Simple Harmonic Motion

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Submitted by bperet on Thu, 02/24/2011 - 23:16

Simple Harmonic Motion (Direction Reversals)

In order to create simple harmonic motion in Larson's Reciprocal System, the outward, scalar expansion of the Universe must reverse itself at regular intervals at specific locations, but not necessarily all locations. Larson gives no reason for this “direction reversal”23 where, at the end of each “unit” of motion, the progression can just decide to reverse itself and go inward rather than outward—and does it with clock-like regularity. Students have had a problem with this description for decades, citing that a direction reversal would generate a square or triangle wave, not a sine wave, and a truly random function would not be the perfect wave that the photon exhibits. Larson provided no mechanism for this reversal to occur but requires it to build his system of theory.

With the understanding of uniform and dependent motion provided by RS2, we know that simple harmonic motion is an accelerated motion and must therefore be a dependent motion, derived from two or more uniform motions. The RS2 model is based on Nehru's paper, “The Photon as Birotation” that uses two dimensions of uniform, angular motion (rotation) to represent the photon. These uniform dimensions of motion, acting in opposition24, create the simple harmonic motion commonly associated with the sine wave of the photon. Euler's formula25, using complex quantities, can be used to represent this relationship:

Where R1 and R2 are the two, uniform angular velocities (rotations) and λ is the resulting dependent motion: simple harmonic motion. Note that the two-dimensional system of rotation is reduced to a single dimension of linear vibration.26 No “direction reversals” required, no question as to the wave shape or randomness of direction and a direct, predictable, and consistent coupling between the scalar dimensions and the resulting wavelike motion.

Simulating Yin: Larson's “Rotational Base”

Because Larson's Reciprocal System did not include the yin aspect of motion, he could have “motion without something to move”—providing it was linear motion—but could not have “rotation without something to rotate.” Since the Universe requires both yang and yin to function, Larson had to come up with a way to simulate the yin aspect of motion, which was lacking in the RS.

To circumvent this lack, he used the linear vibration created by the “direction reversal” to create a structure that could be rotated, which he termed the rotational base—his version of yin. Even Larson admits the rotational base has no observed physical properties,27 which is what you get if you had started with polar geometry to begin with.

Table 1: Comparison of the Derivation of Yin-Yang in RS and RS2

In RS2, neither the direction reversal nor the rotational base are necessary structures, as both concepts are embodied in the fundamental concept of the uniform and dependent motion. Lex parsimoniae.

23 Larson, Dewey B., The Structure of the Physical Universe, 1959: “From the foregoing it is apparent that where n units of one component replace a single unit in association with one unit of the other kind in a linear progression, the direction of the multiple component must reverse at each end of the single unit of the opposite variety. Since space-time is scalar the reversal of direction is meaningless from the space-time standpoint and the uniform progression, one unit of space per unit of time, continues just as if there were no reversals. From the standpoint of space and time individually the progression has involved n units of one kind but only one of the other, the latter being traversed repeatedly in opposite directions. It is not necessary to assume any special mechanism for the reversal of direction. In order to meet the requirements of the First Postulate the multiple units must exist and they can only exist by means of the directional reversals. It follows that these reversals are required by the Postulate itself.”
“When viewed from the standpoint of a reference system which remains stationary and does not participate in the space-time progression the resultant path of the oscillating progression takes the form of a sine curve.”
Note that a “sine curve” is an accelerated (dependent) motion, not a uniform motion. His conclusion is logically inconsistent in that a single, uniform motion (scalar space-time) can produce an non-uniform (accelerated) motion without a second, uniform motion to alter its behavior.

24 The two rotations are actually complex conjugates of each other, one of three forms of “opposites” used in RS2.

25 Euler's formula: z = x + iy = |z| (cos θ + i sin θ) = rei.

26 This reduction in the number of dimensions where counter-rotations interact to produce a wave structure is called “dimensional reduction” and plays a key part in physical interactions, such as superconductivity.

27 Larson, Dewey B., “Outline of the Deductive Development of the Universe of Motion,”, Item 68: “Where a one-unit positive rotational displacement is applied to a one-unit negative vibration, the net total speed displacement (a scalar quantity) is zero. This combination of motions has no effective deviation from unit speed (the physical datum), and therefore has no observed physical properties. We will call it the rotational base of the material system. A similar combination with positive vibration and negative rotation is the rotational base of the cosmic system.”