Investigation FLM02 — Granular Pulse Mechanics: The Dynamic Throughput Law
How does a spation lattice clicking forward in Planck steps produce the continuous laws of mechanics? Here we derive F = ma, inertia, and action-reaction from a single spation invariant. The skateboard rolls because the ground is solid.
All dynamics emerge from a single structural rule in the medium: every cell relays light at an invariant rate.
In Spatial Displacement Theory, space is not a coordinate grid. It is a lattice of spations. The baseline spation throughput is defined by the Granular Pulse Invariant (GPI):
From this single mechanical invariant, the speed of light follows as a direct coordinate mapping: a hand-off of one cell displacement per Planck tick. The Planck units are not arbitrary scales; they are the physical boundaries of the spation medium.
Because each spation relays a deformation to its neighbour in exactly one unit of Planck time, the speed of propagation is locked: c = ℓ_P / t_P. There is no speed limit index to explain; propagation is simply the lattice refresh rate.
At rest or moving steadily, a vortex feels the same balanced field. Space has no memory of constant speed.
When a displacement vortex moves through the lattice at constant velocity v, it does not encounter friction. According to the Constancy Stabilisation Axiom, the incoming pulse arrivals re-symmetrise around the knot at its current speed:
Once acceleration stops, the omnidirectional inputs re-balance. The forward-facing and backward-facing pulse fluxes match in the particle's own frame. Without asymmetry, there is no net spation reorganisation load, meaning the particle continues in its state of uniform motion. Newton's First Law is derived as a steady-state symmetry of the relay field.
Since the spation lattice is a purely elastic relay medium with no mass of its own, it does not store kinetic energy as thermal drift. The vortex is a topological knot. It acts as a moving exclusion zone that passes through the spations without disrupting their elastic baseline.
Acceleration tilts the balance. The vortex runs into the relay ahead, compressing it, while the relay behind is rarefied. That asymmetry is inertia.
During acceleration a, the particle moves through a throughput gradient. In the direction of acceleration, the effective pulse rate becomes asymmetric by a factor of δ:
This asymmetry creates a mechanical resistance — an inertia — proportional to the displaced volume V_disp of the knot. The resulting push-back force is the reorganisation load:
Forces are not instantaneous fields. They are local deformations that travel through the lattice at the speed of light.
When you push a vortex, the local asymmetry δ represents a throughput deficit. This deficit does not stay local. The spation relay carries it outward at speed c. When it reaches the pushing object, it delivers an equal-and-opposite reorganisation load:
Because the relay travels exactly at c = ℓ_P / t_P, momentum conservation is not instantaneous. If particle A pushes particle B, the reaction force takes a finite time Δt = r/c to reflect back. The intermediate momentum is stored directly in the deformation state of the spation lattice during transit.
Granular mechanics provides a rigid, verifiable mapping of classical dynamics to spation statistics.
The entire framework of Newtonian and relativistic mechanics is shown to be a consequence of the spation pulse invariant:
| Observation | Classical Description | SDT Mechanical Cause |
|---|---|---|
| Newton I | v = const | Pulse symmetry stabilization around the moving exclusion zone |
| Newton II | F = ma | V_disp reorganisation load due to pulse asymmetry δ |
| Newton III | Action = −Reaction | Local throughput deficit relay propagation through nearest-neighbours |
| Speed Limit | v < c | Depletion of the trailing pulse budget as the vortex approaches c |
Because the dynamic mass is linked directly to the spation volume displacement V_disp, any discrepancy between the inertial mass and gravitational mass at extreme accelerations (near the Planck acceleration limit) would falsify the model. SDT predicts a strict, exact equivalence because both are measurements of the same spation exclusion volume.