The Tri-Outcome Redshift Model

A Structural Alternative to Expansion-Based Cosmology

Tri-Outcome Redshift Model Illustration

The Tri-Outcome Redshift Model is a cosmological upgrade proposed by Pattern Field Theory (PFT), replacing velocity-based interpretations of redshift with structurally coherent curvature dynamics of the pattern field.

The Three Redshift Mechanisms

  1. PPC – Pattern Phase Curvature: Redshift from field curvature. 
    z_PPC = Δλ / λ₀ = γκ(r) ≈ κ·r
  2. IPD – Inter-Pattern Drift: Redshift from phase desynchronization. 
    z_IPD = Δφ / φ₀
  3. Combined: 
    z_total = (1 + z_PPC)(1 + z_IPD) - 1

Redshift Comparison Table

Concept Classical Formula PFT Formula
Redshift definitionz = (λ_obs - λ₀)/λ₀Same — curvature-based cause
Velocity redshiftz = v/cNot used
Relativistic redshiftz = √[(1+v/c)/(1−v/c)] − 1Not applicable
PPCN/Az_PPC = κ·r
IPDN/Az_IPD = Δφ/φ₀
CombinedN/Az_total = (1 + z_PPC)(1 + z_IPD) − 1

Historical Attribution

Redshift has been misinterpreted for over a century due to reliance on velocity-based models. While Zwicky proposed an early alternative and Hubble observed the data without understanding the cause, Pattern Field Theory reframes these observations under structural curvature and pattern resonance — resolving redshift without invoking spatial expansion or dark energy.

Redshift Attribution and Formulae:

  • Aristotle (384–322 BCE): Proposed intrinsic purpose (telos) in matter — an early model of goal-directed motion.
  • Christiaan Huygens (1629–1695): Advanced wave theory of light, suggesting propagation through a medium — a precursor to field logic.
  • Isaac Newton (1642–1727): Defined universal gravitation in an absolute space and time framework.
  • James Clerk Maxwell (1831–1879): Unified electricity and magnetism; proved light is an electromagnetic field wave.
  • Albert Einstein (1879–1955): Introduced relativistic spacetime curvature and gravitational redshift.
  • Fritz Zwicky (1898–1974): Proposed “tired light” — redshift without expansion.
  • Edwin Hubble (1889–1953): Observed redshift-distance relationship, but relied on Doppler assumptions.
  • Halton Arp (1927–2013): Documented anomalous redshifts suggesting flaws in standard interpretations.
  • Pattern Field Theory (James Johan Sebastian Allen, b. 1969): Replaces all velocity- and expansion-based interpretations with curvature dynamics and resonance desynchronization in a structured field.

PFT Redshift Equations: zPPC = κ · r
zIPD = Δφ / φ₀
ztotal = (1 + zPPC)(1 + zIPD) − 1 This new model removes the requirement for expansion velocity, reframing redshift as a structural and temporal echo of pattern divergence.

Conclusion

This new model explains redshift without invoking cosmic velocity or dark energy — it is the whisper of structure expanding in recursive curvature.