Abstract

According to existing theory the matter wave emerges from the Fourier addition of component waves. The wave packet propagates at velocity V. The potential and kinetic components of a wave retain their phase during a Fourier localization. The Fourier process cannot change the phase of a wave. The matter wave is commonly described with Euler formula. The Euler formula is given in Equation #1. 1,2 e i t = cost + i sint Equation #1 The Euler formula describes the simple harmonic motion of a standing wave. The cos component represents the potential energy of a standing wave. The sin component represents the kinetic energy of a standing wave. The potential and kinetic components are displaced by 90 degrees. The localization of a traveling wave through the Fourier addition of component waves retains the phase of the component waves. To employ this method of localization and then to describe a wave of any velocity with the Euler formula is inconsistent. According to the Born interpretation the matter wave is not material. The matter wave is not constructed of potential and kinetic components. It is only a function of probability. This author contends that the matter wave is real. Disturbances in the matter wave propagate at luminal velocities. These disturbances are restrained by forces. The angular separation of matter=s potential and kinetic energy is variable. The phase of the angular separation establishes matter's relativistic properties.