How Does Spacetime “Tell an Electron How to Move”?

Abstract

Minkowski spacetime provides a background framework for the kinematics and dynamics of classical particles. How the framework implements the motion of matter is not specified within special relativity. In this paper we specify how Minkowski space can implement motion in such a way that ’quantum’ propagation occurs on appropriate scales. This is done by starting in a discrete space and explicitly taking a continuum limit. The argument is direct and illuminates the special tension between ’rest’ and ’uniform motion’ found in Minkowski space, showing how the formal analytic continuations involved in Minkowski space and quantum propagation arise from the same source.