Special Relativistic Kinematics from Wave Phase Coherence

TL;DR

This paper develops a wave phase coherence-based formulation of special relativity, deriving relativistic kinematics from phase invariance principles without new dynamics.

Contribution

It introduces a wave-mechanical perspective on special relativity, reconstructing kinematics from phase coherence and invariance, linking proper time and Minkowski interval to wave phase.

Findings

Relativistic relations follow from phase invariance along particle trajectories.

Proper time is operationally identified as phase count of an internal clock.

Minkowski interval arises as a quadratic form consistent with phase invariance.

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.