Explaining Laws in Special Relativity :: Science Mathematics Papers

Explaining Laws in Special Relativity Wesley Salmon has suggested that the two leading views of scientific explanation, the â€Å"bottom-up† view and the â€Å"top-down† view, describe distinct types of explanation. In this paper, I focus on theoretical explanations in physics, i.e., explanations of physical laws. Using explanations of E=mc2, I argue that the distinction between bottom-up explanations (BUEs) and top-down explanations (BUEs) is best understood as a manifestation of a deeper distinction, found originally in Newton’s work, between two levels of theory. I use Einstein’s distinction between ‘principle’ and ‘constructive’ theories to argue that only lower level theories, i.e., ‘constructive’ theories, can yield BUEs. These explanations, furthermore, depend on higher level laws that receive only TDEs from a ‘principle’ theory. Thus, I conclude that Salmon’s challenge to characterize the relationship between the two types of explanation can be met only by recognizing the close relationship between types of theoretical explanation and the structure of physical theory. The two leading views of scientific explanation, Salmon’s â€Å"bottom-up† view and the Friedman-Kitcher â€Å"top-down† view, give what appear to be prima facie incompatible characterizations of scientific explanation. According to the bottom-up view, we explain a given phenomenon when we uncover the underlying causal mechanisms that are responsible for its occurrence. The top-down view, on the other hand, maintains that we explain a phenomenon by deriving it from the general principles or laws that best unify our knowledge. In this paper, I focus on theoretical explanations in physics, i.e., explanations of physical laws. I first show that, as Salmon suggests (1989, p. 180-182), it seems promising to treat these two approaches not so much as different views about explanation but rather as descriptions of two distinct types of scientific explanations; there are clear cases of laws that have bottom-up explanations (BUEs) while others receive only top-down exp lanations (TDEs). I then argue, using explanations of mass-energy equivalence in Special Relativity (SR), that this disparity (why should some laws receive only TDEs after all?) is best understood as a symptom of a deeper distinction, first introduced by Newton, between two levels of physical theory. At one level, there is the collection of general principles and definitions of physical terms, i.e., a theoretical framework, from which one derives general constraints for all physical processes. At a lower level, there are laws that identify and describe specific physical interactions like gravitation and electromagnetism.