement to have their interactional effects countable in partials of positively displaced units of 1D1d_{R} or 2D1d_{R} motion.

Each unit of motion of a multi-unit photon is a contiguous but separate unit represented in the same dimension; otherwise, photons could not exhibit the photoelectric effect or fluorescence effect. There seems to be no logical requirement for all units of negative 1D2d_{L} motion, which are part of the base photons, to maintain the same identical geometric dimensional probability positioning. That is to say; the following requirement does not necessarily follow, that all unitary parts of a given frequency 1D2d_{L} displacement rotate together with all rotationally represented units of displacement motion required for the particular atomic representation.

In the basic structure of atoms each linear unit equivalent of rotationally represented positively displaced motion is directly associated with a negatively displaced vibrational unit, but not vice versa. This is caused by the sequential ordering of representation. The vibrational frequency of the photons being combinationally represented in the representation as atoms of matter is specific but all factors related to their precise relation to required rotational displacements and specific rotations is not yet clear. At the present stage of development of the theory, the required number of vibrational units involved with required rotational representations does not extend beyond *vibration two** *requirements for atomic structures. There seems to be a lack of anything other than continuity (representation in the same dimension) required of the units of vibration of the basic frequencies of the photons. Determination of specific presence of non-rotating units of vibration for potential association with the required rotating units has yet to be confirmed and shown to be a requirement.

In order to extend rotation beyond unit equivalence with the oppositely directed 1D2d_{L} displacement of one unit, and maintain minimum net displacement from unity, additional units of vibration must be brought into effective presence. Until extension is required the system is said to be rotating on a *vibration one** *status. Immediately upon requiring rotational representation equivalent to two linear units around any dimension, another unit of vibration must be present to prevent equivalence destruction of the photonic vibration. This is the reason the M 2-2-(2) notation was unstable. The atomic interacting system avoids this unstable situation by increasing the vibrational frequency of one or both photons being rotated.

The force effect of one unit of rotationally represented displacement, having specific rotation t = 2, is less than unit value, ln t = 0.693. Rotational notation value 2 having specific rotation t = 3; ln t = 1.0986; is effective. Thus, the first series of eight elements is seen to have inactive force dimensions until additional vibrational units are brought into rotation.

The symbol t used in the force equations is called the *specific rotation** *because it reflects the required number of units of rotational motion effective in the three dimensionality of space with respect to each atomic Notational Reference Point. The value of t is obtained directly or indirectly from the notation for each kind of atom. Because extension to *vibration two** *status in the photon vibrations is required for certain orientational associations, as well as, at certain positions in the building process of atomic structures, conversion of the rotational representation to other values for *vibration two** *conditions may occur for any atom beyond atomic number one.

Extension of rotation to a second unit of vibration is a function of the total displacement being represented for a given atom, rotational and linear equivalencies, approaching the absolute limit of one effective linear displacement from unity in each dimension. Offsetting rotations in a specific temporal dimension for chemical association between atoms often requires other shifts of rotational representation, as a result of positional relationships and environmental factors. These shifts are part of what effectively causes the requirement of recognizing the rotation of the extra units of negative 1D2d_{L} displacement. As a result of the probability positioning of the units required for a second vibration unit to become effective, the specific rotation values shift in the appropriate dimensions to half units of specific rotation. The primary controlling factors for determining the specific rotation in each dimension of each atom are seen to be the identity of the atom and the orientational associations required; i.e., normal electric, neutral, or magnetic. The next most important factors are probability functions. These factors are part of what makes the calculation of all atomic interactional, as well as, absorption and emission phenomena difficult.

The electric dimension of rotational representation for the double photon doubly rotating system is the axis for rotational representation of the entire magnetically rotating structure. Electric displacement values may extend by whole units or half units because an electric unit is a rotational representation for both photonic bases. Half units of specific rotation are not necessarily required in the electric dimension although they may be present without overt evidence of their presence. Specific electric rotation values may follow the sequence 2, 2½, 3, 3½, 4, 4½, 5, 5½, 6, 6½ , 7, 7½, etc. or any intermediate sequence up to the other extreme of 2, 3, 4, 5, 6, 7, 8, 8½, 9, 9½, 10, etc., up to 16.

The sequence of specific magnetic rotations for the different elements may follow the pattern 2, 2½, 3, 3½, 4, 4½, and 5 in either, but not the same in both, magnetic dimensions for corresponding elements from one magnetic row to the next. The sequence of specific magnetic rotations may be at the other extreme 2, 3, 4, 4½, 5. The shift to the vibration two status may be at any intermediate position of the sequence.

In Equation 8 of Chapter 6 [page 75], t is evaluated on the basis of a one dimensional force effect. Equation 10 may appear to assume that the displacement in each of the magnetic dimensions of the atom in question is the same. Squaring a function has exactly the same meaning as obtaining the product of similar functions because the direction in space of any time dimension is completely indeterminate. For an atom exhibiting different displacement values, such as those of the 3-2 and 4-3 magnetic rotational groups, the effective distribution is that of a spheroid having an effective t value determined from the relation^{25}

$$\left( t^2_p \times t_s \right )^{1/3} = t_{eff}$$

t_{p} is the specific rotation effective in the two equal dimensions of the spheroid and is associated with the principal magnetic rotation which is sometimes the larger value and sometimes the smaller value. t_{s} is the specific rotation effective in the single dimension and similarly can be either the smaller or the larger value. Of course t’ is the specific rotation effective in the electric dimension which may or may not be correlated with the spheroidal distribution of the magnetic dimensions.

Net positive rotational displacement is absolutely required for stability in the material sector of the universe, and in an environment of atomic orientations a totally positive rotational displacement is more probable than any combination of positive and negative displacements where the negative displacements are not definitely required for orientational association, and even then, the effective specific rotation of the negative speed displacement must be determined from the equivalent positive displacement.

Remember, positive or negative displacement, inward or outward, is all the same in either generalized dimensional aspect relative to the atom as a scalar reference point. *Specific rotation** *is like the absolute value of a signed number, it has no sign, it is a value. Neutral orientations for normally first order negative valence elements are considered to be the result of totally positive displacement combinations, as well as, for determining the specific rotations involved. When magnetic orientation, enhanced orientation, or neutral orientation is involved, vibration two status for several rotational displacements is automatically demanded. The corresponding specific rotation of an atom in associational relation whether with other atoms of the same kind (the elemental form) or with atoms of a different kind is determined by the orientation required or possible for the atoms involved.

Interatomic distances must be calculated between each pair of atoms in chemical formula units and subsequently arranged relative to geometric probabilities for determination of crystal geometries and molecular or radical shapes, all in accord with relative negativities. The t value entered into the final force equation used to determine the interatomic distance in a specific spatial direction is t_{eff}. For metallic elements and alloys of Division I elements, t_{eff} is the geometric mean of the specific rotations of adjacent atoms. For elements of Division IV and for normal compounds, negative displacements are balanced or offset by positive displacements resulting in the effective displacement between any two atoms being the sum of the displacements of those atoms in the line of orientation. Elements of Divisions II and III may utilize the 8-x neutral orientations thereby creating a pseudo-balancing of displacements for their interatomic orientations. Neutral orientations are almost always interspersed among positive orientations and positive-neutral orientations causing quite complex interatomic situations. Negative to negative orientations seldom have sufficiently high probabilities for existence .to require consideration at this stage of the development of the theory.

A little study of the Charts 1, 2, 3, and 4, in the Appendix will show the positions at which shifts to vibration two status has occurred for one or more of the required rotationally represented displacements in the elemental forms. Where vibration two status is required for binary compounds of the NaCl type arrangement, the specific rotations are also listed.

Vibration two status may result from maximum distribution effects. The fact that a maximum distribution from minimum displacement prevents equivalence alignment of rotational components with linear vibrational components is fortuitous from our point of view of analysis and correlation with the observed material sector of the physical universe. Equivalence alignments result in reduction to and separation of one or more rotationally represented displacement units to linear vibrational form. In many cases a simple sub-atomic compound motion is separated (either an electron, a positron, or a neutron) while in other cases the simplest of atomic compound motion structures having zero electric rotational displacement (a helium atom) is separated. These separations are identified as radioactive decay. Radioactive decay is only one type of decay mechanism by which spontaneous destruction or decay of a specific compound motion could occur.

Quite often a required shift to vibration two status contributes to the cause of a chemical process being endothermic, rather than a heat balance being totally a chemical reorientation effect. The opposite effect may also be true. Photochemical reactions are often initiated on this basis, also.

The actual atomic environment dictates the extent of the shift to vibration two status for the rotational displacement units of the individual atoms. This means that the question of the identity of adjacent atoms is very important, as is the temperature of the system and the flux density of other frequencies of radiation. The applicable probability functions for the possible geometric arrangements of the atoms involved are also affected by these factors. Do not expect the specific rotation of any given element to be the same throughout a given complex molecule or in all possible atomic arrangements: i.e., in all compounds, as well as the elemental form, or to remain constant in a specific chemical reaction.

Since the specific rotations of all atoms of a given Division I element are equal and the magnitude of the “forces” in an isometric crystalline form is equal in all directions in space, it is to be expected that each should have an isometric crystal form. Elements of the other Divisions are not quite so simple, especially those with high probability for negative electric rotations. Even though all Division II elements do have an isometric form, the higher values of the specific electric rotations and the possibility of the opposite neutral orientation of alternating atoms in a given array in the three dimensionality of space require a certain probability for additional geometries.

The solid phase of matter results from the orientation of the motions of the atoms which allows the atoms to move to equivalent space positions inside one natural unit of extension space. Variation in the magnitude of the specific rotations from one orientation to another in complex compounds causes the apparent magnitude of the forces and, therefore, the distances between each pair of atoms in the array to be the same in two dimensions or no two of the dimensions; i.e., different in one or all three dimensions, respectively. The actual magnitude of the specific rotation in each dimension of each atom involved in the overall array determines the required interatomic distance for each pair of atoms and thus, the resulting geometry in space.

## Photon Interactions

Photons of radiation consist of either positive or negative 1D2d_{L} displacements which are representable only as an effect of interaction in the generality of space; i.e., the displacement has no directly discernible effect in and of itself in the unit of primary motion of which it is a part; it cannot be perceived without interaction. Photons of all frequencies are interface phenomena because they have displacement in only one dimension, and thereby, become effective and identifiable in either of the three dimensional aspects of motion, when, and only when, they interact with other photons or with atoms or sub-atoms of matter, either material or cosmic. It is the addition of rotationally represented displacement motion to oppositely displaced 1D2d_{L} motion that gives rise to the effects identified as atoms and sub-atoms of matter of either the material or the cosmic sector.

The overall displacement motion represented within the NRP is responsible for these effects: atomic mass, vectorial motion, heat, electric charge, and magnetic charge. In the normal region outside unit distance the net rotational displacements that constitute the atoms of matter have the effect of mass, something entirely separate from the quantities of energy which may be absorbed by or emitted from atoms. Components representable as opposition to the outward linear motion of the natural progression may be represented within the same unit space in two different ways. The one dimensional application of energy, as 1D1d_{L} displacement, to a material structure is represented with the other displacement motions in such a manner as to give the effects we presently identify as vectorial motion. Lack of relative motion, other than thermal motion, among atoms and molecules in the solid phase allow contiguous structures to share 1D1d_{L} displacement motion. The other way of representing opposition to the normal outward progression is by the addition of low frequency 1D2d_{L} displacement in that dimension.

Photons of radiation either do or do not have resonance with the various atoms or atomic groupings in such a way as to give rise to the phenomena of absorption, reflection, and transmission. The large scale effects of each of these phenomena are thoroughly discussed in available conventional physics texts. Refraction effects, absorption effects, and reflection effects are sufficiently different so as to require different treatment both conceptually and mathematically. The phenomenological descriptions of the interactions of photons with atoms of matter are still in the process of being investigated in terms of the Reciprocal System of theory, as are most other phenomena. However, the phenomena which result from absorption to any degree have been studied in sufficient detail to provide calculations of some spectral effects, heat effects, and electrical and magnetic effects. Threshold effects are often part of absorption phenomena, thus giving clues to the specific identification of some required scalar motion interactions.

## Heat as a Distributed Motion

The mathematics and useable behavioral characteristics of heat processes are thoroughly discussed from the viewpoint of experimental analysis in most elementary physics and chemistry courses while more technical details and practical applications of heat processes are presented in thermodynamics courses. The theoretical aspects of thermal energies are seldom attempted even at advanced levels. The mathematics of the theoretical description of heat with respect to the Reciprocal System of theory have yet to be completed, although the qualitative aspects are fully in accord with experimental observation.

To effectively remain as a temporary part of atoms or groups of atoms for any reasonable period of time, an added motion must be associated with the units of the background primary motion and with the atoms, jointly, or with the atoms, only. In order to not be incorporated as permanent constituents in the motion of atoms or groups of atoms the added motion must have a displacement represented in a different mode from that which defines the identity of the atoms. The added motion may be represented in the same dimension as that of primary motion, but is not necessarily required. One directional rotationally distributed positive or negative displacements are the kind of displacements that are permanent parts of atoms, and therefore, cannot be the kind of motion that has only temporary association with identifiably specific atoms. The only types of displacement motion that can satisfy the requirements of direction and mode are positive 1D1d_{L}, 1D2d_{L}, and positive or negative 1D2d_{R}, and only negative 2D2d_{R} displacement motion.

Since the direction of the normal progression in equivalent space is inward toward the zero of generalized dimensional space, the inward direction of representation of a positive 1D2d_{L} displacement motion is not effective. The representation of 1D2d_{L} motion in the outward direction from zero is inward toward unity and is effective. The outward direction from zero toward unity is coincident with the effective direction of the force effect of the rotational displacements that make up the atoms of the group. Adding the outward effect of the positive displacement 1D2d_{L} motion to the effect of the rotationally represented displacements of the atoms or groups of atoms causes an outward shift in the point of equilibrium between the force effect of the primary progression and the net force effect of displacement motion represented in that direction in generalized space. The net effect is similar to that of a force of tension among the atoms or groups of atoms. This shift increases the equivalent distance of separation in direct proportion to the distributed magnitude of the 1D2d_{L} motion added on a temporary basis. Thus, positive 1D2d_{L} displacement having only temporary association with a group of atoms or a single atom in the dimension of the primary progression is identified as the motion responsible for the phenomena of heat. As implied by referring to groups of atoms, the average distance of separation can be modified between individual atoms or specific polyatomic groupings of atoms in polyatomic groups. Each atom or group of atoms is referred to as a *thermal unit** *or *thermal group**.*

Thermal 1D2d_{L} displacement motion is distributed among all possible directions of the time region dimensions specified by the inter-regional ratio, not ALL directions as rotationally represented motions are. For solid to liquid phase change to occur, the distributed magnitude of the 1D2d_{L} displacement component must be sufficient, not only to bring the net motion to unit value in one reference point dimension of a sufficiently large number of thermal groups, but it must be capable of maintaining that value for a specific proportion of the sample in question. The sample in question refers to the specific physical size of the microcrystal, not to the overall sample. The specific ratio of solid to liquid phase thermal units is determined for each substance by geometric considerations for the structure of the microcrystals.

Of course, for reorientations among the atoms of polyatomic groupings to occur conditions must exist for a specific orientation of the atoms present in the polyatomic group. The number of orientations of each type and the mass effect of the displacements represented within a polyatomic grouping determine the magnitude of 1D2d_{L} displacement motion required before reorientation of the atoms within the polyatomic group can occur. Reorientation of atoms may change which atoms are grouped together in the subsequent thermal groups, thereby causing changes in the formulas of the resulting compounds. If atomic reorientations can supply the required energy and if the necessary activation energy is available, then a change of composition of the solid phase is observed, sometimes with concomitant formation of either a liquid or gas phase component which is, of course, dependent on the total energy available at the energy state at which transition occurs.

If atomic reorientation energy is not available, the molecules or other crystal structure components acquire net translationa1 motion in one dimension. Freedom from the restrictions of an orientation position in one of the time dimensions (which is randomly oriented in generalized space) including distance of separation in space, may increase for a large enough number of the individual components of a crystal structure for total collapse of the spatial arrangement. This is the process of melting which shows that each thermal unit and individual combination of thermal units has its own melting point or decomposition point.

To be sure, statistical analysis for critical size and configuration for geometrical components in a crystal structure play an important part in the determination of melting points. It is the distribution of thermal energy throughout the geometric structures under consideration that determines the temperature range for an observed melting process. This is why powdered samples give more precise results in melting point determinations; small crystals provide greater surface area which provides a much larger surface area to volume ratio and smaller physical volumes over which the thermal motions must be distributed. At the temperature of collapse for the crystal structure, the identifiable melting point, added heat energy is channeled as a result of probability distribution into continuing the thermal destruction of the crystalline form. For the liquid phase to persist, the net thermal force effect must be maintained at unit value or greater in one dimension of the individual coordinate system without any contribution from rotationally represented components in that dimension.

If freedom from restriction of orientation position in the time region and geometric position in space do not occur simultaneously, then a gradual change in the geometry occurs as observed in the spatial aspect. Gradual changes of this sort are classified as softening, as in glasses. Regular geometric positioning, whether in the spatial aspect as for the recognized crystal structures or with part of the order in the temporal aspect as for substances classified as glasses, thereby lacking apparent regularity of geometric positioning of atoms in space, is a result of the types of orientations involved among the atomic constituents and thus whether the particular interatomic distance taken between each pair of atoms in the overall array is specific or merely an average. In substances like silicon dioxide, the inclusion of very small amounts of other atomic components disrupts the spatial regularity although a crystal like regularity continues to exist by considering the three dimensionality of time.

Thermal motion is continually being redistributed within each sample of matter and with its environment. Each quantity of 1D2d_{L} motion added to the system under consideration causes further distribution of the units of thermal energy available. Redistribution changes the number of thermal units having sufficient thermal energy exceeding unit value distributed in all three dimensions of generalized space, thereby making possible the transition to three dimensions of freedom representative of the gas phase. From this concept the *critical temperature** *of many substances has been calculated.

Since pressure is a measure of the total thermal energy per unit volume in the gas phase, the vapor pressure of a liquid depends on the distribution of the available thermal energy among the thermal units, which controls the number of thermal units in the gas phase. Each thermal unit must have sufficient thermal energy to continue in the gas phase or it will degrade back to the liquid or solid phase on an individual unit basis by collision or statistical distribution by condensation with cooler thermal units. In the redistribution process some of the 1D2d_{L} motion is redistributed by contacts among the groups of molecules in the expanded phase or by collisions of gas phase molecules with either of the condensed phases. Evidence of this transition is observed for collision of low energy thermal units with other compound motion structures with which they can orient, dew formation, or as a result of higher energy collisions by which transfer of some of the positive 1D2d_{L} motion can be accomplished, cloud formation. It is the 1D1d_{L} spatial velocity equivalent of the 1D2d_{L} motion of the individual molecule that changes to some value less than the *critical *energy in all three dimension for that type of thermal unit that allows condensation to form the liquid or solid phase. A dynamic equilibrium of phases is established at any set of temperature-pressure conditions below that of the *critical** *conditions.

Remembering that all of the heat energy of the system is displacement motion in the equivalent space of the molecules, and that contact between motions in that region with the outside region or the next contiguous equivalent space region are point contacts, and that all motions (even the imputed vectorial motions that bring displaced units of motion together) are continuous at points of contiguity, transfer of motion is one dimensional upon contact between compound motion structures. Radiation of thermal vibration energy is a different dimensional matter entirely.

Collisions among thermal units having critical energy or greater result in pure elastic collisions minus whatever thermal energy transfer can and does occur for equilibration purposes. Thus, not only specific heats, but melting points, vapor pressures at specific temperatures (and thus, boiling points), and critical temperatures and pressures are calculable directly from this theory. Vander Waals constants, London forces, and many other constants are purely empirical “fudge factors” and have no significance relative to any specific representable scalar motion.

## Absorption and Emission of Photons

Other than heat transfer interactions, the most obvious and fundamental phenomena in which photons interact directly with atoms and molecules of matter are absorption and emission spectra. The interaction upon which many other phenomena owe their interpretation is the presently accepted interpretation for emission spectra of hydrogen. The presently accepted theoretical interpretation of spectra depends on complete acceptance of the nuclear model of atoms. Considering the fact that the Reciprocal System of theory starts with the idea of motion and constructs all entities and phenomena from the representation of scalar motion in dimensional systems, the analysis of atomic spectra must be in terms of motion.

From the previous discussions in which speed displacements have been in terms of full units of motion, it may seem that gaps must exist in the availability of intermediate values of total motion to be represented in either of the three dimensional aspects. The specific quantities of rotationally represented displacement motion have determined the identities for the atoms of matter. The inter-regional ratio indicates the scalar relationship of the alignment relations among the dimensions of equivalent space and generalized space. The requirement for primary motion to be represented in one of those directions provides the basis for the representation of 1D1d_{L} and/or 1D2d_{L} displacements leading to the phenomena of translational movement and thermal movement, respectively. BUT, because these displacements are concurrent with complex motion structures having effects distributed in all directions in the time region, equivalent space, as well as in generalized space, the linearly represented displacements cannot be mathematically represented in the same way as the rotationally represented displacements, either magnitudinally or directionally.

It is because of the reciprocal relation of space and time that the equivalence of the formulation of that relationship as motion, s/t, or as energy, t/s, becomes understandable. A specific total motion or speed of n/1 is equivalent to an energy of 1/n, as also a speed of 1/n is equivalent to an energy of n/1, but each is not equal to the other even though each can be added to the other as long as the net total motion represented in all three geometric dimensions of a given compound representable motion in the material sector has a net value less than unity. The displaced motion that is being rotationally represented causes the mass effect. It is a three dimensionally distributed motion. The displaced motion that is being co-represented at the same Notational Reference Point in a linear manner is not a three dimensionally distributed motion although it is distributed three dimensionally by the generalization of the spatial reference system of normal experience. Because of this difference of representation of the displacements, the effect of the distributed linear displacements is instantaneously in one direction with an inherently one dimensional effect; energy instead of mass.

In the generalized spatial system the zero starting point of energy has been considered to be some value close to, but not equal to, zero space velocity. From the previous conceptual viewpoint, units of motion and units of energy were treated as being of similar magnitude in the same manner as were the magnitudes of space and time units. For continuity of the everyday conceptual view of this world it is normally assumed that space and time have a limited relationship and that they are of the same order of magnitude. The magnitude of one second of time is usually treated as though conceptually equivalent to about one centimeter of space, and that both space and time are infinitely divisible, while in the development of the Reciprocal System of theory both are quantized and one second of time is equivalent to over one hundred eighty six thousand miles of space. Increments of energy having been viewed strictly from the naive position of being an effect having the same zero reference as vectorial motion, rather than as the reciprocal of displacement motion, as it theoretically exists in the natural reference system of the universe of motion, has caused the normally accepted view of this world and universe to be very skewed.

If a scale is set up with low speed, 1/n, near one end and high speed, n/1, near the other with unit speed in the middle, we find that high energy is at the same end as low speed and low energy at the end with high speed. From our position near zero of a three dimensional reference system, either zero speed or zero energy as the reference level for a summation of speed and energy seems to show that the scalar directions of deviations in speed and energy are oppositely directed. BUT, the energy under consideration is a displacement motion, not primary motion. In the natural reference system outward from unity is the same scalar direction regardless of its specific direction or magnitude in a three dimensional reference system.^{26}

Adding more increments of one Dimensional linearly represented displacement motion, whether they cause a change of thermal energy or of translational movement, brings the total displacement closer to the equivalent of primary motion; NOT toward primary motion.

All added motions are to individual Notational Reference Point systems and are, thereby, inside unit space which requires the squaring of that quantity of motion for measurement in the outside region. A positive displacement being inward in the spatial aspect and outward in the temporal aspect has the effect of adding directly to the time aspect of the compound motion in a specific spatially linear direction. Considering the energy representation at a Notational Reference Point, this additional unit of displacement moves the total motion of the NRP closer to the equivalent of primary motion in one direction. Thus, the starting value is represented as 1 - 1/n^{2}. The added, motion, energy, is 1/m^{2}. The net displacement motion of the individual system would be represented by the relation:

$$\frac{s}{t} = \left( 1 - \frac{1}{n^2} \right )+ \frac{1}{m^2} = 1 + \frac{1}{m^2}-\frac{1}{n^2}$$

but since ordinary motions are so close to zero relative to equivalent primary motion, that value must be subtracted out for ordinary work in a stationary spatial reference system. Thus, the energy equivalent for the increment becomes:

*Equation 16*

$$\frac{t}{s} = \frac{1}{m^2} - \frac{1}{n^2}+ 1 - 1 = \frac{1}{m^2} - \frac{1}{n^2}$$

n < m, where n and m represent some number of units of deviation from the natural datum. For n < m, the net energy represented for the final state from zero space is farther from zero, but is actually a greater deviation from unit t/s. n & m are the number of effective units of displacement from primary unity, not equivalent primary motion. From the zero reference of the spatial reference system n and m appear to be in the opposite order. Don’t get confused by trying to stick with interpreting values of displacement as being from the zero of spatial velocity. Reiterating from Chapter Two in the section on Essential Considerations: “One of the first essentials for an understanding of the system of motions that constitutes the theoretical universe of motion defined by the Reciprocal System is to relate all motions to the natural reference system.”

Since energy is normally formulated as t/s and is, therefore, a one dimensional relation, the expression or effect in dimensional space is a change of one dimensional speed which is recognized as a linear velocity. The added energy causes the net deviation from equivalent unity to be less in one dimension of space and, thereby, seems to be moving in a particular direction rather than remaining stationary. The emission of photons causes the net deviation from unity of the emitting structure to be farther from equivalent unity and nearer to the equilibrium condition of its surroundings in dimensional space because absorption of energy caused greater deviation from those equilibrium conditions. Since the actual displaced motion of photons of radiation can be expressed as energy, t/s, the emitted radiation from excited (having greater than the ambient or average energy as measured from the zero of space) atoms of an element can be represented mathematically by the change in total energy of the atom from before emission, (1 - 1/m^{2}), to that after emission (1 - 1/n^{2}), of the radiation. Thus, ΔE = 1/n^{2} - 1/m^{2}. 1/n^{2} represents the state farthest from equivalent unity or the nearest to primary motion; i.e., the least displacement possible from the environment and, thereby, from primary unity.

If the radiation is emitted by an atom having equivalent positive electric displacement of one unit, the smallest numerical values consistent with units of energy which that kind of atom can absorb or emit would be in small whole number multiples of unit motion or unit energy. Thus, in an arbitrary system of measure such as that which we use on this planet, the numerical value found to be consistent with the units of measure of that system is representative of unit speed in that system. The quantity identified as the Rydberg constant for mass one hydrogen is thus the magnitude of unit motion, unit frequency, or unit energy, depending on how we wish to express the value.

It is noted that the inefficient method of increasing net speed from the zero of space by adding displacement units of energy has a limiting value of unity in that dimension, equivalent primary motion. Thus, the speed of light is a very real barrier to one dimensional translational motion in space for any compound displacement motion structure. One dimensional movement is the only kind of motion directly representable in three dimensional space; therefore, that must be our reference for observation and analysis.