Special Relativistic Kinematics from Wave Phase Coherence

Abstract

We present a phase-based formulation of special relativity in which the kinematical structure of the theory is reconstructed from the requirement of phase coherence of localized wave states. Starting from the assumption that physical propagation is associated with surfaces of constant phase and that matter admits an intrinsic rest-frame oscillation, we show that the relativistic relations for time dilation, energy, and momentum follow from the invariant accumulation of phase along particle trajectories. In this framework, proper time is identified operationally as the phase count of an internal clock, and the Minkowski interval arises as the quadratic form consistent with phase invariance across inertial observers. The relation between mass and rest-frame frequency emerges naturally, providing a unified interpretation of relativistic kinematics in wave-mechanical terms. This formulation does not introduce new dynamics but offers a coherent structural perspective that bridges relativistic kinematics and wave propagation.