Technical Specification: The DMG Voxel
The DMG Voxel ($\mathcal{V}_i$) is the fundamental, discrete quantization of spatial angular momentum. It acts simultaneously as a computational bit, a mechanical gyroscope, and a superfluid element. It does not exist in space; a connected lattice of Voxels constitutes space.
Symbol: $\mathcal{V}_i$ — The voxel at coordinate $i$
This document provides the formal specification of the Voxel in the Digital Matrix Gravity framework. The Voxel is not a passive box of empty space—it is the active hardware of reality. It is the smallest possible "gear" in the universe. It does not occupy space; it is space. The entire 3D universe is a crystallized ocean of these gears, packed together in a dense lattice at the Planck scale ($\ell_P \approx 10^{-35}$ m), updating at the Planck frequency ($\omega_P \approx 10^{43}$ Hz).
1. Internal State Variables
Each voxel is defined by a local state vector $|\psi_i\rangle$ governed by four parameters:
| Variable | Definition | Physical Role |
|---|---|---|
| $\omega_c$ (Carrier Spin) |
The intrinsic rotation frequency of the voxel's primary axis.
Value: $\omega_c \leq \omega_P$ ($\approx 10^{43}$ Hz)
|
The rate of Time flow (Chronon). The "System Clock." |
| $\hat{n}$ (Orientation Vector) |
The unit vector pointing along the Carrier Spin axis.
Value: $\hat{n} \in S^2$ (unit sphere)
|
Coherence of $\hat{n}$ across neighbors defines the Gravitational Field. |
| $\omega_L$ (Precession Frequency) |
The rate at which $\hat{n}$ wobbles around a secondary axis.
Value: Variable (e.g., $\sim 10^{20}$ Hz for light)
|
Electromagnetic Energy ($E = \hbar\omega_L$) |
| $\theta$ (Tilt Angle) |
The angle between the vacuum expectation axis (Z) and current orientation $\hat{n}$.
Value: $\theta \in [0, \pi/2]$
|
Mass/Matter State. At $\theta = \pi/2$, the voxel is "flipped." |
The voxel as a precessing quantum gyroscope with two distinct motions
Primary Axis
Points "Down"
Wobble = Light
Flip = Mass
2. The Fundamental Conservation Law
The Voxel operates under a strict finite-resource constraint. The total rotational energy is bounded by the Planck Energy ($E_P$):
Equivalently, in frequency space:
This is the Bandwidth Limit—the voxel cannot spin infinitely fast on all axes. It is a zero-sum system.
- Time Dilation: As interaction energy ($\omega_L$) increases, the carrier frequency ($\omega_c$) must decrease to satisfy the limit. The "system clock" slows down.
- Gravitational Decoupling: If $\omega_L$ approaches $\omega_P$ (saturation), the voxel loses the bandwidth required to maintain the orientation of $\hat{n}$. The gravitational vector becomes undefined ($\vec{g} \to \emptyset$).
3. Phenomenological Modes
The voxel manifests physically different properties based on its geometric regime:
| Mode | State Parameters | Physical Description |
|---|---|---|
| Vacuum (Void) | $\omega_L = 0$, $\theta = 0$ | Laminar Flow. The gyroscope is upright at $\omega_P$. The vector $\hat{n}$ is aligned with neighbors. Space is "smooth." Observer sees: "Empty Space." |
| Electromagnetism | $\omega_L > 0$, $\theta < \pi/2$ | Precession (Wobble). The carrier axis traces a cone. This transverse oscillation propagates through the lattice as light. |
| Mass (Matter) | $\theta = \pi/2$ (Critical Lock) | Toroidal Lock. The voxel is tilted 90° and locked into a rolling state. This "defect" in the grid creates inertial drag (Mass). Observer sees: "Solid Matter." |
| Singularity | $\omega_c \to 0$ | Bandwidth Starvation. The voxel has zero capacity for Time/Gravity. The "refresh rate" hits zero. Event Horizon. |
4. The Qubit Logic
Since the voxel is fundamentally a Bosonic Qubit, it follows quantum mechanical logic rather than classical mechanics:
State $|0\rangle$ — The Vacuum
Geometry: The gyroscope is upright ($\theta = 0$).
Physics: Perfect alignment. No wobble. Superfluid Laminar Flow.
State $|1\rangle$ — The Particle
Geometry: The gyroscope is flipped flat ($\theta = \pi/2$).
Physics: Maximal wobble. A "Knot" in the flow. Stable defect.
Superposition — The Wave Function
Geometry: The gyroscope is in a probabilistic haze between $|0\rangle$ and $|1\rangle$.
Physics: It is coherently entangled with its neighbors. The "Angle" is not locally defined but shared across a cloud of voxels. Observer sees: A delocalized probability cloud (e.g., an electron in an orbital).
5. Collective Dynamics (The Lattice)
The Voxel is not isolated; it is a node in a spin network.
Voxels are fixed in the universe frame — they do not move. They ARE space. The vacuum state is a Bose-Einstein Condensate where information and phase states propagate through the lattice with zero viscosity. This collective hum is the "Lorentzian Bath."
Gravity as Coherence Gradient
Gravity is defined as the negative gradient of orientation coherence:
Gravity is the statistical tendency of voxels to realign their $\hat{n}$ vectors to maximize lattice coherence. Matter creates regions of misalignment; the surrounding voxels "point toward" the defect to restore order.
The Electron as Topological Soliton
An electron is not a single voxel—it is a Toroidal Vortex Ring. A closed loop of voxels where the phase angle $\phi$ winds around the ring (Hopf Fibration), locking the constituent voxels into the Mass State ($\theta = \pi/2$).
- It flows through the grid like a smoke ring through air.
- It is stable because of the topological winding—the internal twist prevents the ring from collapsing.
6. Summary: What Does a Voxel Do?
And crucially: it can only do so much at once.
Overload it with one, and it drops the others.
A Voxel is a precessing quantum bit of spacetime where the trade-off between its internal clock speed (Time) and its external oscillation (Energy) creates the phenomenology of Gravity and Mass.