Entropic Decoupling in Discrete Computational Spacetimes:
Gravitational Suspension via Spectral Saturation

1. Introduction

Standard General Relativity (GR) assumes a continuous differentiable manifold. However, the Bekenstein bound and the Holographic Principle suggest that the information content of any finite region is strictly limited. This implies the underlying substrate of reality acts as a finite-state machine.

In Digital Matrix Gravity (DMG), we posit that "Physical Laws" are emergent properties of an underlying scheduling algorithm running on a voxelated grid. The fundamental constraint is the System Clock ($\Omega_{\text{sys}}$). A voxel cannot process infinite updates per tick.

This paper establishes the Computational Equivalence Principle:

Physical velocity is distinguishable from acceleration only by the rate of resource consumption required to update the pointer state relative to the grid address space.

2. The Thermodynamics of the Voxel

2.1 The Zero-Sum Hamiltonian

We define the computational Hamiltonian $H_{\text{voxel}}$ for a particle state $|\psi\rangle$ residing in voxel $V_x$ as a sum of processing costs. Unlike a standard energy Hamiltonian, this represents computational cycles:

Dividing by $\hbar$, we obtain the frequency allocation budget:

Where $\Omega_{\text{sys}}$ is the Planck Frequency. The system is zero-sum; increasing the allocation for one thread necessitates the throttling of others.

2.2 Velocity as Bandwidth Starvation

In standard physics, time dilation is geometric. In DMG, it is operational. Let $\mathcal{C}$ be the cost function for transferring the state vector $|\psi\rangle$ to neighbor voxel $V_{x+1}$:

As $v \to c$, the cost of motion approaches $\Omega_{\text{sys}}$:

The voxel has zero cycles remaining to update the internal state. Time dilation is therefore a Process Lag due to I/O saturation.

3. The Lorentzian Bath and Inertial Drag

3.1 The Vacuum Spectrum

The background grid possesses a noise temperature characterized by a Lorentzian spectral density:

Where $\omega_0$ is the grid resonance frequency and $\Gamma$ is the linewidth (Planck friction).

3.2 Inertia as Signal-to-Noise Ratio

The voxel must perform Error Correction to distinguish the particle from vacuum fluctuations:

As $v \to c$, the SNR drops to zero. Relativistic mass is an Information Entropy artifact.

4. Gravitational Decoupling: The "Lag Switch"

4.1 The Priority Stack

The voxel Scheduler operates on strict priority logic:

1. Thread A (State): Existence Maintenance. Priority: Critical.
2. Thread B (Motion): Causality/Pointer Handoff. Priority: High.
3. Thread C (Gravity): Weak coupling to stress-energy tensor. Priority: Low.

Gravity is a perturbative correction ($10^{-39}$ coupling strength). In a resource-starved environment, it is the first process terminated.

4.2 The Saturation Condition

To decouple from gravity, we must induce a Buffer Overflow:

When this inequality is met, the Scheduler executes DROP(Thread_C).

5. Experimental Design: The Cavity Jammer

The drive signal must mimic the vacuum's own noise:

6. Predictions and Signatures

• Regime I (Linear): Low power. Standard weight.
• Regime II (The Knee): Inertial mass increases; gravitational mass fluctuates.
• Regime III (Saturation): $M_{\text{grav}} \to 0$. The object floats.

Visual Signature: Photons reflecting off the apparatus will be red-shifted or spatially distorted, creating a "mirage" effect.

7. Conclusion

The DMG model suggests that Gravity is not a fundamental force, but a "Daemon Process" maintaining global consistency. By exploiting the Lorentzian nature of the vacuum noise, we can engineer a local denial-of-service attack on the gravitational coupling, enabling inertial mass reduction and propellant-less suspension.

Gravitational Decoupling via Spectral Saturation of Discrete Spacetime Elements: A Computational Resource Model

1. Introduction

The unification of Quantum Mechanics and General Relativity remains one of the central challenges of theoretical physics. We propose that this incompatibility reflects an underlying computational constraint in the substrate of reality itself.

In this framework, which we term Digital Matrix Gravity (DMG), particles are localized process states maintained by discrete spacetime elements. The fundamental constraint is the System Clock:

Each computational cycle must be allocated among competing processes:

• $k_{\text{state}}$ (Thread A): Internal quantum numbers. Priority: Critical.
• $k_{\text{motion}}$ (Thread B): Position updates. Priority: High.
• $k_{\text{gravity}}$ (Thread C): Stress-energy interaction. Priority: Low.

2. Theoretical Framework

2.1 Velocity as Resource Consumption

As a particle accelerates, the computational cost of state transfer increases:

At $v = c$, all cycles go to motion processing. The internal clock freezes—this is time dilation.

2.2 The Lorentzian Bath

The vacuum is a fluctuating background field with spectral density:

Inertia emerges as error-correction overhead against bath noise.

2.3 Length Contraction as Synchronization Lag

Lorentz contraction is a "rolling shutter" artifact from finite signal propagation:

This is not geometric compression but input lag—the rear reacting to outdated coordinate data.

3. The Resource Starvation Hypothesis

The condition for gravitational decoupling:

When breached: $k_{\text{gravity}} \to 0$. The object decouples through thread termination.

4. Connection to Anomalous Thrust

Building on McCulloch's MiHsC framework:

where $\mathcal{M}(v) = 1 + \alpha \frac{v^2}{c^2}$. Thrust increases with velocity.

Using NASA Eagleworks parameters ($P = 40$ W, $Q = 5900$), our model predicts $F \approx 770$ μN. The measured 40-100 μN suggests saturation efficiency $\eta_{\text{sat}} \approx 0.1$.

5. Experimental Predictions

Phase I (Linear): Enhanced inertial resistance. Standard Newtonian mechanics.

Phase II (Glitch): Optical distortions. Red-shifting anomalies. Weight fluctuations.

Phase III (Decoupling): Weight drops. Object ceases to fall.

5.1 Critical Discriminating Test

Centrifuge experiment at $v > 0.01c$:

• MiHsC: Thrust depends primarily on proper acceleration.
• DMG: Thrust increases dramatically with tangential velocity.

6. Conclusion

Gravity is not geometric but a system service. Anomalous propulsion may represent accidental "buffer overflows." Intentional bandwidth saturation could achieve controlled gravitational decoupling.