Everything here still belongs entirely to the Reciprocal System. DFT will not yet reinterpret anything. But these structures—integer displacements, 2-D rotations, and the scalar arithmetic of speed deviation—will eventually become essential to the dual-frame view. For now, the goal is to lay down the structure exactly as Larson developed it.
1. From Simple Motions to Compound Rotations
RS builds the universe from the single datum of unit scalar motion: a uniform progression at the natural speed
Rotation enters when the vibrating unit is turned about an axis. Because the vibrational units are discrete and not tied together, adding a rotational component to one unit “peels” it away from the rest and creates a new, internally stable compound motion. The details matter: rotation only has physical content when the axis is perpendicular to the vibration. Rotating about the vibrational axis makes no observable difference; rotating about either of the two perpendicular axes creates new structure. Rotation only has physical content when the axis is perpendicular to the vibration. This is because only the perpendicular components introduce the 2-D spatial alternation necessary for a compound motion.
This immediately implies a limit. A vibrating line can first sweep out a disk, and rotating that disk sweeps out a sphere. There is no third independent perpendicular direction remaining for another 2-D rotation of the same photon. Thus the fundamental atomic rotation is two-dimensional, not three.
2. Speed Displacement: Measuring Motion From Unity Instead of Zero
A crucial step in RS is the shift from measuring speed relative to zero to measuring it relative to unity. Everything is built on the natural speed
Slower-than-unity motion
Faster-than-unity motion
The sign does not denote “good” or “bad”; it denotes whether the alteration from unity is accomplished by adding time (positive displacement) or adding space (negative displacement). The sign indicates which aspect—space or time—absorbs the deviation from unity, not which component the motion "belongs" to. Because both are counted as simple integers, the displacements add algebraically. This additivity makes sense only when speed is understood as a scalar property of motion, not a vector property.
The scalar arithmetic of displacement is what later allows rotational combinations to cancel or reinforce each other. That cancellation becomes the foundation of stability.
3. The Rotational Base and the Rule of Alternation
Take a photon with a vibrational displacement—either positive or negative. Add a unit of inward two-dimensional rotation. If the rotation has the opposite sign from the vibrational displacement, they neutralize each other. The result is a compound motion whose net speed displacement is zero, but which nevertheless possesses a definite rotational direction.
This is the rotational base: the simplest structure capable of supporting further rotation. It is “zero displacement” only in the sense that the total deviation from unity vanishes. The rotational direction remains real and is the seed from which all atomic structures grow.
Larson emphasizes an important rule: stable compound motions almost always consist of displacements of opposite sign. Negative vibration combined with positive rotation (or vice versa) leads to structures that resist disintegration. Combinations of identical signs tend to fall apart because their displacement units add in the same direction and are easily disrupted.
This alternation principle is not optional; it is the key to why atoms exist at all.
4. Two-Dimensional Rotation and the Integer Structure of Matter
Because the basic atomic rotation is two-dimensional, its effective magnitude grows quadratically. If the displacement in each dimension is
(in units of 1-D electric displacement).
in electric-displacement units.
Because 2-D rotation grows quadratically while 1-D rotation grows linearly, the magnetic displacement tends to dominate whenever an increment in displacement is needed. Probability favors small displacements and symmetry between dimensions, pushing the system toward the smallest symmetric 2-D patterns available. Electric displacement then fills in the gaps.
This explains why the periodic table naturally separates into 8-, 18-, and 32-element groups. Each corresponds to the size of the electric-displacement “interval” between successive magnetic levels.
5. The RS Displacement Notation
Rotational combinations are expressed by the triplet:
where
and negative values of
This notation captures the full rotational content of an atom or particle in the material sector.
Some fundamental examples:
Hydrogen emerges by adding one negative electric displacement to helium:
Helium is the smallest complete double-rotating system:
Neon appears when both magnetic displacements become
The atomic number is simply the net electric equivalent of the total displacement—magnetic equivalents plus the net electric displacement. This equivalence is not a physical assumption; it follows directly from the scalar arithmetic of displacements.
In this way, the entire periodic table emerges from integer combinations of rotational content, without any reference to particles, forces, or extraneous assumptions.
6. Sub-Atomic Particles and the Material/Cosmic Bases
Below the level of the hydrogen atom, rotational combinations can exist that are too small to form complete double systems. These are the sub-atomic particles, which RS treats as incomplete atoms—not constituents of atoms.
For convenience, RS uses a slightly different notation for particles, showing only effective displacements and prefixing them with:
- M for the material base (positive rotation neutralizing negative vibration),
- C for the cosmic base (negative rotation neutralizing positive vibration).
- Rotational base:
- Electron:
- Positron:
- Massless neutron:
- Neutrino:
Mass only appears when a rotation spans three dimensions. A particle may have rotation in one or two dimensions and still be massless in the RS sense. When sufficient rotational content accumulates, or when two rotations combine, a three-dimensional displacement emerges and mass appears.
This explains the structural origin of the proton and neutron without invoking constituents. They are compound motions, not assemblies of parts.
7. Why This Matters for DFT
This post concludes the strictly RS portion of the project. Up to now we have avoided introducing the dual-frame idea, projection maps, or the motion budget as a general principle. But the material just covered is the keystone:
- RS reveals that matter consists of integer rotational modes arising from a single scalar progression.
- These rotational modes are limited by geometry, scaled by displacement arithmetic, and organized by probability.
- The result is a discrete spectrum of allowed structures: photons, electrons, protons, neutrons, atoms, isotopes.
DFT-8 will be the first post that explicitly shifts from RS foundations to the dual-frame formulation—showing how the S-frame and T-frame arise as complementary representations of the same scalar motion, and how RS displacement structures become a specific case of general projection geometry.