Finite-Response Coupled Field Dynamics: Substrate-Coupled Field Excitations

“This work establishes internal consistency and testable structure; full cosmological fitting is a subsequent program.”

Abstract

Finite-Response Coupled Field Dynamics (FRCFD) is formulated as a 3+1-dimensional field theory in which the vacuum is modeled as a finite-response substrate with a maximum stress capacity S_max. This replaces the implicit infinite-capacity assumption underlying classical geometric gravity with a saturating response structure.

The theory is defined in terms of a scalar substrate field S, a matter field Ψ, and a response function f(S) = exp(-S / S_eff(σ)), where the effective capacity S_eff depends on a local invariant stress scale σ = |∇S|². The nonlinear substrate dynamics enforce bounded response in high-stress regimes, preventing divergent behavior in the field equations.

In the weak-field limit, the theory recovers the standard post-Newtonian structure of General Relativity through an infrared fixed point S_eff → 1, ensuring consistency with Solar-System constraints. In strong-field regimes, the running capacity induces controlled deviations, providing a potential phenomenological window for testing the framework in compact astrophysical systems.

The formalism admits an operational interpretation in which substrate stress governs effective curvature, and the response function f(S) modulates local temporal and causal structure. This yields a self-regulating feedback mechanism: increasing stress drives a reduction in effective response rate, limiting the growth of field gradients and preventing singular behavior.

FRCFD therefore provides a finite-response alternative to geometric gravity in which divergences are regulated dynamically. The framework is constructed to be empirically testable through post-Newtonian parameters, strong-field observables, and cosmological propagation effects, though several sectors (particularly cosmology and quantum extensions) remain under active development.

Wave–Particle Duality in FRCFD: A Substrate-Dependent Field Description

In standard quantum mechanics, the notion of “wave–particle duality” reflects a mismatch between classical categories and the underlying mathematical structure of the theory. The fundamental object is neither a classical wave nor a classical particle, but a quantum state whose behavior depends on the measurement context.

Finite-Response Coupled Field Dynamics (FRCFD) provides a natural field-based interpretation of this behavior without invoking dual classical descriptions.

1. Ontology: Substrate-Coupled Field Excitations

In FRCFD, matter is described by a field Ψ evolving according to: 

∂²Ψ/∂t² − v²∇²Ψ + μΨ + λ|Ψ|²Ψ = κ S Ψ

The field Ψ represents a physical excitation whose dynamics are coupled to the substrate field S. The propagation and interaction of this excitation are therefore not intrinsic, but depend on the local substrate state.

The fundamental object is thus:

A substrate-coupled field excitation with state-dependent dynamics.

2. Wave-Like Regime (Low Substrate Stress)

In regions where the substrate is near its ground state: 

S ≈ 0

the coupling term becomes negligible, and the equation reduces to: 

∂²Ψ/∂t² − v²∇²Ψ ≈ 0

In this limit, the excitation propagates as a nearly linear field mode, exhibiting interference and dispersion characteristic of wave-like behavior.

This regime corresponds to standard quantum field propagation in weakly perturbed backgrounds.

3. Localization Regime (High Substrate Stress)

In regions of elevated substrate stress: 

S → finite, increasing

the coupling term κ S Ψ modifies the effective dynamics of the field. This introduces:

  • State-dependent effective mass or potential
  • Nonlinear self-interaction effects
  • Reduced propagation efficiency through the substrate

These effects can lead to increased localization of the excitation under appropriate conditions. In this regime, the behavior resembles that of particle-like excitations.

This localization is an emergent property of the coupled field dynamics and is not assumed a priori.

4. Interpretation

Within FRCFD, wave-like and particle-like behaviors arise as limiting cases of a single underlying entity: a substrate-coupled field excitation.

The apparent duality reflects the dependence of observable behavior on the local substrate state, rather than the existence of two distinct ontological descriptions.

FRCFD therefore replaces wave–particle duality with a unified, state-dependent field description.

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