What is the physical meaning of mass in view of wave-particle duality? A   proposed model
  Mass is an important concept in classical mechanics, which regards a particle as a corpuscular object. But according to wave-particle duality, we know a free particle can behave like a wave. Is there a wave property that corresponds to the mass of a particle? This is an interesting question that has not been extensively explored before. We suggest that this problem can be approached by treating the mass on the same footing as energy and momentum. Here we propose that, all particles are excitation waves of the vacuum and different particles are represented by different excitation modes. Based on such a model, we found that mass is not an intrinsic property of the particle. Instead, mass is basically a measure of the particle energy. The relations between energy and mass can be directly derived based on the wave properties of the particle. This work explains why some particles are "wave-like" while others are "particle-like". Furthermore, this work has several interesting implications. It directly explains why photons can interact with a gravitational field. It also suggests a possible origin of dark matter; they are thought to be composed of excitation waves that fail to interact with each other. From this model, one can easily see why our universe has more dark matters than visible matters. 
Donald C. Chang