Discrete Motion at Quantized Velocities

Prodigious effort has been expended to unveil the fundamental natures of space and matter but relatively little effort to unveil the fundamental nature of motion – by which I mean settling the question as to whether motion is discrete or continuous. Yet since motion is evidently a property of matter and presumably a property of space, the fundamental nature of motion should be a pointer to the fundamental natures of space and matter. This relative neglect of the fundamental nature of motion is also apparent in the construction of gravitational theories. Gravitation being a special form of accelerated motion implies that the fundamental nature of motion is necessarily part of a complete theory of gravity since any gravitational theory must fit within the framework of the model of motion. This paper proposes an integrated quantum theory of motion that would be an integral part of a well-conceived theory of quantum gravity. The model proposes that all subluminal velocities are derivatives of two fundamental velocities – specifically, elements of the set S = {c, 0}, where c is the velocity of light. We show that when applied to gravitation this model implies the existence of a quantum of mass, and when applied to general motion it implies the existence of a periodic mechanism by which a particle in motion sheds and reclaims its mass. In the conclusion, we predict the main features of a well-conceived theory of quantum gravity based on the implications of this model of motion.