Nonlocality and Entanglement as Resonant Coherence in Harmonic Vacuum Fields

Abstract

This paper investigates quantum nonlocality and entanglement through the framework of the Electromagnetic Permittivity Variation and Orbital Dynamics (EPVOD) theory. Rather than treating entanglement as a non-causal statistical correlation, we propose that entangled particles remain in resonance through a shared harmonic deformation of the vacuum structure. This resonance permits instantaneous coherence of curvature phase states, independent of spatial separation, by way of a continuous, non-energetic coupling through spacetime tension. Entanglement thus arises from geometric coherence between spatially distributed harmonic nodes, enabling a deterministic interpretation of phenomena traditionally described probabilistically.

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1. Introduction

Entanglement challenges classical notions of locality by exhibiting correlated outcomes across arbitrarily large distances, as demonstrated in Bell test experiments. The standard quantum interpretation offers no mechanism for causal linkage, attributing correlations to nonlocal wavefunction collapse. The EPVOD model introduces a physical substrate for coherence: shared vacuum harmonic structure.

2. Entanglement as Harmonic Synchronization

Two particles become entangled when their respective deformation fields resonate through matched phase, curvature, and boundary conditions. This harmonic synchronization creates a unified tension field across spacetime that couples the particles' internal states.

Let particles A and B be initially co-located. Their combined vacuum deformation Φ(x,t) is coherent and stable. Upon spatial separation, their harmonic imprint remains coupled via a resonant standing-wave configuration in vacuum tension:

$$
Φ_{AB}(x,t) = Φ_A(x,t) + Φ_B(x,t) + ext{Interference Terms}
$$

This implies no energy transmission is necessary to sustain coherence; only phase alignment within the harmonic field.

3. Vacuum Field Topology and Resonant Modes

Vacuum is modeled as a deformable medium sustaining curvature oscillations. When entangled particles are formed, the topology of the shared curvature field establishes a mode that spans both positions. As long as external perturbations do not disrupt this field, the entanglement remains intact.

Key implications:

• Nonlocality emerges from extended curvature harmonics
• Wavefunction collapse is the local decoherence of the shared harmonic node
• Measurement corresponds to phase locking with an external curvature boundary, breaking coherence

4. Temporal Invariance and Instantaneity

The tension field supporting entanglement exists in a tensionless equilibrium, and thus lacks a propagation delay. Changes in one particle's configuration instantaneously reflect in the other due to curvature field conservation. This does not violate causality but reframes it as conservation of harmonic boundary conditions across the entangled system.

5. Decoherence as Harmonic Boundary Disruption

Loss of entanglement corresponds to the disturbance of the shared vacuum mode:

• Thermal noise introduces incoherent fluctuations
• Measurement imposes boundary constraints
• Gravitational or electromagnetic gradients distort field topology

These mechanisms introduce phase decoherence, collapsing the shared curvature field into isolated local minima.

6. Experimental Predictions

• Phase-sensitive interferometry may detect residual vacuum tension between entangled particles
• Entanglement longevity increases in vacua with minimal curvature gradients
• Curvature topological simulations may model entanglement stability zones across extended configurations

7. Conclusion

Entanglement and nonlocality, when viewed through EPVOD, are emergent phenomena of resonant harmonic coupling in a deformable vacuum. Spatial distance is irrelevant when coherence is defined by curvature phase alignment rather than signal propagation. This interpretation supports deterministic evolution of entangled systems through vacuum geometry, enabling a geometric bridge between quantum phenomena and gravitational structure.

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