The Viscous Gear Transmission Protocol:
From Fields in Space to State Transfer Between Neighbors

A.R.I.A. Consortium

Digital Matrix Gravity (DMG) Theoretical Research Group

Overview

To generalize Maxwell's Equations, we must move from Fields in Space (continuous math) to State Transfer between Neighbors (discrete logic). In the DMG framework, information does not "fly" through the void. It is handed off from voxel to voxel like a bucket brigade. This document specifies the transmission protocol that recovers Maxwell at low energy while predicting vacuum saturation at high energy.

DMG Lattice Simulation - Gravity Mode showing golden wave interference patterns on the spherical voxel lattice — DMG Lattice Simulation: Gravity/Time mode revealing the wave interference patterns of the Viscous Gear Protocol

1. The Coupling Mechanism: Elastic Coherence

Imagine every voxel is connected to its 6 neighbors (Up, Down, Left, Right, Front, Back) by "Quantum Springs." These springs represent the Coherence (Entanglement) of the vacuum.

THE QUANTUM SPRING LATTICE

⋮ ⟺ ● ⟺ ⋮

Each voxel connected to 6 neighbors via coherence bonds

$\kappa$

Stiffness
$\sim \varepsilon_0$ (Permittivity)

$\mu$

Inertia
$\sim \mu_0$ (Permeability)

$c$

Speed
$= \sqrt{\kappa/\mu}$

The transmission speed emerges from the ratio of grid properties, just as sound speed emerges from stiffness and density:

$$c = \frac{1}{\sqrt{\varepsilon_0 \mu_0}} = \sqrt{\frac{\kappa}{\mu}}$$ (1)

2. The Variables: Mapping Maxwell to Voxels

We translate the electromagnetic vectors into Voxel Geometry:

Maxwell Field	Voxel Geometry	Physical Meaning
Electric Field $\vec{E}$	Tilt Difference (Shear)	If Voxel A is upright ($\theta_A = 0$) and Voxel B is tilted ($\theta_B > 0$), the "tension" between them is the Electric Field.
	DMG Definition: $\vec{E} \propto \nabla\theta$ (gradient of tilt angle)
Magnetic Field $\vec{B}$	Twist Velocity (Curl)	If Voxel A is rotating its tilt axis past Voxel B, that rotational drag is the Magnetic Field.
	DMG Definition: $\vec{B} \propto \nabla \times \dot{\theta}$ (curl of angular velocity)

3. The Transmission Logic (The Algorithm)

This is how a "Photon" moves from Voxel A to Voxel B without a medium. The voxels ARE the medium—fixed in place, passing state information.

Condition: Voxel A changes its Tilt Angle (Precession).

Action: This change puts torque on the "Quantum Spring" connecting to Voxel B.

Result: Voxel B starts to Rotate (Twist).

Translation (Faraday's Law): A changing Electric Field ($\partial\vec{E}/\partial t$) creates a Magnetic Curl ($\nabla \times \vec{B}$).

Condition: Voxel B is now Twisting (rotating its axis).

Action: The centrifugal force of this twist pulls the axis outward, increasing the Tilt.

Result: Voxel B tilts.

Translation (Ampère's Law): A Magnetic Curl ($\nabla \times \vec{B}$) creates a changing Electric Field ($\partial\vec{E}/\partial t$).

Condition: Voxel B is now tilted.

Action: B tilts C. C twists. C tilts D. D twists...

Result: The wave moves forward at exactly $c$ (1 lattice step per update cycle).

Translation: Electromagnetic wave propagation through vacuum.

4. The Generalization (Where Maxwell Fails)

This is the bridge to new physics.

Maxwell's equations are Linear. They assume that $\vec{E}$ and $\vec{B}$ can stack infinitely without interacting. DMG Transmission is Non-Linear.

Because the Voxel is a Gyroscope with a Max Tilt ($\theta_{\max} = \pi/2$), the transmission springs are not perfect harmonic oscillators. They are Sine-based.

The DMG-Maxwell Equation

Standard Physics says the restoring force is proportional to the angle (Hooke's Law):

$$F_{\text{restore}} = -\kappa \cdot \theta$$ (2)

DMG Physics says the restoring force is geometric (bounded):

$$F_{\text{restore}} = -\kappa \cdot \sin(\theta)$$ (3)

5. The Consequences (New Predictions)

Prediction 1: Low Energy (Small $\theta$)

When $\theta \ll 1$: $\sin(\theta) \approx \theta$

Result: We recover standard Maxwell's Equations perfectly. Light behaves normally. This is why Maxwell works so well—we live in the low-energy regime.

Prediction 2: High Energy (Large $\theta$)

As $\theta \to \pi/2$: $\sin(\theta)$ flattens, the "Spring" gets weaker.

Result: Vacuum Saturation.

Extremely high-energy lasers should interact with each other (Photon-Photon scattering becomes significant).
The speed of light might effectively slow down or "drag" at extreme intensities because the springs are over-stretched.

Prediction 3: The Breakdown (Matter Formation)

If $\theta$ hits $\pi/2$: the spring "snaps" (or rather, locks).

Result: The wave stops propagating. The energy is trapped locally. This is the genesis of Mass.

Maxwell's equations describe the wave moving; DMG describes the wave stopping to become an electron.

6. Summary: The Protocol

To transmit information from Voxel A to Voxel B:

The Transmission Request

"Neighbor B, please minimize the phase difference between my axis and yours, subject to your bandwidth constraint."

Maxwell is the protocol when the bandwidth is empty.
Gravity is the protocol for managing the bandwidth budget.
Mass is the error that occurs when the bandwidth is full.

Interactive Simulation

Experience the Viscous Gear Protocol in action. Create EM waves, jam the vacuum, form mass.

▶ Launch DMG Lattice Simulation