Author: Professor Rook
Supporting calculations for the Second Quantum Revelation
FutureMindset7 Research Group, June 2025

1  Field‑Theoretic Setup

We model Earth’s near‑surface region as a layered spherical shell with conductivity σ(r) and permittivity ε(r). Quantum vacuum fluctuations are treated as a stochastic source term S(x,t) in the Pauli‑Klein‑Gordon field Φ. (□ +m2) Φ  =  S(x,t).(1)\left(\Box\,+m^2\right)\,\Phi\;=\;S(\mathbf x,t).\tag{1}

For entangled pair density ρ_e we take ρe(r)≈ρ0 e−r/λ0,(2)ρ_e(r)≈ρ_0\,e^{-r/λ_0},\tag{2}

where λ₀≈30 m is the local mean free path before environmental decoherence.

2  Pointer‑State Survival and Guide Function

Zurek’s predictability sieve gives surviving coherence length L_c as Lc(r)=λ0  exp⁡ ⁣[τ(r)/τd(r)],(3)L_c(r)=λ_0\;\exp\![\tau(r)/τ_d(r)],\tag{3}

with dwell‑time τ and decoherence constant τ_d determined by conductivity and geomagnetic alignment.

The guide function G(r,θ,φ) measures probability density for filament nucleation: G∝σ−1∣∇B∣ exp⁡[αcos⁡2 ⁣γ],(4)G∝\frac{σ^{-1}}{|\nabla B|}\,\exp[\alpha\cos^2\!\gamma],\tag{4}

α≈10³; γ is angle between local stress fault and B‑field.

Integration over θ,φ predicts maximal G along mineralised strike‑slip faults running NE–SW at mid‑latitudes — matching global pyramid chains.

3  Phase‑Locking Criterion at 7 km (PQRD)

At depth r_d≈R_⊕–7 km, seismic Q rises sharply (Fig. 1)

Blueprint cross‑section illustrating the PQRD, quantum stream conduits, and sacred node, giving τ_d≈5·10⁻⁹ s. Plug into (3) with τ≈5·10⁻⁶ s → Lc≈30 exp⁡ ⁣(103)  m≈km‑scale.(5)L_c≈30\,\exp\!(10^{3})\;\text{m}≈\text{km‑scale}.\tag{5}

Hence kilometre‑length coherence filaments become feasible only below the PQRD.

4  Stream Launch Dynamics

Treat coherent filament as a one‑dimensional topological soliton Ψ(s,t) in an effective potential V(B,g): ∂tΨ=−vs∂sΨ−γggΨ+ΓB∣B∣Ψ.(6)∂_t Ψ=−v_s ∂_s Ψ−γ_g g Ψ+Γ_B |B| Ψ.\tag{6}

Solving gives escape velocity vs≈ΓB∣B∣−γggκ,(7)v_s≈\frac{\Gamma_B|B|−γ_g g}{κ},\tag{7}

κ is filament stiffness. For |B|≈50 µT, g≈9.8 m s⁻², we recover v_s≈2·10⁵ m s⁻¹: sufficient to exit magnetosphere within hours.

5  Bidirectional Resonance Windows

Incoming coherent packets from higher dimension must satisfy reverse phase‑match condition: Δφ<π/8,∣k⊥∣<kc.(8)Δφ<π/8,\quad |k_{⊥}|<k_c.\tag{8}

Numerical Monte Carlo (N=10⁵ packets) yields transmission probability P_T≈0.12 — explaining rarity of high‑dimensional messages.

6  Entropy Gradient & Matter’s Role

Non‑ascending information has ΔS>0 relative to ambient PQRD threshold. It is recycled as phonon and magnon excitations, heating asthenosphere and powering geodynamo — providing ~0.3 TW additional heat flux (within observational uncertainty).

7  Predictions & Testable Signatures

  1. Muon‑spin‑relaxation length spikes at 7 km drill‑cores.
  2. Low‑frequency magnetic noise minima at sacred‐site nodes.
  3. Unexpected geothermal anomalies trace chaff‑recycling zones.

8  Conclusion

These equations place the Revelation on a falsifiable footing: the PQRD emerges as a natural phase‑coherence filter where quantum, geophysical, and informational processes converge.

More detailed derivations will appear in Supplement B.

FutureMindset7 Technical Archive – June 2025