Thus far we have been dealing with linear motion only. Rotational motion is also permitted by the geometry of three-dimensional space (or time), but before rotation can take place there must be something that can rotate, and rotational motion therefore cannot be generated directly from the motion of the space-time progression. The existence of a one-dimensional oscillating unit, the photon, now provides the necessary “something.” Our next task will be to examine the theoretical aspects of the rotation of the photon. We will first consider the characteristics of rotational motion per se, and then the special features that result from the fact that it is a photon that is rotating rather than something else.

A significant feature of rotation is that it accomplishes a reversal of the vectorial direction of the motion without a reversal of the scalar direction. As previously pointed out, the oscillating progression of the photon first moves forward one unit and then backward over the same unit, reversing the scalar direction when it reverses the vectorial direction. But an object that is rotating forward continues moving forward regardless of the changes in vectorial direction that are occurring. The difference between these two situations can be emphasized by returning to the automobile analogy. If this car periodically reverses direction, so that it moves back and forth over the same path, as in the case previously considered, a speedometer that runs in reverse during backward motion will register zero after any number of complete cycles, whereas if the car moves around in a circle it will accomplish the same result from a directional standpoint—that is, each complete cycle will put it back where it started—but the speedometer will continue registering forward mileage.

For a closer analogy, let us now assume that this automobile is operating on the surface of a very large balloon, and let us further assume that the speedometer is connected with the inflation mechanism of the balloon in such a manner that a positive speedometer registration causes the balloon to expand, whereas a negative registration causes it to contract. Finally, let us assume that the path of travel, linear in one case and circular in the other, is clearly identified by appropriate markings. Regardless of whether the car moves back and forth on the linear path or moves around the circle, it stays on the painted strip; that is, it remains in the same location on the surface of the balloon. But the back and forth motion makes no change in the size of the balloon and consequently the separation between the original car and any other similar car on the surface of the balloon remains constant, whereas the motion in a circle causes either an expansion or a contraction of the balloon, depending on whether the motion is forward or backward. In this case the separation between any two such cars increases or decreases, even though each remains in a fixed location on the balloon surface.

In the physical situation the mechanism is less complicated, but otherwise quite similar. The oscillating motion of the photon, like the back and forth motion of the motor car, has a scalar resultant of zero, but the rotational motion of the photon maintains the same scalar direction continuously, and it therefore alters the separation between this and every other rotating photon, just as the circular motion of the cars on the balloon surface, under the assumed conditions, changes the distance between them.

One important difference between the two situations is that rotation of the photon can take place only in the negative, or inward scalar direction. For an explanation of this fact we need to consider the limits to which rotational motion is subject. Rotation at unit speed in the outward scalar direction is meaningless, since unit outward speed is the physical zero, the physical equivalent of nothing at all, and no rotation cannot be distinguished from no translation. Motion of any kind in space at a speed in excess of unity is impossible, as we have already noted, and since there are no fractional units, outward rotation of the photon is totally excluded. But rotation at unit speed in the inward scalar direction does have a physical significance; it nullifies the outward motion of the progression and reduces the net speed to zero. Furthermore, it is possible to have one additional unit of inward motion, two full units altogether, without exceeding the limiting value of one net unit. The photon therefore rotates in the inward scalar direction.

A rotating photon thus reverses the normal outward progression and moves inward in space toward all space-time locations as if it were located on a contracting balloon. This inward motion of each individual unit cannot be detected in any direct manner, but since all such rotating photons are moving inward, the visible effect of the motion is that each is moving toward all others, as if they were exerting mutual forces of attraction.

We are now ready to make some more identifications. By the same procedure as before, we identify the rotating photons, with certain exceptions that we will discuss later, as atoms. Collectively, the atoms constitute matter, and the inward motion due to the inherently scalar nature of the rotation is *gravitation*.

As in the case of radiation, the development of this new and accurate theory resolves the seemingly insuperable difficulties that have hitherto stood in the way of a clear understanding of the gravitational phenomenon. The origin of gravitation is now evident. The same thing that accounts for the existence of the atom, the rotation in the inward scalar direction, also causes it to gravitate. Furthermore, the nature of this gravitational motion explains those peculiar characteristics of the phenomenon that have been so baffling to previous investigators. As nearly as can be determined from observation, gravitation acts instantaneously, without an intervening medium, and in such a manner that its effects cannot be screened off or modified in any way, but all attempts to account for these characteristics in terms of previous physical theories have been so fruitless, and seemingly so hopeless, that the task has long since been abandoned. For many decades, all theoretical developments in this area have been based on the premise that, for some unknown reason, the physical observations are giving us false information; that notwithstanding all of the observational evidence to the contrary, gravitation must be propagated at a finite velocity, through a medium or something with the properties of a medium, and that screening or “anti-gravity” measures would probably be feasible if the right methods could be discovered.

The findings of the Reciprocal System now show that the observations are not misleading; they give us a true picture of the situation. The instantaneous action, the absence of a medium, and the impossibility of screening are all explained by the fact that gravitation is not an action of one mass upon another, as it appears to be. In reality each atom of matter is following its own course independently of all others, and the apparent interaction is an illusion created by the fact that all atoms are moving inward in space simultaneously, and hence each is moving toward all others. There is no propagation of an effect of one upon another, and no need for a medium to transmit such an effect.

Both the outward motion of the photon and the inward motion of the atom are scalar motions of the same general character. There is a difference, however, in the way in which these two motions manifest themselves in three-dimensional space. In both cases the direction of the motion with reference to a three-dimensional coordinate system is determined by chance, since a scalar motion has no inherent vectorial direction. The direction of movement of the photon is determined at the moment of emission, and inasmuch as this photon remains permanently in the same absolute location there is no change in direction unless the photon encounters an obstacle of some kind. The atom, on the other hand, is moving in opposition to the space-time progression, and is therefore continually passing from one space-time unit to another. Each such change of absolute location involves a re-determination of the spatial direction of the scalar motion, another chance event, and in the long run the motion of each atom is distributed over all spatial directions; that is, the atom is moving inward in space in all directions. From geometrical considerations we deduce that at distance d from the atom the motion is distributed over a spherical surface of radius d, and the portion of the total motion that is directed toward a unit area at this distance depends on the ratio of that unit area to the total area of the spherical surface, which means that it is inversely proportional to d2. This is the familiar inverse square relation: the (apparent) gravitational effect is inversely proportional to the square of the intervening distance.

Gravitation is generally visualized in terms of force rather than in terms of motion, and it will be desirable to establish the relation between these two concepts. For this purpose, let us consider a situation in which an object is moving in one direction with a certain velocity, and is simultaneously moving in the opposite direction with an equal velocity. The net change of position of the object is zero, and instead of looking at the situation in terms of two opposing motions, we may find it convenient to say that the object is motionless, and that this condition has resulted from a conflict of two forces tending to cause motion in opposite directions. On this basis we define force as that which will cause motion if not prevented from so doing by other forces, and we define the magnitude of the force as the product of mass and acceleration.

This kind of a conceptual device, which replaces the true relationship with an equivalent that can be more easily manipulated, is a perfectly legitimate scientific tool, but its use is subject to certain hazards because the boundary conditions of the substitute are not usually the same as those of the original concept. In the present instance, there is a definite limit to the velocity that can be attained in space, but the concept of force contains no hint of any such limitation, and its existence has not been recognized. This, in turn, has led to some misconceptions concerning the behavior of related quantities.

The basic error in this case is the assumption that a force applied to the acceleration of a mass remains constant irrespective of the velocity of the mass. If we look at this assumption only from the standpoint of the force concept it appears entirely logical. But when we look at the situation in its true light as a combination of motions, rather than through the medium of an artificial representation by means of the force concept, it is immediately apparent that there is no such thing as a constant force. The space-time progression, for instance, tends to cause objects to acquire unit velocity, and hence we say that it exerts unit force. But it is obvious that a tendency to impart unit velocity to an object which is already at a high velocity is not equivalent to a tendency to impart unit velocity to a body at rest. In the limiting condition, when the mass already has unit velocity, the force of the space-time progression (the tendency to cause unit velocity) has no effect at all, and its magnitude is zero.

By way of analogy, we may consider the case of a container partially filled with water. If the container is rotated, the speed of rotation is gradually communicated to the water. At low water velocities, the effective force, and consequently the acceleration, are approximately constant. But even though there is no change in the source from which this “constant” force originates, the acceleration decreases and approaches a zero limit as the water speed approaches the speed of the container. Similarly, the source of the “constant” force of present-day physical experiments—an electric potential, for instance—may remain unchanged, but the effect of the force decreases as the limiting unit velocity is approached.

It is evident, on this basis, that the full effect of any force is attained only when it is exerted on a body at rest, and that the effective force component in application to an object in motion is a function of the difference in velocities. Ordinary terrestrial velocities are so low that the corresponding reduction in effective force is negligible, and at these velocities a force such as that due to an electric potential can be considered constant. Experiments indicate, however, that acceleration decreases rapidly at very high velocities and approaches zero as the velocity of the mass to which the force is applied approaches unity. Relativity theory explains the experimental results by the assumption that the mass increases with velocity and becomes infinite at unit velocity (the velocity of light). In the theoretical universe being developed from the postulates of the Reciprocal System this explanation is not acceptable, as mass is constant, but the same results are produced by the decrease in the effective force as the velocity increases. In mathematical terms, the limiting zero value of a in the expression a = F/mm (which is the fact determined by experiment) is not due to an infinite value of m but to a zero value of F.

The conclusion to be drawn here is not that the use of the concept of force should be abandoned, but that due care should be used in its application, so that the benefits of this convenient device can be realized without falling into serious errors. Much the same can be said of the use of the concept of “gravitational force.” As has been brought out, there actually is no such thing; the truth is that one mass has no effect whatever on another. But within certain limitations masses behave as if they were exerting mutual forces of attraction, and dealing with them on this basis is a convenient practical expedient. In the subsequent discussion, therefore, we will follow common practice and refer to gravitation as a force exerted by masses upon other masses, except where recognition of its true status as motion is necessary in order to avoid erroneous implications.

It is essential to keep in mind, however, that the gravitational force with which we will be dealing is not a real force. It is only an “as if” force, and it does not have all of the properties of a real force. In particular, it involves no transmission or propagation. The “gravitational waves” that are now being sought so assiduously are wholly non-existent. Gravitational effects, changes in the “as if” gravitational forces, can be detected, of course. For example, the gravitational effect of the moon, as experienced at any specific terrestrial location, is continually changing, and if the results now being reported from gravitational detectors of one kind or another are actually of gravitational origin, they are minor variations of a similar, but less regular, nature. They are not waves of the kind that are required by current theory: phenomena analogous to light waves that are capable of transmitting gravitational forces. All of the effects of gravitation appear instantaneously, and there is no interaction time. No screening is possible because there is nothing to screen. The so-called “antigravity” devices must remain a feature of science fiction. In real life the only anti-gravity device is oppositely directed motion.

The next aspect of gravitation that we will want to consider is the effect of mass concentration. According to the theory explained in the preceding pages, each gravitating mass is moving uniformly inward in space toward all space-time locations. Every mass unit occupies both a location in space and a location in time. A rough analogy would be the location of an object on the surface of the earth. Such an object has a location in latitude, measured from the nearest pole, and a location in longitude, measured from the Greenwich meridian. For a complete definition of the position of the object, both of these locations must be specified. The mere fact that a number of objects are all at the same latitude does not mean that they are coincident. If their locations in longitude are random, each of the objects occupies a different position.

The gravitational process in the material universe causes aggregation of matter in space only, while the coexisting progression of time continues unchecked. As a result, the atoms of a material aggregate are contiguous in space but widely dispersed in time. An aggregate of n mass units therefore occupies n space-time locations, even though the entire aggregate may occupy approximately the same space location. Gravitation moves every other mass within the effective limits toward each of these space-time locations independently, and the total motion toward the n-unit mass is therefore n times the motion toward a single unit of mass occupying a single space-time location. The same considerations apply to the reference mass, and the total motion of an n-unit mass toward a specific space-time location is n times that of a single unit of mass.

An issue that is frequently raised by those who encounter this gravitational theory for the first time concerns the response of the gravitational force of mass A to a change of position of some distant mass B. The question that is usually asked runs something like this: “If, as the theory claims, this is not actually an effect transmitted from A to B, but is an independent motion of mass A, how does mass A know what has happened to B, so that the gravitational motion of A can take place in the right amount and in the right direction?”

The answer is that the gravitational motion of mass A never changes, either in amount or in direction. It is always directed from the location of the gravitating unit toward all other space-time locations. But we cannot observe the motion of an object inward in space; we can only observe motion relative to other objects whose presence we can detect. The motion of each object therefore appears to be directed toward the other objects, although, in fact, it is directed toward all locations in space-time irrespective of whether or not they happen to be occupied. Whatever changes take place in the gravitational phenomena by reason of change of relative position of the gravitating masses are not changes in the gravitational motions (or forces) but changes in our ability to detect those motions.

Let us assume an object X occupying location a. This object is moving gravitationally toward all other space-time locations. Inasmuch as we cannot observe time locations, we will consider only the space locations, two of which we will designate b and c. If these locations are not occupied, then we cannot detect the gravitational motion at all. But if location b is occupied by object Y, then we see X moving toward Y; that is, we can now observe the motion of X toward location b, but the motion of X toward location c is still unobservable. The observable gravitational motion (or force) of Y is toward X and has the direction ba.

Now, if Y moves to location c, what happens? The essence of the theory is that the motion of X is not changed at all; it is entirely independent of the position of object Y. But we are now able to observe the motion of X toward c because there is a physical object at that location, while we are no longer able to detect the motion of X toward location b, even though that motion exists just as definitely as before. The direction of the gravitational motion (or force) of X thus appears to have changed, but what has actually happened is that some previously unobservable motion has become observable, whereas some previously observable motion has become unobservable. The same is true of the motion of object Y. It now appears to be moving in the direction ca rather than in the direction ba, but here again there has actually been no change. Gravitationally, Y is moving in all directions at all times.

Having examined those aspects of gravitation that are relevant to the discussion in the subsequent pages, we are now ready to begin consideration of the details of the atomic rotation of which gravitation is one aspect. It is evident at the outset that the photon, a one-dimensional oscillation, cannot rotate around itself as an axis. Such a rotation would be indistinguishable from no rotation at all. But it can rotate around either or both of the axes perpendicular to the path of oscillation at its midpoint. One such rotation generates a two-dimensional figure, a disk. Rotation of the disk in another dimension then generates a three-dimensional figure, a sphere. Since this exhausts the available dimensions, further rotation in the same scalar direction is impossible, and the basic rotation of the atom is therefore two-dimensional.

But even though no further rotation of the same kind is possible, a rotation can take place in the opposite scalar direction around the third axis. Since the basic two-dimensional rotation is distributed through all three dimensions of space, the reverse rotation is not required for geometric stability, and it is therefore only a possibility, not a necessity. The rotational motion of the atom thus consists of a two-dimensional rotation, with or without a one-dimensional rotation in the opposite scalar direction.

Another important point is that two separate two-dimensional rotations may be combined in one physical unit. The nature of this combination can be illustrated by two cardboard disks interpenetrated along a common diameter C. The diameter A perpendicular to C in disk A represents one linear oscillation, and the disk A is the figure generated by a one-dimensional rotation of this oscillation around an axis B perpendicular to both A and C. Rotation of a second linear oscillation, represented by the diameter B, around axis A generates the disk B. It is then clear that disk A may be given a second rotation around axis A, and disk B may be given a second rotation around axis B without interference at any point, as long as the rotational velocities are equal.

Here, again, the second rotating system is not necessary for stability. Units in which there is only one two-dimensional rotation can and do exist. But as a general principle low numbers are more probable than higher numbers and symmetrical combinations are more probable than asymmetrical combinations. Hence, if a second two-dimensional displacement is added to a one-unit rotation, probability considerations require the added displacement to generate a second rotating system rather than adding to the existing rotation. The combinations with only one two-dimensional rotation are therefore limited to those which do not possess more than one unit of rotational displacement.

For convenience in the subsequent discussion it will be desirable to introduce some new terminology to identify the various features of the atomic rotation. We will call the one-dimensional rotation electric rotation, and the corresponding axis the electric axis. Similarly we will refer to the two-dimensional rotation as magnetic rotation around the magnetic axes. If the displacements in the two magnetic dimensions are unequal the rotation is distributed in the form of a spheroid, and in this case the rotation that is effective in two dimensions of the spheroid will be called the principal magnetic rotation and the other will be the subordinate magnetic rotation. Designation of these rotations as electric and magnetic does not indicate the presence of any electric or magnetic forces in the structures now being described. This terminology has been adopted because it not only serves our present purposes, but also sets the stage for the introduction of electric and magnetic phenomena in a later phase of the development.

Each of these rotations may assume any one of a number of possible displacement values. This means that many different combinations can exist, and since the physical behavior of the atoms depends on the magnitude of these rotational displacements, the various rotational combinations can be distinguished by differences in their physical behavior, by differences in their properties, we may say.

We will now identify these rotational combinations as the chemical elements, each rotating unit of a particular kind constituting an atom of that element. For convenience in referring to the various combinations of rotational displacement a notation in the form 2-2-3 will be used in the discussion, the three figures representing the displacements in the principal magnetic, the subordinate magnetic, and the electric rotational dimensions respectively.

It should be noted at this point that the value taken as the unit of magnetic displacement is somewhat arbitrary, as the magnitude of an increment of this two-dimensional displacement, in terms of the basic unit, the electric unit, is variable. At the single unit level dimensional distinctions disappear; that is, 1^{2} is equal to 1, and the magnetic unit is therefore equivalent to the electric unit. However, in those rotational combinations with two magnetic rotations, the combinations that we recognize as atoms of matter, both rotations must have the same speed, in order to avoid interference, and the equivalent of two of the single units is therefore required to give the structure as a whole one unit of magnetic rotation. It will be convenient to define this double unit as the magnetic rotational unit in the material atoms, retaining the single unit, the natural unit, in the subatomic combinations. The electric (one-dimensional) equivalent of n magnetic (two-dimensional) units, as thus defined for the atoms of matter, is 2n^{2}.

In applying this 2n^{2} relation between the magnetic and electric units it is necessary to take into account some mathematical characteristics of the space-time progression. In the undisplaced condition all progression is by units. We have first one unit, then another similar unit, yet another, and so on, the total up to any specific point being n units. There is no term with the value n; this value appears only as the total. The progression of displacements follows a different mathematical pattern because in this case only one of the space-time components progresses, the other remaining fixed at the unit value. The progression of 1/n, for instance, is 1/l, 1/2, 1/3, and so on. The progression of the reciprocals of 1/n is 1,2,3… n. Here the quantity n is the final term, not the total. Similarly, when we find that the electric equivalent of a magnetic displacement n is 2n^{2}, this does not refer to the total from zero to n; it is the equivalent of the nth term alone.

Inasmuch as motion is a relation of space to time, motion of an existing physical unit—that is, addition of motion of a different type—requires a displacement with the opposite space-time direction. Where the displacements have the same direction, an addition merely modifies the quantity of the existing type of motion. The rotating units that constitute atoms may therefore be linear space displacements rotating with net time displacement, or linear time displacements rotating with net space displacement. The latter combinations, however, do not constitute matter, and for the present, the discussion will be confined to those combinations with net rotational time displacement. Unless otherwise specified the displacement values that are given will refer to time displacement. If space displacement is present it will be identified by enclosing the applicable figure in parentheses.

Looking first at those combinations which have zero electric displacement, a single unit of magnetic time displacement results in the combination 1-0-0. This single displacement unit merely neutralizes the oscillating unit of space displacement, and the result is the rotational base, a unit with a net displacement of zero; that is, the rotational equivalent of nothing. One additional unit of magnetic time displacement produces the combination 1-1-0. This combination still does not have the properties that we recognize as those of matter, as it has only one effective magnetic displacement unit and hence only one magnetic system of rotation. The first combination that qualifies as matter requires one more unit of magnetic displacement, bringing the system up to 2-1-0, which can be identified as the element helium. Additional units of magnetic displacement produce a series of elements that we can recognize as the inert gases. The complete series is as follows:

Displacement | Element | Atomic No. | ||
---|---|---|---|---|

2-1-0 | Helium | 2 | ||

2-2-0 | Neon | 10 | ||

3-2-0 | Argon | 18 | ||

3-3-0 | Krypton | 36 | ||

4-3-0 | Xenon | 54 | ||

4-4-0 | Radon | 86 | ||

5-4-0 | Unstable | 118 |

The number of possible combinations of rotations is greatly increased when electric displacement is added to these magnetic combinations, but the combinations that can actually exist as elements are limited by the probability relations. The magnetic displacement n is numerically less than the equivalent electric displacement 2n^{2}, and is correspondingly more probable. Any increment of displacement consequently adds to the magnetic rotation if possible rather than to the electric rotation. This means that the role of the electric displacement is confined to filling in the intervals between successive additions of magnetic displacement.

On this basis it can be seen that if the atomic rotation involved nothing but time displacement, the series of elements would start at the lowest possible magnetic combination, helium, and the electric time displacement would increase step by step until it reached a total of 2n^{2} units, at which point the relative probabilities would result in conversion of these 2n^{2} units into one additional unit of magnetic time displacement, whereupon the building up of the electric displacement would be resumed. This behavior is modified, however, by the fact that electric displacement in matter, unlike magnetic displacement, may take either space-time direction.

As previously mentioned, a net rotational time displacement is required in order to produce those properties that are characteristic of matter. It necessarily follows that the magnetic displacement, which is the major component of the total, must also be a time displacement. But as long as the larger component has the time direction, the system as a whole can meet the requirement of a net time displacement even if the smaller component, the electric displacement, is a space displacement. It is possible, therefore, to increase the net time displacement a given amount either by direct addition of the required number of units of electric time displacement, or by adding magnetic time displacement and then adjusting to the desired intermediate level by adding the appropriate number of units of the oppositely directed electric space displacement.

Which of these alternatives will actually prevail is again a matter of probability, and from probability considerations we deduce that the net displacement will be increased by successive additions of electric time displacement until n^{2} units have been added. At this point the probabilities are nearly equal, and as the net displacement increases still further, the alternate arrangement becomes more probable. In the second half of each group, therefore, the normal pattern involves adding one unit of magnetic time displacement and then reducing to the required net total by adding electric space displacement, eliminating successive units of the latter to move up the atomic series.

By reason of this availability of electric space displacement as a component of the atomic rotation, an element with a net displacement less than that of helium becomes possible. This element, 2-1-(1), which we identify as hydrogen, is produced by adding one unit of electric space displacement to helium and thereby, in effect, subtracting one displacement unit from the equivalent of four units (above the 1-0-0 datum) that helium possesses. Hydrogen is the first in the ascending series of elements, and we may therefore give it the atomic number 1. The atomic number of any other element is equal to its equivalent electric time displacement less two units.

One electric time displacement unit added to hydrogen eliminates the electric space displacement and brings the combination back to helium, atomic number 2, with displacement 2-1-0. This displacement is one unit above the initial level of 1-0-0 in each magnetic dimension, and any further increase in the magnetic displacement requires the addition of a second unit in one of the dimensions. With n=2 the electric equivalent of a magnetic unit is 8, and the next group therefore contains eight elements. In accordance with the probability principles, the first four elements of the group are built on a helium type magnetic rotation with successive additions of electric time displacement. The fourth element, carbon, can also exist with a neon type magnetic rotation and four units of electric space displacement. Beyond carbon the higher magnetic displacement is normal, and the successive steps involve reduction of the electric space displacement, the final result being neon, 2-2-0, when all space displacement has been eliminated. The following elements are included in this group:

Displacement | Element | Atomic No. |
---|---|---|

2-1-1 | Lithium | 3 |

2-1-2 | Beryllium | 4 |

2-1-3 | Boron | 5 |

2-1-4 | Carbon | 6 |

2-2-(4) | ||

2-2-(3) | Nitrogen | 7 |

2-2-(2) | Oxygen | 8 |

2-2-(1) | Fluorine | 9 |

2-2-0 | Neon | 10 |

Another similar group with one additional unit of magnetic displacement follows. When this group is complete at element 18, argon, 3-2-0, the magnetic displacement has reached a level of two units above the rotational datum in both magnetic dimensions. In order to increase the rotation in either dimension by an additional unit, 2 × 32 or 18 units of electric displacement are required. This results in a group of 18 elements, which is followed by a similar group differing only in that the magnetic displacement is one unit greater.

The effective magnetic displacement now steps up to 4 in one dimension, and consequently there are 32 members in each of the final two groups. Only about half of the elements in the second of these groups have actually been identified thus far, but theoretical considerations indicate that the group could be completed under favorable conditions. At 5-4-0 the displacement is 4 units above the 1-0-0 datum in both magnetic dimensions. As indicated in previous publications where the atomic rotation was covered in more detail, this represents the limit at which the rotational character of the motion is lost and the displacement reverts to the linear basis. The next preceding element, 5-4-(1), atomic number 117, is therefore the heaviest element that can be stable under the most favorable conditions.

The three rotational displacement values that are characteristic of each element are the factors, individually, in total, and in the various modifications to which they are subject in association with other elements, that determine the magnitudes of the properties of the elements. For example, when the appropriate values are inserted in an equation given in the first book of the present series, the result is the corresponding inter-atomic distance. Similar mathematical relations, some already published and others still awaiting publication, enable computation of many other physical properties. The ability o? these theoretical expressions to reproduce the observed values in so many different areas is conclusive evidence of the validity of the theoretical system from which they were derived, but the subject matter to which they apply has no direct bearing on the objective of this present volume, and since the evidence contributed by these mathematical expressions is not actually needed for present purposes it will not be considered here.

Even without this great mass of additional confirmation, the items already discussed are more than ample to show that, in the description of the nature and basic features of the atoms of matter, as in the areas previously covered, the new theoretical system is an accurate representation of the physical facts. Once again, a development of the consequences of the postulated properties of space and time has led us to a totally new explanation of an important feature of the physical universe, and again we find a full agreement with observation. In a universe of motion, atoms of matter are, of course, combinations of motion, and our analysis shows that the number of different types of atoms (elements) that are known to exist, and the arrangement of these elements into groups defined by their properties, are exact duplicates of the number and arrangement of the rotational combinations that can theoretically exist above a certain minimum.

In this universe of motion, the rotational combinations that can exist, but are below the minimum required for qualification as atoms of matter, are sub-atomic particles. On this basis, sub-atomic particles are not constituents of atoms, as present-day theory sees them, they are incomplete atoms. The status of all physical entities as nothing more than combinations of motion is the explanation for the observed interconvertibility of these entities: a finding that has delivered the coup de grace to the concept of a universe of matter. If matter is basic, it cannot be converted to motion or to anything else. But it can be converted to motion; hence it is not basic. This is the simple indisputable fact that demolishes the “matter” concept.

In a universe of motion, where matter is motion, and sub-atomic particles are motion, and radiation is motion, and linear change of position is motion, where what is and what it does are both motion, anything physical can be converted into anything else physical, by appropriate processes, because all this amounts to is altering the form of the motion.

Perhaps, at last, man is probing. to that level of understanding where there is no clear distinction between what is and what happens, where the components of the world and the interaction of those components, one with another, are indistinguishable ideas. (K. W. Ford)^{19}

Yes, Dr. Ford, that is how it is.

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