Title:

Intertheory relations in physics : case studies from quantum mechanics and quantum field theory

I defend three general claims concerning intertheoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the lowlevel (purportedly more accurate and encompassing) model to that of the highlevel (purportedly less accurate and encompassing) model that approximately commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account systemspecific details in providing a full derivation of the highlevel theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of systemspecific details. After discussing these points of general methodology, I go on to demonstrate their application to a number of particular intertheory reductions in physics involving quantum theory. I consider three reductions: first, connecting classical mechanics and nonrelativistic quantum mechanics; second,connecting classical electrodynamics and quantum electrodynamics; and third, connecting nonrelativistic quantum mechanics and quantum electrodynamics. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory  the Everett and Bohm theories  as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity.
