Section D
Rotational Motion
 Another type of motion that is permitted by the postulates is rotation.
Before such a motion can take place, however, there must exist something
that can rotate; that is, there must be some identifiable unit that
can be distinguished from the general progression. The photon is the
only primary unit that meets this requirement, and simple rotation
is therefore a rotation of the photon.
 Rotation is motion in which there is a continuous change in vectorial
direction. Unlike the situation in simple harmonic motion, however,
the scalar direction of the simple rotation remains constant. To illustrate
this point, let us return to the automobile analogy, and this time
let us assume that the car is operating on a circular track. The vectorial
direction of this car is continually changing as it moves around the
circle, but its scalar direction is constant. If the car starts moving
forward, it continues to move forward.
 Inasmuch as vectorial directoin is not an inherent property of a
motion, rotation cannot be distinguished from translation on the natural
basis. Adding a unit of rotational motion in the positive scalar direction
(the direction of the normal progression) to the photon would therefore
result in a continuation of the progression, rather than an actual
rotation. Thus, the photon can rotate only in the negative scalar
direction. In the automobile analogy, the equivalent statement would
be that for some reason the car can only run backward around the circle.
 A rotating photon is thus traveling backward along the line of progression,
moving inward in space (or time).
 The vectorial direction corresponding to this inward (negative)
scalar direction, like the vectorial direction of the nonrotating
photon, is a result of viewing the motion in the context of an arbitrary
reference system, rather than an inherent property of the motion itself.
The vectorial direction is therefore determined entirely by chance
in both cases. However, the nonrotating photon remains in the same
absolute location permanently (unless acted upon by an outside agency)
and the direction determined at the time of emission is therefore
permanent. The rotating photon, on the other hand, is continually
moving from one absolute location to another as it travels back along
the line of progression, and each time it enters a new location, the
vectorial direction is redetermined by the chance proess. Inasmuch
as all directions are equally probable, the motion will be distributed
uniformly over all directions in the long run. A rotating photon will
therefore move inward toward all space (or time) locations
other than the one that it happens to occupy momentarily.
 Since space and time locations cannot be identified by observation,
neither inward nor outward motion can be recognized as such. It is
possible, however, to observe the changes in the relations between
the moving units and other physical objects. The photons of radiation,
for instance, are observed to be moving outward from the emitting
objects. Similarly, each rotating photon is moving toward all other
rotating photons, by reason of the inward motion in space (or time)
in which all participate, and the change in relative position in space
can be observed. This second class of identifiable objects in the
theoretical universe thus manifests itself to observation as a number
of individual units which continually move inward toward each other.
 As in the case of the photon, the identification is obvious. The
rotating photons are atoms. Collectively they constitute
matter, and the inward motion in all directions is gravitation.
 In threedimensional space, the fraction of the inward motion directed
toward a unit area at distance d from an atom of matter is inversely
proportional to the total area at that distance; that is, to the surface
of a sphere of radius d. The effective portion of the total inward
motion is therefore inversely proportional to dē. This is the inverse
square law to which gravitation conforms.
 On the basis of the foregoing, gravitation in the theoretical universe
being developed from the postulates is not an action of one aggregate
of matter on another. Each atom and each aggregate of atoms is pursuing
its own course independently of all others, but because each observable
unit is moving inward in space, it is moving toward all others, and
this gives the appearance of a mutual interaction. However, if we
examine the characteristics of the force that each atom or aggregate
appears to be exerting upon the others, we find that this is a force
of a very peculiar nature. The gravitational "force" acts instantaneously,
without an intervening medium, and in such a manner that it cannot
be screened off or modified in any way. These observed characteristics
are so difficult to explain theoretically that most theorists have
taken the rather unscientific stand that the observations must, for
some reason, be wrong, and that notwithstanding the observational
evidence to the countrary, the gravitational effect must be propagated
through a medium, or something with the properties of a medium, at
a finite velocity. It is particularly significant, therefore, that
the theoretical characteristics of gravitation, as derived from the
postulates, are in full agreement with the observations. Motions which
are totally independent of each other will necessarily have just the
kind of characteristics that are observed in gravitation.
 In the foregoing paragraphs, it has been noted parenthetically that
the gravitational motion may be regarded as a force. The relation
between the two concepts can be illustrated by a simple example. Let
us assume a motion x existing coincidentally with an equal and oppositely
directed motion, y. In this case, we can either take the position
that both motions exist and that one neutralizes the other, or we
can say that there are two forces tending to cause motion,
but that no motion results because the forces counterbalance each
other.
 As noted in items 5 and 6, gravitation may take place either in
space or in time. When it acts in space, the atoms of matter continue
to occupy random locations in time, and vice versa. In an observable
aggregate of matter the atoms are therefore widely dispersed in time
even though they are are continguous in space. The inverse type of
aggregate in which the atoms are continguous in time, but widely dispersed
in space, is unobservable.
 In dealing with the magnitude of the gravitational effect, we will
need to take into account this point that spatial locations have no
independent existence. A spatial location is merely one aspect of
a spacetime location. Gravitation therefore moves the atoms of matter
toward all spacetime locations, even though the inward
movement is limited to space. Because of the random locations in time,
an aggregate of n units of motion occupies n widely dispersed locations
in spacetime. In the apparent interaction of an aggregate of n effective
units of motion with one of m effective units, each of the n units
is moving toward each of the m units, and the magnitude of the gravitational
effect at unit distance will therefore be nm. The factors that necessitate
the use of the term “effective” in the foregoing statement
will make their appearance later in the development.
 All matter is subject to gravitation by reason of the same
thing that makes it matter; that is, the rotational motion of the
atoms. Gravitation is therefore the second of the basic motions (or
forces) that determine the course of physical events.
 Each atom of matter is carried outward by one of these motions,
the progression of the absolute location that it occupies, while coincidentally
it is moving inward by reason of the other basic motion, the scalar
effect of its rotation. The net resultant of the two opposing motions
is determined by their relative magnitude. At the shorter distances,
gravitation predominates, and in the realm of ordinary experience,
all aggregates of matter are subject to net gravitational motions
(or forces). But the motion of the progression is constant at unit
speed, while the opposing gravitational motion is attenuated by distance
in accordance with the inverse square law. At some distance, the gravitational
limit of the aggregate of matter under consideration, the motions
reach equality. Beyond this point, the net movement is outward, increasing
toward the speed of light as the gravitational effect continues to
decrease.
 All aggregates of matter smaller than the largest existing units
are under the gravitational control of larger aggregates; that is,
they are within the gravitational limits of these larger units. Consequently
they are not able to continue the outward movement that would take
place in the absence of the larger bodies. The largest existing aggregates
are not limited in this manner, and according to item 14, any two
such aggregates that are outside their mutual gravitational limits
will recede from each other at speeds increasing with distance. In
the observed physical universe, the largest aggregates of matter are
galaxies, and the behavior of these galaxies is in full agreement
with the theoretical behavior of the largest aggregates of matter
in the theoretical universe. Current scientific opinion explains the
observed recession of the distant galaxies by the ad hoc
assumption of a gigantic explosion which hurled the galaxies out into
space at their present velocities. The necessity for any such highly
questionable assumption, with its accompaniment of difficult questions
of a collateral nature, such as what caused the explosion,
is eliminated by the theoretical finding that the galactic recession
is a natural and logical result of the most basic properties of matter.
