The Ja Model: A Motion Centered Language for Irreversible Processes

This work presents the Ja Model, a descriptive framework that uses motion cycles (counts of a reference periodic process) as the primary evolution parameter instead of conventional time. The model introduces a dimensionless comparative index, MUja, constructed from force, displacement, mass, energy, and a dimensionless entropy factor Φ = ΔS / k_B. The framework is dimensionally consistent and explicitly acknowledges that it is a reparametrisation of non‑relativistic, time‑based physics: the reference cycle period τ₀ (e.g., 1/9,192,631,770 s for cesium) is a constant that carries the dimensions of time. The model does not eliminate time but offers an alternative descriptive language for certain dissipative (irreversible) processes within the non‑relativistic domain. A separate methodological companion (Khawaldeh, Jalal Y. A. 2026f) provides numerical reconstruction and empirical illustration using a reconstructed damped oscillator and real orbital decay data from the GRACE‑FO 1 satellite, demonstrating that MUja remains finite, decreases with dissipation, and exhibits stable statistical distributions across thousands of cycles. Unresolved issues include the treatment of inertial motion (force‑free cases), massless particles, reversible (conservative) systems, relativistic frames, and a motion‑based probability calculus. The Ja Model is presented as a research program and a pedagogical reinterpretation, not as a predictive physical theory.