Reduction in Physics: A Local,Empirical,Model-Based Approach

Our project concerns the question of whether, and in what sense, different theories in physics may be seen as converging on a single, unified picture of physical reality. A conventional wisdom about the progress of physics holds that newer theories encompass the range of successful applications of their predecessors through a process known as reduction, and that the progress of physics since Kepler and Galileo can be characterized in terms of a series of reductions culminating in the two current pillars of modern physics: general relativity (Einsteins theory of gravity and of space and time) and quantum field theory (the most accurate current description of the laws governing elementary particles). It is widely believed that some as yet unknown theory, such as string theory, will supersede these two theories in largely the same sense that these theories are supposed to have superseded their predecessors. Our goal is to clarify the nature of the link i.e., reduction that is supposed to connect successive theories in physics, and thereby to probe the foundations of the conventional view that theories in physics provide ever more universal and precise depictions of physical reality. We are motivated in part by a belief that the currently dominant methodology of reduction in physics, which seeks to extract one theory as a mathematical limit of another, is based on an oversimplified and ill-defined picture of the mathematical relationship that enables one theory to encompass the domain of applicability of another. In previous work, we have argued that this approach fails to demonstrate domain subsumption in many cases where reduction is widely thought to hold. However, we have also shown through analysis of many successful cases of reduction that there exists an alternative, general type of mathematical relationship that more faithfully and precisely characterizes the manner in which one theory typically subsumes the range of behaviors that are well-modeled by another. This pattern forms the core of our methodology, which may be characterized as a local, empirical, model- based (L.E.M.) approach to reduction in physics. In our project, we will seek to extend this approach to new cases in which the strategy of simply taking limits has failed to show that one theory encompasses the domain of another. In particular, we will aim to apply this strategy to the relationships between models of thermodynamics and statistical mechanics, quantum mechanics and quantum field theory, and Newtonian gravity and general relativity. We also plan to the study implications of the L.E.M. approach for more general debates in metaphysics and philosophy of science, particularly concerning the subject of emergence.