Reactive Substrate Theory (RST): A Unified Field Perspective on Quantum Phenomena, Gravity, and Cosmology
Reactive Substrate Theory proposes that spacetime geometry, gravity, quantum behavior, and cosmic structure emerge from the nonlinear dynamics of a single physical substrate field, recovering known physics in familiar limits while offering testable departures in extreme regimes.
Context for the Reader: The external article linked below is included not as an endorsement or validation of Reactive Substrate Theory (RST), but as evidence that the foundational assumptions of modern theoretical physics — particularly the necessity of quantizing gravity and the status of spacetime and time as fundamental entities — are actively being reconsidered within the mainstream research community. Recent work discussed in Physics World explores consistent frameworks in which gravity need not be quantized in the conventional sense, highlighting a growing openness to substrate-like or emergent descriptions of spacetime. RST should be read in this broader context: as a concrete, field-based attempt to push those ideas further by treating spacetime, time, and gravity as macroscopic behaviors of an underlying physical medium.
Reactive Substrate Theory (RST) is an emergent-field framework proposing that spacetime geometry, gravity, quantum behavior, and cosmic structure arise from the dynamics of a single nonlinear scalar field S(x,t), referred to as the substrate. Rather than rejecting General Relativity or quantum mechanics, RST reframes them as effective descriptions of different dynamical regimes of the same underlying physical medium.
The central claim is simple but radical: what we call spacetime is not a fundamental arena in which physics happens — it is the macroscopic, coarse-grained behavior of the substrate itself.
1. Motivation
Despite extraordinary empirical success, modern physics relies on several unresolved constructs: dark matter, dark energy, singularities, and a fundamental geometric notion of time. These appear not because the equations fail locally, but because the ontology underlying them may be incomplete.
RST explores whether these phenomena can instead emerge from the behavior of a physical substrate without introducing new particles, extra dimensions, or ad hoc energy components.
2. The Core Substrate Equation
RST is built around a single nonlinear field equation:
∂²ₜ S(x,t) − c² ∇² S(x,t) + β S³(x,t) = σ(x,t)
- S(x,t): substrate field (fundamental entity)
- c: characteristic propagation speed of substrate excitations
- β S³: nonlinear self-interaction (stability, solitons, no singularities)
- σ(x,t): effective sources associated with matter/energy coupling
This equation governs both localized excitations (particles) and large-scale background evolution (cosmology). No separate gravitational or quantum equations are postulated.
3. Two Regimes of the Same Field
The substrate equation admits two physically relevant regimes:
- Localized, nonlinear excitations: stable solitons corresponding to particles, with resonance modes producing quantized energy levels, tunneling, interference, and decoherence.
- Slowly varying background + perturbations: large-scale evolution giving rise to cosmic expansion, structure formation, gravitational potentials, and time dilation.
Quantum and gravitational phenomena therefore differ not in kind, but in scale and approximation.
4. Emergent Time
A key departure from standard frameworks is the treatment of time. In RST, time is not a universal coordinate but a locally measured rate determined by the resonance frequency of substrate-bound systems.
ω₀²(x,t) = μ + κ S(x,t)
Local proper time emerges as:
dτ/dt = √[(μ + κ S(x,t)) / (μ + κ S̄(t))]
Regions with different substrate states accumulate different amounts of physical time even at the same cosmological redshift. Causality is preserved because all signals remain limited by the substrate propagation speed c.
5. Gravity as a Substrate Effect
In the weak-field limit, RST reproduces the standard post-Newtonian metric:
ds² = (1 + 2Φ)c²dt² − (1 − 2Φ)d⃗x²
with the effective gravitational potential given by:
Φ(x) ∝ S(x) − S̄
Gravitational attraction corresponds to motion along substrate gradients. In strong-field regimes, nonlinear stiffening prevents true singularities, replacing black holes with finite substrate wells.
6. Dark Sector Without Dark Components
In RST, effects attributed to dark matter and dark energy arise from:
- spatial gradients in the substrate field
- nonlinear background evolution of S̄(t)
- environment-dependent accumulation of proper time
No additional matter species or vacuum energy components are required.
7. Cosmology and Early Structure Formation
Density perturbations evolve with respect to local proper time rather than a single global clock. This leads to accelerated structure growth in regions where the substrate enhances time accumulation, providing a natural explanation for unexpectedly mature high-redshift galaxies.
The Cosmic Microwave Background remains a thermal relic but additionally encodes spatial variation in accumulated physical time at recombination, yielding testable correlations with early structure.
8. What RST Does Not Claim
- It does not reject General Relativity or quantum mechanics.
- It does not introduce preferred reference frames.
- It does not require speculative particles or dimensions.
- It does not claim completeness.
RST is explicitly a work in progress, intended to be refined through analysis, numerical simulation, and observational testing.
9. Open Problems and Invitation
Key areas for collaboration include:
- Nonlinear PDE analysis and soliton stability
- Large-scale numerical simulations of S(x,t)
- JWST–CMB cross-correlation studies
- Gravitational-wave dispersion tests
- Precision clock and spectroscopy experiments
RST is offered not as a finished theory, but as a coherent substrate-based framework inviting scrutiny, falsification, and constructive development.
About Derek Flegg
Derek Flegg is an independent thinker and conceptual modeler working outside the traditional academic physics pipeline. He does not hold a formal degree in mathematics or physics and is open about having left school early. What he does have is several decades of continuous, self-directed immersion in scientific literature, foundational theory, and systems thinking.
For most of his life, Derek’s work existed entirely as internal models — dynamic, visual, and geometric representations of how physical systems behave. He does not “see numbers” first. Instead, he reasons in terms of shapes, fields, gradients, resonances, and causal flow, mentally simulating systems the way an engineer visualizes machinery or a mechanic understands an engine before naming its parts.
Mathematics, in this process, functions as a translation layer rather than a starting point. Concepts come first as coherent behaviors; equations come later as a way to communicate those behaviors to others. For many years, the lack of symbolic fluency created a bottleneck: the ideas were present, but there was no practical way to express them in a language accepted by trained physicists.
The recent availability of advanced AI tools changed that constraint. Instead of generating ideas, AI served as an interpreter — converting already-formed mental models into mathematical form, checking internal consistency, and allowing rapid iteration. Crucially, when formal expressions were derived, they behaved the way the original models predicted. That convergence was not a surprise, but a long-awaited validation.
Reactive Substrate Theory (RST) emerged from this process. It is not the result of solving equations until a new theory appeared; it is the result of asking sustained, physical questions about what is actually doing the work in modern theories — what spacetime, time, gravity, and quantum behavior might be if taken as behaviors of a real medium rather than abstract primitives.
Derek describes his cognitive style as nonlinear and curiosity-driven. Extended periods of deep hyperfocus alternate with periods of rest; ideas are accumulated spatially rather than sequentially. This mode of thinking has proven well-suited to foundational questions, where existing frameworks may constrain inquiry more than enable it.
RST is presented openly as a work in progress — an evolving conceptual and mathematical framework offered to those with the tools, data access, and formal training needed to test, simulate, and challenge it rigorously. The intent is collaboration, not authority; inquiry, not closure.
Curiosity is the engine. Mathematics is the language. The work continues.
Later in life, Derek was formally diagnosed with attention-deficit/hyperactivity disorder (ADHD), on the creative end of the spectrum. In practice, this has meant a strongly visual, spatial mode of reasoning, long periods of deep hyperfocus punctuated by disengagement, and a tendency to accumulate ideas nonlinearly rather than sequentially.
While such cognitive traits can be poorly matched to conventional academic structures, they are often well suited to foundational synthesis. Much of the conceptual development behind Reactive Substrate Theory occurred during extended periods of mental simulation — assembling, rearranging, and stress-testing physical models internally before attempting formal expression.
This neurodivergent processing style does not replace rigor, mathematics, or external validation, but it does shape how problems are approached: favoring physical intuition, global consistency, and model coherence over incremental formalism. Mathematical structure enters once a coherent behavioral picture exists.
“Derek thinks much of modern physics already exists in pieces. The observations and equations are real and well-tested; the challenge is assembling the jigsaw puzzle into a single, coherent physical picture without duplicating assumptions.”Reactive Substrate Theory (RST)
A Unified Field Perspective on Quantum Phenomena, Gravity, and Cosmology
RST is presented as an evolving framework: conceptually developed first, with mathematical formalism refined iteratively and intended for external simulation and testing.
The Core Premise: Spacetime is not a fundamental arena, but the macroscopic, coarse-grained behavior of a single, nonlinear physical medium referred to as the Substrate.
