Finite-Response Coupled Field Dynamics (FRCFD): From Strong-Field Astrophysics to Cosmological Redshift

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

Finite-Response Coupled Field Dynamics (FRCFD): From Strong-Field Astrophysics to Cosmological Redshift

Derek Flegg
Southern Ontario, March 2026

Table of Contents

Abstract

Finite-Response Coupled Field Dynamics (FRCFD) is a non-geometric framework in which gravitational, inertial, and cosmological phenomena emerge from a finite-capacity substrate field S(x,t) coupled to a matter field Ψ.

2. Core Framework

2.1 Lagrangian

L = 1/2 (∂S)^2 − (β/4) S^4
  + (∂Ψ)^2 − m^2 |Ψ|^2 − g S |Ψ|^2

2.2 Coupled Field Equations

∂²S/∂t² − c²∇²S + βS³ = g|Ψ|²
∂²Ψ/∂t² − v²∇²Ψ + (m² + gS)Ψ = 0

2.3 Response Function

f(S) = exp(−S / Smax)

2.4 Foundational Assumptions

The FRCFD framework is defined by the following minimal postulates:

  • The vacuum is a finite-response substrate characterized by a scalar field S(x,t)
  • The substrate has a maximum capacity Smax
  • Matter fields Ψ couple to S through a local interaction term gS|Ψ|²
  • Signal propagation depends on a response function f(S)
  • The response function is monotonic and bounded: 0 < f(S) ≤ 1
f(S) = exp(−S / Smax)

This form ensures:

  • Linear recovery for weak fields
  • Finite suppression at saturation
  • Path-integrable behavior

3. Emergent Metric

ds² = f(S)² dt² − f(S)⁻² dr² − r² dΩ²

4. Weak-Field Limit

f(S) ≈ 1 − S/Smax
S(r) ≈ GM / r

f(S)^2 ≈ 1 − 2GM / (r Smax)

Matching GR requires:

Smax ≈ 1

6. Photon Sphere & Shadow

Derivation Condition

b^2 = r^2 / f(r)^2

d/dr [r^2 / f(r)^2] = 0

7. ISCO Constraint

The ISCO is determined by stability conditions:

  • dV_eff/dr = 0
  • d²V_eff/dr² = 0

Equivalent condition:

  • dL²/dr = 0

11. Cosmological Redshift

dν / ν = − dS / Smax

ln(1 + z) = ∫ (S(x) / Smax) dx

This preserves phase coherence and avoids scattering-based energy loss.

16. Consistency Check

  • Weak-field gravity recovered
  • Light deflection matches GR limit
  • Time dilation unified
  • Predicts strong-field deviations

17. Limitations

  • No full cosmological solution yet
  • No perturbation theory
  • Rotation partially modeled
  • Quantum consistency unresolved

18. Core Insight

FRCFD replaces geometric ontology with:

  • Geometry → Response dynamics
  • Curvature → Impedance gradients
  • Singularity → Saturation limits

19. Conclusion

The theory stands or falls on observation.

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