Lorentz Structure from Coherent Translating Standing-Waves

This paper presents a constructive and physically transparent derivation of Lorentz time dilation and length contraction for an extended standing-wave eigenform undergoing uniform translation. Using only phase coherence and wave-closure arguments, the analysis shows that the intrinsic spatial and temporal scales of the eigenform rescale by the Lorentz factor, without invoking synchronization conventions, preferred frames, or axiomatic postulates. The resulting structure naturally motivates the standard covariant formulation of relativistic wave equations and provides an intuitive bridge to spinorial descriptions of fermionic states. An explicit appendix derives the Lorentz scaling relations step by step using elementary geometry and trigonometry, emphasizing physical closure rather than coordinate abstraction. The work is intended as a companion to foundational discussions of wave-based particle models and offers an accessible physical interpretation of Lorentz invariance grounded in coherent standing-wave dynamics.