Productive Laws in Relativistic Spacetimes

One of the most intuitive views about the metaphysics of laws of nature is Tim Maudlin's idea of a Fundamental Law of Temporal Evolution. So-called FLOTEs are primitive elements of the universe that produce later states from earlier states. While FLOTEs are at home in traditional Newtonian and non-relativistic quantum mechanical theories (not to mention our pre-theoretic conception of the world), I consider here whether they can be made to work with relativity. In particular, shifting to relativistic spacetimes poses two threats to FLOTEs. First, the lack of a privileged spacelike hypersurface in relativistic spacetime makes it unclear how to understand what produces what. A survey of several conceptions of the nomic production relation compatible with relativity reveals all of them to be lacking. Second, relativity motivates a four-dimensional block universe conception of time, according to which all events that will ever occur already exist. On such a view, it's unclear what work there is to be done by FLOTEs. I consider how a proponent of FLOTEs might respond, but conclude that these combined threats seriously undermine the prospects of a productive conception of laws. In short, if spacetime is relativistic, laws are not productive.