Reactive Substrate Theory (RST): A Unified Quantum–Cosmic Framework
Abstract: S(x,t) — The scalar substrate field; in RST, spacetime itself is this substrate, not a separate entity. Matter, energy, and time emerge from its dynamics.
Reactive Substrate Theory (RST) presents a unified physical framework in which a single non‑linear scalar substrate field S(x,t) constitutes the fundamental reality. In this view, spacetime is not a separate geometric arena but the substrate itself — the void, the aether, the medium whose configuration defines all physical structure. Matter, energy, and time emerge from the dynamics, excitations, and gradients of this substrate. We show that RST reproduces weak‑field predictions of General Relativity while naturally explaining early cosmic structure formation without invoking exotic dark matter or dark energy. Key mathematical formalism, cosmological implications, and a roadmap for numerical and observational tests are outlined.
1. Introduction
Modern physics remains divided between quantum mechanics, which governs microscopic behavior, and general relativity, which governs gravitation and cosmology. Despite their successes, unresolved anomalies persist — including the unexpectedly early formation of massive galaxies and the reliance on unobserved dark components. Reactive Substrate Theory (RST) addresses these issues by positing a single scalar substrate field S(x,t) as the fundamental physical entity. Spacetime is this substrate; its state and evolution define the geometry we observe. Matter, energy, inertia, and time arise as emergent properties of substrate dynamics.
2. The Scalar Substrate Field
RST assumes a continuous scalar field S(x,t) obeying a nonlinear dynamical equation:
∂²S/∂t² − c² ∇²S + β S³ = σ(x,t)
Here β controls nonlinear self‑interaction, while σ(x,t) represents localized sources associated with matter‑energy excitations. The substrate potential is:
V(S) = (β / 4) · S⁴
2.1 Emergent Proper Time
Local proper time τ is not fundamental but emerges from the substrate state:
dτ = dt · [ 1 + α · δS(x,t) ]
where δS = S − ⟨S⟩ and α is a coupling constant. Regions with higher substrate values accumulate more proper time, accelerating local physical evolution relative to the cosmic average.
3. Matter as Solitons
Particles arise as stable, localized soliton excitations of the substrate field. These solutions follow from the static, spherically symmetric form of the substrate equation, with regularity at r = 0 and vacuum asymptotics as r → ∞. Mass, charge, and internal structure emerge from the soliton’s configuration, not from independent fields. Quantum‑like behavior — including discrete energy levels, interference, and entanglement — arises from resonant and collective substrate dynamics.
4. Cosmological Implications
4.1 Background Evolution
For a homogeneous background S̄(t), the evolution equation becomes:
S̄¨ + 3H S̄˙ + β S̄³ = σ̄(t)
where H is the Hubble parameter. This governs cosmic expansion analogously to the Friedmann equations, but without requiring dark energy as a separate component.
4.2 Structure Formation
Perturbations δS(x,t) satisfy:
δS¨ + 3H δS˙ − c² ∇²δS + meff²(t) · δS = δσ(x,t)
with effective mass meff² = 3β S̄²(t). Regions with higher substrate values accumulate more proper time, causing density perturbations to grow faster than in standard ΛCDM. This naturally explains the early appearance of massive, evolved galaxies at high redshift.
A linearized growth equation for density contrast δ is:
d²δ/dτ² + 2H · dδ/dτ · (1 − α δS) ≈ 4πG ρm δ · (1 − 2α δS)
4.3 CMB Interpretation
RST predicts that CMB anisotropies encode both standard density perturbations and spatial variations in accumulated proper time. Observed uniformity constrains:
δSrec ≲ 10⁻⁵
5. RST versus General Relativity
RST reproduces weak‑field GR predictions through an effective potential:
Φ(x) = (κ² μ / 2) · (S − S̄)
ds² = (1 + 2Φ) c² dt² − (1 − 2Φ) d⃗x²
In strong‑field regimes, RST diverges from GR: no true event horizons, potential dispersive gravitational waves, and substrate‑dependent deviations at high energy.
6. Black Hole Rotation
In contrast to Kerr frame‑dragging, RST describes black holes as static substrate wells. Angular momentum resides entirely in matter, not in spacetime itself. This eliminates singularities and provides alternative rotational dynamics.
7. Unified Quantum–Cosmic Framework
Soliton excitations explain quantum phenomena, while large‑scale substrate evolution governs cosmology. Substrate gradients generate gravity and inertia; emergent time mediates dynamics across scales. Spacetime, matter, energy, and time all arise from the substrate, which is the underlying physical reality.
8. Roadmap for Numerical and Observational Tests
- Compute static soliton profiles for particle modeling.
- Simulate substrate perturbation growth to compare with observed galaxy distributions.
- Identify correlations between CMB anisotropies and mature high‑redshift structures.
- Analyze gravitational wave propagation for frequency‑dependent dispersion.
- Validate weak‑field correspondence with solar system tests.
9. Discussion and Conclusion
RST offers a self‑consistent framework linking quantum, relativistic, and cosmological phenomena. Proper‑time modulation explains early galaxy formation naturally. The theory predicts specific deviations from GR in strong fields and high‑energy regimes, offering clear observational tests.
