Relativistic Doppler Shift Reinterpreted Through Propagation-State Deviation in Extended Classical Mechanics

The relativistic Doppler effect provides a well-established mathematical description of the wavelength shift observed when a source and an observer are in relative motion. Within the standard formulation, the observed wavelength is determined by the relative recession velocity between the source and the observer, while the underlying mathematical relation remains independent of the physical origin of that relative motion. This article presents an alternative physical interpretation of the relativistic Doppler relation within the framework of Extended Classical Mechanics (ECM) without modifying its mathematical structure.

ECM distinguishes between a normalized propagation state, represented by u = fꜱ λꜱ, and an observed propagation state, represented by v = fᴏʙꜱ λᴏʙꜱ. The observed wavelength is interpreted as a measurable displacement from the normalized source wavelength,

where the wavelength shift Δλ is regarded as the manifestation of a propagation-state deviation rather than merely the kinematic consequence of relative recession. Within this interpretation, the normalized and observed propagation states are related by

where Δu denotes the propagation-state deviation between the normalized and observed conditions. Consequently, ECM supplements the standard relativistic Doppler formalism by attributing the measurable wavelength displacement to an underlying propagation-state transition while preserving the established Doppler equation. The proposed interpretation provides an alternative conceptual framework for understanding wavelength displacement through propagation-state dynamics and offers a foundation for extending the analysis of phase-, frequency-, and manifestation-dependent physical processes within ECM.