One-dimensional relativistic dynamics with scaling formalism

In one dimension, we investigate dynamics using special relativity only, but make no statement regarding any particular insight into the nature of the spacetime continuum. Indeed, we do away completely with any kind of formal tensor algebra or differential topology, but do incorporate scaling into our calculations. The purpose here is primarily pedagogical, as an extension to the standard undergraduate treatment of special relativity, but it is also a calculational tool, to be able to determine the motion of objects in a one-dimensional case even with accelerations and forces, without having to use the full general relativistic treatment. To illustrate this, we directly compare relativistic to Newtonian or non-relativistic motions for particularly instructive selected systems.