Amplitude–Phase Conjugacy from a Primeon Euler–Lagrange Action: A Dynamical Origin of the Relativistic Time–Inertia Lock

In standard presentations of Special Relativity (SR), time dilation and the velocitydependence of inertial response are often treated as conceptually distinct phenomena.In this work we show that they arise from a single dynamical constraint when spacetime motion is described through a primeon wavefunction with coupled amplitude and phase degrees of freedom. Starting from an Euler-product primeon wavefunction, we derive an effective amplitude–phase action. A kinetic cross term appears naturally when the macroscopic phase is constructed as a prime-weighted bundle whose weightsdepend on the amplitude background. The resulting Euler–Lagrange equations mix the canonical momenta, proving that amplitude and phase are conjugate variables. We show that the familiar relativistic time-dilation and inertial enhancement factors are two projections of this single constraint, and that the cross term provides a principled locus for generalized relativistic dynamics.