Reactive Substrate Theory (RST) — Core Equations

⚛️ Reactive Substrate Theory (RST) — Core Equations (Plain Text)

RST is built on four foundational equations that describe how the Substrate Field (Σ) generates matter, energy, motion, and emergent reality. Written in plain text, they are:

  • Energy–Momentum Relation:
    E² = (p c)² + (mΣ c²)²
    This shows the balance between energy (E), momentum (p), and mass (mΣ) as stored tension in the substrate.
  • Equation A — Baseline Nonlinear Wave Dynamics:
    (1/c²) ∂²Σ/∂t² − ∇²Σ = λ Σ³
    A nonlinear wave equation describing how Σ propagates through spacetime. The cubic self‑interaction term (λ Σ³) allows stable soliton structures to form, identified as matter particles.
  • Equation B — Emergent Reality and Feedback:
    (∂t² S − c² ∇² S + β S³) = σ(x,t) ⋅ FR(C[Ψ])
    This extends Equation A by coupling Σ dynamics to emergent matter distributions (σ) and informational feedback (FR(C[Ψ])), linking physical reality with coherence and consciousness.
  • RST Action and Field Response:
    S_Σ = ∫ from t₁ to t₂ of τ(x, ẋ, t) dt
    d/dt [ ∂τ / ∂ẋ ] − ∂τ / ∂x = 0
    These express the principle of least tension in Σ. The first line defines total integrated substrate tension along a soliton’s trajectory. The second line is the Euler–Lagrange analogue, showing how Σ restores equilibrium when disturbed.

Together, these four equations unify motion, energy, gravity, electromagnetism, quantum behavior, and emergent complexity as different manifestations of Σ dynamics. They demonstrate that the “laws of physics” are not abstract rules but the direct consequences of the substrate’s effort to minimize tension and maintain stability.

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