DFT-3: Linear Vibration and the First Independent Motions
Posted: Tue Dec 02, 2025 10:34 pm
In the previous post I focused on Larson’s argument for the natural reference system: a continually outward-moving scalar progression that exists because every unit of motion necessarily contains one unit of space and one unit of time. When an object has no independent motion, it simply remains at its absolute location, and therefore appears—relative to any stationary spatial frame—to be receding at unit speed. This outward progression is not imposed on the system; it is the system’s basic form.
Once this foundation is accepted, the next question is: What kinds of independent motion can exist on top of this progression? Larson addresses this at the beginning of Chapter 4 NBM, and it is one of the most important transitions in the entire Reciprocal System. The postulates allow independent units of motion to exist in addition to the background progression, but they also impose strict limitations on what those motions can be. Any independent motion must still be scalar in nature, must be continuous, must be uniform, and must respect the discrete-unit boundary. Inward and outward are permissible scalar directions, but because the outward progression already occupies the positive side completely, an independent outward motion cannot be added; less-than-unit space does not exist. The only possibility for an independent unidirectional motion is therefore inward, and even that cannot eliminate the outward progression. The net effect is always a deviation from unity, rather than a true reversal.
But a simple inward motion alone is not yet enough to constitute an ongoing physical effect. It does not create a sustained structure; it merely alters the effective speed relative to unity. To obtain something stable enough to behave like a physical entity, the system must permit a kind of motion that is continuous, uniform, and reversible in a way that does not violate the discrete-unit boundary. Larson identifies this possibility as simple harmonic motion. Although SHM involves reversals of scalar direction, those reversals are continuous when viewed as the projection of circular motion. The scalar speed varies continuously from +1 to 0 to –1 and back again, without discontinuity and without any need for an additional mechanism.
The key point is that SHM is not a vibration of something. In a universe composed entirely of motion, there is nothing “behind” the motion to be shaken. The vibration itself is the entity. What we are identifying is the first independent form of motion that can exist as a self-contained unit. It oscillates across one unit of space (or time), and while confined to that single unit, it is simultaneously being carried outward at unit speed by the progression of the natural reference system. The combined effect, when observed from a fixed spatial frame, is a sinusoidal path—what we normally recognize as a “wave.”
This is the origin of the photon in the Reciprocal System. Larson’s identification is not a metaphor or analogy; it is a direct result of the postulates. A vibrating unit satisfies every empirical characteristic of radiation: it is discrete, it has frequency, it is emitted and absorbed as a particle, it is transmitted with wave-like form due to the geometry of the progression, and it requires no medium to propagate because it does not actually move through space. It remains at its absolute location; the natural reference system moves past it. The traditional wave-particle paradox dissolves once this is understood.
Another longstanding puzzle disappears at the same time. In ordinary theory the propagation of radiation seems to require a medium, and because no such medium was ever observed, space itself was reinterpreted as possessing “physical properties” capable of transmitting waves. Larson shows that this reinterpretation is unnecessary. The outward movement we observe is not a property of space at all; it is the natural reference system progressing uniformly relative to the stationary reference grid we impose. Radiation, in the RS framework, does not propagate through an ether or a vacuum; it is simply carried outward by the scalar progression that defines the universe itself.
From this standpoint, the vibrating unit is not an optional add-on or an empirical guess. It is the first unavoidable consequence of allowing independent motion to exist in a universe whose basic constituent is motion. We have, in this one construction, the first physical “object,” the first physically effective deviation from unity, the first appearance of frequency, the first reconciliation of particle and wave behavior, and the first explanation of how radiation travels without a medium. All of these arise directly from the logic of the postulates.
This completes the initial layer of structure needed before we can proceed to more complex motions. Translational motion will reappear later as a combination of the background progression with independent inward deviation. Rotational motion will enter when additional constraints are imposed on the relations between space and time within a unit. And the rich hierarchy of atomic, gravitational, and electrical effects will come from combining these basic motions in systematic ways. But none of that can be addressed until the foundation—scalar progression, absolute location, inward and outward magnitudes, and simple harmonic vibration—is firmly in place.
In the next installment, I plan to continue following Larson’s sequence and look carefully at how translational, rotational, and vibrational motions coexist within the same framework, how they differ in their spatial and temporal aspects, and how these independent motions begin to build the structures we later identify as matter.
Once this foundation is accepted, the next question is: What kinds of independent motion can exist on top of this progression? Larson addresses this at the beginning of Chapter 4 NBM, and it is one of the most important transitions in the entire Reciprocal System. The postulates allow independent units of motion to exist in addition to the background progression, but they also impose strict limitations on what those motions can be. Any independent motion must still be scalar in nature, must be continuous, must be uniform, and must respect the discrete-unit boundary. Inward and outward are permissible scalar directions, but because the outward progression already occupies the positive side completely, an independent outward motion cannot be added; less-than-unit space does not exist. The only possibility for an independent unidirectional motion is therefore inward, and even that cannot eliminate the outward progression. The net effect is always a deviation from unity, rather than a true reversal.
But a simple inward motion alone is not yet enough to constitute an ongoing physical effect. It does not create a sustained structure; it merely alters the effective speed relative to unity. To obtain something stable enough to behave like a physical entity, the system must permit a kind of motion that is continuous, uniform, and reversible in a way that does not violate the discrete-unit boundary. Larson identifies this possibility as simple harmonic motion. Although SHM involves reversals of scalar direction, those reversals are continuous when viewed as the projection of circular motion. The scalar speed varies continuously from +1 to 0 to –1 and back again, without discontinuity and without any need for an additional mechanism.
The key point is that SHM is not a vibration of something. In a universe composed entirely of motion, there is nothing “behind” the motion to be shaken. The vibration itself is the entity. What we are identifying is the first independent form of motion that can exist as a self-contained unit. It oscillates across one unit of space (or time), and while confined to that single unit, it is simultaneously being carried outward at unit speed by the progression of the natural reference system. The combined effect, when observed from a fixed spatial frame, is a sinusoidal path—what we normally recognize as a “wave.”
This is the origin of the photon in the Reciprocal System. Larson’s identification is not a metaphor or analogy; it is a direct result of the postulates. A vibrating unit satisfies every empirical characteristic of radiation: it is discrete, it has frequency, it is emitted and absorbed as a particle, it is transmitted with wave-like form due to the geometry of the progression, and it requires no medium to propagate because it does not actually move through space. It remains at its absolute location; the natural reference system moves past it. The traditional wave-particle paradox dissolves once this is understood.
Another longstanding puzzle disappears at the same time. In ordinary theory the propagation of radiation seems to require a medium, and because no such medium was ever observed, space itself was reinterpreted as possessing “physical properties” capable of transmitting waves. Larson shows that this reinterpretation is unnecessary. The outward movement we observe is not a property of space at all; it is the natural reference system progressing uniformly relative to the stationary reference grid we impose. Radiation, in the RS framework, does not propagate through an ether or a vacuum; it is simply carried outward by the scalar progression that defines the universe itself.
From this standpoint, the vibrating unit is not an optional add-on or an empirical guess. It is the first unavoidable consequence of allowing independent motion to exist in a universe whose basic constituent is motion. We have, in this one construction, the first physical “object,” the first physically effective deviation from unity, the first appearance of frequency, the first reconciliation of particle and wave behavior, and the first explanation of how radiation travels without a medium. All of these arise directly from the logic of the postulates.
This completes the initial layer of structure needed before we can proceed to more complex motions. Translational motion will reappear later as a combination of the background progression with independent inward deviation. Rotational motion will enter when additional constraints are imposed on the relations between space and time within a unit. And the rich hierarchy of atomic, gravitational, and electrical effects will come from combining these basic motions in systematic ways. But none of that can be addressed until the foundation—scalar progression, absolute location, inward and outward magnitudes, and simple harmonic vibration—is firmly in place.
In the next installment, I plan to continue following Larson’s sequence and look carefully at how translational, rotational, and vibrational motions coexist within the same framework, how they differ in their spatial and temporal aspects, and how these independent motions begin to build the structures we later identify as matter.