Chapter 5 by John Foster July 29, 2025

Quantum Entanglement and Non-Local Interactions

~20,000 words 6 sections Key Frequency: 1.5 × 10¹³ Hz

Quantum entanglement represents one of the most profound mysteries of quantum mechanics, where particles share correlations that persist instantaneously across arbitrary distances. In Dimensional Relativity, entanglement emerges from 2D field networks oscillating at f_entangle ≈ 1.5 × 10¹³ Hz, enabling non-local interactions through quantum foam dynamics.

Key Concepts

  • Entanglement as 2D field sharing between particles
  • Non-local correlations through foam networks
  • EPR paradox and Bell inequality violations
  • Applications to quantum computing and FTL communication

5.1 Quantum Entanglement: Core Principles

Quantum entanglement is the phenomenon where two or more particles share a two-dimensional (2D) energy field, resulting in correlated properties that persist across arbitrary 3D spatial distances. In Dimensional Relativity, entanglement is mediated by quantum foam's 2D fields, oscillating at:

fentangle ≈ Efield / h

where Efield = 10⁻²⁰ J and h = 6.626 × 10⁻³⁴ J·s:

fentangle ≈ 10⁻²⁰ / 6.626 × 10⁻³⁴ ≈ 1.5 × 10¹³ Hz

Einstein-Podolsky-Rosen (EPR) Paradox

The EPR paradox, proposed in 1935, questioned whether quantum mechanics could be complete if particles exhibited "spooky action at a distance." In Dimensional Relativity, this apparent paradox is resolved through 2D field sharing, where entangled particles maintain instantaneous correlations via quantum foam networks.

Key Insight

The foam's fractal network (Df ≈ 2.3) with high connectivity (kavg ≈ 10) ensures robust field interactions, supporting entanglement across cosmic distances through non-local 2D field substrates.

Diagram 9: Entangled Field Network

3D cube (1m × 1m × 1m) showing two entangled particles connected by 2D field sheet oscillating at f_entangle ≈ 1.5 × 10¹³ Hz. Fractal edges (Df ≈ 2.3) span the cube with correlation time < 10⁻¹⁵ s.

Applications

Quantum Computing

Using entanglement for parallel processing and quantum algorithms

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FTL Communication

Leveraging non-local correlations for instantaneous signaling

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Cosmology

Probing early universe entanglement in CMB patterns

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5.2 Network Theory and Entanglement

Entanglement is modeled as a network phenomenon, with 2D fields forming a computational lattice within quantum foam. Nodes represent entangled particles, and edges represent energy flows at fentangle ≈ 1.5 × 10¹³ Hz.

Quantum Foam Network Properties

10⁶⁰ nodes/m³
10⁶¹ edges/m³
~10 avg degree k
3.3×10⁻⁴⁴ s propagation time
tprop ≈ l / c ≈ 10⁻³⁵ / 2.998 × 10⁸ ≈ 3.3 × 10⁻⁴⁴ s

Entanglement Network Visualization

Bell Inequality Testing

Bell Parameter (S)
S = 2.8

Classical limit: |S| ≤ 2 | Quantum limit: |S| ≤ 2√2 ≈ 2.83

Bell Inequality Violated - Quantum Non-locality Confirmed!

5.3 Frequency in Entanglement Dynamics

Dimensional Relativity Frequency Spectrum

Quantum foam: 1.5 × 10¹³ Hz
Entanglement: 1.5 × 10¹³ Hz
Gravity waves: 1.5 × 10¹³ Hz
Synchrotron: 1.6 × 10¹² Hz
Virtual particles: 1.5 × 10¹⁵ Hz

Frequency Coherence

Entanglement stability depends on frequency matching between particles. Decoherence occurs when environmental interactions cause frequency drift, breaking the 2D field connection at fentangle.

5.4 Non-Local Interactions in Quantum Foam

fentangle ≈ Efield / h ≈ 1.5 × 10¹³ Hz

Diagram 10: Non-Local Correlation Map

3D spacetime cube (10m × 10m × 10m) with entangled particles at opposite corners, connected by 2D field sheet.

5.5 Space/Time and Entanglement

Gμν = (8πG / c⁴) Tμν

ER=EPR Conjecture

The ER=EPR conjecture links entanglement (EPR) to wormhole-like connections (Einstein-Rosen bridges). In Dimensional Relativity, entanglement redefines spacetime connectivity through 2D field networks.

5.6 Engineering Entanglement Technologies

Proposed Technologies

📡
Quantum Communicators

Using entangled particles for instantaneous signaling, bypassing light-speed limits

Range: Unlimited Speed: Instantaneous Protocol: EPR correlations
💻
Quantum Computers

Enhancing qubit coherence with foam-mediated entanglement networks

Qubits: Foam-stabilized Coherence: Extended Processing: Distributed
🚀
Spacetime Modulators

Tuning f_entangle to manipulate spacetime for FTL propulsion

Frequency: 1.5 × 10¹³ Hz Application: Warp drives Method: Foam modulation

Chapter Summary

Key Findings

  • Entanglement emerges from shared 2D fields oscillating at f_entangle ≈ 1.5 × 10¹³ Hz
  • Non-local correlations operate through quantum foam networks with propagation times of 3.3 × 10⁻⁴⁴ s
  • Bell inequality violations confirm quantum non-locality via frequency-driven field coherence
  • Entanglement transcends spacetime through 2D field bridges, supporting ER=EPR conjecture
  • Engineering applications enable FTL communication and enhanced quantum computing

Implications

Quantum entanglement through 2D field networks revolutionizes our understanding of non-locality and spacetime connectivity. The characteristic frequency f_entangle provides a practical foundation for developing quantum technologies that transcend classical limitations.