Photon and Motion of a Material Body as Wave Processes: A Relativistic Phase Interpretation

A unified wave-phase description of the photon and of the motion of a material body is proposed. The construction is based on the description of wave processes and on the preservation of their phase state as a fundamental principle. It is shown that from phase invariance, linearity of transitions between descriptions, and the structural linkage between parameters of the wave process, Lorentz-like transformations and an invariant quadratic form naturally arise, which after coordinate interpretation takes the form of Minkowski spacetime structure. In this approach the physically significant characteristic of a wave process is not the absolute phase but the phase state preserved during evolution of the process and manifest only through relations to other processes. The Doppler shift is interpreted as a manifestation of phase relation between wave processes, while the relative velocity of a material body corresponds to phase asymmetry between two oppositely directed light-like components of its wave description. The wave invariant associated with the motion of a material body is factorized through two light-like components Q+ and Q−, whose product after normalization takes the form Q+Q− = 1. In this representation the parameters of the wave process of motion are not independent quantities: the combined characteristic of the components defines the temporal part of the phase description, while their asymmetry defines the spatial part and the associated parameter of relative motion. On the basis of this kinematic structure, phase action is introduced as an integral measure of the evolution of the invariant phase. For a normalized process of motion it is shown that such action leads to a phase-theoretic analogue of the relativistic Hamilton–Jacobi equation. After spacetime and dynamic calibration this description acquires correspondence with the standard relativistic quantities of energy, momentum, and mass. In this sense mass is regarded not as an initial characteristic of the phase formalism but as a derived quantity arising in the physical interpretation of the internal phase structure of the process.