  This fact calls into question certain received views about the nature of intertheoretic relations. The wave theory, for example, is surely the fundamental theory. Nevertheless, these considerations seem to show that that theory is itself explanatorily deficient. There are phenomena within its scope whose explanations require examining the asymptotics of the appropriate equation. This involves paying attention to mathematical structures called characteristics and wavefronts. See Bóna and Slawinski 2011. These mathematical investigations of the deep asymptotic structure of hyperbolic equations are not at all like the straightforward derivations from initial data that are typical of in principle derivations often referred to in carrying out the dictates of Nagel style explanatory reductions. A similar situation arises in the asymptotic domain between quantum mechanics and classical mechanics where Planck’s constant can be considered asymptotically small. (See Belot 2005 for an alternative point of view.)