Inferring Conservation Laws in Particle Physics: A Case Study in the Problem of Induction

This paper develops a means-ends analysis of an inductive problem that arises in particle physics: how to infer from observed reactions conservation principles that govern all reactions among elementary particles. I show that there is a reliable inference procedure that is guaranteed to arrive at an empirically adequate set of conservation principles as more and more evidence is obtained. An interesting feature of reliable procedures for finding conservation principles is that in certain precisely defined circumstances they must introduce hidden particles. Among the reliable inductive methods there is a unique procedure that minimizes convergence time as well as the number of times that the method revises its conservation principles. Thus the aims of reliable, fast and steady convergence to an empirically adequate theory single out a unique optimal inference for a given set of observed reactions–including prescriptions for when exactly to introduce hidden particles. 1 Epistemology In Practice One of the goals of the philosophy of science is to connect general epistemology with scientific practice. In their pursuit of knowledge, scientists face epistemic problems at every step. The epistemologist can learn much from the ways in which they cope with these problems. Conversely, general epistemology should have something to say about particular problems concerning belief and knowledge, theory and evidence, that arise in scientific practice. This paper studies a particular problem of inductive inference arising in particle physics from the point of view of a general inductive epistemology. The inference problem is this: Given a set of observations of particle reactions, find a theory that makes the correct predictions about what reactions–observed and unobserved–are possible. The central epistemological tenet of this paper is that inquiry ought to reliably lead to true beliefs. Though science may err in the short run, it ought to correct itself and eventually settle on a correct theory of the phenomena