Study on the Wave Nature of Mass

In the wave-particle duality, a free particle can be considered as a wave packet. Is there a wave property that corresponds to the rest mass of the particle? We suggest that this problem can be approached by treating the rest mass on the same footing as energy and momentum. Here we demonstrate that, by assuming that the matter wave of a particle is an excitation of a real physical field in the vacuum, one could derive the mass-energy relation from the solution of a simplified wave equation describing a free particle. This solution suggests that the rest mass of a particle is associated with a "transverse wave number", which characterizes the radial variation of the wave function in the transverse plane. This model has several appealing features. For example, it predicts that a massless particle must travel at the constant speed of light.