Abstract Relative motion of particles is examined in the context of relational space-time. It is shown that de Broglie waves may be derived as a representation of the coordinate maps between the rest-frames of these particles. Energy and momentum are not absolute characteristics of these particles, they are understood as parameters of the coordinate maps between their rest-frames. It is also demonstrated the position of a particle is not an absolute, it is contingent on the frame of reference used to observe the particle. Version of Record This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this article is published in Foundations of Physics, and is available online at https://doi.org/10.1007/s10701-023-00715-9