The flow of time in the theory of relativity

Abstract: Dennis Dieks advanced the view that the idea of flow of time is implemented in the theory of relativity. The 'flow' results from the successive happening/becoming of events along the time-like worldline of a material system. This leads to a view of now as local to each worldline. Each past event of the worldline has occurred once as a nowpoint, and we take there to be an ever-changing present now-point 'marking' the unfolding of a physical system. In Dieks' approach there is no preferred worldline and only along each worldline is there a Newtonian-like linear order between successive now-points. We have a flow of time per worldline. Also there is no global temporal order of the now-points of different worldlines. There is, as much, what Dieks calls a partial order. However Dieks needs for a consistency reason to impose a limitation on the assignment of the now-points along different worldlines. In this work it is made the claim that Dieks' consistency requirement is, in fact, inbuilt in the theory as a spatial relation between physical systems and processes. Furthermore, in this work we will consider (very) particular cases of assignments of now-points restricted by this spatial relation, in which the now-points taken to be simultaneous are not relative to the adopted inertial reference frame.