The 4 Rules of Motion

The 4 Rules of Motion are the implementing rules of the Law of Conservation of Momentum which operates on the Spatial Layer, to be explained in Chapter 5.

These 4 Rules match the 4 properties of waves.

Rule 1: No Void

No identity moves into the place of another body unless at the same time that other body moves into the place of another identity.

This is given by the equation: ∇ • v = 0

• ∇: continuous plenum
• v: velocity

Rule 2: Straight or Circular

Every moving identity moves in a straight line when alone, and in a curve or a circle when moving with others. When in a circle, it moves away from the center.

This leads to spin and vortex rotation, producing fractal patterns.

This gives the equations:

1. No vortex: d²r / dt² = 0
2. Within a vortex: d²r / dt² = −Ω × (Ω × r) − 2Ω × dr / dt

This captures Descartes’ three clauses: straight line alone, curve/circle with others, and (in the rotating frame) the striving away from the center via a_cf.

Rule 3: Collisions

When a weaker identity hits a stronger, it will be deflected. When a stronger hits a weaker, it will transfer some of its force to the weaker

This emphasizes the phenomenon of balance and natural limits and is given by the equation: v1′ = [ Θ(2 - α) - 1 ]v1 + ΘαVc where:

• the left side is the original state activation (This is displacement)
• the right side is the shared state activation (This is rotation)

Rule 4: State Continuity

Each identity remains as much as it can always in the same state. It is never changed except by external causes.

This is the concept of inertia in Physics and state in quantum mechanics.

P_Δ = 1 - |⟨Ψ₀|U_ext|Ψ₀⟩|²

change operator: U_ext = e^{-(i/ℏ) ∫ H_ext dt}

Rules 1 and 4 are related to each other just as Rule 2 and 3 are related.

We call:

• Rules 1 and 4 as feminine
• Rules 2 and 3 as masculine