Reciprocal System Research Society

In the last post I stopped at the first independent motion: linear vibration of a unit in the presence of the outward scalar progression. That gives us radiation and the photon, understood as a discrete unit of simple harmonic motion carried outward by the natural reference system. Before we can say anything meaningful about matter, however, another key form of motion has to appear in the theory: rotation.

Here I will stay strictly within Larson’s own development in Nothing But Motion, Chapters 4–5, and only describe how rotation, gravitation, and familiar vectorial motions arise in a universe of motion. Dual-Frame Theory will only enter later, after this entire structure is in place.

At the level we are working, everything is still scalar. A single scalar motion has a magnitude (outward or inward when represented in a fixed frame), but no inherent vectorial direction. Because of this, a single scalar motion cannot produce rotation on its own. Rotation is a directional structure: you cannot have “going around” without some sort of object that has a definite radius and orientation in a reference system.

Larson’s first step is therefore geometric: before there can be rotation, there must already be an independent motion that can be rotated. Motion can exist without anything moving, but rotation cannot. At this stage, there is only one such physical object available: the photon, the independent vibrating unit we identified previously. Simple rotation, then, is rotation of the photon.

In everyday life we think of rotation as a vectorial motion: a wheel turning around a fixed axis in a stationary coordinate system. If nothing else changes, the rotating object stays put in that system and only its orientation changes. But in the realm we are now examining, there is still no mechanism for inherently vectorial motion. All motion is still fundamentally scalar, and any vectorial direction we see is the way that scalar motion is represented in a chosen fixed reference frame.

The crucial point is this: the net scalar direction of independent motion must be inward. The outward progression at unit speed is already “occupied” by the natural reference system. Independent motion can only deviate from unity by adding inward components. However, the vectorial direction that this inward motion takes, once represented in a stationary three-dimensional grid, is determined by how that motion is related to that grid; it is not built into the motion itself. The same inward scalar motion can appear with any vectorial direction that is admissible in 3D space.

Rotation is one such possibility. A scalar rotation is a motion whose vectorial direction is continuously changing in 3D space in a way that traces out a circle, while the scalar magnitude remains inward. This differs from the vibration of the photon in one important respect: in simple harmonic motion the scalar direction alternates between inward and outward (as seen in the projection), producing back-and-forth behavior. In scalar rotation, the changes are entirely in vectorial direction; the scalar direction remains inward throughout. The result is one motion that has both a rotational aspect and an inward translational effect. Larson compares this to a rolling motion, where the rotation of a wheel carries it forward; here the rotation carries the photon inward, even though the underlying mechanism is different.

If it is still unclear how scalar inward motion works, Larson’s balloon analogy helps. A non-rotating photon remains at a fixed absolute location while the expanding balloon (the natural reference system) carries it outward from all other locations. A rotating photon, on the other hand, has an inward component in the scalar sense. Seen in a fixed reference system, this inward motion corresponds to a “spot” on the surface of a contracting balloon: it moves inward toward all other locations. The outward motion is the representation of increasing scalar magnitude; the inward motion represents decreasing scalar magnitude. When that inward magnitude passes through zero, it continues as an increasing inward (negative) quantity. If nothing intervenes, the object passes through a given location and keeps going.

Now we have two classes of independent units:

• Non-rotating vibrating units (photons), which remain in the same absolute locations and appear as radiation moving outward in all directions.
• Rotating photons, whose scalar rotation produces an inward motion in space and which move toward all other locations (again, as seen in a fixed reference system).

The second class is what we recognize as atoms and particles. Collectively, they are matter.

The inward motion itself is gravitation. There is no additional “force” being transmitted through space; there are simply material units whose internal rotational motions include an inward scalar component. Each unit moves inward in space toward all space-time locations other than its current one. Because we cannot identify space and time locations directly, we only see these motions through the changes in the relations between material aggregates. To an observer, matter appears to attract matter, but what is actually happening is that each mass is pursuing its own inward course independently, and we only see the changing separations.

From this standpoint, many of the puzzling features of gravitation fall into place:

• There is no need for a propagating gravitational field or waves in a medium. The inward motion is a built-in property of the rotating units themselves.
• The effective action is instantaneous in the sense that the relative position of two masses changes as soon as they continue their independent inward motions. There is nothing that has to travel from one to the other.
• Gravitational “energy” behaves quite differently from radiant energy. Radiation transfers discrete units of energy between aggregates and is freely convertible between different forms. Gravitational potential energy is strictly a function of position: a mass at point A has a certain potential relative to another mass; if it moves to point B, a fixed amount of energy is released or absorbed, but that energy is not transmitted as “gravitational energy” from place to place. It appears as kinetic, heat, etc. once the motion has taken place.

Larson emphasizes that gravitational energy is not a general “capability of doing work” in the same sense as other forms of energy. It will only do one thing: move masses inward toward one another. If that motion is not allowed to occur, the gravitational energy cannot be tapped. This is quite unlike radiation or electrical energy, and it is one reason why treating gravitation as if it were carried by waves analogous to electromagnetic radiation leads to conceptual difficulties.

The next important consequence arises when we consider how the inward motion is distributed in extension space. The progression of the natural reference system originates everywhere and has the same unit magnitude regardless of position. Gravitation, by contrast, originates at specific locations where matter exists and its effect at a distance is spread over a sphere centered on each mass. In three dimensions, the fraction of the total inward motion directed through a unit area at distance 𝑑 from the mass is inversely proportional to the surface area of that sphere, 4𝜋𝑑². This gives an inverse-square law for the effective gravitational motion. Inside some radius, for a given aggregate, the inward motion dominates over the outward progression; beyond that radius, the progression wins.

That radius is the gravitational limit of the aggregate. Inside its gravitational limit, the net motion is inward and aggregates are gravitationally bound. Beyond that limit, the net motion is outward, asymptotically approaching the unit progression as the gravitational contribution falls off. Larson points out that this provides a natural explanation for the observed recession of distant galaxies, without needing an ad hoc initial explosion: sufficiently large aggregates beyond each other’s gravitational limits simply recede, with speeds increasing with distance up to the speed of light where gravitation becomes negligible.

The same logic also resolves the old argument that a Newtonian inverse-square gravitational field in Euclidean geometry must cause all matter to collapse into a single clump. That argument assumes a net gravitational force everywhere. In a universe of motion, there is only a net inward motion inside gravitational limits; outside, the net is outward progression. Each galaxy is a finite island of matter within its own gravitational limit, but on larger scales the matter distribution can remain approximately uniform while still obeying an inverse-square law in Euclidean space.

Finally, all of this sets the stage for the emergence of the kind of motion we are most familiar with: vectorial motion in a fixed reference frame. Within a gravitationally bound system (a galaxy, a star system, etc.), matter is held within a certain region of extension space by the balance between gravitation and the outward progression. On top of this balance, additional motions can and do occur relative to the fixed coordinate system we choose. These motions have inherent vectorial directions and are always motions of something—planets orbiting, projectiles moving, laboratory objects sliding.

Larson points out that because these are the motions most directly accessible to experience, we tend to assume their characteristics—being “of something,” having a built-in direction—are universal properties of motion. But from the standpoint of the Reciprocal System, this is backwards. Vectorial motion is a special case that arises within gravitationally bound systems. The basic motions of the universe are scalar; their “directions” are inward or outward in the scalar sense, and they only acquire vectorial directions when we represent them in a chosen reference frame.

The observed motion of any object we examine is actually a composite of:

• the outward progression of the natural reference system,
• the inward rotational motion (gravitation), and
• any additional vectorial motions relative to the bound-system reference frame.

For some objects—photons, neutrinos—the net result is motion at the speed of light in our coordinates, which actually corresponds to the absence of independent motion in the natural reference system. For atoms, the inward rotational motion partially cancels the outward progression, leaving small net speeds in ordinary situations. Recognizing this composite character is essential; without it, many features of basic phenomena remain obscure.

At this point we have, still within Larson’s framework, a surprisingly rich structure:

• scalar progression and absolute locations,
• independent linear vibration (radiation),
• scalar rotation of the photon (atoms and particles),
• gravitation as inherent inward motion,
• gravitational limits and outward cosmic recession,
• and the emergence of vectorial motion in gravitationally bound systems.

In subsequent posts I will start to connect this structure to the dual-frame formalism: how the same underlying motions can be seen as “translational” and “rotational” in different interpretive frames, and how DFT tries to formalize the constraints linking those interpretations without discarding any of Larson’s achievements.