Entanglement as Recursive Coherence: A Test of Temporal Flow Physics

Entanglement as Recursive Coherence: A Test of Temporal Flow Physics

By John Gavel

 Background

In standard quantum theory, entanglement is often treated as a kind of abstract relational bookkeeping — a mysterious global correlation with no clear mechanism for how it propagates or persists.

In Temporal Flow Physics (TFP), we propose a radically different perspective:

Entanglement is not passive correlation—it is recursive cooperation under tension.

Entangled systems are not just "linked" by a rule, but held together by a constraint geometry that recursive flow must resolve. These recursive flows propagate across a network of motifs (local phase-locked structures), and entanglement emerges only when coherence is maintained across motif boundaries under finite friction (δ) and topological constraint.

So we asked:

Can we model entanglement as a recursive coherence field and predict where and how it collapses?

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The Experiment

We constructed a small motif graph (6 nodes) where each node has a local phase Ψₖ ∈ [0, 2π]. Motifs are linked by edges, and the edges carry recursive strain if the phase difference between motifs is large.

We tested how recursive coherence propagates across this motif network under constraints using the following steps:

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 1. Phase Field (Ψₖ)

Each motif node has a phase:

Ψ = [2.3533, 5.9735, 4.5993, 3.7615, 0.9803, 0.9801]

This could represent phase alignment in coherent flow, recursive state, or loop phase.

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 2. Entanglement Tensor Eₖⱼ

We compute local recursive strain between connected motifs as:

Eₖⱼ = sin²( (Ψₖ − Ψⱼ) / 2 )

This encodes how much phase misalignment exists between motifs. Large values mean high recursive strain — the flow across the edge is under tension.

This tensor acts as a constraint map: it shows where recursive phase continuity is hard to achieve.

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3. Recursive Coherence Kernel Kₖⱼ

This is the nonlinear transformation from strain to flow capacity:

Kₖⱼ = exp(−Eₖⱼ / ε_threshold)

Where ε_threshold is the threshold sensitivity to strain — analogous to δ_eff (informational friction) in TFP.

• High Eₖⱼ → Low Kₖⱼ: recursive flow suppressed

• Low Eₖⱼ → Kₖⱼ ≈ 1: recursive coherence propagates easily

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Code Summary

Here’s the core of the simulation in Python:

import numpy as np

# Motif node phases (in radians)
Ψ = np.array([2.3533, 5.9735, 4.5993, 3.7615, 0.9803, 0.9801])

# Edges (undirected)
edges = [(0,1), (1,2), (2,3), (3,4), (4,5), (5,0)]

# Recursive strain (entanglement tensor)
E = np.zeros((6,6))
for i,j in edges:
    E[i,j] = E[j,i] = np.sin( (Ψ[i] - Ψ[j]) / 2 )**2

# Recursive coherence kernel
ε_threshold = 0.5
K = np.exp( -E / ε_threshold )

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Results

--- Node Phases ---

Ψ[0] = 2.3533
Ψ[1] = 5.9735
Ψ[2] = 4.5993
Ψ[3] = 3.7615
Ψ[4] = 0.9803
Ψ[5] = 0.9801

--- Entanglement Tensor Eₖⱼ ---

[[0.     0.1331 0.     0.     0.     0.0687]
 [0.1331 0.     0.0687 0.     0.     0.    ]
 [0.     0.0687 0.     0.0419 0.     0.    ]
 [0.     0.     0.0419 0.     0.1391 0.    ]
 [0.     0.     0.     0.1391 0.     0.    ]
 [0.0687 0.     0.     0.     0.     0.    ]]

--- Recursive Coherence Kernel Kₖⱼ ---

[[0.     0.2641 0.     0.     0.     0.5033]
 [0.2641 0.     0.503  0.     0.     0.    ]
 [0.     0.503  0.     0.6578 0.     0.    ]
 [0.     0.     0.6578 0.     0.2489 0.    ]
 [0.     0.     0.     0.2489 0.     0.9999]
 [0.5033 0.     0.     0.     0.9999 0.    ]]

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Interpretation

 High Entanglement Strain:

• E₀₁ = 0.1331, E₃₄ = 0.1391

  • These are bottlenecks: recursive coherence is strained here.

  • Corresponds to phase discontinuities—motifs that do not easily align.

 Perfect Coherence:

• E₄₅ = 0.0

  • Ψ₄ ≈ Ψ₅ → phase-locked → ideal coherence anchor.

  • K₄₅ = 0.9999 → full recursive permeability.

 Coherence Corridors:

• K₂₃ = 0.6578

  • Moderate recursive flow allowed.

  • Recursive coherence can percolate here without strong collapse.

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 What This Confirms About TFP

Recursive coherence is sensitive to phase strain.

Entanglement emerges as a recursive flow property over motifs, not as static state overlap.

Recursive strain Eₖⱼ inhibits coherence via exponential suppression.

Frustrated edges (like 0↔1, 3↔4) form entanglement tension points — they may cause decoherence unless coherence can reroute or resolve.

Perfectly aligned motifs (like 4↔5) act as coherence attractors — they stabilize entanglement domains.