RST in a Single Equation (Pedagogical Form)

RST in a Single Equation (Pedagogical Form)

For teaching and intuitive understanding, Reactive Substrate Theory can be reduced to its minimal dynamical core: 

∂t2 S − c2 ∇2 S + β S3 = ρ

Interpretation

  • S(x,t): physical substrate field
  • Wave term: propagation of disturbances
  • Cubic term: nonlinear stiffening and stability
  • ρ: coherent excitation density

All higher-level phenomena are derived:

  • Gravity → gradients of S
  • Time → local oscillation rates
  • Particles → stable localized solutions
  • Black holes → deep but finite substrate wells

This formulation fits on a single slide, is numerically tractable, and makes no metaphysical commitments.

RST v1.1: Justified Extensions Only

Design principle: RST v1.1 may introduce only structures that are logically forced by correspondence with General Relativity and Quantum Mechanics, or that are required for numerical stability and observational testing. No speculative additions are permitted.

Allowed Extensions (v1.1)

  • Time-averaged resonance functional
    Replace explicit phase dependence with a coarse-grained measure: 
    FR[C[Ψ]] = <ρ>T
    Justification: aligns cosmological behavior with effective field theory practice and avoids unobservable phase sensitivity.
  • Explicit weak-field metric map
    Φ = A ( S − S̄ )
    Justification: makes recovery of GR’s weak-field limit explicit and testable.
  • Optional numerical damping (non-physical)
    + γ ∂t S
    Justification: stabilizes simulations only; removable regulator with no physical interpretation.

Explicitly Forbidden in v1.1

  • Additional fundamental fields
  • Extra dimensions
  • Nonlocal operators
  • Ad hoc potentials or tuned functions
  • Higher-order polynomial terms without observational motivation
  • Claims of propulsion or engineered spacetime manipulation

RST v1.1 is about closing the system, not expanding the ontology.

Reactive Substrate Theory as a Grant-Ready Proposal

Central hypothesis: A single nonlinear scalar field can reproduce weak-field gravity, quantum coherence, and large-scale structure without quantizing spacetime itself.

Why This Merits Funding

  • Uses existing mathematical methods
  • Leverages existing astronomical and laboratory datasets
  • Emphasizes low-cost data re-analysis rather than new instrumentation
  • Targets known tensions in modern theory (early structure, horizons, time)

What Is New

  • Time treated as an emergent rate, not a fundamental coordinate
  • Gravity arising from substrate gradients, not geometric postulates
  • Black holes modeled as finite, dynamical configurations

What Will Be Tested

  • CMB phase and timing residuals
  • JWST early-structure anomalies
  • Clock-rate interferometry constraints
  • Strong-field relaxation behavior

What Failure Looks Like

  • No stable numerical solutions
  • No deviations from ΛCDM beyond experimental noise
  • Inability to reproduce post-Newtonian limits

Either outcome is scientifically useful.

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