RST vs ΛCDM Expectations
RST v1.0 — One-Page arXiv-Style Preprint
Title: Reactive Substrate Theory v1.0: A Minimal Classical Substrate Framework Recovering GR and QM Limits
Author: Derek Flegg
Abstract:
Reactive Substrate Theory (RST) proposes that spacetime geometry, gravitational effects, and quantum observables arise as effective behaviors of a continuous scalar substrate field S(x,t), coupled to a coherence field Ψ(x,t). RST does not replace General Relativity (GR) or Quantum Mechanics (QM), but reinterprets them as emergent descriptions valid in distinct dynamical limits. We present a minimal, closed formulation (v1.0) consisting of two coupled nonlinear wave equations, demonstrate consistency with weak-field GR and standard QM probability interpretation, and outline clear paths to numerical and observational falsification.
1. Field Equations (Minimal Closure)
∂²ₜ S − c²∇²S + βS³ = σ(x,t)|Ψ|²
∂²ₜ Ψ − v²∇²Ψ + μΨ + λ|Ψ|²Ψ = κSΨ
2. Correspondence Limits
- GR: Weak-field limit recovered via Φ = A(S − S̄)
- QM: |Ψ|² interpreted as conserved probability density
3. Claims and Scope
- RST is classical at the substrate level
- No quantization of spacetime required
- No dark sector assumed
4. Falsifiability
Failure to reproduce known GR/QM results, numerical instability, or lack of predicted residuals at higher precision would falsify RST v1.0.
RST v1.0 — Minimal GitHub README (for Simulators)
This repository implements the minimal Reactive Substrate Theory (RST v1.0) system for numerical exploration. The goal is to test stability, soliton formation, and correspondence limits — not to optimize parameters.
Core System
∂²ₜ S − c²∇²S + βS³ = σ(x,t)|Ψ|² ∂²ₜ Ψ − v²∇²Ψ + μΨ + λ|Ψ|²Ψ = κSΨ
Requirements
- Python / Julia / C++ numerical environment
- Finite difference or spectral PDE solver
- Second-order time stepping (leapfrog / Verlet)
Suggested Parameters (Dimensionless Units)
- c = 1, v = 1
- β ≈ 1
- λ ≈ 1
- κ ≈ 1
Initial Conditions
- Ψ(x,0): Gaussian or localized packet
- S(x,0): uniform background
- All time derivatives initially zero
Success Metrics
- Stable localized Ψ structures
- Bounded S response
- Energy conservation
Non-Goals
- No cosmological tuning
- No quantum gravity claims
- No experimental predictions beyond v1.0 scope
RST v1.0 — Observational Signature Checklist
RST v1.0 predicts subtle, testable deviations from ΛCDM and standard GR/QM interpretations, while preserving all confirmed first-order results.
RST vs ΛCDM Expectations
| Observable | ΛCDM / GR Expectation | RST v1.0 Expectation |
|---|---|---|
| Weak-Field Gravity | Metric curvature | Substrate gradient (equivalent) |
| Galaxy Rotation Curves | Dark matter halos | Persistent substrate deformation |
| Clock Rates | Pure metric dilation | Local resonance-dependent variation |
| CMB Residuals | Uniform phase evolution | Slight time-rate modulation |
| Quantum Probability | |Ψ|² postulate | |Ψ|² as conserved substrate coherence |
Low-Risk Tests
- VLBI timing residual re-analysis
- Clock-comparison experiments
- Numerical soliton stability studies
Immediate Falsifiers
- Observed violations of GR/QM correspondence limits
- Absence of predicted residual structure at higher precision
- Numerical instability across reasonable parameter space
