Simple Harmonic Motion
All of the statements in Section B, aside from those dealing
with the terminology utilized in this work, can be deduced directly from
the postulates. Hereafter, the deductions will be cumulative; that is,
each statement may be a consequence, wholly or in part, of some conclusion
or conclusions previously stated.
- While the progression is normally outward (positive), it is possible,
within the limits imposed by the postulates, for certain motions to
take place in the inward (negative) scalar direction. One such possibility
is a single negatively directed unit of translational motion. This
makes possible the existence of simple harmonic motion, in
which the scalar direction of movement reverses at the end of a unit
of space, or time. In such motion, each unit of space is associated
with a unit fo time, as in unidirectional translational motion, but
in the context of a stationary, three-dimensional spatial (or temporal)
reference system, the motion oscillates back and forth over a single
unit of space (or time), and from the standpoint of such a system
of reference, this is a vibratory motion in which one unit of space
(or time) is associated with n units of time (or space).
- At this stage of the development, no mechanism is available whereby
changes can take place, and only continuous processes are
possible. At first glance, therefore, it might appear that the reversals
of scalar direction at each end of the basic unit are inadmissable.
However, the changes of direction in simple harmonic motino are actually
continuous, as can be seen from the fact that such motion is a projection
of circular motion on a diameter. The algebraic sum of hte positive
and negative motions varies continuously from +1 at the midpoint of
the forward movement to zero at the positive end of the path of motion,
and then to -1 at the midpoint of the reverse movement and zero at
the negative and of the path.
- As indicated in Section B, the inherent scalar direction (positive
or negative) of a motion in space (or in time) has a direction with
reference to any stationary coordinate system, a vectorial direction,
we may call it. This vectorial direction is independent of the scalar
direction, except to the extend that the same factors may, in some
instances, affect both. As an analogy, we may consider a motor car.
The motion of this car has a direction in three-dimensional space,
while at the same time, it has a scalar direction, in that it will
be moving either forward or backward. As a general proposition, the
vectorial direction of this vehicle is independt of its scalar direction.
The car can run forward in any vectorial direction, or backward in
any direction. However, if it is traveling on a very narrow road,
and going forward when it moves south, then it must reverse the scalar
direction and travel backward in order to move north. Similarly, the
simple harmonic motion reverses both the scalar and the vectorial
directions at each end of its one-unit path. This unit of space (or
time) therefore remains stationary in the dimension of the motion
when viewed in the context of a stationary three-dimensional coordinate
- But the linear motion of the vibrating unit has no component in
the dimensions perpendicular to the line of oscillation, and the normal
progression of space-time is therefore operative in these dimesions.
The absolute location of the vibrating unit consequently moves outward
at unit speed in a direction perpendicular to the line of vibration.
The combination of a vibratory motion and a linear motion perpendicular
to the line of vibration results in a path which has the form of a
sine curve. The vectorial direction of the progression is purely a
matter of chance, and if a substantial number of these vibrating units
originate coincidentally, it will be observed that they move outward
in all directions from the point of origin. traveling at unit speed,
and following a wave-like path.
- Inasmuch as the theoretical phenomena emerge from the development
without labels it is necessary to identify the physical phenomenon
corresponding to a theoretical derivation before the two can be compared.
However, this identification is easily accomplished by comparing the
characteristics of the physical and theoretical phenomena. In most
cases, the correlation is obvious, and in any event, the verification
of the identification is automatic, as any error will quickly show
up as a discrepancy.
- The identity of the physical counterpart of the theoretical vibrating
unit is obvious. This unit is a photon. The process of emission
and movement of the photons is radiation. The space-time
ratio of the vibrations is the frequency of the radiation,
and the unit outward speed of movement is the speed of radiation,
more familiarly known as the speed of light.
- One of the most difficult problems with respect to radiation has
been to explain how it can be propagated through space without some
kind of a medium. This problem has never been solved other than by
what has been described as a "semantic trick"; that is, assuming,
entirely ad hoc, that space has the properties of a medium.
In the theoretical universe this problem does not arise, as the photon
remains in the same absolute location in which it originates. With
respect to the natural system of reference it does not move at
all, and the movement that is observed in the context of a stationary
reference system relative t othe stationary system, not a movement
of the photon itself.
- Another serious problem has been to provide an explanation for the
fact that the photon behaves in some respects as a particle, whereas
in other respects it behaves as a wave. Here, again, there is no problem
at all in the theoretical universe. The theoretical photon acts as
a particle in emission or absorption because it is a particle
(that is, a discrete unit). It travels as a wave because the combination
of its own inherent oscillating motion and the forward progression
of space-time has the form of a wave.